math, is it just physics?

[sobriquet]

We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm of
idealized forms.

For instance in the intro to this recent yt contribution:

On the other hand there seems to be mounting evidence that the patterns
in physics match up in intriguing ways with abstractions on a conceptual
level.

So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed in
the behavior and properties of things like elementary particles such as
electrons or fields.

[FromTheRafters]

We often hear claims that math has nothing to do with reality and is just
something that exists in our imagination or some platonic realm of idealized
forms.
http://youtu.be/dzuDSTamzrE
On the other hand there seems to be mounting evidence that the patterns in
physics match up in intriguing ways with abstractions on a conceptual level.
http://youtu.be/-OxVsVUesSc
So in a way one could claim that concepts like integers and their properties
and relationships can be more or less empirically observed in the behavior
and properties of things like elementary particles such as electrons or
fields.

There's also this:

https://math.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

[sobriquet]

Post by FromTheRafters

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm
of idealized forms.
http://youtu.be/dzuDSTamzrE
On the other hand there seems to be mounting evidence that the
patterns in physics match up in intriguing ways with abstractions on a
conceptual level.
http://youtu.be/-OxVsVUesSc
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles
such as electrons or fields.

https://math.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

I'm learning german and french, so I ask chat gpt to pronounce every
sentence in english, german and french. It does so with a very strong
english accent. I tell it to get rid of the accent. it does so and it
sounds pretty good. However as soon as I paste the next paragraph, the
strong english accent is back. I remind it that I want it to pronounce
the text without an accent and it complies. However, as soon as I go
to the next paragraph, the strong accent returns.. AAARRRRggh!!!!

[Ross Finlayson]

Post by sobriquet

Post by FromTheRafters

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm
of idealized forms.
http://youtu.be/dzuDSTamzrE
On the other hand there seems to be mounting evidence that the
patterns in physics match up in intriguing ways with abstractions on
a conceptual level.
http://youtu.be/-OxVsVUesSc
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles
such as electrons or fields.

https://math.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

I'm learning german and french, so I ask chat gpt to pronounce every
sentence in english, german and french. It does so with a very strong
english accent. I tell it to get rid of the accent. it does so and it
sounds pretty good. However as soon as I paste the next paragraph, the
strong english accent is back. I remind it that I want it to pronounce
the text without an accent and it complies. However, as soon as I go
to the next paragraph, the strong accent returns.. AAARRRRggh!!!!

I often say that a strong mathematical platonism arrives at
numbers are quite concrete and that there's a theory with
both a strong mathematical platonism, AND, a strong logicist
positivism, quite all scientific with an ontology for the
empiricist mind, yet still fundamentally founded by a continuous
thread of a theory of logical and mathematical truth.


Consider something like Derrida on Husserl's pre-geometric
and pre-scientific world, with regards to why these quite
logicist-positivist minded thinkers have it very strongly
so that mathematics is always present, then also as with
regards to "the ubiquitous success of mathematics in physics".

Then, the mathematical universe hypothesis of a sort,
also has that physics is just mathematics.

[sobriquet]

Post by Ross Finlayson

Post by sobriquet

Post by FromTheRafters

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm
of idealized forms.
http://youtu.be/dzuDSTamzrE
On the other hand there seems to be mounting evidence that the
patterns in physics match up in intriguing ways with abstractions on
a conceptual level.
http://youtu.be/-OxVsVUesSc
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles
such as electrons or fields.

https://math.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

I'm learning german and french, so I ask chat gpt to pronounce every
sentence in english, german and french. It does so with a very strong
english accent. I tell it to get rid of the accent. it does so and it
sounds pretty good. However as soon as I paste the next paragraph, the
strong english accent is back. I remind it that I want it to pronounce
the text without an accent and it complies. However, as soon as I go
to the next paragraph, the strong accent returns.. AAARRRRggh!!!!

I often say that a strong mathematical platonism arrives at
numbers are quite concrete and that there's a theory with
both a strong mathematical platonism, AND, a strong logicist
positivism, quite all scientific with an ontology for the
empiricist mind, yet still fundamentally founded by a continuous
thread of a theory of logical and mathematical truth.
Consider something like Derrida on Husserl's pre-geometric
and pre-scientific world, with regards to why these quite
logicist-positivist minded thinkers have it very strongly
so that mathematics is always present, then also as with
regards to "the ubiquitous success of mathematics in physics".
Then, the mathematical universe hypothesis of a sort,
also has that physics is just mathematics.

But we don't want to confuse the map with the territory.
It's a bit like arithmetic and the claim that computers are not really
doing arithmetic, since only biological organic beings like humans can
do real arithmetic and computers are only simulating doing arithmetic,
but they are not really doing arithmetic. So only a human actually is
able to add 5 and 7 and produce the sum of 12 and if you use a
calculator or computer, it looks like it's doing the same thing and it
even comes up with the same result 12, but it's not really doing
addition, just simulating the mental process of addition that only a
human being can perform.
This seems a nonsense claim, but that is similar to nonsense claims that
computers can't really be conscious or subjectively experience things,
even if they end up with exactly the same results as a human claiming
he's conscious and not a philosophical zombie like a computer that can
only behave like it's conscious without actually being conscious or
having a subjective experience. So what is the difference between
simulating addition and actual addition if we end up with identical
outputs for a given combination of inputs?
Can a simulation or model be identical to reality? I would say yes.
You can do a simulation of the formation of ice crystals with actual
water as a model where you control the circumstances to simulate nature
outside the laboratory. As opposed to doing a computational simulation
of water with some kind of math that models certain aspects of water to
explore the way water undergoes a phase change from liquid to solid.

In any case, if we unify math and physics, it would just be two sides
of the same coin.. so it's kind of like claiming everything is energy,
since matter is just a form of energy or claiming that everything is
matter, since energy is just a form of matter.

Regarding the unreasonable effectiveness of math in the natural sciences
I would say.. well, you wouldn't have expected that, would ya? We
abstract from reality to obtain math and lo and behold, the math is very
suitable to model reality.

[Ross Finlayson]

Post by sobriquet

Post by Ross Finlayson

Post by sobriquet

Post by FromTheRafters

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm
of idealized forms.
http://youtu.be/dzuDSTamzrE
On the other hand there seems to be mounting evidence that the
patterns in physics match up in intriguing ways with abstractions on
a conceptual level.
http://youtu.be/-OxVsVUesSc
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles
such as electrons or fields.

https://math.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

I'm learning german and french, so I ask chat gpt to pronounce every
sentence in english, german and french. It does so with a very strong
english accent. I tell it to get rid of the accent. it does so and it
sounds pretty good. However as soon as I paste the next paragraph, the
strong english accent is back. I remind it that I want it to pronounce
the text without an accent and it complies. However, as soon as I go
to the next paragraph, the strong accent returns.. AAARRRRggh!!!!

I often say that a strong mathematical platonism arrives at
numbers are quite concrete and that there's a theory with
both a strong mathematical platonism, AND, a strong logicist
positivism, quite all scientific with an ontology for the
empiricist mind, yet still fundamentally founded by a continuous
thread of a theory of logical and mathematical truth.
Consider something like Derrida on Husserl's pre-geometric
and pre-scientific world, with regards to why these quite
logicist-positivist minded thinkers have it very strongly
so that mathematics is always present, then also as with
regards to "the ubiquitous success of mathematics in physics".
Then, the mathematical universe hypothesis of a sort,
also has that physics is just mathematics.

But we don't want to confuse the map with the territory.
It's a bit like arithmetic and the claim that computers are not really
doing arithmetic, since only biological organic beings like humans can
do real arithmetic and computers are only simulating doing arithmetic,
but they are not really doing arithmetic. So only a human actually is
able to add 5 and 7 and produce the sum of 12 and if you use a
calculator or computer, it looks like it's doing the same thing and it
even comes up with the same result 12, but it's not really doing
addition, just simulating the mental process of addition that only a
human being can perform.
This seems a nonsense claim, but that is similar to nonsense claims that
computers can't really be conscious or subjectively experience things,
even if they end up with exactly the same results as a human claiming
he's conscious and not a philosophical zombie like a computer that can
only behave like it's conscious without actually being conscious or
having a subjective experience. So what is the difference between
simulating addition and actual addition if we end up with identical
outputs for a given combination of inputs?
Can a simulation or model be identical to reality? I would say yes.
You can do a simulation of the formation of ice crystals with actual
water as a model where you control the circumstances to simulate nature
outside the laboratory. As opposed to doing a computational simulation
of water with some kind of math that models certain aspects of water to
explore the way water undergoes a phase change from liquid to solid.
In any case, if we unify math and physics, it would just be two sides
of the same coin.. so it's kind of like claiming everything is energy,
since matter is just a form of energy or claiming that everything is
matter, since energy is just a form of matter.
Regarding the unreasonable effectiveness of math in the natural sciences
I would say.. well, you wouldn't have expected that, would ya? We
abstract from reality to obtain math and lo and behold, the math is very
suitable to model reality.

Perhaps an idea to consider is that there is
any theory, at all, with no paradoxes, at all.

Then, there's still allthe humans lives in the human condition,
and like other finite thinking feeling beings, may attain to
the infinite and continuous in the mathematical, yet there is
one that is to be attained to.

Relaying subjectivity and inter-subjectivity if considered
"higher thinking of the human condition" with regards to
humans being the highest thinkers in this world, or at
least of a sort of at least capable thinker, makes for
some reading of Cassirer reading Montaigne.

There are many _kinds_ of energy and _in_ the entelechy,
it's fair to say that conflating energy with regards to
conservation in a given space of content by continuity
the entelechy, it's similar with arithmetic, for example
having increment versus division instead of iteration and
inverses, arriving at the modular in the middle.

[Stefan Ram]

Post by sobriquet
addition

What would be "really doing addition"?

[sobriquet]

Post by Stefan Ram

Post by sobriquet
addition

What would be "really doing addition"?

There might be a difference between adding numbers by inspecting their
structure and going through some kind of algorithm that composes a new
number digit by digit based on the digits of the numbers it's adding.
As opposed to a kind of look-up table with pre-computed sums where it
just looks up the particular combination of inputs to find the
associated output.

Just like if you have some complicated function that takes long to
compute which is showing down your algorithm, you can compute it once
and keep the results in a kind of table that enables you to retrieve the
precomputed value without going through the same calculations repeatedly
and discarding the results every time.

[sobriquet]

Post by sobriquet

Post by sobriquet
addition

   What would be "really doing addition"?

There might be a difference between adding numbers by inspecting their
structure and going through some kind of algorithm that composes a new
number digit by digit based on the digits of the numbers it's adding.
As opposed to a kind of look-up table with pre-computed sums where it
just looks up the particular combination of inputs to find the
associated output.
Just like if you have some complicated function that takes long to
compute which is showing down your algorithm, you can compute it once
and keep the results in a kind of table that enables you to retrieve the
precomputed value without going through the same calculations repeatedly
and discarding the results every time.

uh.. slowing down your algorithm, that is.

[sobriquet]

Post by Stefan Ram

Post by sobriquet
addition

What would be "really doing addition"?

There might be a difference between adding numbers by inspecting their
structure and going through some kind of algorithm that composes a new
number digit by digit based on the digits of the numbers it's adding.
As opposed to a kind of look-up table with pre-computed sums where it
just looks up the particular combination of inputs to find the
associated output.

Just like if you have some complicated function that takes long to
compute which is showing down your algorithm, you can compute it once
and keep the results in a kind of table that enables you to retrieve the
precomputed value without going through the same calculations repeatedly
and discarding the results every time.

[WM]

Post by sobriquet
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed in
the behavior and properties of things like elementary particles such as
electrons or fields.

Or bricks, marbles, people etc. The natural numbers have been abstracted
from reality. The laws like "the existence of n implies the existence of
n+1" were so evident, that no axioms appeared necessary before Dedekind,
Peano, Schmidt etc. Only Cantor's assumption of an actual set with |ℕ|
being a fixed quantity greater than all numbers is not abstracted from
reality.

Regards, WM

[joes]

Post by WM

Post by sobriquet
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles such
as electrons or fields.

Or bricks, marbles, people etc. The natural numbers have been abstracted
from reality. The laws like "the existence of n implies the existence of
n+1" were so evident, that no axioms appeared necessary before Dedekind,
Peano, Schmidt etc. Only Cantor's assumption of an actual set with |ℕ|
being a fixed quantity greater than all numbers is not abstracted from
reality.

Oh PLEASE show me something physically infinite.

[sobriquet]

Post by joes

Post by WM

Post by sobriquet
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles such
as electrons or fields.

Or bricks, marbles, people etc. The natural numbers have been abstracted
from reality. The laws like "the existence of n implies the existence of
n+1" were so evident, that no axioms appeared necessary before Dedekind,
Peano, Schmidt etc. Only Cantor's assumption of an actual set with |ℕ|
being a fixed quantity greater than all numbers is not abstracted from
reality.

Oh PLEASE show me something physically infinite.

How about space? Or would you claim that if we emit photons in opposite
directions on a straight line/trajectory, they would eventually meet up,
provided they don't run into anything else?

[Stefan Ram]

Post by sobriquet
How about space?

Take the finite quotient of differences of position and time of
a car and you get an approximation to its current speed. Now let
the difference become /infinitely small/ and you get the exact value
of the current speed of the car in that moment /in the real world/.

Achilles can never overtake the tortoise? Calculate the
/infinite series/ and get the correct answer: Achilles
can overtake the tortoise /in the real world/.

So, infinity is everywhere!

|Look into infinity, all you see is trouble.
Bob Dylan

[sobriquet]

Post by Stefan Ram

Post by sobriquet
How about space?

Take the finite quotient of differences of position and time of
a car and you get an approximation to its current speed. Now let
the difference become /infinitely small/ and you get the exact value
of the current speed of the car in that moment /in the real world/.
Achilles can never overtake the tortoise? Calculate the
/infinite series/ and get the correct answer: Achilles
can overtake the tortoise /in the real world/.
So, infinity is everywhere!
|Look into infinity, all you see is trouble.
Bob Dylan

We have a concept of infinity, but perhaps it's a misconception. Maybe
things are finite and in our fantasy we can go to infinity, but in
reality it doesn't work that way.
Things often look continuous because they are composed of such minuscule
units and in our imagination we can take a quantity of gold and
subdivide it into smaller quantities of gold and we can repeat that step
infinitely often.
But we know that we will reach atoms of gold eventually and we can not
split them up into smaller quantities of gold.
The same might be true for space and time itself. So it would be
premature to claim that infinity exists or doesn't exist while we still
have no comprehensive theory that accounts for everything (space, time,
information, energy, matter).

[Stefan Ram]

Post by sobriquet
We have a concept of infinity, but perhaps it's a misconception. Maybe
things are finite and in our fantasy we can go to infinity, but in
reality it doesn't work that way.

Reality's out of our reach. To get a good look at the world up
close, you need some serious juice. There are certain distances
we'll never be able to check out 'cause even all the energy in
the universe wouldn't cut it.

By the same token, there are spots in the cosmos so far out that
we'll never catch a glimpse of what's beyond them. They're booking
it away from us faster than light can make the trip.

As for the infinite or infinitesimal in physics, it's just
a simplified way of thinking about how things work at
the largest or tiniest levels. It gets the job done for
a lot of purposes, while reality is out of our reach.

|There are times when I look in the mirror,
|I expect to see a younger man.
|We are living in the real world,
|And we can't get out.
"Real World" - Peter Green Splinter Group

[Jim Burns]

Post by joes

Post by WM

Post by sobriquet
So in a way one could claim that concepts like
integers and their properties and relationships
can be more or less empirically observed
in the behavior and properties of things like
elementary particles such as electrons or fields.

Or bricks, marbles, people etc.
The natural numbers have been abstracted from reality.
The laws like
"the existence of n implies the existence of n+1"
were so evident, that no axioms appeared necessary
before Dedekind, Peano, Schmidt etc.
Only Cantor's assumption of
an actual set with |ℕ| being a fixed quantity
greater than all numbers
is not abstracted from reality.

Oh PLEASE show me something physically infinite.

I can't show it to you, but
what if physical evidence showed that
something physically infinite might exist?
That strikes me as just.as.good.as showing you,
for the purpose of deciding whether
mathematicians should be allowed to speak of
infinite things.

Consider the cosmos,
of which our observable universe is
a small and possibly.infinitesimal part.

Our observations to date are best explained by
a cosmological curvature with a value in
a narrow range around 0.

If our local patch is typical,
and what we observe locally holds throughout,
then
an observed curvature > 0 indicates
a finite cosmos much bigger than the observable,
and
an observed curvature ≤ 0 indicates
a infinite cosmos.

The latest I've heard,
the finite/infinite question is still up in the air.
I consider that to be where it should be
until we have good reasons which bring it down.


Math, is it just physics?

Mathematicians will do what mathematicians do,
but some of what they do will be encouraged,
if it is found to be useful elsewhere.
Including, but not limited to, in physics.

The idea (suggested in other threads) that
mathematicians should only do useful.elsewhere math
has the way this works exactly backwards.

Mathematicians can't limit themselves to
what will some day find a use elsewhere.
How could they possibly know that?

Physicists, faced with a new problem,
look at what math has already been done
for help in describing and reasoning about it.

Bernhard Riemann (1826 -- 1866)
did not work on differential geometry
_for general relativity_ (1915)
He couldn't have.

Einstein couldn't know someone else's work
was useful before that work was done.
He couldn't have.

[Ross Finlayson]

Post by joes

Post by WM

Post by sobriquet
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles such
as electrons or fields.

Or bricks, marbles, people etc. The natural numbers have been abstracted
from reality. The laws like "the existence of n implies the existence of
n+1" were so evident, that no axioms appeared necessary before Dedekind,
Peano, Schmidt etc. Only Cantor's assumption of an actual set with |ℕ|
being a fixed quantity greater than all numbers is not abstracted from
reality.

Oh PLEASE show me something physically infinite.

0 m/s = ? s/m, ..., ?

[Ross Finlayson]

Post by Ross Finlayson

Post by joes

Post by WM

Post by sobriquet
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles such
as electrons or fields.

Or bricks, marbles, people etc. The natural numbers have been abstracted
from reality. The laws like "the existence of n implies the existence of
n+1" were so evident, that no axioms appeared necessary before Dedekind,
Peano, Schmidt etc. Only Cantor's assumption of an actual set with |ℕ|
being a fixed quantity greater than all numbers is not abstracted from
reality.

Oh PLEASE show me something physically infinite.

0 m/s = ? s/m, ..., ?

[Ross Finlayson]

Post by Ross Finlayson

Post by Ross Finlayson

Post by joes

Post by WM

Post by sobriquet
So in a way one could claim that concepts like integers and their
properties and relationships can be more or less empirically observed
in the behavior and properties of things like elementary particles such
as electrons or fields.

Or bricks, marbles, people etc. The natural numbers have been abstracted
from reality. The laws like "the existence of n implies the
existence of
n+1" were so evident, that no axioms appeared necessary before Dedekind,
Peano, Schmidt etc. Only Cantor's assumption of an actual set with |ℕ|
being a fixed quantity greater than all numbers is not abstracted from
reality.

Oh PLEASE show me something physically infinite.

0 m/s = ? s/m, ..., ?

http://youtu.be/EyWpZQny5cY

So, "zero meters per second is infinity seconds per meter".

There's also that in any change of motion, there are
infinitely-many higher orders of acceleration,
nominally both non-zero and vanishing.

Then, there's that if there were finitely-many particles,
then relations among those are also physical objects,
as are those as are those ad infinitum.

Of course most usual field theories have
that there's a continuous manifold, and
there's no real shortest distance or
there are either no straight lines or
no right angles, which would be absurd.

So, the infinite abounds in physics.


Of course, the regular singular points of
the hypergeometric are well-known as
zero, one, and infinity, and this quite
before ordinary Russell's retro-thesis.


Anyways, infinity abounds in physics.

[Stefan Ram]

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm of
idealized forms.

A ton of math stuff is just us taking real-world connections and
boiling them down to their essence. So it's no shocker that we can
turn around and spot these stripped-down ideas out in the wild again.

[Mild Shock]

sci.physics has probably never heard of emergence.
You can easily have the following case:

- As a substrate a System A, with Laws X
- On top of it a System B, with Laws Y

Just look at Game of Life by Convay. Its all
patterns and in the linguistics of the observer,

that we interpret blinking cells as a glider.
But Convay was not the first, von Neuman pionieered:

John von Neumann's universal constructor is a self-
replicating machine in a cellular automaton (CA)
environment. It was designed in the 1940s, without
the use of a computer.
https://en.wikipedia.org/wiki/Von_Neumann_universal_constructor

Mostlikely Physics fails for such emergent behaviours,
it even cannot deploy its tools of order reduction,
where micro levels are modelled by macro levels,

so how did Physics get dismissed from its Garden of Eden?

Post by Stefan Ram

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm of
idealized forms.

A ton of math stuff is just us taking real-world connections and
boiling them down to their essence. So it's no shocker that we can
turn around and spot these stripped-down ideas out in the wild again.

[Mild Shock]

But there will be not a revival of study of emergence,
or interest in genetic programming, because the field

has been sliently overtaken by a) Deep Learning and
b) Chinese People, just watch what they are doing:

2011 Paper: Bilinear Deep Learning for Image
Classification (Zhong et al.)
stochastic gradient descent (SGD) with momentum

Since randomized algorithms are used so basically
forms of genetic programming that mimic evolution.

The 2011 paper marks the beginning of deep learning,
it received further refinements in the 2014.

Post by Mild Shock
sci.physics has probably never heard of emergence.
- As a substrate a System A, with Laws X
- On top of it a System B, with Laws Y
Just look at Game of Life by Convay. Its all
patterns and in the linguistics of the observer,
that we interpret blinking cells as a glider.
John von Neumann's universal constructor is a self-
replicating machine in a cellular automaton (CA)
environment. It was designed in the 1940s, without
the use of a computer.
https://en.wikipedia.org/wiki/Von_Neumann_universal_constructor
Mostlikely Physics fails for such emergent behaviours,
it even cannot deploy its tools of order reduction,
where micro levels are modelled by macro levels,
so how did Physics get dismissed from its Garden of Eden?

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm of
idealized forms.

   A ton of math stuff is just us taking real-world connections and
   boiling them down to their essence. So it's no shocker that we can
   turn around and spot these stripped-down ideas out in the wild again.

[Mild Shock]

Sabine Hossfelder is probably the king in lamenting
the loss of Garden of Eden in physics. In one video

she discusses emergence a little bit:

This New Idea Could Explain Complexity

But she doesn't have a single video about genetic
programming (GP). Which refers to:

HOLLAND J. H. 1975. Adaption in Natural and
Artificial Systems. University of Michigan
Press, Ann Arbor.

On the other hand she refers to:

The term "lumpability" was first introduced by John
G. Kemeny and J. Laurie Snell in their 1976
book "Finite Markov Chains."

Which could be indeed helpful in the context
of Deep Learning.

Post by Mild Shock
But there will be not a revival of study of emergence,
or interest in genetic programming, because the field
has been sliently overtaken by a) Deep Learning and
2011 Paper: Bilinear Deep Learning for Image
Classification (Zhong et al.)
stochastic gradient descent (SGD) with momentum
Since randomized algorithms are used so basically
forms of genetic programming that mimic evolution.
The 2011 paper marks the beginning of deep learning,
it received further refinements in the 2014.

Post by Mild Shock
sci.physics has probably never heard of emergence.
- As a substrate a System A, with Laws X
- On top of it a System B, with Laws Y
Just look at Game of Life by Convay. Its all
patterns and in the linguistics of the observer,
that we interpret blinking cells as a glider.
John von Neumann's universal constructor is a self-
replicating machine in a cellular automaton (CA)
environment. It was designed in the 1940s, without
the use of a computer.
https://en.wikipedia.org/wiki/Von_Neumann_universal_constructor
Mostlikely Physics fails for such emergent behaviours,
it even cannot deploy its tools of order reduction,
where micro levels are modelled by macro levels,
so how did Physics get dismissed from its Garden of Eden?

Post by sobriquet
We often hear claims that math has nothing to do with reality and is
just something that exists in our imagination or some platonic realm of
idealized forms.

   A ton of math stuff is just us taking real-world connections and
   boiling them down to their essence. So it's no shocker that we can
   turn around and spot these stripped-down ideas out in the wild again.