From kmatsuno Wed Apr 20 10:53:45 1994
To: bio-info@net.bio.net
Subject: one-to-one ?
Status: RO
In article <Co26KI.4vu@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov (Tom
Schneider) wrote:
>Koichiro Matsuno wrote:
>|...If the physicist is the only allowed observer, the one-to-one mapping
>|would remain invincible and the reversibility of computation would be
>|guaranteed.
>Although I understand the idea that if the atoms could be reversed in their
>paths one would return to the original state, this is not possible by any
>means we know now.
First of all, I have to say the physicists are very strange, though competent,
people. They have been educated to accept the presence of an ideal world first,
then followed by each awkward step toward the messy reality. Only after
learning a frictionless world (e.g., the idea of inertia), they are allowed
to face the frictional world (e.g., irreversibility). This is the rule of the
game for the physicists. Of course, you can blame them as far as you restrain
yourself from joining the game. It is perfectly legitimate to say that there
is no means to reverse the velocities of all of the molecules moving around in
your office. But, the physicists don't care, because they quite naturally
assimilate themselves as inhabitnats in the ideal world unless forcibly
ousted. It is easy for them to think of reversing the directions of all the
velocities without being annoyed by how to implement them unless the freedom
of thought is threatened. They do this while they are sitting on the
armchairs as waving their hands. In contrast, the problem of implementation
is the problem in our messy actual world, but not the one in the fantasy
world of the physicist.
In other words, the physicists approach our messy world by tinkering with
a hierarchy of abstractions, only. If one sort of abstration turns out to be
not quite good, their strategy would be to figure out an alternative
abstraction. Their objective is always to construct an abstraction of the
reality. As far as they admit that what they are doing is an abstraction,
there would be no problem. Only when they happen to claim the reality of the
abstraction, some people like you, Tom, would become uneasy. Me, too. The
abstraction of the reality does not automatically cash in the reality of the
abstraction. Curiously enough, however, most physicists are quite happy with
the abstraction of the reality. Think of a physical experiment on an "almost"
frictionless puck sliding on the ice rink designed to convince the high-school
student of the idea of inertia. This type of experiments has been a superb
example to show how marvelously abstractions work in physics. The one-to-one
law is the abstraction of the "physical" reality par excellence. There,
nothing like noises is allowed to intervene, because the one-to-one law
claiming the definitude of every detail is just incommensurable with the idea
of noises. Noises are noises to those that cannot boast of having that
definitude.
|I'm not convinced of that. As I said above, even if systems are one-to-one, a
|small molecular machine embedded in a larger system cannot predict the impacts
|of the larger system even thought they are predictable from a more
|knowledgeable viewpoint. So the design of the molecular machine must be "as
|if" it were irreversible (or
noisy). How curious!
Once the one-to-one law is taken for granted, there is no need to
distinguish between the small and the large or between being microscopic and
macroscopic. In this fantasy world of abstraction, everything has to be
definite independent of its size, scale or content of whatever sort. However,
the problem does emerge when one comes to feel sick and tired with the
fantasy world of the one-to-one. If you would like to distinguish between the
small and the large or would like to refer to noises, the price you have to pay
would be to abandon the one-to-one law. Don't forget that I am your company in
this regard. The rule of the game has to be changed to either a many-to-one
or a one-to-may, or an arbitrary mix of the two of your choice.
The problem of physical implementation is really a serious matter for both
the many-to-one and the one-to-many, though the one-to-one people can dismiss
with a legitimate excuse the problem of implementation, embedding, noises and
the like as maintaining that there are no such words in their dictionary to
consult with. It is a matter of choice. Which do you like to pick up, the
physical implementation of the molecular machine or the one-to-one law? This
is a mutually exclusive choice. My guess is that you would like to face the
implementation problem more squarely. If so, this means that you have to pay
the price. You have already parted with the idea of the one-to-one law.
Incidentally, thermodynamics based upon the many-to-one mapping of
methodological origin is quite at home with noises because noises are taken
as the residue spilled over from the many-to-one mapping applied to the
underlying microdynamics whatever
it may be.
>|The one-to-one camp is completely happy with its reversible computation and
>|need not worry about whatever complaints the many-to-one side may say about
>|an irreversibility or its look-alike.
>Oh ho! The trouble is that no matter what they do, they will be embedding
>a small system inside a larger system, and they won't be able to predict
>the noise from the larger system. The only escape is to have a noise-free
>system, and that looks like a
tough thing to attain.
A sound assessment. At the same time, the one-to-one people would not care
much about your points because there is no dichotomy between the small and the
large nor noises to their mind. Even the idea of noise-free is foreign to
them. The time when your verdict becomes really serious is when the one-to-one
people happens to step outside their territory absent-mindedly, whether
intentionally or not. If you find them, push them back to where they
originally were or corner them.
>To my surprise, the one-to-many and the one-to-one models still lead to the
>same
>molecular machine model because a molecular machine can't predict external
>impacts. The one-to-many mapping
is the toughest, I agree.
If you really mean that a molecular machine can't predict external
impacts, you are already a maverick leaving the horde in the one-to-one
camp. I mean you have implicitly accepted the position of the one-to-many
law.
Regrards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <Cou4Ar.4K3@ncifcrf.gov>
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Status: RO
In article <9404200153.AA03908@voscc.nagaokaut.ac.jp>
kmatsuno@VOSCC.NAGAOKAUT.AC.JP (koichiro
matsuno/7129) writes:
| If you would like to distinguish between the
| small and the large or would like to refer to noises, the price you have to pay
| would be to abandon the one-to-one law. Don't forget that I am your company in
| this regard. The rule of the game has to be changed to either a many-to-one
| or a one-to-may, or an arbitrary mix of the two of your choice.
| ...
| It is a matter of choice. Which do you like to pick up, the
| physical implementation of the molecular machine or the one-to-one law? This
| is a mutually exclusive choice. My guess is that you would like to face the
| implementation problem more squarely. If so, this means that you have to pay
| the price. You have already parted with the idea of the one-to-one law.
| ...
| If you really mean that a molecular machine can't predict external
| impacts, you are already a maverick leaving the horde in the one-to-one
| camp. I mean you have implicitly accepted the position of the one-to-many
| law.
Your wonderful exposition nearly had me stumped. I ascribe to the possibility
that the world operates by a one-to-one mapping of the past into the future,
yet I also ascribe to the concept of noise! You are saying that the former
excludes the latter, leaving me in
a quandary.
I think I know the way out. Consider the genetic evolution of computer
programs, a rather popular pastime these days. In this model, which Bob Moore
has told us about, we allow a population of computer programs to be modified
"randomly" and then we allow each to do its job. Then we kill the ones that
did worse and allow the better ones to replicate. If it can be set up for a
particular problem, this turns out to be a very effective way of getting a
program that does a complex task for which we cannot articulate or design a
direct analytical solution.
Now the mother program that does this contains several modules. One module
contains the little programs that are evolving, the other contains a so-called
pseudo random generator. The module that contains the program corresponds to
Newtonian physics, in that everything that happens there is one-to-one. Given
each little program, how well it does on its task is precisely defined. So the
overall choice of which program survives and which dies is precisely defined.
In other words, it's one-to-one.
The other module is used to generate mutations in the little programs. This
module could contain a radioactive substance or be measuring the voltage across
a hot resistor. But that's not what people do because it is much more
expensive compared to pseudo random number generators. Such a generator starts
with a "seed" number and modifies it to get the next number in the "random"
series. A simple example will make
this clear.
Start with a seed of 1. The algorithm is to take the current seed, multiply by
7 and throw away all digits above 9. So we get: 1, 7, 9, 3, 1, ... This is
the random series. The example is obviously too small to be useful but all one
needs to do is multiply by a bigger number. Whole books have been written on
how to chose numbers so that the series is as "random" as possible. But no
matter how the algorithm is written, every seed is precisely predictable from
the previous seed.
So the pseudo random number generator
is also "Newtonian" and one-to-one.
That is, the concept of "noise" or random mutation is useful for thinking about
this problem, but the evolution operates in a system which is globally
one-to-one. The same thing can apply to molecular machines. The critical
point is that the selection is performed on individuals who do not have access
to the global state. Thus the individuals have no "choice" but to act as if
the "noise" impacting on them is random. In making a model of molecular
machines we also must model the impacts as "noisy" and "random" even if the
entire universe is one-to-one. A curious twist is that it doesn't matter
whether or not the universe contains truly random events, as some people say
exist in quantum mechanics. We have
to treat it as random.
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: info on info theory
Message-Id: <Cou5Mv.53L@ncifcrf.gov>
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Date: Mon, 25 Apr 1994 22:11:18 GMT
Status: RO
In article <CoLIAC.68w@freenet.carleton.ca> ag659@FreeNet.Carleton.CA (Dr. John
D. Collier) writes:
| I certainly agree that this is the crux of the issue here, and I agree
| that information is a difference. I think, though, that entropy must
| also be a difference. Consider the following: A system will approach
| equilibrium as constraints are removed, and the equilibrium point will
| not depend on how the constraints are removed. The entropy change from
| the starting condition to the finishing (equilibirum) condition will
| depend only on what constraints were in place, and which were removed.
| Now if there is an absolute entropy for a system, then there must be
| a condition in which all constraints are removed. I would maintain
| that we know of no such state, and also that entropy calculations
| never [take] all constraints into consideration in any case, so entropy
| as it is used is always a difference.
My understanding is that the entropy is zero in a perfect crystal at 0 Kelvin.
According to the Definitions in my CRC, "Third law of thermodynamics - the
statement that every substance has a finite positive entropy, and that the
entropy of a crystalline substance is zero at the temperature of absolute
zero." So according to this the entropy has an absolute scale and need not be
always a difference.
| We can look at it differently, in terms of temperature, on which
| entropy depends. Temperature is average kinetic energy per degree
| of freedom. However, the number of accessible degrees of freedom
| depends on the energies available (and given quantum mechanics,
| the amount of time one is able to wait). So temperature is not
| an absolute measure either, in
practice.
On temperature, my CRC says "The fundamental temperature scale is the absolute,
thermodynamic or Kelvin scale in which the temperature measure is based on the
average kinetic energy per molecule of a perfect gas." Degrees of freedom are
not mentioned.
This raises an interesting issue with respect to our discussion of the units of
entropy. If temperature is (roughly??) energy per moles, then entropy, being
energy per temperature would reduce to ... moles! What I find interesting is
that this almost connects to the idea of bits measuring choices. There is a
piece still missing to the puzzle, in that it should be the log of the number
of moles, not moles. Anyway, a change in entropy would correspond to a change
in the countable objects (ie, moles). So we are almost there in making sense
out of the joules per degree Kelvin.
If temperature were per degree of freedom (which I haven't ruled out, perhaps
John or someone has some idea about this), I find it getting confusing because
I think of degrees of freedom as the dimensionality of the space Shannon
spheres are in, and the only impact of that for these problems is the amount
that the spheres intersect. The dimensionality stays constant during a
molecular machine operation. Certainly the dimensionality is not the entropy
change (which is measured by the log of the number of little spheres inside the
big gumball machine and all that
:-).
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: abooth@cix.compulink.co.uk ("Anthony Booth")
Subject: Re: one-to-one ?
Message-Id: <Cov5z1.H91@cix.compulink.co.uk>
Date: Tue, 26 Apr 1994 11:16:13 GMT
X-News-Software: Ameol
Status: RO
In a reply to Koichiro Matsuno, Tom
Schneider wrote:
> From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
> Message-ID: <Cou4Ar.4K3@ncifcrf.gov>
>
> ............ A curious twist is that it doesn't matter
> whether or not the universe contains truly random events, as some
> people say exist in quantum mechanics. We have to treat it as random.
>
> Tom Schneider
What beats me is why you think this is a curious twist. Also it matters
just as little whether the universe contains truly causal events as it
does truly random ones because the reasoning would run just the same! It
can only mean that you spontaneously or inherently still believe before
all else that causal processes are universal, and this in spite of the
message in which you write it saying "treat it as the contrary"! I doubt
that this is merely some rhetorical device you are using. Listen
carefully to these words of your own and apply them to every aspect of
your thinking. There is only virtue in proclaiming that something is
causal so long as there is a condition where it is worth treating it as
causal.
The reason that I dwell on these points is that I believe that we can
only make good theories for complex things like information or entropy
when we see, and sense directly, that the care with which we fix our
frames of reference (boundaries of systems, identities of observers etc.)
always determines limits to our certainty because there are limitlessly
many alternative views. It is possible to improve things by making this
care more explicit, but we are mostly just not in the habit of doing it
as we battle within conventional
frameworks.
As I read the correspondence in this net dealing with these issues I
often feel frustrated by the sense that the proponents (with exceptions
like Koichiro) are just looking in the wrong direction. They frequently
fail to see that the issues of disagreement within the terms of an
argument are illusory and caused merely by confusion of alternative
points of view. Why don't we move the endeavour to extending these
frameworks in clear and attractive ways instead of trying to bring rigour
to inadequate ones?
If anybody is so inclined to reply to this by saying "Why don't you do it
then?", I must say that the couple of attempts I have made here to start
that have drawn practically no fire. Perhaps it would be better for me
to continue in the path of the arguments of Koichiro; I shall try to do
that if this little piece is not
blown out of the water.
Thank you all for the debate.
Tony Booth Streatham London England
abooth@cix.compulink.co.uk
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 26 Apr 1994 19:57:07 -0700
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In article <Cou4Ar.4K3@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov (Tom
Schneider) writes:
>I ascribe to the possibility
>that the world operates by a one-to-one mapping of the past into the future,
>yet I also ascribe to the concept of noise! You are saying that the former
>excludes the latter, leaving
me in a quandary.
I am listening to you...
>Consider the genetic evolution of computer
>programs, a rather popular pastime
these days.
No problem! Many people do.
>Now the mother program that does this contains several modules. One module
>contains the little programs that are evolving, the other contains a so-called
>pseudo random generator. The module that contains the program corresponds to
>Newtonian physics, in that everything that happens there is one-to-one.
...
>The other module is used to generate mutations in the little programs...
>Such a [pseudo random number] generator starts
>with a "seed" number and modifies it to get the next number in the "random"
>series.
...
>So the pseudo random number generator
is also "Newtonian" and one-to-one.
>That is, the concept of "noise" or random mutation is useful for thinking about
>this problem, but the evolution operates in a system which is globally
>one-to-one. The same thing can apply to molecular machines. The critical
>point is that the selection is performed on individuals who do not have access
>to the global state. Thus the individuals have no "choice" but to act as if
>the "noise" impacting
on them is random.
I think I can follow your logic. The model of your choice, the one-to-one
law supplemented by random noise, does not cause me any inconvenience unless
you come up with other competing models to compare. Things would become
complicated only when more than one model are proposed in order to describe
what the world looks like. The problem is with the communication between
seemingly different models. Newtonian mechanics is a prototype of all of the
possible one-to-one laws with no noise. Even if the number of degrees of
freedom in motion is greater than the Avogadro's, the one-to-one law with no
noise does work. On the other hand, there has been a tough physical problem
of how to reach the one-to-one law supplemented by noise from the one-to-one
with no noise or, in short, how to get the Langevin equation from the
Hamiltonian dynamics. What physicists have accomplished up until now is that
if you know the nature of noise well in advance, you can get the one-to-one
with noise from the one-to-one without noise. If you want to know more about
this, perhaps ask Ron Fox.
My point is that in order to get noise, you have to first know what the
noise is. The situation is similar to distinguishing between music and noise
as listening to the same physical sound. The noise to somebody may not be
noise at all to somebody else. Neither the one-to-one with no noise nor
the one-to-one with noise can police the other. We need an impartial third
party, if any, to settle the matter. The biggest problem with the one-to-one
law with noise is how to distinguish between the one-to-one law and noise
and then to integrate the both.
As far as the one-to-one law with no noise goes, we have the difficulty in
how to justify the occurrence of irreversibility in our empirical world.
Likewise, if we start from the one-to-one with noise, the origin of noise
remains as a mistery. Historically, noise has come from thermodynamics. The
many-to-one mapping of thermodynamics (see Wolfgang Porod's posting a month
or two ago) is able to define noise as the residue spilled over from the
mapping. Noise thus defined is methodological in its origin, depending upon
what sort of many-to-one mapping would be available in the first place. The
many-to-one mapping of thermodynamics by itself does not say anything
specific about the nature of the underlying microdynamics, whether a
one-to-one or whatever else. The present methodological incompetence of
thermodynamics leaving the nature of the underlying microdynamics
unspecified prohibits us from saying that the thermodynamic system should
follow the one-to-one law with noise.
In spite of this, you can model the themodynamic system by your one-to-one
with noise as far as you maintain that model is model, and no more. As far as
you distinguish between the model of a dynamic and the dynamic of the model,
no problem would come up. The one-to-one law with noise is a model of
thermkodynamics, but does by no means represent thermodynamics to be modeled.
Because of this, the price you have to pay for taking the law of one-to-one
law with noise as a model of thermodynamics turns out to be that you have to
keep yourself ambivalent about whether or not the underlying dynamics is
reversible. You have the both at the same time; the first part of
"the one-to-one with noise" refers to reversibility, whereas the second part
noise to irreversibility. Of course, it is legitimate to say that unless
equipped with model of whatever sort, one cannot even talk about what the
reality should be. At issue here is what model has been employed for defining
and deciphering noise.
I believe that both of us agree on that thermodynamics provides the
frame of reference for figuring out what noise is all about. However,
thermodynamics is peculiar and strange in defining noise negatively, not
positively, that is to to say, as those contributions that influence
but are not included in thermodynamic variables themselves (e.g, entropy).
If you say that the noise appearing in the one-to-one law supplemented by
noise comes from thermodynamics and admit thermodynamics at the same time,
you would also have to have the thermodynamics from the one-to-one with
noise, being contrary to the observation that thermodynamics does not say
anything specific about the underlying microdynamics. As a matter of fact,
what is really nice about thermodynamics is that it is undercomplete as a
theoretical model. Quantum mechanics, another nicety, is undercomplete,
too.
In short, noise is an aweful concept to define positively. The only
alternative might be to define it negatively as thermodynamics does. You
can define the pseudo random number positively, but noise cannot be the
pseudo noise. Noise hides behind itself something whose every detail all
of us want to know in private but afraid to ask in public. Noise is
noise, period. The best one can hope may be to try to approach what looks
like noise without talking about noise explicitly. To repeat, I have no
problem with selling the idea of the one-to-one law with noise as a model.
The difficulty I have with it is that the one-to-one with noise, once taken
too seriously, comes to force itself to be the only model to approach
thermodynamics.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: abooth@cix.compulink.co.uk ("Anthony Booth")
Subject: Re: one-to-one ?
Message-Id: <Cox18p.7zA@cix.compulink.co.uk>
Date: Wed, 27 Apr 1994 11:29:12 GMT
X-News-Software: Ameol
Status: RO
I would like to say how much I appreciate the contributions by Koichiro
Matsuno (are we supposed to use capitals for Japanese names?) However,
in relation to his latest piece:
> From: kmatsuno@VOSCC.NAGAOKAUT.AC.JP (koichiro matsuno/7129)
> Message-ID: <9404270251.AA17296@voscc.nagaokaut.ac.jp>
> ..... On the other hand, there has been a tough physical
> problem of how to reach the one-to-one law supplemented by noise from
> the one-to-one with no noise or, in short, how to get the Langevin
> equation from the Hamiltonian dynamics. What physicists have
> accomplished up until now is that if you know the nature of noise well
> in advance, you can get the one-to-one with noise from the one-to-one
> without noise. If you want to know more about this, perhaps ask Ron
> Fox.
.... two points:
1 Please can we have a simple textbook reference if possible for
the Langevin equation. My engineering background has not brought it
before me.
2 I don't recall Ron Fox appearing on the network -- presumably a
personal reference to Tom Schneider's acquaintance. If it is an
important input, is there anything from Tom Fox which we can read in
print or on the net please?
Thanks,
Tony Booth Streatham London England
abooth@cix.compulink.co.uk
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From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
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In article <Cov5z1.H91@cix.compulink.co.uk> abooth@cix.compulink.co.uk
("Anthony Booth") writes:
| In a reply to Koichiro Matsuno, Tom Schneider wrote:
|
| > From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
| > Message-ID: <Cou4Ar.4K3@ncifcrf.gov>
| >
| > ............ A curious twist is that it doesn't matter
| > whether or not the universe contains truly random events, as some
| > people say exist in quantum mechanics. We have to treat it as random.
| >
| > Tom Schneider
|
| What beats me is why you think
this is a curious twist.
It is a little strange (to ME! :-) because it means that one can use classical
statistics to describe molecular machines whether or not underlying events are
random. It's one less thing I have
to really worry about!
| Also it matters
| just as little whether the universe contains truly causal events as it
| does truly random ones because
the reasoning would run just the same!
Right.
| It
| can only mean that you spontaneously or inherently still believe before
| all else that causal processes are universal, and this in spite of the
| message in which you write it saying "treat it as the contrary"! I doubt
| that this is merely some rhetorical device you are using. Listen
| carefully to these words of your own and apply them to every aspect of
| your thinking.
Sorry, I lost you here. I never used the phrase "treat it as the contrary" in
the recent postings. Perhaps you could be a little more specific? What are
"these words of your own"
that I should be applying to my thinking?
| There is only virtue in proclaiming that something is
| causal so long as there is a condition where it is worth treating it as
| causal.
No, suppose that the universe is one-to-one causal for everything. That is, it
is deterministic so that everything that follows in the future is completely
predictable from the present state. Even if this were the case, one would
still find evolving systems that act as if the universe were unpredictable.
Perhaps another example is the use of "if" statements in computer programs,
where it is obvious that in any particular instance there is only one correct
path for the computer to take through the program. That is, the result of the
program is deterministic (ignoring errors). If it is deterministic, ask
yourself why we need "if"
statements!
| The reason that I dwell on these points is that I believe that we can
| only make good theories for complex things like information or entropy
| when we see, and sense directly, that the care with which we fix our
| frames of reference (boundaries of systems, identities of observers etc.)
| always determines limits to our certainty because there are limitlessly
| many alternative views. It is possible to improve things by making this
| care more explicit, but we are mostly just not in the habit of doing it
| as we battle within conventional
frameworks.
I agree that we need to be explicit, but I don't think 'information' or
'entropy' as complex things - they are simply measures of the change of state
of a system or the state of a system (respectively). My information theory
primer is an attempt to make them more understandable. Perhaps that would be
useful for you to reread?
| As I read the correspondence in this net dealing with these issues I
| often feel frustrated by the sense that the proponents (with exceptions
| like Koichiro) are just looking in the wrong direction. They frequently
| fail to see that the issues of disagreement within the terms of an
| argument are illusory and caused merely by confusion of alternative
| points of view. Why don't we move the endeavour to extending these
| frameworks in clear and attractive ways instead of trying to bring rigour
| to inadequate ones?
It don't think my direction is a wrong one, since it has done rather well at
predicting results at the lab bench. (Note: there are many possible "right"
directions.) Making things more clear - that's a good challenge! Perhaps you
could point out unclear passages in my papers? Or do you see another approach
that would be more clear?
| If anybody is so inclined to reply to this by saying "Why don't you do it
| then?", I must say that the couple of attempts I have made here to start
| that have drawn practically no fire. Perhaps it would be better for me
| to continue in the path of the arguments of Koichiro; I shall try to do
| that if this little piece is not
blown out of the water.
I think I've responded to most if not all of your postings, hopefully in a
useful way.
| Thank you all for the debate.
Thank you for continuing to stick
with this!
| Tony Booth Streatham London England
abooth@cix.compulink.co.uk
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 27 Apr 1994 19:49:20 -0700
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In article <Cov5z1.H91@cix.compulink.co.uk> abooth@cix.compulink.co.uk
("Anthony Booth") writes
>Why don't we move the endeavour to extending these
>frameworks in clear and attractive ways instead of trying to bring rigour
>to inadequate ones?
>
>If anybody is so inclined to reply to this by saying "Why don't you do it
>then?", I must say that the couple of attempts I have made here to start
>that have drawn practically no
fire.
No! Tony. You make us very busy
for finding the fire extinguisher.
In article <Cox18p.7zA@cix.compulink.co.uk> abooth@cix.compulink.co.uk
("Anthony Booth") writes
> .... two points:
>
> 1 Please can we have a simple textbook reference if possible for
>the Langevin equation. My engineering background has not brought it
>before me.
I am not updated about the subject matter. But, I could find the following
two books in my bookshelf might be
relevant:
Nicolis, G. and Prigogine, I., 1977. Self-Organization in Nonequilibrium
Systems: From Dissipative Structures to Order through Fluctuations
(John Wiley & Sons, New York)
Haken, H., 1977. Synergetics (Springer-Verlag,
New York).
I have also treated some aspect of
the agenda in my book:
Matsuno, K., 1989. Protobiology: Physical Basis of Biology (CRC Press,
Boca Raton Florida).
The best I can recommend to you is
to ask Ron Fox.
> 2 I don't recall Ron Fox appearing on the network -- presumably a
>personal reference to Tom Schneider's acquaintance. If it is an
>important input, is there anything from Tom Fox which we can read in
>print or on the net please?
Ron Fox wrote a good review article on the Langevin equation and the
Markov Process in the journal named "Physics Reports" some years ago,
though I forgot which year or which
volume. Good Luck!!
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP) wrote:
: In article <Cou4Ar.4K3@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov (Tom
: Schneider) writes:
: >I ascribe to the possibility
: >that the world operates by a one-to-one mapping of the past into the future,
: >yet I also ascribe to the concept of noise! You are saying that the former
: >excludes the latter, leaving
me in a quandary.
: My point is that in order to get noise, you have to first know what the
: noise is. The situation is similar to distinguishing between music and noise
: as listening to the same physical sound. The noise to somebody may not be
: noise at all to somebody else. Neither the one-to-one with no noise nor
: the one-to-one with noise can police the other. We need an impartial third
: party, if any, to settle the matter. The biggest problem with the one-to-one
: law with noise is how to distinguish between the one-to-one law and noise
: and then to integrate the both.
Sorry for butting in here, I have only been half following the thread, so I
shall have to look up the archive for the rest.
I tend to try to think about everything in terms of probability distributions:
Bayes theorem and all that. Surely 'noise' is just a tag which is used to refer
to all of the contributions to a *measurement* which do not give an increase
in our information about the value
which the measurement is intended to determine.
In fact we are taught to consider noise to be those contributions which can be
made arbitrarily irrelevant by more/longer/etc measurements. That is their
contribution averages to zero. (The contributions which do not make our a posteriori
probability distribution more localised, and which cannot be eliminated in this way
are tagged systematic errors)
I don't think we need any court of last appeal. We must simply be careful about
how we define our system. If we consider every particle's position & momentum &c,
so that the microstate is totally defined, then there is no noise, and the one-to-one
mapping is clear.(Quantum
fluctuations may or may not prevent us from reversing time and following the
path backwards- I like to think not, but that's another question). In systems
of the sizes considered in thermodynamics
we have no hope of doing this measuremetnt.
If we are only
concerning ourselves with those macroscopic quantities like temperature, then we
use the term noise to refer to the fluctuations in these quantities as the system
ergodically wanders through it's phase space. It is quite feasible to measure these
variables, and many students do so,
so the idea of noise is easy to deal with.
If we were to use a system for which
thermodynamics was truly valid (it is only the limiting case of a model at infinite
system size) then those fluctuations would be zero, because of the averaging over the
infinite system. Even in this last case, we can only talk about a one to one mapping
if we consider the microstate, because the macroscopic variables do not fully
describe the system.
In summary, were are stuck with our thermodynamics appearing noisy because the
maths requires the systems to be infinite, but we can't manage that. If we want to
get rid of the noise then we are left with the options of completely characterising
the system microscopically (equally impossible) or of using a system so small that
the approximations of thermodynamics
are no longer valid at all.
Once again, the typed screenful does not seem to represent what is in my head, but
I would appreciate any comments.
If I'm completely off the thread then I probably deserve some flames for not
reading up the rest of the thread
properly. In which case I apologise!
Charlie
Charlie Cook
Department of Physics
Loughborough University of Technology
Loughborough
UK
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <Cozv9I.BAL@ncifcrf.gov>
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In article <CoxMI7.Eyx@lut.ac.uk>
phceac@lut.ac.uk (C.E.A.Cook) writes:
| In summary, were are stuck with our thermodynamics appearing noisy because the
| maths requires the systems to be infinite, but we can't manage that. If we want to
| get rid of the noise then we are left with the options of completely [characterizing]
| the system microscopically (equally impossible) or of using a system so small that
| the approximations of thermodynamics
are no longer valid at all.
Consider Johnson's experiment and Nyquist's theory, as presented in the pair of
back-to-back papers:
@article{Johnson1928,
author = "J. B. Johnson",
title = "Thermal agitation of electricity in conductors",
journal = "Physical Review",
volume = "32",
pages = "97-109",
year = "1928"}
@article{Nyquist1928,
author = "H. Nyquist",
title = "Thermal agitation of electric charge in conductors",
journal = "Physical Review",
volume = "32",
pages = "110-113",
year = "1928"}
One takes a sensitive oscilloscope and attaches it to a resistor. One sees on
the screen a wiggly voltage. The distribution of the voltage is Gaussian, with
mean zero. It does not go away by having a bigger resistor. The interesting
thing they did was to place the resistor at different temperatures, and they
found that the noise power (I think) was proportional to the temperature.
Nyquist then built his theory which
led to N = WkT.
Consider a molecular dynamics simulation of the resistor atoms and of electrons
flowing through. The dynamics can be purely one-to-one and Newtonian. Yet one
will see a nice Gaussian in the voltage "measured" in the simulation. It
wouldn't be hard to do, simply measure the velocity of one particle in a cloud
of particles inside the simulation.
It will be Gaussian.
So the one-to-one model does not have to have noise added, it comes out simply
from the nature of a complex system.
One can take the same system and gather all the particles into one corner.
Then start the simulation. They will spread out, and the measured entropy of
the system will increase as they bounce around. (You could measure entropy
from the distribution of numbers of particles in marked out regions of the
box.) Reverse all the paths and they go back to the corner and then spread out
again. Would someone like to program this? It could be done in C with ASCII
graphics for a display. (The positions of the particles would be real numbers
of course, and then the positions
would be rounded for the display.)
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
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In article <9404270251.AA17296@voscc.nagaokaut.ac.jp>
kmatsuno@VOSCC.NAGAOKAUT.AC.JP (koichiro
matsuno/7129) writes:
| I think I can follow your logic. The model of your choice, the one-to-one
| law supplemented by random noise, does not cause me any inconvenience unless
| you come up with other competing
models to compare.
As I said in the other posting, as I understand it, one doesn't "supplement" or
add to the one-to-one model, one gets noise phenomena directly as part of the
model. Any large collection of Newtonian-simulated particles should show
approximately Gaussian distributions
of velocities.
| On the other hand, there has been a tough physical problem
| of how to reach the one-to-one law supplemented by noise from the one-to-one
| with no noise or, in short, how to get the Langevin equation from the
| Hamiltonian dynamics.
The first part may actually be easy! Just use the "law of large numbers" from
statistics! I looked at the Langevin pretty closely for a while and finally
decided that it was not useful to me. It sweeps all the interesting detail of
the noise into a single random variable. I could find no place that it
contributed to molecular machine
theory.
| My point is that in order to get noise, you have to first know what the
| noise is.
For the dynamic simulation, the noise appears automatically without my
knowing anything.
| The situation is similar to distinguishing between music and noise
| as listening to the same physical sound. The noise to somebody may not be
| noise at all to somebody else.
This really confuses the issue. While it is sometimes true that some kid will
blast "noise", that is quite different from the white noise that one measures
on a resistor. Nobody is claiming
to dance to that!
| Neither the one-to-one with no noise nor
| the one-to-one with noise can police the other. We need an impartial third
| party, if any, to settle the matter. The biggest problem with the one-to-one
| law with noise is how to distinguish between the one-to-one law and noise
| and then to integrate the both.
The electrical engineers have a very clear picture of noise and what to do
about it.
| As far as the one-to-one law with no noise goes, we have the difficulty in
| how to justify the occurrence of
irreversibility in our empirical world.
The simulation demonstrates "irreversibility" by the case I mentioned of having
the particles all in one corner at
the start.
| Likewise, if we start from the one-to-one with noise, the origin of noise
| remains as a [mystery].
Again, the "noise" comes about from the dynamics of the complex system
and appears even in a Newtonian dynamic
simulation of bouncing balls.
| Historically, noise has come from thermodynamics. The
| many-to-one mapping of thermodynamics (see Wolfgang Porod's posting a month
| or two ago) is able to define noise as the residue spilled over from the
| mapping. Noise thus defined is methodological in its origin, depending upon
| what sort of many-to-one mapping
would be available in the first place.
That's an interesting point. The "noise" measured in the simulation comes
about because the measurement is only of a very small portion of the entire
simulation. But that is what we should be doing because the molecules only
interact with a portion of the solution they are in. So from a molecule's
viewpoint, the solution is "noisy" even if the entire solution is perfectly
predictable.
| In spite of this, you can model the [thermodynamic] system by your one-to-one
| with noise as far as you maintain
that model is model, and no more.
We are ALWAYS working with models! One can make the Newtonian dynamic
simulation more complex - with water and salts and proteins bouncing around -
but it's not essentially any different
from bouncing balls.
| As far as
| you distinguish between the model of a dynamic and the dynamic of the model,
| no problem would come up. The one-to-one law with noise is a model of
| [thermodynamics], but does by no means represent thermodynamics to be modeled.
| Because of this, the price you have to pay for taking the law of one-to-one
| law with noise as a model of thermodynamics turns out to be that you have to
| keep yourself ambivalent about whether or not the underlying dynamics is
| reversible. You have the both at the same time; the first part of
| "the one-to-one with noise" refers to reversibility, whereas the second part
| noise to irreversibility. Of course, it is legitimate to say that unless
| equipped with model of whatever sort, one cannot even talk about what the
| reality should be. At issue here is what model has been employed for defining
| and deciphering noise.
I like how you try to stick me in a corner! It's the only way we learn... You
say "...you have to keep yourself ambivalent about whether or not the
underlying dynamics is reversible." I'm not ambivalent! The underlying
dynamics is "reversible"! Just tweak all the velocities in the computer to be
negative and all the balls will fly back into their starting corner. (I
neglect effects of roundoff error, which may well prevent that if the
simulation runs too long. The counter would be to have more accuracy in the
simulation. This is only a distracting detail I think. In any case, there
would be a low point in the entropy
as the balls "almost" all regather.)
So I am happy with a one-to-one physics (meaning every moment is predicted
exactly from the previous moment) that is reversible (because one can do that
in simulation by negating the velocities) and that has "noise" as a consequence
of the complexity of a large interacting system (that may be closed) and a
small measuring probe.
| I believe that both of us agree on that thermodynamics provides the
| frame of reference for figuring
out what noise is all about.
Actually, I start from statistics (Gaussian distribution from law of large
numbers) and electrical engineering
(Nyquist's N=WkT).
| In short, noise is an [awful]
concept to define positively.
Is there a problem with N=WkT or
Gaussian distributions?
| The difficulty I have with it is that the one-to-one with noise, once taken
| too seriously, comes to force itself to be the only model to approach
| thermodynamics.
Maybe it's all we need? ;-)
Regards,
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 29 Apr 1994 07:22:21 -0700
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In article <CoxMI7.Eyx@lut.ac.uk> phceac@lut.ac.uk (C.E.A.Cook)
writes:
>I tend to try to think about everything in terms of probability
>distributions: Bayes theorem
and all that.
Some observer with limited capacity must be there. Otherwise, no
probability. Is this observer you
yourself or somebody else?
>In fact we are taught to consider noise to be those
>contributions which can be made arbitrarily irrelevant by
>more/longer/etc measurements. That is their contribution
>averages to zero.
Again, it depends upon who the observer (carrying that sort of
measurement apparatus) is.
>I don't think we need any court of last appeal. We must simply
>be careful about how we define our system. If we consider every
>particle's position & momentum, so that the microstate is
>totally defined, then there is no noise, and the one-to-one
>mapping is clear.
Noise or no noise is up to the observer even if the underlying
dynamics is the one-to-one. By the way, who is we in this case?
We as the omnipotent universal objective
observer or we as...?
>If we are only concerning ourselves with those macroscopic
>quantities like temperature, then we use the term noise to refer
>to the fluctuations in these quantities as the system
>ergodically wanders through it's
phase space.
Is the ergodic motion of the one-to-one mapping the only way to
get the fluctuations?
>If we were to use a system for which thermodynmaics were truly
>valid (it is only the limiting case of a model at infinite
>system size) then those fluctuations would be zero, because of
>the averaging over the infinite system. Even in the last case,
>we can only talk about a one to one mapping if we consider the
>microstate, because the macroscopic variables do not fully
>describe the system.
How about the possibility of conceiving thermodynamics without
considering the underlying microscopic
dynamics explicitly?
You have just raised a panoramic array of a whole bunch of
subtle issues which have importunately bothered those practioners
in statistical physics and information theory during more than
several decades in the past. It would be next to impossible for
me to give you a convincing argument to each point you raised in
the manner that it could also convince anybody to whom it may
concern, though I am not a defeatist. The most difficult part
with me is my incompetence in fathoming what sort of theoretical
framework they are taking as most
fundamental or uncompromisable.
Let me first expose to you my "uncompromisable" framework.
Thermodynamics as the rear base of both statistical physics and
information theory remains indefinite in its implication. This
means that although it definitely provides a unique relationship
among the thermodynamic variables, thermodynamics says nothing
about the contributions from those
other than the variables.
One big issue here is about our understanding of noise within
the framework of thermodynamics. A nice thing about
thermodynamics is that it identifies the nature of noise at least
up to its mean square value. For instance, the mean square
fluctuation of the entropy of a gas determines its specific heat
at constant pressure. Similarly, the mean square fluctuation of
electric currents in a resistor determines its electrical
conductivity (the Nyquist theorem or the fluctuation-dissipation
theorem). The thermodynamic specification of noise in terms of
its mean square value does not exhaustively specify every detail
of the noise. A mean square value of individual quantities does
not say anything specific about each individual quantity. Noise
in the framework of thermodynamics remains indefinite with regard
to its constituent individual events. The Nyquist theorem tells
us only the ensemble property of electric-current fluctuations,
instead of each of individual fluctuations. Only when the
ensemble of individual events is the most fundamental object to
be measured for some reasons, the thermodynamic specification of
noise could remain sufficient. Inadequacy of the ensemble noise
would become visible when the Gaussian noise turns colored from
white.
On the other hand, whether the one-to-one temporal mapping
could give us the thermodynamic limit is another story. Although
it woud be nice to have thermodynamics from the one-to-one
mapping, thermodynamics of itself is no more than a form of
curvature geometry in the space spanned by thermodynamic
variables. In particular, the curvature of the manifold spanned
by the thermodynamic variables represents the contributions from
thermal noise or fluctuation.
Thanks for comments.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 29 Apr 1994 07:28:39 -0700
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In article <Cozx34.Bs0@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov>
(Tom Schneider) writes:
A >The simulation demonstrates "irreversibility" by the case I
>mentioned of having the particles all in one corner at the
>start.
>
B >The "noise" measured in the simulation comes about because the
>measurement is only of a very small portion of the entire
>simulation. But that is what we should be doing because the
>molecules only interact with a portion of the solution they are
>in. So from a molecule's viewpoint, the solution is "noisy" even
>if the entire solution is perfectly predictable.
>
C >So I am happy with a one-to-one physics (meaning every moment
>is predictable exactly from the previous moment) that is
>reversible (because one can do that in simulation by negating
>the velocities) and that has "noise" as a consequence of the
>complexity of a large interacting system (that may be closed)
>and a small measuring probe.
Let me make the situation as simple as possible. You have
admitted the three of phenomenological irreversibility
originating in boundary conditions applied externally in A,
internal measurement from a molecule's viewpoint in B and the
reversible microscopic one-to-one law in C. Physicists have long
since recognized that phenomenological irreversibility due to
boundary conditions and the reversible microdynamics coexist
peacefully. There is no argument about it. Its corollary is
reversible computation as Joao Leao explained in his recent posts
while taking great pains in doing
so.
Now, the problem for us is: Can internal measurement from a
molecule's viewpoint stand alone without offending the two of
phenomenological irreversibility and the reversible
microdynamics? If you say the molecule's viewpoint is just a
metaphor and don't take it seriously, your position would reduce
to that of physicists accepting phenomenological irreversibility,
reversible microdynamics and reversible
computation.
On the other hand, if you ask to take internal measurement
from a molecule's viewpoint seriously, there would appear at
least two different observers observing the same microscopic
process; one is the external observer who said the microdynamics
follows the reversible one-to-one law, and the other is the
internal observer claiming the molecule's viewpoint. At issue is
how these two observers could communicate with each other and
establish the consensus, if any. If the consensus cannot be
reached, then, what would happen? Tom, don't take me wrong. In
doing so, I have tried to corner myself. Some of my attempt for
the way out I tried is in my Protobiology: Physical Basis of
Biology (CRC Press, Boca Raton Florida,
1989).
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: hughb@eng.umd.edu (Hugh Brunk)
Subject: Re: one-to-one ?
Date: 29 Apr 1994 22:47:16 GMT
Message-Id: <2ps2pk$9os@mojo.eng.umd.edu>
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In article <Cozx34.Bs0@ncifcrf.gov>
toms@fcsparc6.ncifcrf.gov (Tom Schneider) writes:
>
>Actually, I start from statistics (Gaussian distribution from law of large
>numbers) and electrical engineering
(Nyquist's N=WkT).
There seems to be a lot being written about Gaussian distributions and
how they come about. If I'm not mistaken, the reason for the
pervasiveness of Gaussian distributions is explained not by the laws of
large numbers, but by the Central Limit Theorem. The Central Limit
Theorem basically says that the sum of N independent and identically
distributed random variables approaches a Gaussian Distribution as N
grows large. In the case of a resistor, the velocities of individual
electrons can be assumed to be identically distributed and essentially
independent due to relatively limited interactions between them.
Velocities of the individual electrons need not be Gaussian; indeed,
solid-state quantum treatments result in discrete distributions. The
Central Limit Theorem says that the voltage observed across the resistor
will be Gaussian in character since it is determined from the sum of the
states of the *large number of* charges in the resistor.
Laws of large numbers, on the other hand, relate the sample averages
of individual realizations of a random process to the probabilistic averages.
Gaussian distributions are not necessary to have the laws of large
numbers hold: One form of LOLN says that, as N goes to infinity, the
number of heads in a sequence of
coin tosses goes to N/2.
From an engineering point of view (my usual one) noise is anything that
is either not predictable or too much trouble to predict. While the
world may certainly operate in a deterministic one-to-one fashion it
seems increasingly obvious that we will never "know" it as such. The
uncertainty principle puts a probabilistic "seed" in nature, as far as
our knowledge of it is concerned. When we try to extrapolate a
reasonable knowledge of a current state into the future the seed of
uncertainty grows, requiring probabilistic methods of analysis.
This is my first posting to this group; I saw a lecture Tom Schneider
gave this week and was excited by his work. I hope to be able to
contribute something to the info-theory side of issues; I certainly
won't be telling anyone anything
about microbiology.
Hugh Brunk
hughb@eng.umd.edu
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 1 May 1994 02:42:46 -0700
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In article <2ps2pk$9os@mojo.eng.umd.edu> hughb@eng.umd.edu (Hugh
Brunk) writes:
>If I'm not mistaken, the reason for the pervasiveness of
>Gaussian distributions is explained not by the laws of large
>numbers, but by the Central Limit
Theorem.
Fine.
I would like to add a few more. The Central Limit Theorem
refers to a fundamental statistical property of any independent
variables each of which is identically distributed. In
particular, in relation to our more specific agenda on whether
the microscopic dynamic variables following the one-to-one
temporal mapping can yield a Gaussian distribution, the question
of "CLT to whom?" or "the one-to-one law to whom?" would become
more urgent. The validity of CLT to statisticians is indisputable
as much as that of the one-to-one law to the Laplacean demon who
is neither the friend nor the relative of the Maxwell's demon,
though. In contrast, CLT is of no use to the Laplacean demon
because the latter is supposed to have the capacity of
recognizing each dynamic variable in relation to all of the
others at every moment. To our fellow statisticians, also, the
one-to-one law taking care of particles of the Avogadro's number
or more would be too much and of no use, although the Cray's
supercomputer may enable them to take care of a few or several
tens of thousands of particles at a time. Each of CLT and the
one-to-one law is legitimate in its own light unless CLT be
forced to the Laplacean demon or the one-to-one law to
statisticians.
The problem would come up only when there appears somebody who
takes the position of the Laplacean demon in one occasion and
that of a statistician in another as looking at the same
phenomenon. Of course, one can avoid unnecessary confusions if
this person declares when (s)he changes the perspective from the
demon's to the statistician's or vice versa every time. It may
be possible in theory, but difficult
in practice.
The situation to physicists and biologists is much more
complicated. They have to face thermodynamics which has nothing
to do with either the statistics or the one-to-one law in the
beginning. It is certainly premature to say that thermodynamics
would be a statistics of mechanics. In spite of this caution,
thermodynamics understood as a form of statistical mechanics to
physicists has been proved to be a great success (e.g,
transistor, pc, e-mail). The present success does not, however,
lead to the hasty conclusion that thermodynamics to a molecule
may reduce to a statistics of mechanics to a physicist, let alone
the statistics of mechanics to the
molecule.
The actuality of molecular recognition proceeding in the
thermodynamic environment urges us to directly confront the
question of "thermodynamics to whom?". How could the
thermodynamics to a physicist be related to the thermodynamics
to a molecule? A clue to both the cohesion of John Collier and
the ontological step for the theorist/designer of Tony Booth may
be found in squarely facing this
question.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: abooth@cix.compulink.co.uk ("Anthony Booth")
Subject: Re: one-to-one ?
Message-Id: <Cp726z.30E@cix.compulink.co.uk>
Date: Mon, 2 May 1994 21:25:46 GMT
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There is a debate in bionet.info-theory over an original posting by
Koichiro Matsuno on the subject:
Re: one-to-one ?
In a part of the debate between toms@fcsparc6.ncifcrf.gov (Tom
Schneider) and myself abooth@cix.compulink.co.uk ("Anthony Booth") the
following exchange occurred:
In part of message-ID: <Coxuv9.Ku4@ncifcrf.gov>
Tom wrote:
>In article <Cov5z1.H91@cix.compulink.co.uk> abooth@cix.compulink.co.uk
>("Anthony Booth") writes:
>|
>| > From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
>| > Message-ID: <Cou4Ar.4K3@ncifcrf.gov>
>| >
>| > ............ A curious twist is that it doesn't matter
>| > whether or not the universe contains truly random events, as some
>| > people say exist in quantum mechanics. We have to treat it as
>| > random.
>| >
>| > Tom Schneider
>|
>| What beats me is why you think
this is a curious twist.
Tom replied:
>It is a little strange (to ME! :-) because it means that one can use
>classical statistics to describe molecular machines whether or not
>underlying events are random. It's one less thing I have to really
>worry about!
>
>| Also it matters just as little whether the universe contains truly
>| causal events as it does truly random ones because the reasoning
>| would run just the same!
>
>Right.
>
>| It can only mean that you spontaneously or inherently still believe
>| before all else that causal processes are universal, and this in
>| spite of the message in which you write it saying "treat it as the
>| contrary"! I doubt that this is merely some rhetorical device you
>| are using. Listen carefully to these words of your own and apply
>| them to every aspect of your thinking.
>
Tom then replies:
>Sorry, I lost you here. I never used the phrase "treat it as the
>contrary" in the recent postings. Perhaps you could be a little more
>specific? What are "these words of your own" that I should be applying
>to my thinking?
>
>| There is only virtue in proclaiming that something is causal so long
>| as there is a condition where it is worth treating it as causal.
>
Tom then replies:
>No, suppose that the universe is one-to-one causal for everything.
>That is, it is deterministic so that everything that follows in the
>future is completely predictable from the present state. Even if this
>were the case, one would still find evolving systems that act as if the
>universe were unpredictable. Perhaps another example is the use of "if"
>statements in computer programs, where it is obvious that in any
>particular instance there is only one correct path for the computer to
>take through the program. That is, the result of the program is
>deterministic (ignoring errors). If it is deterministic, ask yourself
>why we need "if" statements!
..... it continues in similar style.
I thank Tom for his reply from which the above sequence is taken, and I
am particularly grateful in general for his willing, cheery and tolerant
style of handling these sticky areas of thought. It sometimes surprises
me that he can keep it up so well. I value that as a critical new input
where this sort of difference exists, and one which is almost absent in
the usual formal sorts of communications
on these subjects.
By his list of localised comments Tom tempts me, even invites me to reply
again to his remarks, for there are surely many further things which
could be said to develop the shower of little differences which are
evident in this sequence, and that was only part of Tom's reply! Oddly,
I would love to reply (I will willingly do so separately Tom at your
slightest desire either privately or on the net), and true, some of the
points could do with tightening up by any standards of good reasoning (my
points I mean), but to my mind the sequence contains many points of
contention which are traceable to a single and important underlying
difference of approach.
It seems to me that the technique of amplifying individual points of
difference below the level of the main thesis pulls the argument away
from the essence of what needs to be grasped here. That is not true for
all arguments, but it is for those which stand to benefit from the
introduction of new models rather than from the consolidation of existing
ones. So I shall continue to try to hold a general view of the process
of the debate. The little sequence above then is an example of how these
differences can come out in everyday
expressions.
Looking at the entire sequence of this interchange my objective therefore
is still to expose a specific sort of contrast of mind sets which seems
to me to make all the difference as to whether we can handle the sorts of
new ideas needed in the main concerns of this particular news net. (It
happens that I am also interested in the extension of that elsewhere into
the field of engineering design too.
This is a rather general problem.)
To try to focus this basic difference of mind set I suggest the issue I
mentioned above of whether the subject stands to gain most from
development of its models, or from consolidation of existing models.
However I am not about to propose a panacea. For instance I am not
trying to suggest an approach which would exclude the one-to-one models
which are so much a reflex of our scientific world (refer to postings by
Koichiro Matsuno). Rather I am trying, and I think this accords
generally with views posted by Koichiro Matsuno, John Collier and Bob
Ulanowicz in this news net, to add a further space in which the subject
seems almost certain to offer fruitful
development.
This is a problem which emerges in the steering of all sorts of work
where tangible results are sought whilst potential exists for novel
models. Some people call the two necessary thought processes convergent
and divergent respectively. These processes have different disciplines.
Perhaps if this could be grasped then the further issue of whether the
particular subject of info-theory in biology can benefit from either
development of or reinforcement of models could be handled routinely by
conscious thought and corresponding expression instead of relying upon
primal intuitive reflexes. Please do not think that I believe we can
ever escape using primal intuitive reflexes though, it is just that we
can choose to shift the edges of our model domain so that the issues
which we handle consciously are selected
to better effect.
Once this opportunity for extension of models is recognised I believe
there is much more to be said about how we might use the notions of
entropy and information. If we do not recognise this change there will
continue to be much bickering over
details with less than best effect.
Tony Booth Streatham London England
abooth@cix.compulink.co.uk
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 3 May 1994 05:31:21 -0700
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Soon after I put the post "one-to-one ?" on the net on the
19th of April, Tom Schneider, Tony Booth, Charlie Cook and Hugh
Brunk joined and took their time for making their comments on it.
I certainly appreciate that. At the same time, I feel the need
to shift the gear a little bit more
toward the normal position.
In article <Cp726z.30E@cix.compulink.co.uk>
abooth@cix.complink.co.uk ("Anthony
Booth") observes in passing:
>...the one-to-one models which are so much a reflex of our
>scientific world...
In almost the same context, hughb@eng.umd.edu (Hugh Brunk)
writes:
>While the world may certainly operates in a deterministic one-
>to-one fashion it seems increasingly obvious that we will never
>"know" it as such.
in the article <2ps2pk$9os@mojo.eng.umd.edu>.
These two observations remind me of a unique aspect of the
deterministic one-to-one law, namely, a complete absence of the
capacity of recognition or measurement on the part of the law
itself. On the other hand, one of the basic attributes of
information is the capacity of recognition on the side called the
receiver, whatever it may be. A real difficulty with the one-
to-one law is its incompetence in coming to grips with the
quality called recognition or measurement that distinguishes
between the a priori uncertainty and the a posteriori less
uncertainty. No tree inside the wood covered by the one-to-one
law can come up with the capacity of recognition. The one-to-
one law with noise as a derivative of the one-to-one law with no
noise cannot assume the capacity of recognition as the
indispensable attribute of information.
If the issue of information on material grounds is claimed not
to be ill-stated, it should be prerequisite for us to recognize
that molecules have the capacity of recognition in the manner
being incommensurable with the deterministic one-to-one law.
Molecules to Bob Ulanowicz may be touchy-feely fellows, though not
necessarily wishy-washy. (I borrowed this phrasing from Marc
Roussel. Thanks, Marc!).
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
Sender: usenet@lut.ac.uk (Usenet-News)
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Date: Mon, 2 May 1994 16:35:40 GMT
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koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP)
wrote:
: Some observer with limited capacity
must be there.
Yep, sounds like me!! :-)
: . Is this observer you
yourself or somebody else?
What I meant was that it does not matter who the observer is.
Whether (s)he/it is a part of the system or not, whether it
is omnipotent or can only manage to stick in a thermometer,
the universe will still do it's stuff, regardless. Otherwise
we break the unspoken axiom that the laws of physics are the
same for all observers.
: In article <CoxMI7.Eyx@lut.ac.uk> phceac@lut.ac.uk (C.E.A.Cook)
: writes:
: >In fact we are taught to consider noise to be those
: >contributions which can be made arbitrarily irrelevant by
: >more/longer/etc measurements. That is their contribution
: >averages to zero.
: Again, it depends upon who the observer (carrying that sort of
: measurement apparatus) is.
: >I don't think we need any court of last appeal. We must simply
: >be careful about how we define our system. If we consider every
: >particle's position & momentum, so that the microstate is
: >totally defined, then there is no noise, and the one-to-one
: >mapping is clear.
: Noise or no noise is up to the observer even if the underlying
: dynamics is the one-to-one. By the way, who is we in this case?
: We as the omnipotent universal
objective observer or we as...?
Noise or no noise is determined by the observer (whoever that be)
when the model or or parameter being measured is chosen. At the level
of the one-to-one there is no noise (IMHO) . Consider the following
experiment, which is absolutely noise-free:
Given the state of the universe at the present moment, see
what it is like in 24 hours.
I realise that we are in no position to actually fully characterise
the universe at the beginning and end of the experiment, but at the start
we know that the experiment will have a unique outcome. (I ignore the recent
article in Scientific American about time travel) . We also, if we
assume causality (I hope that is theright term) and do not let God
play with the works, know that the condition of the universe at the
end is determined solely by it's state at the beginning.
This is my "uncompromisable framework" - it is not theoretical, and
it has nothing to do with the observer.
I think it's an axiom.
: Is the ergodic motion of the one-to-one mapping the only way to
: get the fluctuations?
It is the only way to get them from
the one to one mapping.
: How about the possibility of conceiving thermodynamics without
: considering the underlying microscopic dynamics explicitly?
Actually, I was first introduced to thermodynamics without any
consideration of the microscopics. The "laws" appeared to be rather
arbitrary to me and I never felt that I possessed any understanding
of them. It was deeply enlightening to be shown that thermodynamics
is just the maths of the dynamics of large numbers of particles.
That was the sort of insight that
drew me to science!
: Let me first expose to you my "uncompromisable" framework.
: Thermodynamics as the rear base of both statistical physics and
: information theory remains indefinite in its implication. This
: means that although it definitely provides a unique relationship
: among the thermodynamic variables, thermodynamics says nothing
: about the contributions from those
other than the variables.
: One big issue here is about our understanding of noise within
: the framework of thermodynamics. A nice thing about
: thermodynamics is that it identifies the nature of noise at least
: up to its mean square value. For instance, the mean square
: fluctuation of the entropy of a gas determines its specific heat
And so it is no longer noise, it is another parameter in the model.
The gas molecules are still doing the same things, but we understand
their collective properties better. If we can measure the next moment
of the entropy, then ( Am I right? I am about to say something which
is mainly intuition ) we are measuring the size of our system of
particles - a nonzero value means that we have hit the edge of our
assumptoin that the LLN is valid.
: On the other hand, whether the one-to-one temporal mapping
: could give us the thermodynamic limit is another story. Although
: it woud be nice to have thermodynamics from the one-to-one
: mapping, thermodynamics of itself is no more than a form of
: curvature geometry in the space spanned by thermodynamic
: variables. In particular, the curvature of the manifold spanned
: by the thermodynamic variables represents the contributions from
: thermal noise or fluctuation.
I agree. We use thermodynamics because it allows us to work out
useful things about large collections of particles in a space with
only a handful of dimensions. Ain't no Cray fast enough to do anything
useful in O( 6E23 ) dimensions!! There is nothing to prevent the use
of more parameters in our models, but things get all complicated. It
would be nice to never have to step out of that beautiful curved space
of thermodynamics, but we can't do
everything in there.
I ramble! Perhaps I have missed your
point.
: Thanks for comments.
I find this fascinating.
Charlie
Charlie Cook
Department of Physics
Loughborough University of Technology
Loughborough
UK
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From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 3 May 1994 23:20:02 -0700
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Charlie Cook has made visible his "uncompromisable" framework.
Thanks, Charlie.
In article <Cp60rG.46H@lut.ac.uk> phceac@lut.ac.uk (C. E. A.
Cook) writes:
>We also, if we assume causality (I hope that is [the right]
>term) and do not let God play with the works, know that the condition
>of the universe at the end is determined solely by it's state at
>the beginning. This is my "uncompromisable framework" - it is not
>theoretical, and it has nothing to do with the observer. I think
>it's an axiom.
Your position is consistent in proposing and accepting the
axiom. Although I am quite happy with the axiom so long as it is
said as an axiom, a few remarks on my understanding of axiomatic
framework may be appropriate. The supreme example of axiomatic
thinking is Euclidean geometry. Even if it may have started from
a set of observational statements, Euclidean geometry, once
distilled as such, turns out to be completely axiomatic with no
reference to observational activities. Euclidean geometry as a
complete form of formal language is structure-oriented in the
sense that anything appearing there can exhaustively be
identified by referring only to the structure of the geometry.
No activity originating in or pointing to the objects outside the
structure is allowed to intervene there. Any axiomatization
enables us to get rid of nasty object-oriented activities latent
in practicing every natural language. This is certainly a nice
aspect of axiomatization. But, the other side of the same coin
reveals that axiomatization lacks its de novo generative competency. That
means that Euclidean geometry is incompetent in generating
Riemannian geometry from its own inside. Some one named G. F. B.
Riemann was called for the job of
constructing the new axiom.
Whatever axiomatization one may be involved in, it would be
legitimate to stick to what the axiom has prescribed so long as
one prohibits oneself from talking about its de novo generative capacity.
However, our empirical world seems full of those outlaws that
disturb the tranquility of axiomatization. Any process born out
of observation or measurement that has the capacity of going
beyond any structure-oriented axiomatization can have the
potential for disturbing the axiomatic formalism once
established, whatever it may be. This is because no axiom claims
the intangible power to tame all of the possible dissidents
completely.
Physics and physicists have been lucky in avoiding any serious
encounter with such outlaws by securing its disciplinary boundary
tight or by excluding biology and sociology from their territory.
But, the time has been changing. Recently, something called
information has been haunting in many places even in physics. If
axiomatization of information is really possible in physics like
many others in the past (of course, Shannon's is one attempt in
this direction), it would certainly be a greatest feast. The only
anxiety I have now with this possibility is I don't know how long
it would take. If it would take too long, my bet would be to do
something else by that time, namely, to face the object-oriented
activities latent in information that have not yet been
structuralized, even though nasty
or messy.
Charlie, I thank you for giving me an impetus for verbalizing
things in the above , even if you
disagree.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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I just read through this whole thread, and I think I see what is
at the root of it. At least, I see the aspect of the discussion
which taxes my poor brain the most!! I am not surprised that it
is also the aspect which none of
my postings have addressed.
I think that Koichiro's position is summed up by the following
two excerpts:
In article <9404291423.AA03156@voscc.nagaokaut.ac.jp> he
writes:
> Now, the problem for us is: Can internal measurement from a
>molecule's viewpoint stand alone without offending the two of
>phenomenological irreversibility and the reversible
>microdynamics? If you say the molecule's viewpoint is just a
>metaphor and don't take it seriously, your position would reduce
>to that of physicists accepting phenomenological irreversibility,
>reversible microdynamics and reversible computation.
>
> On the other hand, if you ask to take internal measurement
>from a molecule's viewpoint seriously, there would appear at
>least two different observers observing the same microscopic
>process; one is the external observer who said the microdynamics
>follows the reversible one-to-one law, and the other is the
>internal observer claiming the molecule's viewpoint. At issue is
>how these two observers could communicate with each other and
>establish the consensus, if any. If the consensus cannot be
>reached, then, what would happen? Tom, don't take me wrong. In
>doing so, I have tried to corner myself. Some of my attempt for
>the way out I tried is in my Protobiology: Physical Basis of
>Biology (CRC Press, Boca Raton Florida, 1989).
>
And again:
koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP) wrote:
: These two observations remind me of a unique aspect of the
: deterministic one-to-one law, namely, a complete absence of the
: capacity of recognition or measurement on the part of the law
: itself. On the other hand, one of the basic attributes of
: information is the capacity of recognition on the side called the
: receiver, whatever it may be. A real difficulty with the one-
: to-one law is its incompetence in coming to grips with the
: quality called recognition or measurement that distinguishes
: between the a priori uncertainty and the a posteriori less
: uncertainty. No tree inside the wood covered by the one-to-one
: law can come up with the capacity of recognition. The one-to-
: one law with noise as a derivative of the one-to-one law with no
: noise cannot assume the capacity of recognition as the
: indispensable attribute of information.
Correct me if I am wrong about the
above, Koichiro.
Here are some thoughts of my own.
They may be best ignored!
At the level of the one-to-one law there is no need for a capacity for
measurement. To be more precise- the one to one law is only of use as
a working model to a "universal, omnipotent observer". Armed with it,
and a single measurement of state, and a suitable universal computer,
this observer can exactly predict the state of the universe at any
time in the future. Given the nonlinear nature of even very simple
mechanical systems (consider the three body problem, let alone 6E23)
we find ourselves to be very far
from omnipotent!!
So we find ourselves to be in the woods, to use Koichiro's metaphor,
and they are dark and deep. To find out about them we must perform
measurements. Philosophy offers us many models for the absolute
structure of them, none of which we can prove to be true, because of
the limited nature of the measurements we can perform. There may be a
one-to-one law in operation, or it may just be that a benign deity makes
it look that way. Whatever is out there, we are in here. This is just as
true at the molecular level: I am a piece of EcoRi - Am I in a cell or
am I in a test tube? It doesn't matter as all I can measure is whether
I am on a site which I recognise.
Now, to get back to the issue of communication as described in the first
of the two posts I have included above, there is no way of establishing
a two way consensus between the different models. Whilst the unibersal
observer can look at the measurements done by Charlie Cook, and say that
they are consistent with the output of the program on the computer, how
can CC even conceive the scale of that computer. Equally, whilst I may
look at EcoRi in a test-tube and find that it's behaviour is consistent
with my model for binding, how can it conceive of anything more complex
than yes or no. In the latest post:
: If the issue of information on material grounds is claimed not
: to be ill-stated, it should be prerequisite for us to recognize
: that molecules have the capacity of recognition in the manner
: being incommensurable with the deterministic one-to-one law.
The EcoTi is a two state machine, it only knows either `got it` or
`haven't got it`. Only at the level of the CC observer or above can it
be said that EcoRi has `recognised` CGATT (or whatever it does - sorry
to all the bio*ists out there :-)) . It is only if the two levels of
measurement of information start getting muddled that things
become ill-stated.
Similarly, I (Charlie) might make a set of measurements of a piece of
string and say that I have determined that it is 50.0cm +/-0.2cm long.
The universal observer would say that I measured:
1) (length of string, 50.128467839457....cm) + (0.0238747cm due to position
of my head with respect to the scale) + ( -0.193487289345cm due to
inaccuracy of ruler) + ....
2) similarly for the second measurement, etc
Both Charlie and the UO are talking about the same acts but have different
capacities for describing those acts.
Somewhere in the above there may lurk some sense. It is late and I may
have strangled it in the writing,
Charlie
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <CpAxFJ.2E4@ncifcrf.gov>
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In article <2ps2pk$9os@mojo.eng.umd.edu> hughb@eng.umd.edu (Hugh Brunk) writes:
| In article <Cozx34.Bs0@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov (Tom Schneider) writes:
|
| >Actually, I start from statistics (Gaussian distribution from law of large
| >numbers) and electrical engineering (Nyquist's N=WkT).
|
| There seems to be a lot being written about Gaussian distributions and
| how they come about. If I'm not mistaken, the reason for the
| pervasiveness of Gaussian distributions is explained not by the laws of
| large numbers, but by the Central
Limit Theorem.
OOps! Thanks for the correction.
| This is my first posting to this group; I saw a lecture Tom Schneider
| gave this week and was excited by his work. I hope to be able to
| contribute something to the info-theory side of issues; I certainly
| won't be telling anyone anything
about microbiology.
Welcome to the group!
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <CpAxBJ.2Co@ncifcrf.gov>
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In article <9404291423.AA03156@voscc.nagaokaut.ac.jp>
kmatsuno@VOSCC.NAGAOKAUT.AC.JP (koichiro
matsuno/7129) writes:
| In article <Cozx34.Bs0@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov>
| (Tom Schneider) writes:
| Now, the problem for us is: Can internal measurement from a
| molecule's viewpoint stand alone without offending the two of
| phenomenological irreversibility and the reversible
| microdynamics? If you say the molecule's viewpoint is just a
| metaphor and don't take it seriously, your position would reduce
| to that of physicists accepting phenomenological irreversibility,
| reversible microdynamics and reversible computation.
|
| On the other hand, if you ask to take internal measurement
| from a molecule's viewpoint seriously,
I think we don't have much choice, that it is hard to even think about
molecular biology without thinking about what happens to individual molecules.
Whether it is a "measurement" is something else, but that they interact as
individuals is not in doubt from
the wealth of experimental data.
| there would appear at
| least two different observers observing the same microscopic
| process; one is the external observer who said the microdynamics
| follows the reversible one-to-one law, and the other is the
| internal observer claiming the molecule's viewpoint. At issue is
| how these two observers could communicate with each other and
| establish the consensus, if any. If the consensus cannot be
| reached, then, what would happen? Tom, don't take me wrong. In
| doing so, I have tried to corner myself. Some of my attempt for
| the way out I tried is in my Protobiology: Physical Basis of
| Biology (CRC Press, Boca Raton
Florida, 1989).
You are right, there are two viewpoints. The "chemical" viewpoint tends to be
the macroscopic one. In this view one treats huge numbers of molecules and
talks about their concentrations. For many problems this works quite well.
However, for the problem of how a single molecule of EcoRI finds its binding
site precisely, it doesn't make sense to talk about their concentrations
because a single molecule does it independently of all the other molecules in
solution (assuming that there is not too much crowding). I find it amusing
that we can use the tools of molecular biology to determine the kinds of things
the individuals do, even though we are (almost!) always working with huge
numbers of molecules. Recent experiments are actually starting to work with
single molecule interactions and so the game is shifting in an interesting
direction. There is no conflict between the two views as long as we keep clear
about which view we are taking. That is, I don't know of cases where the
population effects are inconsistent with single molecule actions. Of course
one can get oneself into trouble easily, for example, by trying to explain why
EcoRI is precise by talking about
concentrations of the molecules.
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <CpAzAx.2zz@ncifcrf.gov>
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In article <9405031225.AA21935@voscc.nagaokaut.ac.jp>
kmatsuno@VOSCC.NAGAOKAUT.AC.JP (koichiro
matsuno/7129) writes:
| Soon after I put the post "one-to-one ?" on the net on the
| 19th of April, Tom Schneider, Tony Booth, Charlie Cook and Hugh
| Brunk joined and took their time for making their comments on it.
| I certainly appreciate that. At the same time, I feel the need
| to shift the gear a little bit
more toward the normal position.
I think that I speak for a lot of people to say that we also appreciate your
efforts in this discussion!
| These two observations remind me of a unique aspect of the
| deterministic one-to-one law, namely, a complete absence of the
| capacity of recognition or measurement on the part of the law
| itself. On the other hand, one of the basic attributes of
| information is the capacity of recognition on the side called the
| receiver, whatever it may be. A real difficulty with the one-
| to-one law is its incompetence in coming to grips with the
| quality called recognition or measurement that distinguishes
| between the a priori uncertainty and the a posteriori less
| uncertainty. No tree inside the wood covered by the one-to-one
| law can come up with the capacity of recognition. The one-to-
| one law with noise as a derivative of the one-to-one law with no
| noise cannot assume the capacity of recognition as the
| indispensable attribute of information.
|
| If the issue of information on material grounds is claimed not
| to be ill-stated, it should be prerequisite for us to recognize
| that molecules have the capacity of recognition in the manner
| being incommensurable with the
deterministic one-to-one law.
This is an important problem. If we have a box with one-to-one physics, how
can we also have a recognition process? From the omniscient viewpoint it isn't
necessary. But living things don't have an omniscient viewpoint because they
are finite. Molecules within a living thing are even "more" finite (eg, most a
precise number of atoms). So the question is whether it makes sense for
recognition to be there. I think the answer is "mu": you're asking the wrong
question (perhaps you could give a better definition, I hope mine is at least
approximately right! :-). The reason is that living things exist - so even if
the universe is perfectly deterministic, we go on our bumbling way. Evolution
continues despite. Those who throw up their arms and moan "what's the use!"
and then kill themselves... are selected against and don't contribute to the
gene pool further! So we have this crazy survival instinct even if there is no
purpose to existence...
We might as well enjoy it and have
fun!
The point here is to keep in mind the special feedback loop of evolutionary
selection. This is one of the features that crisply distinguishes biology from
physics. In physics it doesn't matter if recognition happens or not, but in
biology what happens drives evolution.
One way to think about this problem on a more finite scale is a big molecular
simulation of water DNA and EcoRI. The simulation is finite and closed, so it
is deterministic. The EcoRI would move around and eventually find its GAATTC
sites, just as in the "real" world. Recognition would proceed within the
one-to-one physics of the simulation.
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
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In article <Cp726z.30E@cix.compulink.co.uk> abooth@cix.compulink.co.uk
("Anthony Booth") writes:
| I thank Tom for his reply from which the above sequence is taken, and I
| am particularly grateful in general for his willing, cheery and tolerant
| style of handling these sticky areas of thought. It sometimes surprises
| me that he can keep it up so well.
Thanks. I suppose the reason that I keep it up is because it is so critical to
my work. It may be that a small remark by someone here has enormous
consequences for the direction of my or other people's research. Basically I'm
testing my world view against yours. If I'm wrong, then (boo hoo) I'll have to
accept that. John Spouge and I had many wonderful sparing contests before this
group formed. Some of them were pretty disturbing to me, but my understanding
of the theory did turn out stronger in the end. (I'm thinking about the time
that John pointed out that he could beat Shannon's channel capacity by doing
temperature shifts with materials with special heat capacity properties over
the shift range. This disturbed me a lot and it took a while to find out how
to get around it: molecular machines operate at only one temperature! That
has the neat consequence of allowing
the integration of dS>=dq/T).
| I value that as a critical new input
| where this sort of difference exists, and one which is almost absent in
| the usual formal sorts of communications
on these subjects.
The neat thing about this method of communication is that everybody can speak
(we are not moderated) until everybody is either exhausted (! ;-) or
understands everyone else...
| By his list of localised comments Tom tempts me, even invites me to reply
| again to his remarks, for there are surely many further things which
| could be said to develop the shower of little differences which are
| evident in this sequence, and that was only part of Tom's reply! Oddly,
| I would love to reply (I will willingly do so separately Tom at your
| slightest desire either privately or on the net), and true, some of the
| points could do with tightening up by any standards of good reasoning (my
| points I mean), but to my mind the sequence contains many points of
| contention which are traceable to a single and important underlying
| difference of approach.
As usual, it would be better to do
it on the net, if you have the energy.
| It seems to me that the technique of amplifying individual points of
| difference below the level of the main thesis pulls the argument away
| from the essence of what needs to be grasped here. That is not true for
| all arguments, but it is for those which stand to benefit from the
| introduction of new models rather than from the consolidation of existing
| ones. So I shall continue to try to hold a general view of the process
| of the debate. The little sequence above then is an example of how these
| differences can come out in everyday
expressions.
Fortunately we can split off another
thread!
| To try to focus this basic difference of mind set I suggest the issue I
| mentioned above of whether the subject stands to gain most from
| development of its models, or from
consolidation of existing models.
I personally am trying to consolidate my models, but I think that other people
should do whatever they want, perhaps develop competing models to mine. Then
we can have a derby at the lab bench!
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <CpCDAq.6B@ncifcrf.gov>
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Date: Thu, 5 May 1994 18:13:35 GMT
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In article <9405051333.AA00823@voscc.nagaokaut.ac.jp>
kmatsuno@VOSCC.NAGAOKAUT.AC.JP (koichiro
matsuno/7129) writes:
| In short, I can see that
| the one-to-one physics can simulate the capacity of recognition
| surviving in thermodynamics to the extent that the one-to-one law
| can generate thermodynamics, though this is a tough job as
| Charlie Cook noted. The one-to-one physics can accordingly
| provide a rich catalogue of simulated biological functions. We
| can even name several peer-reviewed technical journals devoted
| to this subject matter of simulation. Up to this point, both of
| us, I believe, are on the same
boat.
Yes, good.
| Now, what concerns me is that the simulation of recognition
| is not recognition itself, though this may look just as quibbling
| over the terms in its sheer outlook. Whether this is only a
| matter of quibbling over the terms may be seen in the light that
| both you and Charlie observe that the one-to-one law has no need
| for a capacity of recognition, observation or measurement.
| Impressive to the one-to-one physics is that it can simulate the
| process of simulation even if it is completely foreign to the
| conception of recognition. If you see no difference between the
| simulation of recognition and recognition itself, you would be
| certainly right when you say I
am chasing the wrong target.
No, that's a valid point. I do not think that the simulation of recognition is
the same as recognition itself. Simulation of recognition is a model.
Recognition itself is what happens when I put the water, DNA and EcoRI together
in a test tube. I can't see what happens directly, so I make models. One
point about a model is that it does not capture all of the reality. But it is
testable. So I make up models about recognition - perhaps including
simulations or maybe Gedankin simulations (as we have been doing here) and then
see if predictions from the model
match the real world.
| But, the difference between the simulation of recognition and
| recognition itself can become obvious when one decides to commit
| oneself to a grandiose project of getting something looking like
| "life" while fooling around a test-tube in which every bit of
| every likely chemical is mixed together. The serious essence of
| the project is to intend to get a fantastic organization of
| recognition capabilities from a mere mixture of ingredient
| chemicals. Some one calls the project the simulated laboratory
| synthesis of life.
It doesn't need to be as grandiose as you are thinking. One can put together
some rather complex reactions "in vitro". One that comes to mind is DNA
replication, which is of course fundamental to most living things on the planet
(there are RNA viruses). We can do this using using "template" DNA, DNA
polymerase, the four nucleotides, some salt and usually a "primer". The primer
is a short piece of synthetic DNA that will stick to the template by
complementary bases, displacing one of the strands. The DNA polymerase will
find the end of the primer and extend it using the nucleotides. People have
gotten this to work for many different polymerases and many DNAs. (The latest
trick, reported yesterday in the bionet.journals.contents, is to create a
mismatched region of DNA instead of a primer, and Ecoli RNA polymerase will
start there!) Two cases where people use this ability very heavily are PCR and
sequencing. In PCR (polymerase chain reaction, Nobel prize to Kary Mullis last
fall) one sets up a pair of primers and then does multiple rounds of
replication by using temperature shifts. This "amplifies" small pieces of
DNA. It is truly spectacular: one can amplify a single molecule of DNA from a
sperm a million fold! The other heavy use of this "technology" is in DNA
sequencing, where one poisons the replication reaction with fluorescent dyes
attached to nucleotides which cannot be used for further reactions. Another
use is to do a "coupled transcription translation system" in which one allows
RNA to be made, and this is then translated into protein - all in a test tube.
Granted, nobody can take all these parts and make the "blob" yet, but we have
come quite a good distance toward making "life in the test tube" or at least
copying nature.
| The best way to reach the concept of recognition from the one-
| to-one [physics], which doesn't know recognition, is through
| thermodynamics.
Yes, and I think you need to add some concepts from biology also - such as the
"importance" of the recognition to an organism. Otherwise the failure of a
system to show recognition would have no consequence and so there would not be
any way even to know that recognition
took place.
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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From: smb18@mole.bio.cam.ac.uk (Simon Brocklehurst (Bioc))
Subject: Re: one-to-one ?
Date: 5 May 1994 19:21:55 GMT
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toms@fcsparc6.ncifcrf.gov (Tom Schneider)
writes:
>However, for the problem of how a single molecule of EcoRI finds its binding
>site precisely, it doesn't make sense to talk about their concentrations
>because a single molecule does it independently of all the other molecules in
>solution (assuming that there
is not too much crowding).
I'm probably getting something screwed up here, but _in general_
(not necessarily in the specific case of EcoRI) doesn't this argument
about the need to consider only one molecule depend on whether the
"recognition event" is directed somehow, or is the result of a random
collision? That is, if it's directed then considering one molecule
is enough - if not then won't you
need to consider many molecules?
-- Simon
!-----------------------------------------------------------------------
Simon M. Brocklehurst
Cambridge Centre for Molecular Recognition
Department of Biochemistry
University of Cambridge
Cambridge
UK
E-mail: s.m.brocklehurst@bioc.cam.ac.uk
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From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 4 May 1994 18:24:16 -0700
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Charlie's latest piece on "one-to-one ?" touches upon the
inner core of our whole issue in a very sharp way. You hit the
mark.
In article <Cp8x6J.64J@lut.ac.uk> phceac@lut.ac.uk (C. E. A.
Cook) writes:
>At the level of the one-to-one law there is no need for a
>capacity for measurement. To be more precise- the one to one
>law is only of use as a working model to "universal, omnipotent
>observer".
Agreed.
>Armed with it, and a single measurement of state, and a suitable
>universal computer, this observer can exactly predict the state
>of the universe at any time in
the future.
Give me a break here. If I accept the idea of state which you
mentioned in the above, I would also have to admit that
everything would proceed along the line you have already set. The
reservation I would like to keep for myself is that the
conception of state and its identification are feasible only to
the universal objective observer. It doesn't matter whether the
object whose "state" is of interest is a molecule in a test-
tube or a string in the Cosmos. Once the idea of state is applied
to whatever material object, its identification has to be
simultaneous globally irrespective of how large or small it may
be. The conception of state and its global identifiability at
every moment, combined together, allows only the universal
objective observer. Of course, you can mimick the universal
observer, but you also see you are
not the full-sized UO.
So long as you say you are mimicking the universal objective
observer, there should be no difference to be mentioned between
the two of you. If you say the difference turns out to be
serious, on the other hand, you would not be mimicking the other
party any more.
Perhaps, you may agree that physics has long been quite at
home with the idea of state and the universal objective observer.
Its immediate consequence is the preservation of an invariance
under certain symmetric operations that keeps the universality
of the observer. The one-to-one law is a superb example
demonstrating the symmetric law keeping such a universality.
Precisely for this reason, symmetry-breaking phenomena have been
thought as being no more than trivial appendages to the
privileged symmetric laws. (Think about a source of symmetry-
breakings for phase transitions which solid state physicists have
come up with or a big fuss about the Higgs particle for high
energy physicists around the failed
SSC).
What concerns me most here is information. If we can hope to
understand information in terms of symmetric laws supplemented
by minor symmetry-breakings out of the blue, it may be said that
the duo of state and the universal objective observer could take
care of us. Conversely, if symmetry-breakings are rather the rule
for information, we would have to get rid of the stipulation of
state and the universal observer. One circumstantial evidence
demonstrating information as an attribute of symmetry-breaking
phenomena is the presence of the people who are sympathetic to
the Bayesian approach to probability distinguishing between the
a priori uncertainty and the a posteriori less uncertainty. The
price we have to pay for adopting the symmetry-breaking between
the a priori and the a posteriori would be to abandon the
conception of state no matter how useful it may be for other
purposes. Instead, the idea of events or the idea of difference
would come to the fore, although we are still not well accustomed
to thinking of events or differences without employing the idea of
state.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 5 May 1994 06:39:02 -0700
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In article <CpAzAx.2zz@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov
(Tom Schenider) writes:
>...a big molecular simulation of water DNA and EcoRI. The
>simulation is finite and closed, so it is deterministic. The
>EcoRI would move around and eventually find its GATTC sites,
>just as in the "real" world. Recognition would proceed within
>the one-to-one physics of the
simulation.
Also, in article <Cozx34.Bs0@ncifcrf.gov>
TS writes:
>So I am happy with a one-to-one physics (meaning every moment
>is predicted exactly from the previous moment) that is
>reversible ...
Okay, Tom. Let me try how well, or poorly, I can follow what
you are saying. The magic word is "simulation". Your system of
water DNA and EcoRI can be a model of the one-to-one physics. I
accept that. I also accept the association of the touch-and-go
of EcoRI with a simulated recognition. In short, I can see that
the one-to-one physics can simulate the capacity of recognition
surviving in thermodynamics to the extent that the one-to-one law
can generate thermodynamics, though this is a tough job as
Charlie Cook noted. The one-to-one physics can accordingly
provide a rich catalogue of simulated biological functions. We
can even name several peer-reviewed technical journals devoted
to this subject matter of simulation. Up to this point, both of
us, I believe, are on the same boat.
Now, what concerns me is that the simulation of recognition
is not recognition itself, though this may look just as quibbling
over the terms in its sheer outlook. Whether this is only a
matter of quibbling over the terms may be seen in the light that
both you and Charlie observe that the one-to-one law has no need
for a capacity of recognition, observation or measurement.
Impressive to the one-to-one physics is that it can simulate the
process of simulation even if it is completely foreign to the
conception of recognition. If you see no difference between the
simulation of recognition and recognition itself, you would be
certainly right when you say I am
chasing the wrong target.
But, the difference between the simulation of recognition and
recognition itself can become obvious when one decides to commit
oneself to a grandiose project of getting something looking like
"life" while fooling around a test-tube in which every bit of
every likely chemical is mixed together. The serious essence of
the project is to intend to get a fantastic organization of
recognition capabilities from a mere mixture of ingredient
chemicals. Some one calls the project the simulated laboratory
synthesis of life.
The real problem with any simulation is what to simulate by
what. If one employs termodynamics as a means of simulating
something else, one can expect to incorporate the capacity of
recognition being possible in thermodynamics also in the
simulated. The highest hurdle for actualizing the simulated
laboratory synthesis of life from the random mixture of likely
chemicals is in the apparent inadequacy of the capacity of
recognition that the thermodynamics
of the mixture could provide.
Of course, you can demonstrate the thermodynamic capacity of
recognition between EcoRI and DNA if thermodynamics of the system
of EcoRI and DNA is guaranteed. What is really significant to
thermodynamics, to my mind, is that it carries the capacity of
recognition or the methodological incompleteness such that
thermodynamics alone does not specify, unless supplemented by,
say, the atomic gas theory, the value of each thermodynamic
variable, while the value has been determined in retrospect. Only
in this sense, the one-to-one physics can be said to come up with
the simulated recognition when it
generates thermodynamics.
The best way to reach the concept of recognition from the one-
to-one physicis, which doesn't know recognition, is through
thermodynamics.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@vosc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 6 May 1994 04:58:24 -0700
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In article <2qbh0j$d88@lyra.csx.cam.ac.uk>
smb18@mole.bio.cam.ac.uk (Simon Brocklehurst
(Bioc)) writes:
>..., but _in general_ (not necessarily in the specific case of
>EcoRI) doesn't this argument about the need to consider only one
>molecule depend on whether the "recognition event" is directed
>somehow, or is the result of
a random collision?
Perhaps, my tentative answer to your question, one of the
deepest questions in information-biology,
is, Both.
Thermodynamics of molecular recognition is at least two-
staged; before beginning to recognize the other party and after
that. Molecular biologists concern themselves with what is going
to happen once the concerned parties begin to recognize each
other, or with molecular recognition among intimates in short.
It takes a pretty long time as McClare and Mae-Wan Ho noted. At
this stage, although it is certainly legitimate, thermodynamics
doesn't help molecular biologists much compared to molecular
biology which is more specific. On the other hand, before those
potential partners get close contact with each other, the major
driving factor for the close encounter is thermal agitations or
Brownian motion and certainly not directed. Physicists can
engineer the molecular recognition driven by Brownian encounter
in their labs.
Molecular recognition among intimates for molecular biologists
and molecular recognition driven by Brownian encounter for
physicists are just the polar opposites. Real biology may find
itself somewhere in between.
Molecular recognition among intimates may be seen as directed
in the sense that those intimates are involved at least in
eliminating internal conflicts such as the would-be violation of
the first law of thermodynamics (or "energy is energy" a la Marc
Roussel) while recognizing each other. In contrast, molecular
recognition driven by Brownian encounter may be seen as non-
directed, in which the energy transaction is completed
independently and almost instantaneously compared to molecular
recognition among intimates.
This way of looking at molecular recognition may give us some
hint on John Cairns' directed mutations,
also.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 7 May 1994 00:05:48 -0700
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In article <Cp8x6J.64J@lut.ac.uk> phceac@lut.ac.uk (C. E. A.
Cook) writes:
>..., there is no way of establishing a two way consensus between
>the different models. Whilst the [universal] observer can look
>at the measurements done by Charlie Cook, and say that they are
>consistent with the output of the computer, how can CC even
>conceive the scale of that computer.
Addressing to almost the similar issue, Tom Schneider wrote in
the article <Cozx34.Bs0@ncifcrf.gov>:
>..., there are two viewpoints. The "chemical" viewpoint tends
>to be the macroscopic one. In this view one treats [huge]
>numbers of molecules and talks about their concentrations. For
>many problems this works quite well. However, for the problem
>of how a single molecule of EcoRI finds its binding site
>precisely, it doesn't make sense to talk about their
>concentrations because a single molecule does it independently
>of all the other molecules... There is no conflict between the
>two views as long as we keep
clear which view we are taking.
Both Charlie and Tom are right in their own perspectives,
though a bit different from mine. When I said "There would appear
at least two different observers observing the same microscopic
process; one is the external observer..., and the other is the
internal observer claiming the molecule's viewpoint. At issue is
how these two observers could communicate with each other and
establish the consensus, if any." in the article
<9404291423.AA03156@voscc.nagaokaut.ac.jp>, I had the following
three cases in mind: two different external observers, one
external and one internal observer, and one external and more
than one internal observers. The internal observer is like some
one sitting on the shoulder of each
molecule.
When Charlie says no way of establishing a two way consensus
between the different models, the universal observer and Charlie
Cook, both are the observers external to the object to be
observed. There should be no way and even no need of establishing
the two way consensus, because the object takes care of itself
whatever may happen between UO and
CC.
When Tom says no conflict between the two views, the case he
considered is one external and one internal observer. So long
as each observer sticks to its own model firmly without suffering
forced interferences from its outside, each view can hold. Since
each one of the external and the internal observer is external
to the other, the integrity of each view can be guaranteed when
properly worked out.
Now, the situation would become drastically changed if more
than one internal observers participate. In fact, if we count the
number of molecules interacting among themselves, the number of
the internal observers sitting on the shoulder of each molecule
can be a great many. If we admit that each internal observer has
its own model of itself and its outside, a new difficulty would
come up which both Charlie and Tom could avoid shrewdly and
deliberately. That is the inevitable interferences among those
internal models. Consider, for instance, the energy transaction
perceived and maintained by each internal observer. Unless
properly coordinated among themselves, even the first law of
thermodynamics would get into trouble. This sticky problem is
fortunately absent in both Charlie's
and Tom's case.
My inclination toward facing Bio & Info is to live with how
well our fellow internal observers could manage their business,
including even their day-to-day energy transactions, while
experiencing the unexpected all the
time.
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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To: bio-info@net.bio.net
From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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As Anthony Booth says in <Cp726z.30E@cix.compulink.co.uk> :
"... the technique of amplifying individual points of
difference below the level of the main thesis pulls the argument away
from the essence of what needs to
be grasped here."
That is so true- it's far easier
to see the trees than the forest.
In article <Cp60rG.46H@lut.ac.uk> phceac@lut.ac.uk (C. E. A.
Cook) writes:
>We also, if we assume causality (I hope that is [the right]
>term) and do not let God play with the works, know that the condition
>of the universe at the end is determined solely by it's state at
>the beginning. This is my "uncompromisable framework" - it is not
>theoretical, and it has nothing to do with the observer. I think
>it's an axiom.
In <9405040521.AA25108@voscc.nagaokaut.ac.jp> Koichiro writes:
"Any process born out
of observation or measurement that has the capacity of going
beyond any structure-oriented axiomatization can have the
potential for disturbing the axiomatic formalism once
established, whatever it may be. This is because no axiom claims
the intangible power to tame all of the possible dissidents
completely. "
This looks like an expression of Godel's Incompleteness theorem. The
point is that if we find that we need to deal with entities for which
our axioms are inadequate, then we must *define* new axioms. I am
quite open to the possibility that my framework could be compromised,
BUT the experiment which does so can only be performed at the level
of the UO, so I shall never see it. For example, consider a "universal
intervener" ( or UO-with-a-spanner ). Whether or not the UI exists is
irrelevant to me, unless it starts tampering in such a way that I find
my uncompromisable framework to be invalid. I shall then retire to a
cave in the hills for the rest of
my days!!
To get closer to the centre of the issue: Koichiro writes in
<9405050118.AA28888@voscc.nagaokaut.ac.jp>
What concerns me most here is information. If we can hope to
understand information in terms of symmetric laws supplemented
by minor symmetry-breakings out of the blue, it may be said that
the duo of state and the universal objective observer could take
care of us. Conversely, if symmetry-breakings are rather the rule
for information, we would have to get rid of the stipulation of
state and the universal observer.
As I wrote
>Armed with it, and a single measurement of state, and a suitable
>universal computer, this observer can exactly predict the state
>of the universe at any time in the future.
"it" being the one-to-one law. In other words, the UO has the ability
to declare all events to be either of probability 0 or 1 . However,
thisis not the only way of describing those events. The UO can still
calculate conditional probabilities, and by marginalising some of the
variables it could arrive at a description of the universe in terms of
H,T,S etc. It would have discarded information in the process, but it
would have a different perspective of the dynamics of the universe.
Scientists often do the same thing when they perform MonteCarlo studies
of processes. The difference between mere mortals and the UO is that
we can only measure the universe imperfectly, so we are stuck with the
asymmetry of knowing less today than we will tomorrow (we hope!). This
lack of symmetry is not a feature of the physical processes taking
place ( the 1-to-1 is symmetric), nor is it "out of the blue", it is
a consequence of the observer's (that's us) limited measurement ability.
The asymmetry does not force us to abandon the 1-to-1 description of
the universe, it just means that we need to try to look for aspects of
the 1-to-1 which we can measure and test and use as tools for predicting
the future. This is fundamental to the hypothesise-predict-test cycle
by which science progresses.
In <9405051333.AA00823@voscc.nagaokaut.ac.jp>, Koichiro writes:
"In article <CpAzAx.2zz@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov
(Tom Schenider) writes:
>...a big molecular simulation of water DNA and EcoRI. The
>simulation is finite and closed, so it is deterministic. The
>EcoRI would move around and eventually find its GATTC sites,
>just as in the "real" world. Recognition would proceed within
>the one-to-one physics of the simulation.
[ paragraph deleted ]
Now, what concerns me is that the simulation of recognition
is not recognition itself, though this may look just as quibbling
over the terms in its sheer outlook.
"
No, no ! Surely recognition is a way of describing what takes place in
both the simulation and in a real tube of chemicals. This is just like
the UO calculating the temperature of a part of the universe from the
velocities it gets as an output of its universal computer. What is
acually happening in both the simulated and the actual test-tube is that
molecules are bouncing around under the influence of forces due to other
molecules. "recognition" is a term used to describe a particular event
which can take place as a result of this bouncing. Just by saying that
'EcoRi has recognised GATTC' we have placed recognition at a level above
EcoRi. EcoRi is a machine of 2 states (1 bit) - bound or unbound. The
recognition of which we speak involves 5 bases at 2bits/base. In the
same way the UO had a far more information-rich description of my
measurements of that piece of string than I did, although in that case
it was by infinite numbers of bits ( since all of its descriptions were
to infinite precision!) .
I am sure that if this distinction is made between the event which we call
recognition and the process leading to it, then much of the confusion
will evaporate. We can divide the process into as many stages as we please,
although it makes sense to ensure that we have a way of describing each
of those stages. However, as long as we only use recognition as a term
for the event at the end then all of the different ways of describing
that process are consistent with each other. Starting with the top level,
the UO's computer gives a set of coordinates for the positions of all the
molecules as a function of time, up to the moment when Ecori slides down
the potential well into its bound state on the nucleic acid molecule.
It is equally possible, and much more useful for us as human observers,
to divide it into 3 stages : Brownian motion of EcoRi in solution,
described by a probability of colliding with a DNA molecule ; movement
along the DNA described by the probabiltity of jumping to the next site;
finally, arrival at GATTC with the ensuing slide into the bound state.
Note that the probabilities are temperature and concentration dependent,
which is where the thermodynamics comes in. Also the slide into binding
is there for the molecular biologists. Note also that this way of
*describing* the process is not possible for an observer with the
perspective of the EcoRi molecule. What IT sees, is :
Ouch( hit by water molecule!)
Ouch( hit by water molecule!)
Ouch( hit by water molecule!)
Ouch( hit by water molecule!)
Ouch( hit by water molecule!)
...
Ah, what's this thing?( on the DNA chain )
Feels sort of bumpy!(moving along it )
Hey, I've stopped moving! ( Bound!!
)
[ NB this is a slightly different description of EcoRi from the one I
used before- now it has 3 states ]
What the EcoRi itself sees is :
State 1 ( unbound state, for some time )
State 2 ( on the chain but unbound, for some further time )
State 3 ( Bound! forever )
I stress that all three of the descriptions of the process ( notice
that it is singular) are equally valid. So indeed are :
> Molecular recognition among intimates for molecular biologists
> and molecular recognition driven by Brownian encounter for
> physicists
but I strongly disagree that they
> are just the polar opposites. Real biology may find
> itself somewhere in between.
They are different ways of describing the same thing. In fact the physicist
will include the molecular biologists work in his/her description. If we
want to talk of directed processes as against non-directed then we are
really just making the distinction between those which are probabilistic
and those which are inevitable.
I was going to express each of the above descriptions in terms of
conditional probabilities, but this
has already got too long.
[ I just spotted the latest post,
and it fits in so nicely....
koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP) wrote:
>Now, the situation would become drastically changed if more
>than one internal observers participate. In fact, if we count the
>number of molecules interacting among themselves, the number of
>the internal observers sitting on the shoulder of each molecule
>can be a great many. If we admit that each internal observer has
>its own model of itself and its outside, a new difficulty would
>come up which both Charlie and Tom could avoid shrewdly and
>deliberately. That is the inevitable interferences among those
>internal models. Consider, for instance, the energy transaction
>perceived and maintained by each internal observer. Unless
>properly coordinated among themselves, even the first law of
>thermodynamics would get into trouble. This sticky problem is
>fortunately absent in both Charlie's
and Tom's case.
Each observer, wherever it is, must have a view which is consistent
with what si actually happening - the universe does it's stuff regardless
of who is watching, and it does the same thing for all observers. It is
therefore impossible for the views of the different observers to be
inconsistent, because they have all been watching the same thing, and
whichever observer does the arbitration must be on a level not below the
highest of those between which it measures consistency. They do not have
to have any active coordination: it is inherent. Has anyone heard of the
odd sock theorem?
Regards
Charlie
Charlie Cook
Department of Physics
Loughborough University of Technology
Loughborough
UK
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From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
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In article <2qbh0j$d88@lyra.csx.cam.ac.uk> smb18@mole.bio.cam.ac.uk (Simon
Brocklehurst (Bioc)) writes:
| ... doesn't this argument
| about the need to consider only one molecule depend on whether the
| "recognition event" is directed somehow, or is the result of a random
| collision? That is, if it's directed then considering one molecule
| is enough - if not then won't you
need to consider many molecules?
What do you mean by "directed"? There is no outside agent which directs the
motions of molecules in cells. That would be vitalism. The molecules have to
locate their binding sites by themselves. This doesn't mean that a bunch of
them might not have to work together though. In many cases more than one
protein binds to a region of DNA and together they form a complex. If the
concentration of one of the necessary components is low, the complex may not
form or may not function. Yet the individuals are still acting as distinct
units, the concentration is an indirect measure of the probability that the
individuals will get together.
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <CpJq1J.GME@ncifcrf.gov>
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In article <CpI1u8.I6F@lut.ac.uk>
phceac@lut.ac.uk (C.E.A.Cook) writes:
| In <9405051333.AA00823@voscc.nagaokaut.ac.jp>, Koichiro writes:
| "In article <CpAzAx.2zz@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov
| (Tom Schenider) writes:
| >...a big molecular simulation of water DNA and EcoRI. The
| >simulation is finite and closed, so it is deterministic. The
| >EcoRI would move around and eventually find its GATTC sites,
| >just as in the "real" world. Recognition would proceed within
| >the one-to-one physics of
the simulation.
You somehow lost one of the As.
The original statement was:
| One way to think about this problem on a more finite scale is a big molecular
| simulation of water DNA and EcoRI. The simulation is finite and closed, so it
| is deterministic. The EcoRI would move around and eventually find its GAATTC
^
| sites, just as in the "real" world. Recognition would proceed within the
| one-to-one physics of the simulation.
| which can take place as a result of this bouncing. Just by saying that
| 'EcoRi has recognised GATTC' we have placed recognition at a level above
EcoRI GAATTC
| EcoRi. EcoRi is a machine of 2 states (1 bit) - bound or unbound. The
| recognition of which we speak involves 5 bases at 2bits/base. In the
6
| Ouch( hit by water molecule!)
cute!
| What the EcoRi itself sees is :
| State 1 ( unbound state, for some time )
| State 2 ( on the chain but unbound, for some further time )
| State 3 ( Bound! forever )
EcoRI will not stay in state 3, it will return to the other two
states eventually, according to a
Boltzmann distribution.
I'm glad to see you starting to think
about how the molecule works.
| Has anyone heard of the odd sock
theorem?
Nope, would you like to explain?
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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From: smb18@mole.bio.cam.ac.uk (Simon Brocklehurst (Bioc))
Subject: Re: one-to-one ?
Date: 9 May 1994 18:52:56 GMT
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toms@fcsparc6.ncifcrf.gov (Tom Schneider)
writes:
>What do you mean by "directed"? There is no outside agent which directs the
>motions of molecules in cells. That would be vitalism. The molecules have to
>locate their binding sites by
themselves.
Sorry, I wasn't referring to an outside agent of some kind. What
I mean by 'directed' is simply that there may something about the structure
of the, say two, molecules that allows them to 'send signals to each
other' to guide the interaction. In this case you would get more
productive collisions than would be expected by a consideration
of random thermal motion.
One of the best examples of this kind of thing is an intramolecular example:
protein folding (my favourite!). We all know that the molecule doesn't
explore all possible conformations randomly - rather the folding is directed
in some way i.e. atoms in the protein 'send signals to each other'. There
is no reason why this kind of thinking cannot be extended to inter-molecular
examples.
On the other hand, there are other examples of where it's just the
relative kinetic energies of the
molecules are important...
Any clearer?
-- Simon
!-----------------------------------------------------------------------
Simon M. Brocklehurst
Cambridge Centre for Molecular Recognition
Department of Biochemistry
University of Cambridge
Cambridge
UK
E-mail: s.m.brocklehurst@bioc.cam.ac.uk
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From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <CpJxpC.L4L@ncifcrf.gov>
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In article <2qm0q8$3gc@lyra.csx.cam.ac.uk> smb18@mole.bio.cam.ac.uk (Simon
Brocklehurst (Bioc)) writes:
| toms@fcsparc6.ncifcrf.gov (Tom Schneider) writes:
|
| >What do you mean by "directed"? There is no outside agent which directs the
| >motions of molecules in cells. That would be vitalism. The molecules have to
| >locate their binding sites by themselves.
|
| Sorry, I wasn't referring to an outside agent of some kind. What
| I mean by 'directed' is simply that there may something about the structure
| of the, say two, molecules that allows them to 'send signals to each
| other' to guide the interaction. In this case you would get more
| productive collisions than would be expected by a consideration
| of random thermal motion.
Yes, a nice example of that is known already: proteins like EcoRI track the
DNA using electrostatic interactions. DNA is negatively charged, making two
"rail road" tracks (with a twist!), EcoRI has positive charges on its surface
that allow it to follow the tracks. People have demonstrated tracking
experimentally, and have worked on the theory of diffusion. It turns out that
since tracking lowers the dimensionality of the search space from 3 to 1
dimension, the rate of finding the
binding site is increased.
So, going back to our previous comments:
| [Tom S wrote:]
| >However, for the problem of how a single molecule of EcoRI finds its binding
| >site precisely, it doesn't make sense to talk about their concentrations
| >because a single molecule does it independently of all the other molecules in
| >solution (assuming that there is not too much crowding).
|
| I'm probably getting something screwed up here, but _in general_
| (not necessarily in the specific case of EcoRI) doesn't this argument
| about the need to consider only one molecule depend on whether the
| "recognition event" is directed somehow, or is the result of a random
| collision? That is, if it's directed then considering one molecule
| is enough - if not then won't you
need to consider many molecules?
No, it doesn't matter whether or not it is directed. The unit which recognizes
GAATTC is a single EcoRI protein, so other molecules are not relevant. This is
one of the advantages of considering only the "before" and "after" states of a
molecular machine operation. The mechanism in between those two states doesn't
matter. So whether EcoRI finds its sites by tracking along the DNA or by
hopping off and back on (or a combination, which is what happens in reality)
doesn't matter for the computation
that says the site has 12 bits.
| One of the best examples of this kind of thing is an intramolecular example:
| protein folding (my favourite!). We all know that the molecule doesn't
| explore all possible conformations randomly - rather the folding is directed
| in some way i.e. atoms in the protein 'send signals to each other'. There
| is no reason why this kind of thinking cannot be extended to inter-molecular
| examples.
An interesting conjunction of ideas: perhaps protein folding IS directed in
the sense you mean, with the mechanism I mentioned. Imagine that the charges
on the protein form a changing electrostatic field in the water or through the
water by polarizing individual molecules. This field could guide folding far
before the chains could come together to interact physically. I have not heard
of anyone trying this approach, but it might be pretty easy to give a first
shot at it by simulating a string of charged and uncharged particles in
Brownian motion. Would the string tend to form something like the finally
folded protein?
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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Tom Schneider (toms@fcsparc6.ncifcrf.gov) wrote:
: In article <CpI1u8.I6F@lut.ac.uk>
phceac@lut.ac.uk (C.E.A.Cook) writes:
: | In <9405051333.AA00823@voscc.nagaokaut.ac.jp>, Koichiro writes:
: | "In article <CpAzAx.2zz@ncifcrf.gov> toms@fcsparc6.ncifcrf.gov
: | (Tom Schenider) writes:
: | >EcoRI would move around and eventually find its GATTC sites,
: You somehow lost one of the As.
The original statement was:
I blame it on Koichiro!! :-) ( Cook's zeroth law:
When In Trouble, Find A Scapegoat
)
: | Ouch( hit by water molecule!)
: cute!
Cute for us, but I bet it's pretty painful for Ecori.
Painful, but not boring!! What bliss
it would be to have no memory!
: | What the EcoRi itself sees is :
: | State 1 ( unbound state, for some time )
: | State 2 ( on the chain but unbound, for some further time )
: | State 3 ( Bound! forever )
: EcoRI will not stay in state 3, it will return to the other two
: states eventually, according to
a Boltzmann distribution.
Yes, on whatever scale, there is always a nonzero probability of
a reaction going the 'wrong' way. in this case I have no feel for
the actual values of the probabilities in the model... what are the
relative sizes of the time constants for the different stages?? I
imagine that Ecori traverses at least several sites on the DNA in
the typical time it spends on the chain.
Stage 3 is a bit vague in this particular description... can chain
scission take place ( needs Mg++ in the mix???), in which case I
would say that recognition has occurred, and that that event ( recogn'n
+ scission ) has made information available to a higher observer with
some electrophoresis gel( or whatever you do !!) . Also the probability
for the transition State1 -> State 2 has changed, since now there is one
less piece of DNA(length A), but two pieces of lengths B,C.
On the other hand, if no irreversible step occurs, then in the end another
event occurs, which might be called
'unrecognition'.
: I'm glad to see you starting to think about how the molecule works.
I must step up my efforts to find a good molbio book ( secondhand!).
My latest find was one on game theory, which might be relevant here on
B.I-T. The problem I have been trying to address is not one of what happens,
but of how we describe what happens. That said, keep on pointing out my
mistakes... as long as you've got
the patience!
: | Has anyone heard of the odd sock
theorem?
: Nope, would you like to explain?
I'm not sure I can, it's just a hazy
memory. I'll try to find out though.
Regards,
Charlie
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From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 9 May 1994 20:07:36 -0700
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Charlie Cook phceac@lut.ac.uk writes in
<CpI1u8.I6F@lut.ac.uk>:
>As Anthony Booth says in <Cp726z.30E@cix.compulink.co.uk>:
>>... the technique of amplifying individual points of difference
>>below the level of the main thesis pulls the argument away from
>>the essence of what needs
to be grasped here.
>This is so true- it's far easier to see the trees than the
>forest.
Charlie, don't forget me sitting in the very same bandwagon
you are pulling with Tony. Believe me when I say that I am quite
comfortable with most of what you have been saying. (Also,
believe in my saying that I am neither a professional diplomat
nor politician seeking compromise day in, day out.) The point is
simply this. You said:
>The observer, wherever it is, must have a view which is
>consistent with what [is] actually happening - the universe
>does it's stuff regardless of who is watching, and it does the
>same thing for all observers. It is therefore impossible for
>the views of the different observers to be inconsistent, because
>they have all been watching the same thing, and whichever
>observer does the arbitration must be a level not below the
>highest of those between which it measures consistency. They
>do not have to have any active
coordination: it is inherent.
My naive question occurred to my mind after reading the above
passage is: Is "the universe does the same thing for all
observers" an axiomatic statement or an observational one? If
this statement is an axiomatic one, you can legitimately dismiss
the disturbing question of "By the way, who said that?" and then
I can join you. On the other hand, if it is an observational one,
the question of "Who at all saw that?" could come up. "The
universe does the same thing for all observers" may look okay de
facto, but its observational confirmation costs our fellow
scientists a fantastic amount of time and money which, perhaps,
they could not afford.
It would certainly be wonderful if the universal objective
observer underwrites and takes care of the consistency of our
empirical world. My only concern is that even if we don't know
how properly the UO is doing its job, it would also be nice to
have a do-it-yourself consistency such that the internal
observers of limited capacity take care of themselves and
eliminate likely internal conflicts constantly in the effect so
as to make the UO also happy. I have talked about only the wood,
not the trees.
Regards,
Koichiro
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 9 May 1994 23:14:10 -0700
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Charlie Cook phceac@lut.ac.uk
witres in <CpJtKr.KJv@lut.ac.uk>
>I blame it on Koichiro!! :-) (Cook's zeroth law: When In Trouble, Find
>A Scapegoat.
Charlie, you are 100% right. Moreover, EcoRI would never take GATTC for
GAATTC. Only me and his company ... (Matsuno's hottest third law: Even if
100% right, still 0% wrong).
Regards,
Koichiro
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From: smb18@mole.bio.cam.ac.uk (Simon Brocklehurst (Bioc))
Subject: Re: one-to-one ?
Date: 10 May 1994 12:12:53 GMT
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toms@fcsparc6.ncifcrf.gov (Tom Schneider)
writes:
>An interesting conjunction of ideas: perhaps protein folding IS directed in
>the sense you mean, with the mechanism I mentioned. Imagine that the charges
>on the protein form a changing electrostatic field in the water or through the
>water by polarizing individual molecules. This field could guide folding far
>before the chains could come together to interact physically. I have not heard
>of anyone trying this approach, but it might be pretty easy to give a first
>shot at it by simulating a string of charged and uncharged particles in
>Brownian motion. Would the string tend to form something like the finally
>folded protein?
Could be interesting - if it's going to work, though, surely something in
the model has got to deal with the
"hydrophobic" effect in some shape or form.
I have a hunch that polarization of so-called non-polar groups is important
in protein folding. Time will tell.
Of course, if someone could devise a model that produces native-like folds
without considering the "hydrophobic effect" at all then that would _very_
interesting.
!-----------------------------------------------------------------------
Simon M. Brocklehurst
Cambridge Centre for Molecular Recognition
Department of Biochemistry
University of Cambridge
Cambridge
UK
E-mail: s.m.brocklehurst@bioc.cam.ac.uk
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From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP) wrote:
: Charlie Cook phceac@lut.ac.uk
witres in <CpJtKr.KJv@lut.ac.uk>
: >I blame it on Koichiro!! :-) (Cook's zeroth law: When In Trouble, Find
: >A Scapegoat.
: Charlie, you are 100% right.
A pleasant change for me!!
Still, there's no excuse for me not putting in the effort to find out
some basic molecular biology. I am sure that I would learn much more
from some of the threads on B.I-T
if I did so.
I must learn some molbio.
I must learn some molbio.
I must learn some molbio.
( to be recited by me daily)
Cheers,
Charlie
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From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
Message-Id: <CpLpsD.AoG@ncifcrf.gov>
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In article <CpJtKr.KJv@lut.ac.uk>
phceac@lut.ac.uk (C.E.A.Cook) writes:
| Cute for us, but I bet it's pretty painful for Ecori.
| Painful, but not boring!! What
bliss it would be to have no memory!
Of course EcoRI really doesn't "feel" anything, I'm sure you recognize. But if
it did, it probably would have evolved to "feel" quite at home with all those
violent impacts, in the sense that a polar bear probably has evolved to feel
quite warm most of the time (there is a cartoon that shows a little polar bear
saying to it's ma, "I don't
care what they say, I'm cold!").
For a long time I thought that the lack of memory would have a consequence in
molecular machine theory, but I could never pin it down. McClare thinks he
did, but I haven't seen it lead anywhere useful. On the other hand, a molecule
like rhodopsin, with two distinct after states, does form a kind of memory, and
people are trying to exploit this.
| : | What the EcoRi itself sees is :
| : | State 1 ( unbound state, for some time )
| : | State 2 ( on the chain but unbound, for some further time )
| : | State 3 ( Bound! forever )
|
| : EcoRI will not stay in state 3, it will return to the other two
| : states eventually, according to a Boltzmann distribution.
|
| Yes, on whatever scale, there is always a nonzero probability of
| a reaction going the 'wrong' way. in this case I have no feel for
| the actual values of the probabilities in the model... what are the
| relative sizes of the time constants
for the different stages??
I don't know the relative numbers, but they are probably all on the order of
seconds. If you or someone else has the time/energy/funding/equipment one
could do some experiments to determine
the transition probabilities.
| I imagine that Ecori traverses at least several sites on the DNA in
| the typical time it spends on the chain.
| Stage 3 is a bit vague in this particular description... can chain
| scission take place ( needs Mg++
in the mix???), in which case I
yes, Mg++ is needed
| would say that recognition has occurred, and that that event ( recogn'n
| + scission ) has made information available to a higher observer with
| some electrophoresis gel( or whatever
you do !!) . Also the probability
Yes, people use electrophoresis to separate the chains, or use a radioactively
(eg 32P or non-radioactive methods) labeled DNA and catch them on
nitrocellulose. (DNA normally goes through, but will be held on the filter by
a protein.) Then count they the
radioactivity on the filter.
| for the transition State1 -> State 2 has changed, since now there is one
| less piece of DNA(length A), but
two pieces of lengths B,C.
right.
| On the other hand, if no irreversible step occurs, then in the end another
| event occurs, which might be called
'unrecognition'.
Yes! If we define "information gain" as what happens when EcoRI binds a site,
then "information loss" or "unrecognition" is the reverse. This has an
important consequence. If one claims that information must always be positive,
then we can't explain this situation, and we get a kind of perpetual motion.
This means that an equation for information that always gives a positive number
can't be right for modeling molecular
machines. (This was discussed in edmm.)
| : I'm glad to see you starting to think about how the molecule works.
| I must step up my efforts to find a good molbio book ( secondhand!).
| My latest find was one on game theory, which might be relevant here on
| B.I-T.
I don't think anyone has explored game theory in this context. I don't
know enough about it to judge if
it is sensible or not.
| The problem I have been trying to address is not one of what happens,
| but of how we describe what happens. That said, keep on pointing out my
| mistakes... as long as you've got
the patience!
I shouldn't take the time but I do. Crossing fields is tough, but once you
reach the other side you will have
an advantage.
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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Tom Schneider (toms@fcsparc6.ncifcrf.gov)
wrote:
: Yes, a nice example of that is known already: proteins like EcoRI track the
: DNA using electrostatic interactions. DNA is negatively charged, making two
: "rail road" tracks (with a twist!), EcoRI has positive charges on its surface
: that allow it to follow the tracks. People have demonstrated tracking
: experimentally, and have worked on the theory of diffusion. It turns out that
: since tracking lowers the dimensionality of the search space from 3 to 1
: dimension, the rate of finding
the binding site is increased.
Interesting- this is similar to how I imagined it. However, isn't the
DNA actually a linear dipole or multipole. It only has a net charge on the acid
group at the end. It's all those
oxygens with their lone pairs!
Either way, I seem to remember a long thread about protein folding
some time last year, but I was working away so I missed most of it.
Can anyone suggest what months of
the archives I should retrieve?
Cheers,,
Charlie
( spending lots of time at the computer
at the moment!! )
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From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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My last followup got eaten when vi failed a write due to me
being over-quota on my disk space.
Here is attempt 2:
koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP)
wrote:
: My naive question occurred to my mind after reading the above
: passage is: Is "the universe does the same thing for all
: observers" an axiomatic statement or an observational one?
For us, as non-universal observers, it has to be accepted as an
axiom in all of our theories. Otherwise there is little point in
continuing with science. Going back to my Bayesian roots, I would
define an axiom as a statement on which all inferences are
conditional. It is, of course, possible that the universe is not
the same for all observers, but this would require us, at the very
least, to redefine science by saying that "under certain conditions
the universe appears to do the same thing for all observers, in which
case these models are applicable( those which we would recognise as
modern science): in other circumstances we must use a description
which is dependent on the observer".
We can never PROVE this axiom, either by measurement (observation) or
otherwise. Personally I do not expect any experimental evidence to come
to light which disproves it, since our measurements are always so very
imperfect. So far science has done quite well at using it as
a basis for reasoning about the physical
world.
: "The
: universe does the same thing for all observers" may look okay de
: facto, but its observational confirmation costs our fellow
: scientists a fantastic amount of time and money which, perhaps,
: they could not afford.
I would say that scientists use it as an assumption and then try to
confirm observations by comparing them with other observations. The
one who said that his/her data could not be explained under this
assumption would be a brave one indeed!
Consider the following experiment:
I give you a piece of string (Ideal String(tm): doesn't
stretch, shrink, no thermal expansion, etc ), and you measure it
to be 12.5cm (+/-0.01cm) long, then you give it back to me. I then
give you the same piece of string again and you measure it to be
4.5cm (+/-0.01cm) long. Gaussian errors.
In this case, your measurements are strong evidence that the
initial assumptioni, that I am honest, is wrong. You can't prove it,
your ruler might be faulty, etc, but you would at least have reason
for thinking that I might have lied about it being the same bit of string.
There are no measurements taken so far that call the axiom into
question in any serious way. We are certainly not capable of definitively
proving it to be false.
: It would certainly be wonderful if the universal objective
: observer underwrites and takes care of the consistency of our
: empirical world.
We don't need anyone to observe that the universe behaves itself. They
could never show us their measuremetns of its consistency anyway. What
is more, any measurements of consistency which we perform will be
imperfect, so we can not even be
sure from them.
: have a do-it-yourself consistency such that the internal
: observers of limited capacity take care of themselves and
: eliminate likely internal conflicts constantly in the effect so
: as to make the UO also happy.
If the axiom is correct, then no such conflicts will occur, and the
consistency of the universe itself will keep everyone happy. Otherwise,
we are all in deep do-do.
Regards,
Charlie
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 10 May 1994 19:19:23 -0700
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Before forgetting, I would like to add a few more to the
remarks Charlie made in his <CpI1u8.I6F@lut.ac.uk>. C. E. A. Cook
phceac@lut.ac.uk writes:
>Note also that this way of *describing* the process is not
>possible for an observer with the perspective of the [EcoRI]
>molecule. What IT sees, is:
>
> Ouch (hit by water molecule)
> Ouch (hit by water molecule)
> ...
Charlie, you hit the mark, again. The way I see what you saw is
through the interplay between the universal objective observer
and the internal observers. One scenario which makes both the UO
and the internal observer sitting on the shoulder of each
molecule happy is:
Ouch, you hit me. Sorry, but blame on the guy hitting me first.
Ouch, you hit me. Sorry, but blame on the guy hitting me first.
...
Ouch, you hit me. Sorry, but blame
on the guy hitting me first.
One more scenario which makes at least the internal observers
happy is:
Ouch, you hit me. Sorry, but I couldn't expect THAT guy behind
you hit me first.
Ouch, you hit me. Sorry, but I couldn't expect 'THAT' guy
behind you hit me first.
...
Ouch, you hit me. Sorry, but I couldn't expect "THAT" guy
behind you hit
me first.
Of course, nothing unexpected could
happen to the mind of the UO.
My point is that we can do serious things even if we don't
refer to the UO frequently. In this regard, I am thinking of
horse-races run by a Municipal Government. Although the Municipal
Government may serve as the Universal Bookmaker that could boast
of having an unlimited source of money at least by selling
municipal bonds, it is difference of opinion that makes horse-
races (Twain). The local bookmakers do their own business very
seriously while taking the risk of estimating various conditional
probabilities. So long as the UB can avoid its bankruptcy, the
ubiquitous little bookmakers could survive, unless attacked by
surprise police-raid, without caring
much about the UB.
Regards,
Koichiro
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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From: toms@fcsparc6.ncifcrf.gov (Tom Schneider)
Subject: Re: one-to-one ?
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In article <CpLoAz.45B@lut.ac.uk>
phceac@lut.ac.uk (C.E.A.Cook) writes:
| ... However, isn't the
| DNA actually a linear dipole or multipole. It only has a net charge on the acid
| group at the end. It's all those
oxygens with their lone pairs!
The charge is not just at the end,
it is at every base pair.
Tom Schneider
National Cancer Institute
Laboratory of Mathematical Biology
Frederick, Maryland 21702-1201
toms@ncifcrf.gov
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To: bio-info@net.bio.net
From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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In article <CpI1u8.I6F@lut.ac.uk> I wrote:
> Has anyone heard of the odd sock theorem?
And Tom Schneider (toms@fcsparc6.ncifcrf.gov) wrote:
> Nope, would you like to explain?
Ok, I had my wires crossed, here's
the story!
The odd sock theorem, I have been told by two people, says that
if one has a bag containing a mixture of socks of two colours,
then one need take out no more than 3 socks, without replacement,
to be certain of getting a pair.
In the general case of an N-footed sock-wearer, and a choice of
M different colours of sock, one needs to draw (N-1)*M + 1 socks
to be certain of having all feet the same colour. It is clear,
therefore that the adoption of footwear is incompatible with
large numbers of legs...when did you last see a centipede witih
clogs on? :-)
What I was actually thinking of, which has some relevance, is an
anecdote used by J.S.Bell to illustrate nonlocality in quantum
mechanics. Dr Bertlmann likes to wear odd socks, red and blue,
but doesn't care which colour goes on which foot. When one sees
him enter the room, one knows instantly, upon noticing that his left sock
is red, that his right sock is blue.
I think that this inherent correlation, due to the nature of Bertlmann's
sock-wearing habits, could be used as an analogy to the correlation
between the observations of different non-UO observers due to the
nature of the universe's sock-wearing habits. ( It's a bit of a
weak analogy, but something may be
revealed by it!)
Ref: Bertlmann's socks and the nature of reality, found in
'Speakable and Unspeakable in quantum mechanics' a collection of papers
by J.S.Bell
Did that help?
Regards,
Charlie
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To: bio-info@net.bio.net
From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 11 May 1994 23:55:34 -0700
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In article <CpLMyp.3Mt@lut.ac.uk> phceac@lut.ac.uk (C. E. A.
Cook) writes:
>koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP)
wrote:
>: It would certainly be wonderful if the universal objective
>: observer underwrites and takes care of the consistency of our
>: empirical world.
>We don't need anyone to observe that the universe behaves itself. They
>could never show us their measuremetns of its consistency anyway. What
>is more, any measurements of consistency which we perform will be
>imperfect, so we can not even be sure from them.>
>
>: have a do-it-yourself consistency such that the internal
>: observers of limited capacity take care of themselves and
>: eliminate likely internal conflicts constantly in the effect so
>: as to make the UO also happy.
>If the axiom is correct, then no such conflicts will occur, and the
>consistency of the universe itself will keep everyone happy. Otherwise,
>we are all in deep do-do.
May I suggest one more example to make clearer the situation
surrounding the universal observer and the internal observers, I would
hope so, instead of aggravating it?
Suppose there are three guys A, B & C who are very hungry and are
served foods at a very slow rate because of some reasons in the kitchen.
The inevitable outcome is the fighting for foods. (Although I DO know
this sort of fighting is severely frowned in some society, give me a few
moment until somebody from the society comes to caution me.) Also, suppose
the UO is watching the situation
with interest.
After a brief moment of severe fighting, the guy A began to talk in a
retrospective manner:
"I was so hungry in the beginning and then I took some from the plate of B"
"Because you took some from me, then I took some from C."
"Because you took some from me, then I took some from A".
- continued in the forward direction
-
The UO may describe the situation in terms of selfishness, altruism,
tit-for-tat, random walk, or whatever you name it. What is common to both the
descriptions by the UO and by the participants is linear causality. The UO
could be happy because the participants followed linear progression of
causes.
On the other hand, the participants right in the high time for the
fighting would describe their own acts a bit differently. Suppose an
angel sent from the UO could interview each of the participants involved
in the fighting:
Angel asked:
"Why you A, took some from the plate of B?"
"Because C next to me surprised me by taking some from mine a moment ago."
"Why you C, took some from A?"
"Because B next to me surprised me by taking some from mine a moment ago."
"Why you B, took some from C?"
"Because A next to me surprised me by taking some from mine a moment ago."
- continued in the backward direction
-
As far as things that have been done are concerned, there should be no
difference between the retrospective description by the participants in the
forward direction and the angel's interview in the backward direction. The
only difference is that the angel's interview in the backward direction has
something called "surprise", while there is nothing like that in the
retrospective description in the forward direction with which the UO is
quite happy. One possibility for subsuming "surprise" in the face of the
first law of thermodynamics is a cohesion exercised among the participants
facing finite energy resources. Those three guys fighting for foods are
quite cohesive among themselves by sharing their foods unexpectedly.
Needless to say, the UO armed with linear causality may look quite a nice
and trustworthy framework. My humble question is how to verbalize such a
cohesion arising from subsuming "surprise" in the language which the
friends of the UO can manage, or
the question itself is an illusion?
Regards,
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of University
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 12 May 1994 02:43:29 -0700
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In article <CpnAy1.5G2@lut.ac.uk> phceac@lut.ac.uk (C. E. A.
Cook) writes:
>What I was actually thinking of, which has some relevance, is an
>anecdote used by J.S.Bell to illustrate nonlocality in quantum
>mechanics. Dr Bertlmann likes to wear odd socks, red and blue,
>but doesn't care which colour goes on which foot. When one sees
>him enter the room, one knows instantly, upon noticing that his left sock
>is red, that his right sock is blue.
>I think that this inherent correlation, due to the nature of Bertlmann's
>sock-wearing habits, could be used as an analogy to the correlation
>between the observations of different non-UO observers due to the
>nature of the universe's sock-wearing habits. ( It's a bit of a
>weak analogy, but something may
be revealed by it!)
Nonlocality in quantum mechanics is consistent with the nonlocality
of the universal objective observer. The UO can dispatch its local
representatives anywhere in the universe. Each local representative of the
UO can thus identify what its fellow local representatives are dtecting
elsewhere at the same moment as consulting its mentor, the UO, every time
(e.g., the Aspect-Grangier-Riger photon polarization experiment). This is,
however, not the instance of actual observation. The trick of simultaneous
nonlocal correlation is within the supposed one-to-one physics on the global
scale. Every tiny portion of whatever macroscopic body following the
one-to-one physics determines itself uniquely in relation to all the rest.
The one-to-one physics guarantees that to know its tiny bits is just
equivalent to knowing all the rest at every moment. This prohibits us from
thinking of every local representative of the UO as a non-UO observer. So long
as one takes the one-to-one physics for granted, the observer that can be
consistent with the physics, whatever it may be, turns out to be the UO
itself or its protege.
Each local represetative of the UO is no other than the life-size UO of
unlimited capacity, a dream of physicists.
What is really intriguing is the possibility of having the observers
of limited capacity like us, as a serious matter on physical or material
grounds.
Charlie, thanks for calling my attention to Bell's. The last time when I
read some of Bell's writings, I missed what taste Dr. Bertlmann has for his
socks.
Regards,
Koichiro
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-21, Japan
kmatsuno@voscc.nagaokaut.ac.jp
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From: phceac@lut.ac.uk (C.E.A.Cook)
Subject: Re: one-to-one ?
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koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP) proposed a rather
nice example (I like this one!) :
: Suppose there are three guys A, B & C who are very hungry and are
: served foods at a very slow rate
because of some reasons in the kitchen.
....
: After a brief moment of severe fighting, the guy A began to talk in a
: retrospective manner:
: "I was so hungry in the beginning and then I took some from the plate of B"
: "Because you took some from me, then I took some from C."
: "Because you took some from me, then I took some from A".
: - continued in the forward direction
-
: The UO may describe the situation in terms of selfishness, altruism,
: tit-for-tat, random walk, or whatever you name it. What is common to both the
: descriptions by the UO and by the participants is linear causality. The UO
: could be happy because the participants followed linear progression of
: causes.
:
: On the other hand, the participants right in the high time for the
: fighting would describe their own acts a bit differently. Suppose an
: angel sent from the UO could interview each of the participants involved
: in the fighting:
: Angel asked:
: "Why you A, took some from the plate of B?"
: "Because C next to me surprised me by taking some from mine a moment ago."
: "Why you C, took some from A?"
: "Because B next to me surprised me by taking some from mine a moment ago."
: "Why you B, took some from C?"
: "Because A next to me surprised me by taking some from mine a moment ago."
: - continued in the backward direction
-
: As far as things that have been done are concerned, there should be no
: difference between the retrospective description by the participants in the
: forward direction and the angel's
interview in the backward direction.
Quite!
: The
: only difference is that the angel's interview in the backward direction has
: something called "surprise", while there is nothing like that in the
: retrospective description in the forward direction with which the UO is
: quite happy.
Now I am getting lost! If the angel watches both of those two conversations
it will be just as surprised to be told "Event1 caused Event2" as to be told
"Event2 was caused by Event1". To any particular questioner, the information
available from A,B and C is the same,
whatever order the story is told in.
The only ones who are surprised are the poor guys who keep finding their
plates empty!!
Have I misunderstood your example,
Koichiro??
Regards,
Charlie
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From: kmatsuno@voscc.nagaokaut.ac.jp (koichiro matsuno/7129)
Subject: Re: one-to-one ?
Date: 12 May 1994 16:26:16 -0700
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In article <Cpp4tz.CDD@lut.ac.uk> phceac@lut.ac.uk (C. E. A.
Cook) writes:
>koichiro matsuno/7129 (kmatsuno@VOSCC.NAGAOKAUT.AC.JP) proposed a rather
>nice example (I like this one!) :
>
>: Suppose there are three guys A, B & C who are very hungry and are
>: served foods at a very slow rate because of some reasons in the kitchen.
>
>....
>
>: As far as things that have been done are concerned, there should be no
>: difference between the retrospective description by the participants in the
>: forward direction and the angel's interview in the backward direction.
>
>Quite!
>: The
>: only difference is that the angel's interview in the backward direction has
>: something called "surprise", while there is nothing like that in the
>: retrospective description in the forward direction with which the UO is
>: quite happy.
>
>Now I am getting lost! If the angel watches both of those two conversations
>it will be just as surprised to be told "Event1 caused Event2" as to be told
>"Event2 was caused by Event1". To any particular questioner, the information
>available from A,B and C is the same, whatever order the story is told in.
>
>The only ones who are surprised are the poor guys who keep finding their
>plates empty!!
>
>Have I misunderstood your example,
Koichiro??
No, no. You haven't misunderstood me!! You are 99.9...9% right. The
remaining 0.0...1% reserved for me is that I have been thinking of those poor
Guys all the time, such as dinosaurs..........
Regards,
Koichiro