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Mathematics and Music

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Mikhail Gorelkin

Mathematics and Music

I would like to return to that Chaitin lesson: it seems that a full and correct definition of mathematics is *impossible*... like a full axiomatization of arithmetic. Mathematics is so complex that an accurate definition of it is equal to doing math (no compression in Chaitin's terminology). It means that all our descriptions are just *references* to discussed subjects. --Mikhail

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

Re: Mathematics and Music

Mikhail Gorelkin wrote:
> I would like to return to that Chaitin lesson:

Well, the problem with focusing on the Chaitin talk is that there were
many things said in the talk, not all of which point in the same
direction. So, it would be better if you would single out a specific
aspect of the talk that bears discussion.

> it seems that a full
> and correct definition of mathematics is *impossible*... like a full
> axiomatization of arithmetic. Mathematics is so complex that an
> accurate definition of it is equal to doing math (no compression in
> Chaitin's terminology). It means that all our descriptions are just
> *references* to discussed subjects. --Mikhail

Hmmm. I maintain my claim that math is a living language by which we
describe aspects of reality. That means I agree completely that a
complete and consistent definition of math is impossible.

But I disagree that an accurate definition of math is equal to doing
math. Because I believe math is a language, defining math is
linguistics (and anthropology and history). Granted, to be specific
about the actual language, one has to know and do some math. After all,
describing, say, the history of the concept of "infinity" requires
enough mathematical understanding to follow the historical thread.

But such "doing math" is a side-effect of the linguistic work. I
suspect that, in defining math, the linguist only has to about the same
amount of math as a linguist has to do when defining, say, French or
Swahili.

Then I again agree that all our descriptions are just references to
discussed objects, because that's the fundamental role of languages.
They provide us with the ability to _refer_ to things (albeit the
"things" that can be referred to may not actually exist or they may be
an artifact of the language being used).

So, I'm in the odd position of having to agree with the beginning of
your argument, disagree with the middle, and agree with the end. [grin]

--
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

Mikhail Gorelkin

Re: Mathematics and Music

Glen, 1) >>I maintain my claim that math is a living language by which we describe aspects of reality.<< and >>But I disagree that an accurate definition of math is equal to doing math.<< I don't know a better definition of math than: it is an *art*. Even more: there is no math but mathematicians who perform their *indefinable* art ("The other sort [of mathematicians] are guided by intuition..." --Henri Poincare "Intuition and Logic in Mathematics"; or "a mathematician who is not something of a poet will never be a good mathematician.") An act of creation is beyond any language but to communicate their ideas, models, results, yes, they need a language and, from this point, it *appears* that math is a language, or, at least, that there is an isomorphism between math and a language. Are the English poetry and the English language the same? Studying only French, can we write, for example, "In Search of Lost Time"?... When we cannot put something into a language, we try to extend and change it. A language is living because an artist (or the Artist, it depends on a point of view) is performing. 2) >>on the Chaitin talk is that there were many things said in the talk<< My perception is: he told about one thing: reality of things is incalculable and even un-nameable with probability one (Borel). It is, probably, why philosophers talk about its divine nature. --Mikhal

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Monday, July 14, 2008 5:08 PM

Subject: Re: [FRIAM] Mathematics and Music

Mikhail Gorelkin wrote:
> I would like to return to that Chaitin lesson:

Well, the problem with focusing on the Chaitin talk is that there were
many things said in the talk, not all of which point in the same
direction. So, it would be better if you would single out a specific
aspect of the talk that bears discussion.

> it seems that a full
> and correct definition of mathematics is *impossible*... like a full
> axiomatization of arithmetic. Mathematics is so complex that an
> accurate definition of it is equal to doing math (no compression in
> Chaitin's terminology). It means that all our descriptions are just
> *references* to discussed subjects. --Mikhail

Hmmm. I maintain my claim that math is a living language by which we
describe aspects of reality. That means I agree completely that a
complete and consistent definition of math is impossible.

But I disagree that an accurate definition of math is equal to doing
math. Because I believe math is a language, defining math is
linguistics (and anthropology and history). Granted, to be specific
about the actual language, one has to know and do some math. After all,
describing, say, the history of the concept of "infinity" requires
enough mathematical understanding to follow the historical thread.

But such "doing math" is a side-effect of the linguistic work. I
suspect that, in defining math, the linguist only has to about the same
amount of math as a linguist has to do when defining, say, French or
Swahili.

Then I again agree that all our descriptions are just references to
discussed objects, because that's the fundamental role of languages.
They provide us with the ability to _refer_ to things (albeit the
"things" that can be referred to may not actually exist or they may be
an artifact of the language being used).

So, I'm in the odd position of having to agree with the beginning of
your argument, disagree with the middle, and agree with the end. [grin]

--
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

glen ep ropella

Re: Mathematics and Music

Mikhail Gorelkin wrote:

>>> Glen between brackets<<
>
> 1) >>I maintain my claim that math is a living language by which we
> describe aspects of reality.<< and >>But I disagree that an accurate
> definition of math is equal to doing math.<<
>
> I don't know a better definition of math than: it is an *art*. Even
> more: there is no math but mathematicians who perform their
> *indefinable* art ("The other sort [of mathematicians] are guided by
> intuition..." --Henri Poincare "Intuition and Logic in Mathematics";
> or "a mathematician who is not something of a poet will never be a
> good mathematician.")

These are fine notions; but ultimately we're just trading opinions,
there, and won't really get very far, at least not over e-mail.

> An act of creation is beyond any language

OK. I explicitly disagree with the claim that an act of creation is
beyond any language. Specifically, I think linguistic constructs are
part of a larger, more general type of sensory-motor interaction that
also includes other forms of communication like pictures, fist-fights,
chair-building, etc. as well as the general interpretation and discovery
of the world around us.

This general sensory-motor category (I'll call it SMI) is the _only_
evidence we have that an external reality even exists. Hence, things in
SMI are the only things we can talk about rationally. All the other
hypothetical occult stuff behind the things in SMI are amorphous shadows
that we can only get at indirectly, if at all.

So, the claim that creation is _beyond_ (behind, more than, etc.)
language (and vision, and interactive exploration, etc.) is a very
strong, realist claim.

There's no problem being a realist and assuming there is _something_ out
there beyond SMI. But accepting such an assumption is a slippery slope.
Once you accept that, you tend to _delude_ yourself into thinking you
can somewhat accurately or precisely determine the difference between
two things hidden behind elements of SMI.

In essence, this is why the scientific method consists largely of a)
repeatability, b) falsification, and c) prediction. Because all that
stuff is on _this_ side of SMI. All else is occluded behind SMI.

So, it is much more conservative to avoid claims about what's behind SMI
and stick with talking about things like the language and the constructs
in the language. Hence, creation is the act of constructing something
in SMI, e.g. a novel, or a chair, or a rigorous statement of a theorem,
using other things in SMI.

Since there are things in SMI other than languages, it is true that math
may not be _merely_ a language. It may consist of other sensory-motor
interactions with our environments. If that's your criticism, then I
accept it and admit that we need to broaden the consideration to other
things in SMI. But I won't accept that we have to appeal to the
"supernatural" to define math.

> Are the English poetry and the English language the same?

Clearly not. Poetry is a sub-language, which is why it's so remarkable
when one sees good poetry. The best artists can do so much within very
tight constraints. (And this demonstrates why I'm not a language artist
... because I'm a wind-bag ... can't say anything in under 1000 words. ;-)

> Studying only French, can we write, for example, "In Search of Lost
> Time"?... When we cannot put something into a language, we try to
> extend and change it. A language is living because an artist (or the
> Artist, it depends on a point of view) is performing.

Yes! The _act_ of transforming one thing into another thing is what
makes the things "living", which is why relational modeling seems so
much more powerful than constituent modeling (though I happen to believe
they're expressively equivalent).

But that doesn't mean we can pierce the ontological veil and directly
see what's behind the elements of SMI.

> 2) >>on the Chaitin talk is that there were many things said in the
> talk<<
>
> My perception is: he told about one thing: reality of things is
> incalculable and even un-nameable with probability one (Borel). It
> is, probably, why philosophers talk about its divine nature. --Mikhal

OK. Well, again, I have to argue with you (without arguing with
Chaitin). [grin] What we are capable of inferring about reality _is_
calculable and nameable. We can count the words we use. We can
categorize and name our beakers, animals, genes, shirts, etc. And we
can quantitatively compare stories (experimental protocols, poems, etc.).

And since we cannot have a clear idea what's behind the elements of SMI,
my claim is that reality _is_ what's in SMI. And, hence, reality is
calculable and nameable, at least to the extent to which we're concerned
with reality.

--
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

Marcus G. Daniels

Re: Mathematics and Music

glen e. p. ropella wrote:
> This general sensory-motor category (I'll call it SMI) is the _only_
> evidence we have that an external reality even exists.
Those characters you think you see on your computer screen. Those
sounds you think you hear coming from your speakers. That us. The
voices in your head. :-)

============================================================
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

Mikhail Gorelkin

Re: Mathematics and Music

In reply to this post by glen ep ropella

Glen, got it :-) We all have *two* me: the one is indefinable "I am" (who thinks, the real one) and the another is the product of thinking of the first one (me as I think about me). The perception of the first one - mostly through intuition, imagination,... - of "external things" is what we call *reality*. The problem is we are mostly unaware about many details of it (they are beneath of our consciousness) or it is very difficult to *articulate* them correctly. Falling in love with a woman is here (try to describe this unique feeling). Another example is: it took a quite some time to recognize the essence of people and become more predictive about their behaviors... The second one organizes our world around his categorization, rationality, causality,... It is the *constructed* reality. There is a gap inside of us: we differently "know" what reality is and what we construct in our rational minds as "reality". Here is an example from that Chaitin's lesson: we intuitively (geometrically) "know" *all* points on the line but rationally can name and compute... almost nothing (zero probability). Our second me perceives everything when it appears in our rational mind as it is created there, but the first one knows that... his companion lives inside of the Matrix. And Godel's theorems exist only in that artificial "reality". Our rational mind tries hard to fix these problems and it cannot. It cannot even leave a zone of zero-probability... The artist - call him a mathematician - is a real me who exists in reality and through his art creates another one and all fancy stuff there like Lie groups :-) --Mikhail

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Monday, July 14, 2008 9:45 PM

Subject: Re: [FRIAM] Mathematics and Music

Mikhail Gorelkin wrote:

>>> Glen between brackets<<
>
> 1) >>I maintain my claim that math is a living language by which we
> describe aspects of reality.<< and >>But I disagree that an accurate
> definition of math is equal to doing math.<<
>
> I don't know a better definition of math than: it is an *art*. Even
> more: there is no math but mathematicians who perform their
> *indefinable* art ("The other sort [of mathematicians] are guided by
> intuition..." --Henri Poincare "Intuition and Logic in Mathematics";
> or "a mathematician who is not something of a poet will never be a
> good mathematician.")

These are fine notions; but ultimately we're just trading opinions,
there, and won't really get very far, at least not over e-mail.

> An act of creation is beyond any language

OK. I explicitly disagree with the claim that an act of creation is
beyond any language. Specifically, I think linguistic constructs are
part of a larger, more general type of sensory-motor interaction that
also includes other forms of communication like pictures, fist-fights,
chair-building, etc. as well as the general interpretation and discovery
of the world around us.

This general sensory-motor category (I'll call it SMI) is the _only_
evidence we have that an external reality even exists. Hence, things in
SMI are the only things we can talk about rationally. All the other
hypothetical occult stuff behind the things in SMI are amorphous shadows
that we can only get at indirectly, if at all.

So, the claim that creation is _beyond_ (behind, more than, etc.)
language (and vision, and interactive exploration, etc.) is a very
strong, realist claim.

There's no problem being a realist and assuming there is _something_ out
there beyond SMI. But accepting such an assumption is a slippery slope.
Once you accept that, you tend to _delude_ yourself into thinking you
can somewhat accurately or precisely determine the difference between
two things hidden behind elements of SMI.

In essence, this is why the scientific method consists largely of a)
repeatability, b) falsification, and c) prediction. Because all that
stuff is on _this_ side of SMI. All else is occluded behind SMI.

So, it is much more conservative to avoid claims about what's behind SMI
and stick with talking about things like the language and the constructs
in the language. Hence, creation is the act of constructing something
in SMI, e.g. a novel, or a chair, or a rigorous statement of a theorem,
using other things in SMI.

Since there are things in SMI other than languages, it is true that math
may not be _merely_ a language. It may consist of other sensory-motor
interactions with our environments. If that's your criticism, then I
accept it and admit that we need to broaden the consideration to other
things in SMI. But I won't accept that we have to appeal to the
"supernatural" to define math.

> Are the English poetry and the English language the same?

Clearly not. Poetry is a sub-language, which is why it's so remarkable
when one sees good poetry. The best artists can do so much within very
tight constraints. (And this demonstrates why I'm not a language artist
... because I'm a wind-bag ... can't say anything in under 1000 words. ;-)

> Studying only French, can we write, for example, "In Search of Lost
> Time"?... When we cannot put something into a language, we try to
> extend and change it. A language is living because an artist (or the
> Artist, it depends on a point of view) is performing.

Yes! The _act_ of transforming one thing into another thing is what
makes the things "living", which is why relational modeling seems so
much more powerful than constituent modeling (though I happen to believe
they're expressively equivalent).

But that doesn't mean we can pierce the ontological veil and directly
see what's behind the elements of SMI.

> 2) >>on the Chaitin talk is that there were many things said in the
> talk<<
>
> My perception is: he told about one thing: reality of things is
> incalculable and even un-nameable with probability one (Borel). It
> is, probably, why philosophers talk about its divine nature. --Mikhal

OK. Well, again, I have to argue with you (without arguing with
Chaitin). [grin] What we are capable of inferring about reality _is_
calculable and nameable. We can count the words we use. We can
categorize and name our beakers, animals, genes, shirts, etc. And we
can quantitatively compare stories (experimental protocols, poems, etc.).

And since we cannot have a clear idea what's behind the elements of SMI,
my claim is that reality _is_ what's in SMI. And, hence, reality is
calculable and nameable, at least to the extent to which we're concerned
with reality.

--
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

Kenneth Lloyd

Re: Mathematics and Music

Lie Groups are fancy?

Simple, elegant, perhaps. Not fancy.

Ken

From: [hidden email] [mailto:[hidden email]] On Behalf Of Mikhail Gorelkin
Sent: Monday, July 14, 2008 11:02 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Mathematics and Music

Glen, got it :-) We all have *two* me: the one is indefinable "I am" (who thinks, the real one) and the another is the product of thinking of the first one (me as I think about me). The perception of the first one - mostly through intuition, imagination,... - of "external things" is what we call *reality*. The problem is we are mostly unaware about many details of it (they are beneath of our consciousness) or it is very difficult to *articulate* them correctly. Falling in love with a woman is here (try to describe this unique feeling). Another example is: it took a quite some time to recognize the essence of people and become more predictive about their behaviors... The second one organizes our world around his categorization, rationality, causality,... It is the *constructed* reality. There is a gap inside of us: we differently "know" what reality is and what we construct in our rational minds as "reality". Here is an example from that Chaitin's lesson: we intuitively (geometrically) "know" *all* points on the line but rationally can name and compute... almost nothing (zero probability). Our second me perceives everything when it appears in our rational mind as it is created there, but the first one knows that... his companion lives inside of the Matrix. And Godel's theorems exist only in that artificial "reality". Our rational mind tries hard to fix these problems and it cannot. It cannot even leave a zone of zero-probability... The artist - call him a mathematician - is a real me who exists in reality and through his art creates another one and all fancy stuff there like Lie groups :-) --Mikhail

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Monday, July 14, 2008 9:45 PM

Subject: Re: [FRIAM] Mathematics and Music

Mikhail Gorelkin wrote:

>>> Glen between brackets<<
>
> 1) >>I maintain my claim that math is a living language by which we
> describe aspects of reality.<< and >>But I disagree that an accurate
> definition of math is equal to doing math.<<
>
> I don't know a better definition of math than: it is an *art*. Even
> more: there is no math but mathematicians who perform their
> *indefinable* art ("The other sort [of mathematicians] are guided by
> intuition..." --Henri Poincare "Intuition and Logic in Mathematics";
> or "a mathematician who is not something of a poet will never be a
> good mathematician.")

These are fine notions; but ultimately we're just trading opinions,
there, and won't really get very far, at least not over e-mail.

> An act of creation is beyond any language

OK. I explicitly disagree with the claim that an act of creation is
beyond any language. Specifically, I think linguistic constructs are
part of a larger, more general type of sensory-motor interaction that
also includes other forms of communication like pictures, fist-fights,
chair-building, etc. as well as the general interpretation and discovery
of the world around us.

This general sensory-motor category (I'll call it SMI) is the _only_
evidence we have that an external reality even exists. Hence, things in
SMI are the only things we can talk about rationally. All the other
hypothetical occult stuff behind the things in SMI are amorphous shadows
that we can only get at indirectly, if at all.

So, the claim that creation is _beyond_ (behind, more than, etc.)
language (and vision, and interactive exploration, etc.) is a very
strong, realist claim.

There's no problem being a realist and assuming there is _something_ out
there beyond SMI. But accepting such an assumption is a slippery slope.
Once you accept that, you tend to _delude_ yourself into thinking you
can somewhat accurately or precisely determine the difference between
two things hidden behind elements of SMI.

In essence, this is why the scientific method consists largely of a)
repeatability, b) falsification, and c) prediction. Because all that
stuff is on _this_ side of SMI. All else is occluded behind SMI.

So, it is much more conservative to avoid claims about what's behind SMI
and stick with talking about things like the language and the constructs
in the language. Hence, creation is the act of constructing something
in SMI, e.g. a novel, or a chair, or a rigorous statement of a theorem,
using other things in SMI.

Since there are things in SMI other than languages, it is true that math
may not be _merely_ a language. It may consist of other sensory-motor
interactions with our environments. If that's your criticism, then I
accept it and admit that we need to broaden the consideration to other
things in SMI. But I won't accept that we have to appeal to the
"supernatural" to define math.

> Are the English poetry and the English language the same?

Clearly not. Poetry is a sub-language, which is why it's so remarkable
when one sees good poetry. The best artists can do so much within very
tight constraints. (And this demonstrates why I'm not a language artist
... because I'm a wind-bag ... can't say anything in under 1000 words. ;-)

> Studying only French, can we write, for example, "In Search of Lost
> Time"?... When we cannot put something into a language, we try to
> extend and change it. A language is living because an artist (or the
> Artist, it depends on a point of view) is performing.

Yes! The _act_ of transforming one thing into another thing is what
makes the things "living", which is why relational modeling seems so
much more powerful than constituent modeling (though I happen to believe
they're expressively equivalent).

But that doesn't mean we can pierce the ontological veil and directly
see what's behind the elements of SMI.

> 2) >>on the Chaitin talk is that there were many things said in the
> talk<<
>
> My perception is: he told about one thing: reality of things is
> incalculable and even un-nameable with probability one (Borel). It
> is, probably, why philosophers talk about its divine nature. --Mikhal

OK. Well, again, I have to argue with you (without arguing with
Chaitin). [grin] What we are capable of inferring about reality _is_
calculable and nameable. We can count the words we use. We can
categorize and name our beakers, animals, genes, shirts, etc. And we
can quantitatively compare stories (experimental protocols, poems, etc.).

And since we cannot have a clear idea what's behind the elements of SMI,
my claim is that reality _is_ what's in SMI. And, hence, reality is
calculable and nameable, at least to the extent to which we're concerned
with reality.

--
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

glen ep ropella

Re: Mathematics and Music

In reply to this post by Mikhail Gorelkin

Mikhail Gorelkin wrote:
> We all have *two* me: the one is indefinable "I am"
> (who thinks, the real one) and the another is the product of thinking
> of the first one (me as I think about me).

Well, OK. I kindasorta agree. But, one has to realize that the latter
me is just as "real" as the former me. These self-referencing loops are
a part of reality. This is one area where English does just fine and
(what we know of) mathematics starts to stumble (but not fall).

> The perception of the
> first one - mostly through intuition, imagination,... - of "external
> things" is what we call *reality*. The problem is we are mostly
> unaware about many details of it (they are beneath of our
> consciousness) or it is very difficult to *articulate* them
> correctly. Falling in love with a woman is here (try to describe this
> unique feeling). Another example is: it took a quite some time to
> recognize the essence of people and become more predictive about
> their behaviors... The second one organizes our world around his
> categorization, rationality, causality,... It is the *constructed*
> reality. There is a gap inside of us: we differently "know" what
> reality is and what we construct in our rational minds as "reality".

It's true that constructed reality is not a perfect match of ... a
priori reality (for lack of a better term). But I have to punctuate
this argument again with the fact that the constructed reality, those
thoughts inside someone's brain, are just as real as the a priori
reality. There is no substantive difference (or at least there won't be
once we get a better handle on neural correlates -- an engineering problem).

There _may_ (emphasis on "may") be a modeling difference. A priori
reality may not be a model of anything, i.e. it may not _refer_ to
anything. Hence, it's a thing in and of itself and can't be used as a
symbol. ... Maybe. In contrast, the constructed reality can be used as
a model, primarily because it is an incomplete match with a priori
reality. (A model cannot, by definition, be an exact match to its
referent ... the map is not the territory.)

But just because one chunk of reality can be used as a model and the
other cannot doesn't mean one is more real than the other.

> Here is an example from that Chaitin's lesson: we intuitively
> (geometrically) "know" *all* points on the line but rationally can
> name and compute... almost nothing (zero probability). Our second me
> perceives everything when it appears in our rational mind as it is
> created there, but the first one knows that... his companion lives
> inside of the Matrix. And Godel's theorems exist only in that
> artificial "reality". Our rational mind tries hard to fix these
> problems and it cannot. It cannot even leave a zone of
> zero-probability... The artist - call him a mathematician - is a real
> me who exists in reality and through his art creates another one and
> all fancy stuff there like Lie groups :-) --Mikhail

Here's where my punctuation blurbs above matter. Those things like
Goedel's result and Lie groups are just as real as apples, chairs, and
the grand canyon. Just because they are constructed (artificial,
synthetic) doesn't mean they hold some lower ontological or formal
status in reality.

What an extreme Platonist might argue is that these constructed
rationale are not only more reflective of reality than chairs and apples
but that they _are_ reality and the rest is illusory ... noise in the
transduction between "out there" and "in here". To steal from Jack:
Where we receive musical scales and party planning, the universe is
transmitting maximally even sets.

In the end, I don't believe either of the two "me"s is more real than
the other. It all lies in the set of sensory-motor interactions, which
may or may not be correlated with an occult "reality" beyond that.

Going back to Chaitin, I agree fully with one of the things he
_intended_ to say but that Feynman said better: What I cannot create, I
do not understand. That states a direct relation between creation and
language. I will also make the dubious claim that: What I cannot
understand (in some medium), I cannot create. And that states the
inverse relation. The point being that, even if it's solely
subconsciously or through movement and action, all we know is what we
can observe, manipulate, and talk about. The rest is supernatural and
magical thinking.

--
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

Mikhail Gorelkin

Re: Mathematics and Music

Glen, 1) >>But, one has to realize that the latter me is just as "real" as the former me.<< Probably, from a point of view of an authentic self, a degree of such "real-ness" is not very significant - zero probability - and may be ignored almost completely. I think it is "real" because this authentic self exists behind it. 2) >>But I have to punctuate this argument again with the fact that the constructed reality, those thoughts inside someone's brain, are just as real as the a priori reality<< Yes, but it's very limited and low reality. We try to think about something, but our Selves know it as it is. This difference is what matters. 3) >>Those things like Gödels result and Lie groups are just as real as apples, chairs, and the grand canyon.<< apples,... are a result of our perception (interpretation) of reality. They are symbols, constructs like Lie groups. But constructs may be also phantoms (illusions) - without a correlation (a kind of an "isomorphism") with something in reality (or bigger reality) and don't "work" in our practical life. They eventually will disappear. 4) >>Feynman said better: What I cannot create, I do not understand.<< In his Nobel lesson, Feynman said that nobody understands quantum mechanic :-) The key word here is "create" and people mostly misuse it. I think that this phrase should sound like this: what I cannot make, I do not understand (algorithmical understanding). Yes, I agree that the inverse phrase is correct as well... The ability to *make* is an attribute of our rational mind. If one person can make something like a chair, than another one can steal his plan (algorithm, understanding), copy it and sell on the market with a price of *commodity*. But a rational mind cannot *create*. Such ability is an attribute of our Genius. We read poetry for only two reasons: to get a glimpse of its original author - this authentic self, and to enjoy his *creation* - art. We cannot sell to a museum our makes but arts. And the Boston Symphony Orchestra will not perform even a technically sophisticated make... Creation of a genius is mysterious for a rational mind of the "author" as for others. It's why "authors" usually withdraw their interpretations and comments or make (invent) them after all. --Mikhail

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Tuesday, July 15, 2008 1:15 PM

Subject: Re: [FRIAM] Mathematics and Music

Mikhail Gorelkin wrote:
> We all have *two* me: the one is indefinable "I am"
> (who thinks, the real one) and the another is the product of thinking
> of the first one (me as I think about me).

Well, OK. I kindasorta agree. But, one has to realize that the latter
me is just as "real" as the former me. These self-referencing loops are
a part of reality. This is one area where English does just fine and
(what we know of) mathematics starts to stumble (but not fall).

> The perception of the
> first one - mostly through intuition, imagination,... - of "external
> things" is what we call *reality*. The problem is we are mostly
> unaware about many details of it (they are beneath of our
> consciousness) or it is very difficult to *articulate* them
> correctly. Falling in love with a woman is here (try to describe this
> unique feeling). Another example is: it took a quite some time to
> recognize the essence of people and become more predictive about
> their behaviors... The second one organizes our world around his
> categorization, rationality, causality,... It is the *constructed*
> reality. There is a gap inside of us: we differently "know" what
> reality is and what we construct in our rational minds as "reality".

It's true that constructed reality is not a perfect match of ... a
priori reality (for lack of a better term). But I have to punctuate
this argument again with the fact that the constructed reality, those
thoughts inside someone's brain, are just as real as the a priori
reality. There is no substantive difference (or at least there won't be
once we get a better handle on neural correlates -- an engineering problem).

There _may_ (emphasis on "may") be a modeling difference. A priori
reality may not be a model of anything, i.e. it may not _refer_ to
anything. Hence, it's a thing in and of itself and can't be used as a
symbol. ... Maybe. In contrast, the constructed reality can be used as
a model, primarily because it is an incomplete match with a priori
reality. (A model cannot, by definition, be an exact match to its
referent .. the map is not the territory.)

But just because one chunk of reality can be used as a model and the
other cannot doesn't mean one is more real than the other.

> Here is an example from that Chaitin's lesson: we intuitively
> (geometrically) "know" *all* points on the line but rationally can
> name and compute... almost nothing (zero probability). Our second me
> perceives everything when it appears in our rational mind as it is
> created there, but the first one knows that... his companion lives
> inside of the Matrix. And Godel's theorems exist only in that
> artificial "reality". Our rational mind tries hard to fix these
> problems and it cannot. It cannot even leave a zone of
> zero-probability... The artist - call him a mathematician - is a real
> me who exists in reality and through his art creates another one and
> all fancy stuff there like Lie groups :-) --Mikhail

Here's where my punctuation blurbs above matter. Those things like
Goedel's result and Lie groups are just as real as apples, chairs, and
the grand canyon. Just because they are constructed (artificial,
synthetic) doesn't mean they hold some lower ontological or formal
status in reality.

What an extreme Platonist might argue is that these constructed
rationale are not only more reflective of reality than chairs and apples
but that they _are_ reality and the rest is illusory .. noise in the
transduction between "out there" and "in here". To steal from Jack:
Where we receive musical scales and party planning, the universe is
transmitting maximally even sets.

In the end, I don't believe either of the two "me"s is more real than
the other. It all lies in the set of sensory-motor interactions, which
may or may not be correlated with an occult "reality" beyond that.

Going back to Chaitin, I agree fully with one of the things he
_intended_ to say but that Feynman said better: What I cannot create, I
do not understand. That states a direct relation between creation and
language. I will also make the dubious claim that: What I cannot
understand (in some medium), I cannot create. And that states the
inverse relation. The point being that, even if it's solely
subconsciously or through movement and action, all we know is what we
can observe, manipulate, and talk about. The rest is supernatural and
magical thinking.

--
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

glen ep ropella

Re: Mathematics and Music

Mikhail Gorelkin wrote:
> >>Glen<<
>
> 1) >>But, one has to realize that the latter me is just as
> "real" as the former me.<<
>
> Probably, from a point of view of an
> authentic self, a degree of such "real-ness" is not very significant
> - zero probability - and may be ignored almost completely. I think it
> is "real" because this authentic self exists behind it.

Perhaps. But there is a consensus reality argument that our conception
of self (and hence our whole behavioral repertoire) is a function of our
inner selves. The argument basically relies on the idea that our inner
self co-emerges ontogenically right along with our physical self. And
to change either one at any stage in ontogenesis is to change the other
in deep and fundamental ways.

There's also an extension of that argument that says a person's identity
is as much a function of their peers as it is of their self.

I'm not saying that these are rock solid arguments. But, to claim that
the inner self's "real-ness" is insignificant is a denial of those
arguments and, to defend the claim properly, you'd have to find some
important fault with those arguments.

> 2) >>But I
> have to punctuate this argument again with the fact that the
> constructed reality, those thoughts inside someone's brain, are just
> as real as the a priori reality<< Yes, but it's very limited and low
> reality. We try to think about something, but our Selves know it as
> it is. This difference is what matters.

I agree that the difference is what matters. But I disagree that our
constructed inner self is "very limited". In fact, I'd say that the
plasticity of our inner self is much greater in some ways than that of
our physical selves precisely because it sits on a (perhaps imperfect)
logical layer of abstraction above the physical self.

In other words, our inner self can contemplate obviously fictitious
things like unicorns and human-traversable wormholes without immediately
being shot down by reality. Our physical selves are "trapped" within
the tight, immediate constraints of physical reality.

But to go back to the main point, those obviously fictitious
constructions we imagine are still _real_ in that they have a
perceptible (sometimes immense) impact on the physical world. (Just
take a look at all the glittery unicorns on pastel colored notebooks in
the school supplies section of your local box store. ;-)

> 3)
>>> Those things like Gödel's result and Lie groups are just as real
>>> as apples, chairs, and the grand canyon.<< apples,... are a
> result of our perception (interpretation) of reality. They are
> symbols, constructs like Lie groups. But constructs may be also
> phantoms (illusions) - without a correlation (a kind of an
> "isomorphism") with something in reality (or bigger reality) and
> don't "work" in our practical life. They eventually will disappear.

I agree with the gist of what you're saying. The fictitious constructs
of no use to the physical self will die off. However, we can't be too
draconian about the word "use". For example glittery, rainbow-colored
unicorns serve no apparent purpose (except to young people and wind-bags
trying to build straw-men ;-), yet they continue unabated. The reverse
logic is that all these constructs, fictitious or not, that currently
exist _must_ be serving some purpose to the physical selves of those who
hold them.

> 4) >>Feynman said better: What I cannot create, I do not
> understand.<< In his Nobel lesson, Feynman said that nobody
> understands quantum mechanic :-) The key word here is "create" and
> people mostly misuse it. I think that this phrase should sound like
> this: what I cannot make, I do not understand (algorithmical
> understanding). Yes, I agree that the inverse phrase is correct as
> well... The ability to *make* is an attribute of our rational mind.
> If one person can make something like a chair, than another one can
> steal his plan (algorithm, understanding), copy it and sell on the
> market with a price of *commodity*. But a rational mind cannot
> *create*. Such ability is an attribute of our Genius. We read poetry
> for only two reasons: to get a glimpse of its original author - this
> authentic self, and to enjoy his *creation* - art. We cannot sell to
> a museum our makes but arts. And the Boston Symphony Orchestra will
> not perform even a technically sophisticated make... Creation of a
> genius is mysterious for a rational mind of the "author" as for
> others. It's why "authors" usually withdraw their interpretations and
> comments or make (invent) them after all. --Mikhail

Hmmm. [grin] You _almost_ convince me! But, I don't hold this
Cartesian Partition so strongly. I believe the activity in the brain is
real activity and can create (by itself) just as mysteriously as the
interplay between hands and brain can create. In fact, it's not clear
to me that the brain, by itself, can _make_ anything in your sense. It
is not regular enough. Perhaps the more autonomic parts of the brain
can act so regular. But, the higher functions seem more artistic than
methodological.

Whether or not such brain activity is "rational" or not is, I think, a
red herring. Rationality is probably a convenient fiction.

Going back to the original point, I maintain that both the act of
creation and the act of making occur within what I call sensory-motor
interactions, not somehow "beyond" or behind them.

--
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

Mikhail Gorelkin

Re: Mathematics and Music

Glen, >>Going back to the original point, I maintain that both the act of creation and the act of making occur within what I call sensory-motor interactions, not somehow "beyond" or behind them.<< No, *nobody* can convince you. He/she can show you but you're the one that has.. to see / experience this difference :-) (this is an axiomatic level) --Mikhail

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Tuesday, July 15, 2008 7:11 PM

Subject: Re: [FRIAM] Mathematics and Music

Mikhail Gorelkin wrote:
> >>Glen<<
>
> 1) >>But, one has to realize that the latter me is just as
> "real" as the former me.<<
>
> Probably, from a point of view of an
> authentic self, a degree of such "real-ness" is not very significant
> - zero probability - and may be ignored almost completely. I think it
> is "real" because this authentic self exists behind it.

Perhaps. But there is a consensus reality argument that our conception
of self (and hence our whole behavioral repertoire) is a function of our
inner selves. The argument basically relies on the idea that our inner
self co-emerges ontogenically right along with our physical self. And
to change either one at any stage in ontogenesis is to change the other
in deep and fundamental ways.

There's also an extension of that argument that says a person's identity
is as much a function of their peers as it is of their self.

I'm not saying that these are rock solid arguments. But, to claim that
the inner self's "real-ness" is insignificant is a denial of those
arguments and, to defend the claim properly, you'd have to find some
important fault with those arguments.

> 2) >>But I
> have to punctuate this argument again with the fact that the
> constructed reality, those thoughts inside someone's brain, are just
> as real as the a priori reality<< Yes, but it's very limited and low
> reality. We try to think about something, but our Selves know it as
> it is. This difference is what matters.

I agree that the difference is what matters. But I disagree that our
constructed inner self is "very limited". In fact, I'd say that the
plasticity of our inner self is much greater in some ways than that of
our physical selves precisely because it sits on a (perhaps imperfect)
logical layer of abstraction above the physical self.

In other words, our inner self can contemplate obviously fictitious
things like unicorns and human-traversable wormholes without immediately
being shot down by reality. Our physical selves are "trapped" within
the tight, immediate constraints of physical reality.

But to go back to the main point, those obviously fictitious
constructions we imagine are still _real_ in that they have a
perceptible (sometimes immense) impact on the physical world. (Just
take a look at all the glittery unicorns on pastel colored notebooks in
the school supplies section of your local box store. ;-)

> 3)
>>> Those things like Gödel's result and Lie groups are just as real
>>> as apples, chairs, and the grand canyon.<< apples,... are a
> result of our perception (interpretation) of reality. They are
> symbols, constructs like Lie groups. But constructs may be also
> phantoms (illusions) - without a correlation (a kind of an
> "isomorphism") with something in reality (or bigger reality) and
> don't "work" in our practical life. They eventually will disappear.

I agree with the gist of what you're saying. The fictitious constructs
of no use to the physical self will die off. However, we can't be too
draconian about the word "use". For example glittery, rainbow-colored
unicorns serve no apparent purpose (except to young people and wind-bags
trying to build straw-men ;-), yet they continue unabated. The reverse
logic is that all these constructs, fictitious or not, that currently
exist _must_ be serving some purpose to the physical selves of those who
hold them.

> 4) >>Feynman said better: What I cannot create, I do not
> understand.<< In his Nobel lesson, Feynman said that nobody
> understands quantum mechanic :-) The key word here is "create" and
> people mostly misuse it. I think that this phrase should sound like
> this: what I cannot make, I do not understand (algorithmical
> understanding). Yes, I agree that the inverse phrase is correct as
> well... The ability to *make* is an attribute of our rational mind.
> If one person can make something like a chair, than another one can
> steal his plan (algorithm, understanding), copy it and sell on the
> market with a price of *commodity*. But a rational mind cannot
> *create*. Such ability is an attribute of our Genius. We read poetry
> for only two reasons: to get a glimpse of its original author - this
> authentic self, and to enjoy his *creation* - art. We cannot sell to
> a museum our makes but arts. And the Boston Symphony Orchestra will
> not perform even a technically sophisticated make... Creation of a
> genius is mysterious for a rational mind of the "author" as for
> others. It's why "authors" usually withdraw their interpretations and
> comments or make (invent) them after all. --Mikhail

Hmmm. [grin] You _almost_ convince me! But, I don't hold this
Cartesian Partition so strongly. I believe the activity in the brain is
real activity and can create (by itself) just as mysteriously as the
interplay between hands and brain can create. In fact, it's not clear
to me that the brain, by itself, can _make_ anything in your sense. It
is not regular enough. Perhaps the more autonomic parts of the brain
can act so regular. But, the higher functions seem more artistic than
methodological.

Whether or not such brain activity is "rational" or not is, I think, a
red herring. Rationality is probably a convenient fiction.

Going back to the original point, I maintain that both the act of
creation and the act of making occur within what I call sensory-motor
interactions, not somehow "beyond" or behind them.

--
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

glen ep ropella

Re: Mathematics and Music

Mikhail Gorelkin wrote:
> >>Glen<<
> >>Going back to the original point, I maintain that both the
> act of creation and the act of making occur within what I call
> sensory-motor interactions, not somehow "beyond" or behind them.<<
> No, *nobody* can convince you. He/she can show you but you're the one
> that has.. to see / experience this difference :-) (this is an
> axiomatic level) --Mikhail

It's not clear to me what you're saying, here. Are you simply saying
that I'm stubborn? [grin] Yes, that's true ... and I'm proud of it. As
a good friend once told me: "If your mind is too closed, nothing can
get in. But if your mind is too open, everything falls out."

Or are you simply saying that a metaphysical/supernatural hypothesis
like your "creation is beyond language" is a belief that cannot be
debated? One either accepts it or one doesn't and no argument is
powerful enough to change one's position?

In that sense, I guess we agree, because I believe the claim: "creation
is beyond language" to be a religious claim. I don't believe the claim.

But, just because it's religious on its face doesn't mean we can't shave
down the concept of "creation" (like you did by distinguishing "making"
from "creation") and construct some type of scientific (testable) claim.
For example, we might propose that: Non-linguistic animals can
spontaneously begin using novel food gathering methods. "Novel" meaning
"never before observed in this species". The we can leave it up to the
metaphysicians as to whether or not "novelty" and "creation" are related.

--
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

Mikhail Gorelkin

Re: Mathematics and Music

Glen, >>Or are you simply saying that a metaphysical/supernatural hypothesis like your "creation is beyond language" is a belief that cannot be debated? One either accepts it or one doesn't and no argument is powerful enough to change one's position?<< Yes, I meant something like this, but I prefer to use another, more appropriate, terminology (it seems that Chaitin mean the same): *reality as it is* ("outside" of our perception). I think that perceived image of reality that we claim as "our reality" is not complete and not very accurate as any interpretation. And our evolution (as our consciousness grows from our current level toward our Higher Selves) is also about extension and clarification of this perception of reality. Or we can say: our "reality" is extending (it's an isomorphic expression). It seems that theologians, mystics, philosophers were first to recognize / experience bigger reality behind our "regular" perception of it, and now we need to extend our languages (references) and models to "work" with the same things. I got from Chaitin's lesson that he tries mathematically to articulate something like that... without using a word "divine" :-) P.S. Sometime we recognized that our references point to different perceptions, images of reality, and this is what I meant as an axiomatic level. It's about *to see*, not *proof* (read "convince") because it's prior any proof, even any language. --Mikhail

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Wednesday, July 16, 2008 12:41 PM

Subject: Re: [FRIAM] Mathematics and Music

Mikhail Gorelkin wrote:
> >>Glen<<
> >>Going back to the original point, I maintain that both the
> act of creation and the act of making occur within what I call
> sensory-motor interactions, not somehow "beyond" or behind them.<<
> No, *nobody* can convince you. He/she can show you but you're the one
> that has.. to see / experience this difference :-) (this is an
> axiomatic level) --Mikhail

It's not clear to me what you're saying, here. Are you simply saying
that I'm stubborn? [grin] Yes, that's true ... and I'm proud of it. As
a good friend once told me: "If your mind is too closed, nothing can
get in. But if your mind is too open, everything falls out."

Or are you simply saying that a metaphysical/supernatural hypothesis
like your "creation is beyond language" is a belief that cannot be
debated? One either accepts it or one doesn't and no argument is
powerful enough to change one's position?

In that sense, I guess we agree, because I believe the claim: "creation
is beyond language" to be a religious claim. I don't believe the claim.

But, just because it's religious on its face doesn't mean we can't shave
down the concept of "creation" (like you did by distinguishing "making"
from "creation") and construct some type of scientific (testable) claim.
For example, we might propose that: Non-linguistic animals can
spontaneously begin using novel food gathering methods. "Novel" meaning
"never before observed in this species". The we can leave it up to the
metaphysicians as to whether or not "novelty" and "creation" are related.

--
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