Mathematics and Life - Comments on Gregory Chaitin Lectures Sweden 2005

[Ann Racuya-Robbins-2]

There are a number of things Chaitin talks about that seem problematic to me. But the mathematical joy remains.

Central to the disconnect for me is a series of related statements beginning with—

"A law has to be simpler than what it explains." "To understand is to compress." "The laws of physics must be simpler than what they explain."

Why does a law have to be simpler? What is simpler?  I suppose that is the reason to be for complexity science that life appears to more likely move from simpler to more complex.

But more than that I am wondering what drives the desire to see the world this way. This point of view, it seems to me, is what stops certain streams of mathematics and philosophy from being able to address life in both the formal in informal senses. Certainly biological life.

To me understanding life and to a very great extent biological life is the human mission. Finding a theory of life based on the statements Chaitin iterates including “to understand is to compress” will most likely not tell us much about life or more precisely living. The experience of death teaches this. The experience of death teaches me the gravity of the distinction between theories based on definitional systems and living and dying...(only yesterday leaving my house for the day I found a hatchling from the oriole nest under the eave had fallen from its nest and lay dying or dead…its body still bloody and wet from leaving its shell and the ants by the thousands eating the chick.)

What I like most about mathematics is the feeling of being able to hold the whole world in my head. It is a very powerful feeling...being able to reduce the enormous complexity and importance even power of the world and hold it in my mind…even more the ability to manipulate its structure through symbols and come up with new conclusions. In some way this experience gives me the feeling of being as powerful as the world. The exchange and sharing of these systems of symbolic manipulation is an extremely exciting and intimate experience. Chaitin’s discussion of “uncomputable numbers” and “countable infinity” gives me this excitement and intimate feeling. For a moment I feel a sense of immortality, of transcending the distance between one and another, transcending our biologically bounded existence. I think it is this experience of transcendence and intimacy that draws people to mathematics and not its cousin philosophy with its endless if beautiful verbosity. To me the message of mathematics is the desire and need for intimacy and transcendence—an overwhelming desire approaching the desire for life itself.

I am uneasy. even disquieted with the logic (mathematics) that simplifying my experience of life or of life itself can make it more comprehensible or meaningful. Rather I think there are as many mathematics as there are lives and each one tells us more about our nature.

 

Ann Racuya-Robbins

Founder and CEO

World Knowledge Bank®

 

https://www.wkbank.com/knowledge/Comments_on_Chaitin

 

https://www.wkbank.com

 

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[Marcus G. Daniels]

Ann Racuya-Robbins wrote:
>
> Why does a law have to be simpler? What is simpler?  I suppose that is
> the reason to be for complexity science that life appears to more
> likely move from simpler to more complex.
>
The most powerful computers in the world can only simulate microseconds
of the many body physics and electrostatics of a million atoms, which is
just a small part of a single cell.   If there is no compression, or
simplification, there is no hope of grasping what happens in organisms.

Marcus

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[Roger Critchlow-2]

On Tue, Jul 15, 2008 at 10:03 AM, Ann Racuya-Robbins <[hidden email]> wrote:

What I like most about mathematics is the feeling of being able to hold the whole world in my head. It is a very powerful feeling...being able to reduce the enormous complexity and importance even power of the world and hold it in my mind…even more the ability to manipulate its structure through symbols and come up with new conclusions. In some way this experience gives me the feeling of being as powerful as the world.

 
I think this feeling is partly the compression of experience into formal systems that Chaitin discusses. 

-- rec --

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[Ann Racuya-Robbins-2]

This makes the problem seem like it is technical not ontological...i.e. what
is need is greater computing power. I think there are many ways of grasping
what happens in organisms beside computer simulation...compassion for
example. This reminds me somewhat of Ptolemy using Platonic Solids to
explain why the universe (the heavens) was not a pyramid.  

Thank you for communicating.
-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf
Of Marcus G. Daniels
Sent: Tuesday, July 15, 2008 10:36 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Mathematics and Life - Comments on Gregory Chaitin
Lectures Sweden 2005

Ann Racuya-Robbins wrote:
>
> Why does a law have to be simpler? What is simpler?  I suppose that is
> the reason to be for complexity science that life appears to more
> likely move from simpler to more complex.
>
The most powerful computers in the world can only simulate microseconds
of the many body physics and electrostatics of a million atoms, which is
just a small part of a single cell.   If there is no compression, or
simplification, there is no hope of grasping what happens in organisms.

Marcus

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[glen ep ropella]

Marcus G. Daniels wrote:
> Ann Racuya-Robbins wrote:
>> Why does a law have to be simpler? What is simpler?  I suppose that is
>> the reason to be for complexity science that life appears to more
>> likely move from simpler to more complex.
>>
> The most powerful computers in the world can only simulate microseconds
> of the many body physics and electrostatics of a million atoms, which is
> just a small part of a single cell.   If there is no compression, or
> simplification, there is no hope of grasping what happens in organisms.

It's not quite true that without compression or simplification, there is
no hope of grasping what happens in organisms.

Actually, this concept of compression is relatively new in the modeling
world.  Modeling, traditionally, consists of taking one concrete thing,
in all its particular gory detail, and studying it side-by-side with
some other concrete thing, in all its gory detail.  Both things, the
model and its referent are replete with the messy details of concrete
existence, yet we can use one to learn about the other, no compression
or simplification needed.

In fact, one might say that this obsessive compulsive fixation on
compression and distillation is a kind of mental disorder.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


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[Marcus G. Daniels]

Ann Racuya-Robbins wrote:
> Why does a law have to be simpler? What is simpler?
> This makes the problem seem like it is technical not ontological...i.e. what
> is need is greater computing power.
If one wants to think about how an organism works without
simplification, and be able to poke and prod at it, one way to go is to
try to capture the chemistry and physical dynamics of its cells, down to
its atoms and electrical fields in a simulation.  One would aim to avoid
proliferation of crude approximated submodels (platonic solids
describing cell types or organs or whatever), in favor of physics.  That
is, you go as down as far as you can using data and to specify
everything.   But doing this is not actually computationally feasible,
even if sufficient data were available, and that's not even close either.

Of course, even a well-informed physics model will still be an
approximation.  My point is that if one wants to capture an organism (or
even just a single cell), without compromising on the mathematical
formulation, and without throwing away details, it is off-the-charts
hard.  Maybe in ten or twenty years it will be possible to do one cell.  
> I think there are many ways of grasping
> what happens in organisms beside computer simulation...compassion for
> example.
Compassion is also a simplification.   There's the animal, and then
there's the way you feel for the animal.   But the way you feel is not
the animal.  You have no way to know what the animal is actually feeling
except from what you can infer by interacting with it, or by scanning it
with a futuristic functional MRI.

Marcus

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[Marcus G. Daniels]

glen e. p. ropella wrote:

>> Ann Racuya-Robbins wrote:
>>    
>>> Why does a law have to be simpler?
> Modeling, traditionally, consists of taking one concrete thing,
> in all its particular gory detail, and studying it side-by-side with
> some other concrete thing, in all its gory detail.  Both things, the
> model and its referent are replete with the messy details of concrete
> existence, yet we can use one to learn about the other, no compression
> or simplification needed.
>  

These inferences can only be made about the compared properties of the
two things.   What is compared is not everything, often times is hard to
measure, and usually is hypothesis driven -- all simplifications.
Put another way, to have a concrete thing in all of its gory detail,
does not mean you have any idea what is important to measure from it, or
whether what is relevant even CAN be measured non-intrusively given its
working form.  It is a matter of inquiry in the form of science,
empathy, intuition, or your favorite thing to make guesses about what to
measure.

In the case of life, "A law has to be simpler than what it explains."
because the precise processes of living things living are too complex to
directly grok (again, in full detail).  Minimally, living things involve
billions of components that interact in non-linear ways.

Marcus


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[Ann Racuya-Robbins-2]

Using your traditional description of modeling "Modeling, traditionally,
consists of taking one concrete thing,
in all its particular gory detail, and studying it side-by-side with
some other concrete thing, in all its gory detail."
What is a concrete thing? I guess by concrete thing you do not mean a living
individual. In this traditional sense of model is there anything that is not
a model? Probably not. But comparing a living individual to a non living
model of a individual highlights the exact divide...life. Compressing the
model it seems to me would not overcome this difficulty in anyway.
I think with living individuals "all its gory details" becomes all its
glorious detail, as many a film/video or novel teaches. Compressing the
model, or a process that results in the compression of the model does make
the model more alive.
Biomimicry changes that formulation so that rather than compressing or
simplifying it does not take a stand of power relations between the two
comparitants.
The possibility of Biomimicry itself is the result of using compassion to
understand two living individuals beginning with oneself.

 
-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf
Of glen e. p. ropella
Sent: Tuesday, July 15, 2008 12:06 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Mathematics and Life - Comments on Gregory Chaitin
Lectures Sweden 2005

Marcus G. Daniels wrote:
> Ann Racuya-Robbins wrote:
>> Why does a law have to be simpler? What is simpler?  I suppose that is
>> the reason to be for complexity science that life appears to more
>> likely move from simpler to more complex.
>>
> The most powerful computers in the world can only simulate microseconds
> of the many body physics and electrostatics of a million atoms, which is
> just a small part of a single cell.   If there is no compression, or
> simplification, there is no hope of grasping what happens in organisms.

It's not quite true that without compression or simplification, there is
no hope of grasping what happens in organisms.

Actually, this concept of compression is relatively new in the modeling
world.  Modeling, traditionally, consists of taking one concrete thing,
in all its particular gory detail, and studying it side-by-side with
some other concrete thing, in all its gory detail.  Both things, the
model and its referent are replete with the messy details of concrete
existence, yet we can use one to learn about the other, no compression
or simplification needed.

In fact, one might say that this obsessive compulsive fixation on
compression and distillation is a kind of mental disorder.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


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[glen ep ropella]

Marcus G. Daniels wrote:
> These inferences can only be made about the compared properties of the
> two things.

Not necessarily (though admittedly that's common).  What one _can_ do
and what we often used to do is study both the model and its referent by
doing similar experiments on both.  In the experiments, one does hone in
on an aspect of both the model and referent.  But, this is not the same
as simplification or compression.  Rather, it consists of _controlling_
the properties one wants fixed and allowing freedom to others.

Such is not a simplification but a constraining or controlling.

> In the case of life, "A law has to be simpler than what it explains."
> because the precise processes of living things living are too complex to
> directly grok (again, in full detail).  Minimally, living things involve
> billions of components that interact in non-linear ways.

Sure, what we denote a "law" must be simpler than what it explains
because the abstractions we denote by "law" are, by definition, simpler
in abstraction than they are when fully applied.  However, an "applied
law" is no simpler than the processes its supposed to explain.  Hence,
in _practice_, laws are no simpler than what they explain.  Only in
academe or in didactic abstraction are laws simpler than what they
explain.  This is especially true in the special sciences like biology
where heterogeneity is the rule.  Natural sciences are, and will forever
remain, dirty.

Don't take my statements as an indication that I think such abstractions
are not useful.  In fact, I'm all for making such
abstractions/compressions.  But the trick with any compression or
encoding is that the simpler the "law", the more complex the codec and
vice versa.  Simple codec means complex law.  Simple law means complex
codec.  And a law is totally useless without its codec, the body of
knowledge that allows one to encode into and decode out of the
compressed form.

The detail doesn't just go away.  It's moved around to suit any
particular purpose.  Hence, in essence, simplification and compression
are _not_ necessary for understanding.  What's necessary is some (any)
route by which we can observe and manipulate the system in a controlled
fashion and some _language_ in which to describe what we did so that
others may criticize us or repeat what we did.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


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[glen ep ropella]

Ann Racuya-Robbins wrote:
> Using your traditional description of modeling "Modeling,
> traditionally, consists of taking one concrete thing, in all its
> particular gory detail, and studying it side-by-side with some other
> concrete thing, in all its gory detail." What is a concrete thing? I
> guess by concrete thing you do not mean a living individual.

No, a living individual is a concrete thing.  In fact, living
individuals are the hardest things to abstract.  Hence, they are the
_most_ concrete, more concrete than, say, rocks, or chairs, or even
mountains and coast lines.  By "concrete" I basically mean "riddled with
niggling details" or "not removable from its context" or "not amenable
to abstraction".  Some concrete things (e.g. rocks) are more easily
removed from their context.  They are "context sensitive", but not
"embedded" or deeply context dependent.  But, for example, a flower, is
much more concrete and is not only context sensitive, it's down right
context dependent.

> In this
> traditional sense of model is there anything that is not a model?
> Probably not.

Yes.  By definition, a model must have a referent.  So, if there's no
observer to _assign_ the model to its referent or if the model is so
excruciatingly concrete that it can't be used to model anything else,
then it would not be a model.  An example of the latter might be, say,
the universe.  it's not clear what the universe could model, since
there's nothing else to which it can refer.  (And it can only be a model
of itself in the most degenerate sens of the word "model".)

Another example would be something that is obviously unique.  Something
so bizarre and pathological that it just isn't similar to anything else.

I'm not suggesting that, practically, there is any real thing that
cannot be used as a model.  Our ignorance is boundless.  So, a very
clueless person can use, say, a coffee mug to model an earthworm if he
wants to.  But such a practice probably wouldn't last very long in a
competitive environment.

> But comparing a living individual to a non living model
> of a individual highlights the exact divide...life. Compressing the
> model it seems to me would not overcome this difficulty in anyway. I
> think with living individuals "all its gory details" becomes all its
> glorious detail, as many a film/video or novel teaches. Compressing
> the model, or a process that results in the compression of the model
> does make the model more alive. Biomimicry changes that formulation
> so that rather than compressing or simplifying it does not take a
> stand of power relations between the two comparitants. The
> possibility of Biomimicry itself is the result of using compassion to
>  understand two living individuals beginning with oneself.

I agree completely.  Compression and simplification are a tiny component
to a successful model.  And, mostly, the compression and simplification
are used to aid in communication rather than as an aid to practice.
Compressions and simplifications are used for indoctrination of the
uninitiated.  The initiated are chock full of exceptions and caveats
that apply when any simplification is applied/used.  Compressions and
simplifications are also used as a "jargon" between the initiated so
they can communicate more efficiently.  But even amongst those who use
them as jargon they still fully decode them into context when they
interact with the real world.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


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[Marcus G. Daniels]

glen e. p. ropella wrote:
> But the trick with any compression or
> encoding is that the simpler the "law", the more complex the codec and
> vice versa.  Simple codec means complex law.  Simple law means complex
> codec.  And a law is totally useless without its codec, the body of
> knowledge that allows one to encode into and decode out of the
> compressed form.
>  
A `codec' is just a function that derives a signal from the set of
observable properties.
Its definition typically would imply an ontology, unless there was
machine learning in use.
The underlying ontology may be objectionable to a potential a user of
the codec, or they may even find the set of properties inadequate.  But
all that's really required to make it science is to declare the
mechanisms of the codec and the properties being observed.   Refusing to
accept any declaration (and to my mind it is valid to call this
`simplification'), is to prefer magic.

Marcus

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[glen ep ropella]

Marcus G. Daniels wrote:
> But
> all that's really required to make it science is to declare the
> mechanisms of the codec and the properties being observed.   Refusing to
> accept any declaration (and to my mind it is valid to call this
> `simplification'), is to prefer magic.

No, it goes beyond _declaring_ mechanisms and properties being observed.
  That's the whole point of the thread, I think.  Human behavior, e.g.
the scientific method, is not so easily declared.  One has to be
trained.  And that training includes implicit as well as explicit knowledge.

So, there are entire cultures around various experimental procedures
that cannot be finitely, completely declared.  And that implicit
knowledge of application is part of the encoding/decoding needed when a
"law" is applied.

It's not a refusal to accept any declaration so much as it's a refusal
to admit that all things can be completely formalized.  Obviously,
anyone who buys into the scientific method, in general, will accept that
some declaration is possible and always that _more_ declaration is
desired.  But, only a few of us believe that science could be pursued by
a specified automaton.  I.e. only a few of us are committed, pure,
formalists who believe everything is susceptible to a computational
(semantic-free) process.

The rest of us admit that implicit and undeclarable knowledge is part of
the codec for any abstracted law.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


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[Marcus G. Daniels]

glen e. p. ropella wrote:
> The rest of us admit that implicit and undeclarable knowledge is part of
> the codec for any abstracted law.
>  
Do you mean undeclarable in the sense of 1) It's unreasonable to expect
a one-time formal, and complete declaration from anyone, or 2) the
knowledge can't be communicated or inferred or modeled, in principle.  
The ethic of `more is better' is what I'm pushing, and yes, toward
machine readability (e.g. semantic web) and automatons.

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[Marcus G. Daniels]

glen e. p. ropella wrote:
> But, only a few of us believe that science could be pursued by
> a specified automaton.
Btw, no, I don't mean that.  I mean a growing, developing automaton.  
Evolving on its own accord as well as with editing by human experts.
Much more useful than a textbook!

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[glen ep ropella]

Marcus G. Daniels wrote:
> Do you mean undeclarable in the sense of 1) It's unreasonable to
> expect a one-time formal, and complete declaration from anyone, or 2)
> the knowledge can't be communicated or inferred or modeled, in
> principle.

I largely mean (2); but I also mean (1) because in any given finite
interval, (1) becomes (2).  They are only distinct if we assume a long
enough time and enough resources to make the knowledge explicit.

 > The ethic of `more is better' is what I'm pushing, and
 > yes, toward machine readability (e.g. semantic web) and automatons.
[...]
> Btw, no, I don't mean [science can be pursued by a specified
> automaton].  I mean a growing, developing automaton. Evolving on its
> own accord as well as with editing by human experts. Much more useful
> than a textbook!

I couldn't agree more.  The only problem with this belief is the vague
concept of "growing" or "progress".  Such a concept is very hard
(probably impossible) to nail down when considering a process like this.

So, because I have no faith that we can define "growing" or "progress"
successfully, I just stick with _drift_.  There's no method for us to
objectively measure the drift of our evolving automaton (currently
consisting of an amalgam of databases, dusty journals, old men in lab
coats, swarthy women building chairs, migrant strawberry pickers, pasty
people pecking at keyboards, the fleas feeding and breeding on our pets,
etc.).

Since there's no way to grok that drift, we can't really claim that we
have strong evidence that the codec can be explicitly declared.  We can
only hope.

--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com


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[Marcus G. Daniels]

glen e. p. ropella wrote:
>> Btw, no, I don't mean [science can be pursued by a specified
>> automaton].  I mean a growing, developing automaton. Evolving on its
>> own accord as well as with editing by human experts. Much more useful
>> than a textbook!
>>    
>
> The only problem with this belief is the vague
> concept of "growing" or "progress".  
Growing in the sense of adding more and more ontologies for different
kinds of experiments.  Growing in the toolbox sense of R or Mathematica
growing.  Growing in the sense of machine-readable
semantically-annotated data stores growing.
So one might imagine internet publication of statistical regularities
from automaton-initiated data mining, and then researchers (or even
robots) testing them in the lab...

Marcus


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[Douglas Roberts-2]

LORDY!

You folks do go on and on.

A humble request:  Could one of you, sort of, ...you know:  Get To The Point?

I mean really.  For *days* we've been inundated with vague postulations about math, music, ABMs, biomimicry (whatever that is) complexity (whatever *that* is) compression, fidelity of resolution, mental disorders (don't ask my opinion on this one), mentalism and calculus (cringe), etc. etc. etc.

But,

What is the point of this particular thread of expostulation?

Because if it is "Complexity is", or some such, could somebody just please just say it?

Thank you very much.

--
Doug Roberts, RTI International
[hidden email]
[hidden email]
505-455-7333 - Office
505-670-8195 - Cell

On Tue, Jul 15, 2008 at 5:49 PM, Marcus G. Daniels <[hidden email]> wrote:

glen e. p. ropella wrote:

>> Btw, no, I don't mean [science can be pursued by a specified
>> automaton].  I mean a growing, developing automaton. Evolving on its
>> own accord as well as with editing by human experts. Much more useful
>> than a textbook!
>>
>

> The only problem with this belief is the vague
> concept of "growing" or "progress".

Growing in the sense of adding more and more ontologies for different
kinds of experiments.  Growing in the toolbox sense of R or Mathematica
growing.  Growing in the sense of machine-readable
semantically-annotated data stores growing.
So one might imagine internet publication of statistical regularities
from automaton-initiated data mining, and then researchers (or even
robots) testing them in the lab...

Marcus

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[Russell Standish]

On Tue, Jul 15, 2008 at 10:03:21AM -0600, Ann Racuya-Robbins wrote:

> There are a number of things Chaitin talks about that seem problematic to
> me. But the mathematical joy remains.
>
> Central to the disconnect for me is a series of related statements beginning
> with-
>
> "A law has to be simpler than what it explains." "To understand is to
> compress." "The laws of physics must be simpler than what they explain."
>
> Why does a law have to be simpler? What is simpler?  I suppose that is the
> reason to be for complexity science that life appears to more likely move
> from simpler to more complex.
>
> But more than that I am wondering what drives the desire to see the world
> this way. This point of view, it seems to me, is what stops certain streams
> of mathematics and philosophy from being able to address life in both the
> formal in informal senses. Certainly biological life.
>

Chaitin's comment is more of an insight into how cognition works. Some
of my colleagues in The Centre for the Mind have said to me privately
that human cognition works this way, and that they expect all
intelligences (eg AI) would work that way too.

There are good evolutionary reasons why we compress. When presented
with a messy signal from the environment, we need to make a snap
decision about whether to fight, flee or ignore some specific
stimulus. Is that shape over there a real lion, or is it just a
lion-shaped rock? By the time we analytically solved the problem using
logic, we would be eaten (if it really was a lion).

Cheers

--

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A/Prof Russell Standish                  Phone [phone] (mobile)
Mathematics                        
UNSW SYDNEY 2052                 [hidden email]
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[Owen Densmore]

I note, all you of many words, Doug was not answered.

    -- Owen

On Jul 15, 2008, at 6:10 PM, Douglas Roberts wrote:

> LORDY!
>
> You folks do go on and on.
>
> A humble request:  *Could one of you, sort of, ...you know:  Get To  
> The
> Point?*
>
> I mean really.  For *days* we've been inundated with vague  
> postulations
> about math, music, ABMs, biomimicry (whatever that is) complexity  
> (whatever
> *that* is) compression, fidelity of resolution, mental disorders  
> (don't ask
> my opinion on this one), mentalism and calculus (cringe), etc. etc.  
> etc.
>
> But,
>
> What is the point of this particular thread of expostulation?
>
> Because if it is "Complexity is", or some such, could somebody just  
> please
> just say it?
>
> Thank you very much.

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[Marcus G. Daniels]

Owen Densmore wrote:
> I note, all you of many words, Doug was not answered.
It is an evolving discussion, and, looking at the archives again, even a
reasonably linear one.   So I have no response for Doug, nor much
concern for his.   I'd rather argue semantics with those actually
contributing to the thread.  It's a trivial manner to fork them.

Marcus

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Meets Fridays 9a-11:30 at cafe at St. John's College
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