sobriquet wrote :
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:
https://www.youtube.com/watch?v=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.
https://www.youtube.com/watch?v=-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
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.
On 28.01.2025 21:56, sobriquet wrote:Oh PLEASE show me something physically infinite.
Or bricks, marbles, people etc. The natural numbers have been abstracted
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.
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.
Am Wed, 29 Jan 2025 09:48:47 +0100 schrieb WM:
On 28.01.2025 21:56, sobriquet wrote:Oh PLEASE show me something physically infinite.
Or bricks, marbles, people etc. The natural numbers have been abstracted
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.
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.
Am Wed, 29 Jan 2025 09:48:47 +0100 schrieb WM:
On 28.01.2025 21:56, sobriquet wrote:
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.
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.
How about space?
sobriquet <dohduhdah@yahoo.com> wrote or quoted:
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.
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.
Mild Shock schrieb:
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?
Stefan Ram schrieb:
sobriquet <dohduhdah@yahoo.com> wrote or quoted:
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. >>>
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?
Stefan Ram schrieb:
sobriquet <dohduhdah@yahoo.com> wrote or quoted:
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. >>
sobriquet <dohduhdah@yahoo.com> wrote or quoted:
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.
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