Rosen, Life Itself

[Phil Henshaw-2]

 
> OK.  So perhaps you might be willing to change your question to:
> "Given
> an INcomplete math representation of a button, how would you derive a
> math representation of a button hole?"  If you did that, then we might
> be able to formulate an answer.  However, although that modified
> question is well-formed, it is too vague.  We'd need to see an example
> math representation of the button to know what's there and what's
> missing.
[ph] As I was saying, my interest in using math to explore the environment
rather than represent it.  So my use of the math would be to frame the
question and point to where the answer might be found more than provide the
answer.  I was just posing the classic question of a simple physical object
that is easy to describe but in a description that is stripped of our
cultural associations as math is, the description of the object itself would
not contain any reasonable hint of what it is for.  The question then might
be rephrased, what kinds of mathematical descriptions contain a hint of what
the thing described is for, linking it to it's context?  

The main one I use is the continuity of a thing's changes, because how
something changes over time connects it with its context.  The curious thing
is that the math of history curves is thought to be mathematically more or
less meaningless but, potentially, accomplishes the bridge across the gap
that makes 'meaningful' math self-referential and disconnected from reality.
It's not 'buttons' we're so concerned with, but networks as complex systems,
that when described as a stand-alone diagram are abstracted from their
context, but as a history of developments are connected to their context.

>
> --
> glen e. p. ropella, 971-219-3846, http://tempusdictum.com
>
>
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[Günther Greindl]

Glen,

> Hmmm.  So, let's just examine the GIT.  What is shown is that, through a
> math technique (Goedel numbering), it can be shown that any particular
> (complex enough) formal system will either allow sentences that are
> undecidable or that can be both valid ("true") and invalid ("false").

You can stay in the system. Then there's only symbols. Whoever said that
it was allowed to go outside the symbols?

And if you analyze one formal system on a higher level formal system,
then, there again, only symbols.

Everything else is philosophy (this is barebones formalism I am
advocating here - but then again - why not? you have to give reasons for
assuming more).

> It seems quite clear that because we can use math to demonstrate that
> formal systems are inadequate to the task of capturing all of math means
> that math is more than formal systems.

You have not demonstrated the above. you have just shown that there is
undecidable stuff in some formal systems (it goes for all of course) -
but then again - whoever says that it has to bottom out somewhere? Maybe
formal systems is all there is.

> I don't believe this requires a prior philosophy of math.

It requires rejecting formalism.

>  All it
> requires is the mechanical rigor of formal systems plus a method for
> counting the sentences in a formal system.  It seems to me that mindless
> inference could infer this (which is just another way of saying that I
> believe the proofs of the GIT that I've seen ... a.k.a. I believe the
> GIT is true ... ;-),

Ok I would agree with this - I see what you mean now. The machine can
see this with self-analysis.
I just reject the notion of some understanding "beyond the machine"
which is usually invoked, but I see that this is not what you mean.

> of any given mechanism into its entailing context.  Meta-math is
> precisely a methodology of "jumping in and out of the context" of any
> given formalism.  And, despite its name, meta-math is just math.

I agree 100%.

> Indeed, that's my point.  Math handles this jumping in and out of any
> particular context (witness category theory where the diagrams apply to
> many different particular bodies of math) but formal systems does not
> because formal systems only works with 1 alphabet, grammar, and set of
> axioms at any given time.  There's been no attempt (as far as I know),
> within formal systems, to hop between formal systems in a rigorous way
> ... to create measures/metrics of them with which to build up spaces of
> them.  Granted, there has been lots of discussion about the differences
> between particular formal systems (e.g. ZFC and its variants).  And,
> also granted, there's been lots of work to demonstrate the equivalence
> of various particular formal systems.

Yes, very interesting, this hopping is just what would be required! But
I think in computer science just this is being done! I mean, an
operating system is doing nothing but switching contexts, right?

But only in a haphazard way (trying to optimize processing throughput) -
if you could devise a mechanism for formal-system jumping in a directed
way depending on environmental requirements, I think you would have
solved the problem of Artificial General Intelligence. It seems to be
difficult *grin*

> No matter how high or low in the hierarchy you may go, you will still be
> using math, but you will not be locked within any given formal system.
> Hence, math is somehow more than (or outside of) formal systems.

Here I disagree - you are reifying the word "math" - but the collection
of all formal systems is not a thing which is good to speak about I think.

"the dao that is named is not the eternal dao" ;-))

> I think the non-FS part of math contains, at least, the method of proof
> this ability to hop about symbolically/semantically/referentially that
> makes math "more" than formal systems.

We have not formalized this hopping about, but it surely is
formalizable. We humans think we can hop about as we like because we
live in tightly constrained environments (our universe, more
specifically Earth, heavily industrialized/civilized/conformed to
primate living requirments) - I would guess our cognitive systems would
crash if sufficiently alien environments were provided (probably
dropping you on Pluto in a spacesuit would be enough to make most people
go insane). So I think this "unmechanistic" jumping is an "inside view"
cognitive illusion.


> And in many ways, this can be used to help justify the idea that math
> _is_ reality, because math, like reality, doesn't seem bound within any
> particular set of fixed rules.
 > There always seems to be a way to
> puncture the formalism and get at some deeper layer underneath.  There's
> always a way to successfully break the rules, to
> reinterpret/remanipulate the situation to one's benefit.  So, while it's
> reasonable to say "reality is math", it is not reasonable to say
> "reality is a formal system".

That is a deep question you are posing here (or a deep assertment you
are making *grin*); it is the crux of the matter.

So, we have the hypothesis that in the end it all boils down to formal
systems (=mechanism; which is nicely defined via computability);
or that it somehow goes beyond the formal - but what should this be? I
wonder...
Of course, computability (I equate it with mechanism here) has one thing
speaking for it: the Church-Turing Thesis. This is a deep principle,
requiring much thought. I would like to end on this philosophical note.
Thanks for your remarks Glen, very stimulating!

Cheers,
Günther

--
Günther Greindl
Department of Philosophy of Science
University of Vienna
[hidden email]

Blog: http://www.complexitystudies.org/
Thesis: http://www.complexitystudies.org/proposal/


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[glen ep ropella]

Günther Greindl wrote:
> I just reject the notion of some understanding "beyond the machine"
> which is usually invoked, but I see that this is not what you mean.

Right.  I (in my more reductionist moments) reject that, too.  I'm not
claiming that there is anything _other_ than formal systems.  I am
claiming that somehow ... I don't know how ... humans can put on and
take off different formal systems as if they were hats or shirts.

When we hop out of a formal system (into a different formal system) and
begin counting the sentences in the first one, we are doing something
that we can't (yet) mechanically automate.  But we are _still_ engaging
in math.  (Witness "model theory".)

> Yes, very interesting, this hopping is just what would be required! But
> I think in computer science just this is being done! I mean, an
> operating system is doing nothing but switching contexts, right?
>
> But only in a haphazard way (trying to optimize processing throughput) -
> if you could devise a mechanism for formal-system jumping in a directed
> way depending on environmental requirements, I think you would have
> solved the problem of Artificial General Intelligence. It seems to be
> difficult *grin*

Right.  We _do_ this type of hopping around all the time in math and
computer science ... in fact, we do it all the time even
psychologically.  (I think it's what allows people to hold strongly to
obviously contradictory or incommensurate convictions.)  The trick is
that we don't have a full-blown _measure_ (or better yet, metric) of the
set of formal systems and a grammar for hopping in and out of them.
Again, I have to qualify that with "as far as I know."  There could
easily be whole branches of math I've never run across and perhaps they
do exactly what I'm saying hasn't been done.... for all I know.

Now, I don't know if I'd go so far as to claim that obtaining such rigor
for a description of "formal systems space" would solve the problem of
artificial (general) intelligence.  But, it would help us build robots
smart enough to do the general work that can be done by most humans.
Designing a robot that could adopt and abandon formal systems when its
interactions with the environment start to go wonky beyond some
threshold would definitely go a long way to achieving general intelligence.

Of course, I don't believe that's possible in the _abstract_, though.
As I've said before, I think the ability to don and doff formal systems
goes hand-in-hand with our embeddedness ... the fact that our CNS is
concretely embedded in the environment via continual, real-time, sensory
motor feedback loops.  Without such embedding, I don't think we can
construct robots that don and doff formal systems at "will."

>> No matter how high or low in the hierarchy you may go, you will still be
>> using math, but you will not be locked within any given formal system.
>> Hence, math is somehow more than (or outside of) formal systems.
>
> Here I disagree - you are reifying the word "math" - but the collection
> of all formal systems is not a thing which is good to speak about I think.
>
> "the dao that is named is not the eternal dao" ;-))

[grin]  "Good"??  Why wouldn't it be good to speak about that
collection?  Do you think it's ill-defined?  I admit that it's vague and
that I'm just yappin' without making any significant contribution... but
I don't think it's necessarily "bad" to talk about such a mathematical
object... even if it's only hypothetical.  I take heart from things like
universal algebras that we can make progress.  But, then again, I'm an
optimist.

I'm hoping that you mentioned the loopy nature of taoism purposefully.
There's a lot of deep analogy between assuming a fixed formal system
(reductionist -- guilty of the fallacy of the perfect solution) versus
allowing math to contain some ill-conceived "glue" between formal
systems and Western versus Eastern thought.  But, again, the path to
enlightenment usually involves being swatted upside the head when you
ask or attempt to answer a loopy question.  That swat in the head that
you get from, say, your Zen master (now only $39.95 from your local
Wal-Mart! ;-) is a reminder that the answer lies in the sensory-motor
coupling between inferential and causal entailment and NOT isolated on
either side.

> We have not formalized this hopping about, but it surely is
> formalizable.

It may not be formalizable.  ... And don't call me Shirley. ;-)

> We humans think we can hop about as we like because we
> live in tightly constrained environments (our universe, more
> specifically Earth, heavily industrialized/civilized/conformed to
> primate living requirments) - I would guess our cognitive systems would
> crash if sufficiently alien environments were provided (probably
> dropping you on Pluto in a spacesuit would be enough to make most people
> go insane). So I think this "unmechanistic" jumping is an "inside view"
> cognitive illusion.

I'm not so sure.  I think there is plenty of inter-individual
variability between humans to argue that _some_ people would go insane
if they were dropped on Pluto but others would not.  Whether the ones
who go insane do so because they believe in a universal formal system or
because they flip out in some runaway hopping process is another more
refined question.  Ultimately, given my previous opinion, if they go
insane it won't be because humans _need_ some fixated formal system.
It'll be because living in a space suit with no other living beings with
which to interact would be an extreme abstraction from the necessary
sensory-motor embedding we all use.

> So, we have the hypothesis that in the end it all boils down to formal
> systems (=mechanism; which is nicely defined via computability);
> or that it somehow goes beyond the formal - but what should this be? I
> wonder...

The minimal conjecture would be that math consists of a set of formal
systems plus methods for describing relations between formal systems.
But such a thing can't be proven because, really, math is just a
_language_ humans invented and use.

> Of course, computability (I equate it with mechanism here) has one thing
> speaking for it: the Church-Turing Thesis. This is a deep principle,
> requiring much thought. I would like to end on this philosophical note.
> Thanks for your remarks Glen, very stimulating!

Yep!  That's a good place to end... in spite of all my rambling above.
Ultimately, when big weighty principles like that enter the discussion,
it's usually an indicator that we've traveled very far down the rabbit
hole and any further descent will be useless (except for mumbo-jumbo
mind expansion ;-).  Regardless of whether or not the universe is
ultimately mechanical or not doesn't remove the (apparent) fact that
lossy compression (as in a human's understanding of the world) is useful
for prediction.  So, in the end, even if everything's ultimately
mechanical, there's still a place for things like "magical thinking",
wisdom, and intuition.

Hence, it's down right silly and wasteful for die-hard reductionists to
spend so much time brow-beating the holists.

And thanks for your patience and vision.  Normally, people just call me
a silly person and walk away. [grin]

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


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[Phil Henshaw-2]

Glen,

..clip

> You can stay in the system. Then there's only symbols. Whoever said
> that
> it was allowed to go outside the symbols?
>
> And if you analyze one formal system on a higher level formal system,
> then, there again, only symbols.
>
> Everything else is philosophy (this is barebones formalism I am
> advocating here - but then again - why not? you have to give reasons
> for
> assuming more).

[ph] Yes that's the key step, having a reason to assume more so that a
process of looking for it is justified.   You can't confirm things outside
your syntax without looking for them and finding them. Otherwise you just
have fiction.  But having clues to where to look for things that are
discoverable is a reliable procedure for going beyond your current model.

Phil



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[glen ep ropella]

Phil Henshaw wrote:
> Günther Greindl wrote:
 >>
>> You can stay in the system. Then there's only symbols. Whoever said
>>  that it was allowed to go outside the symbols?
>>
>> And if you analyze one formal system on a higher level formal
>> system, then, there again, only symbols.
>>
>> Everything else is philosophy (this is barebones formalism I am
>> advocating here - but then again - why not? you have to give
>> reasons for assuming more).

Just to be clear, Günther wrote that part.

> [ph] Yes that's the key step, having a reason to assume more so that
> a process of looking for it is justified.   You can't confirm things
> outside your syntax without looking for them and finding them.
> Otherwise you just have fiction.  But having clues to where to look
> for things that are discoverable is a reliable procedure for going
> beyond your current model.

I agree that your syntax must be somehow inadequate to cause you to look
outside of it.  And, if we believe his argument, Rosen's work culminated
_merely_ into a demonstration of how our modeling language is
inadequate.  (Not to belittle that achievement, of course.)  He didn't
really get very far in extending the language so that it could capture
(Rosennean) complexity.

But, I'm not sure that "having clues to where to look for discoverable
things" is a reliable procedure.  That sounds pretty ad hoc.  If I were
to attempt to create a reliable procedure, it would invariably involve
some concerted (and distributed) hands-on effort to explore reality.  In
fact, I can't think of a better method than what we're already doing in
science today.  The only flaws I can see are a) not quite enough "big
science" and b) not quite enough amateur science.  And, of course, our
society is in a fragile balance between objective truth-seeking versus
self-interested rhetoric.  We could easily fall back into a dark ages
where, say, Monsanto, specified what we consider "biological truth".

So, it would be nice, but perhaps logically impossible, to construct a
really _reliable_ procedure.

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


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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Phil Henshaw-2]

Glen,
You say "But, I'm not sure that "having clues to where to look for discoverable things" is a reliable procedure.  That sounds pretty ad hoc.  If I were to attempt to create a reliable procedure, it would invariably involve some concerted (and distributed) hands-on effort to explore reality.  In fact, I can't think of a better method than what we're already doing in science today."

It's odd that you don't catch my intent to help others understand a very non ad hoc and efficient method, not yet in general use, for doing just that.  To understand my technique you do need to distinguish between information and the physical prosesses from which we get it.. That can be a hangup.  Once you distinguish between those, what works to let your information signal you where to look in physical processes for better information about how they work is the transitions between continuities. That indicates transitions in how they are working, giving you focused questions and a subject to closely examine for more.  

my site is a bit of a mess, but you might think of it as all about the progressions in the continuity and conservation of change that signal where to look to see how complex developmental processes work.

Phil


Sent from my Verizon Wireless BlackBerry

-----Original Message-----
From: "glen e. p. ropella" <[hidden email]>

Date: Fri, 15 Aug 2008 20:08:14
To: The Friday Morning Applied Complexity Coffee Group<[hidden email]>
Subject: Re: [FRIAM] Rosen, Life Itself


Phil Henshaw wrote:
> Günther Greindl wrote:
 >>
>> You can stay in the system. Then there's only symbols. Whoever said
>>  that it was allowed to go outside the symbols?
>>
>> And if you analyze one formal system on a higher level formal
>> system, then, there again, only symbols.
>>
>> Everything else is philosophy (this is barebones formalism I am
>> advocating here - but then again - why not? you have to give
>> reasons for assuming more).

Just to be clear, Günther wrote that part.

> [ph] Yes that's the key step, having a reason to assume more so that
> a process of looking for it is justified.   You can't confirm things
> outside your syntax without looking for them and finding them.
> Otherwise you just have fiction.  But having clues to where to look
> for things that are discoverable is a reliable procedure for going
> beyond your current model.

I agree that your syntax must be somehow inadequate to cause you to look
outside of it.  And, if we believe his argument, Rosen's work culminated
_merely_ into a demonstration of how our modeling language is
inadequate.  (Not to belittle that achievement, of course.)  He didn't
really get very far in extending the language so that it could capture
(Rosennean) complexity.

But, I'm not sure that "having clues to where to look for discoverable
things" is a reliable procedure.  That sounds pretty ad hoc.  If I were
to attempt to create a reliable procedure, it would invariably involve
some concerted (and distributed) hands-on effort to explore reality.  In
fact, I can't think of a better method than what we're already doing in
science today.  The only flaws I can see are a) not quite enough "big
science" and b) not quite enough amateur science.  And, of course, our
society is in a fragile balance between objective truth-seeking versus
self-interested rhetoric.  We could easily fall back into a dark ages
where, say, Monsanto, specified what we consider "biological truth".

So, it would be nice, but perhaps logically impossible, to construct a
really _reliable_ procedure.

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


============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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[glen ep ropella]

[hidden email] wrote:
> It's odd that you don't catch my intent to help others understand a
> very non ad hoc and efficient method, not yet in general use, for
> doing just that.  To understand my technique you do need to
> distinguish between information and the physical prosesses from which
> we get it.. That can be a hangup.

Sorry.  I'm a bit of a literal person and, since we were talking in the
context of Rosen, I keep trying to tie the conversation to what I
understand of Rosen's work.

And in that context, we're (or should be) assuming a very clear
delineation between causal and inferential entailment, a.k.a. "physical
processes" and "information", respectively.

So, at least in the context of Rosen, that distinction is not the
problem.  It's foundational.

> Once you distinguish between
> those, what works to let your information signal you where to look in
> physical processes for better information about how they work is the
> transitions between continuities. That indicates transitions in how
> they are working, giving you focused questions and a subject to
> closely examine for more.

I guess I'm lost.  It's not clear to me how this relates to Rosen and
"Life Itself".  Perhaps you'd be willing to clarify that for me?  Thanks.

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


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[Phil Henshaw-2]

Glen,
Well, of course "having clues to where to look for discoverable things" is
not a reliable procedure ...if you simply speculate.   It's like offering
someone in a clue to where the beer is.   If you don't go get it it's a
hopelessly unreliable way to have one.   You make me crazed!!

> Phil Henshaw wrote:
> > Günther Greindl wrote:
>  >>
> >> You can stay in the system. Then there's only symbols. Whoever said
> >>  that it was allowed to go outside the symbols?
> >>
> >> And if you analyze one formal system on a higher level formal
> >> system, then, there again, only symbols.
> >>
> >> Everything else is philosophy (this is barebones formalism I am
> >> advocating here - but then again - why not? you have to give
> >> reasons for assuming more).
>
> Just to be clear, Günther wrote that part.
>
> > [ph] Yes that's the key step, having a reason to assume more so that
> > a process of looking for it is justified.   You can't confirm things
> > outside your syntax without looking for them and finding them.
> > Otherwise you just have fiction.  But having clues to where to look
> > for things that are discoverable is a reliable procedure for going
> > beyond your current model.
>
> I agree that your syntax must be somehow inadequate to cause you to
> look
> outside of it.  And, if we believe his argument, Rosen's work
> culminated
> _merely_ into a demonstration of how our modeling language is
> inadequate.  (Not to belittle that achievement, of course.)  He didn't
> really get very far in extending the language so that it could capture
> (Rosennean) complexity.
>
> But, I'm not sure that "having clues to where to look for discoverable
> things" is a reliable procedure.  That sounds pretty ad hoc.  If I were
> to attempt to create a reliable procedure, it would invariably involve
> some concerted (and distributed) hands-on effort to explore reality.
> In
> fact, I can't think of a better method than what we're already doing in
> science today.  The only flaws I can see are a) not quite enough "big
> science" and b) not quite enough amateur science.  And, of course, our
> society is in a fragile balance between objective truth-seeking versus
> self-interested rhetoric.  We could easily fall back into a dark ages
> where, say, Monsanto, specified what we consider "biological truth".
>
> So, it would be nice, but perhaps logically impossible, to construct a
> really _reliable_ procedure.
>
> --
> glen e. p. ropella, 971-219-3846, http://tempusdictum.com
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
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[Phil Henshaw-2]

Glen,
Oops, please ignore last quip, a response to an old email having had a
couple extra beers...

My technique is for identifying where physical systems beyond our
information are located, and then how to explore them for interesting
information.  I guess the way that relates to Rosen is as what you should do
if you accept his conclusion that math is inadequate as a representation of
real complex systems.  The alternative I'm suggesting is that you let
complex physical systems represent themselves, and use the math for the
purpose of exploring them instead.  Yes... it turns the world on it's head
in a certain way, or backwards if you prefer, but it sure works better that
way when it comes to systems that distinguish themselves by developing in
individual ways along paths they find by exploring environments there's not
way to describe.  That's why I switch from a representational objective to
an exploratory one.

Phil

> -----Original Message-----
> From: [hidden email] [mailto:[hidden email]] On
> Behalf Of glen e. p. ropella
> Sent: Monday, August 18, 2008 2:59 PM
> To: The Friday Morning Applied Complexity Coffee Group
> Subject: Re: [FRIAM] Rosen, Life Itself
>
> [hidden email] wrote:
> > It's odd that you don't catch my intent to help others understand a
> > very non ad hoc and efficient method, not yet in general use, for
> > doing just that.  To understand my technique you do need to
> > distinguish between information and the physical prosesses from which
> > we get it.. That can be a hangup.
>
> Sorry.  I'm a bit of a literal person and, since we were talking in the
> context of Rosen, I keep trying to tie the conversation to what I
> understand of Rosen's work.
>
> And in that context, we're (or should be) assuming a very clear
> delineation between causal and inferential entailment, a.k.a. "physical
> processes" and "information", respectively.
>
> So, at least in the context of Rosen, that distinction is not the
> problem.  It's foundational.
>
> > Once you distinguish between
> > those, what works to let your information signal you where to look in
> > physical processes for better information about how they work is the
> > transitions between continuities. That indicates transitions in how
> > they are working, giving you focused questions and a subject to
> > closely examine for more.
>
> I guess I'm lost.  It's not clear to me how this relates to Rosen and
> "Life Itself".  Perhaps you'd be willing to clarify that for me?
> Thanks.
>
> --
> glen e. p. ropella, 971-219-3846, http://tempusdictum.com
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org