[ExI] favor for a friend

[Giovanni Santostasi]

It is actually a deep statement with many layers and ramifications.

To simplify (physicist back of envelope solution of the riddle):

True= self consistent.
Mathematics is like a game you establish rules in the beginning (axioms)
and true is any self-consistent statement derived from these axioms.

Exist =Real = regarding the physical world in which we live.

Let's take a simple mathematical concept that is actually not that
abstract, as some of the examples given in other responses to this email.
The ratio between the circumference of a circle and its diameter, or the
constant called Pi.

Pi is true, in the sense that is a well-defined, self-consistent concept
that can be derived from a precise algorithm. We can make statements about
pi that are true in this particular sense for example the the second
decimal place of Pi is 4.
It is a true statement.
But does Pi exist in the real world?
No.
Pi implies by the nature of its definition that it a number that cannot be
written as a fraction of integers, or in other words has an infinite number
of decimals.
If you take any physical circle (or an approximation to a theoretically
perfect circle) and measure the ratio between circumference and diameter
you get an approximation to the pure mathematics Pi.
You can improve the "roundness" of the circle to the point that it is an
atomic level of perfection and precision (something we cannot do
technologically right now but maybe one day) and still you would not get an
infinite number of decimal places. Even if you transcend some of the
technological limitations at a point you will clash with the fact space and
time is quantized and there is a length scale where the meaning of length
itself is meaningless (Plank's scale).

Real numbers are not real at all. They are abstractions and they represent
processes that can in theory continue forever and they don't have an
endpoint ( until the universe dies?).
The mystery is in how effective mathematics is (that is an abstraction of
the real world that implies infinite process and infinite divisible
quantities, vs a real-world that has finite length scale, finite time scale
(Plank's time), and finite times to accomplish processes (heat death of the
universe) in actually being able to describe this quantized and finite
universe.
Why an approximation of pi is good enough (I think NASA uses 5 decimal
places at most) to send probes to Mars with all the precision every needed
for such a mission?
Why the true pi has an infinite number of digits and the "real" and useful
pi needs only 5?
That is the deep question.
Some philosophy schools, for example the Platonists (modern example of this
is R. Penrose), tried to resolve this riddle by putting upside the problem
and claiming (without any evidence) that the world of math is the Real
world and the physical world is like an imperfect representation of that
ideal world (like a 2D shadow of the 3D real, platonic world). I think
this  "solution" is huge bs and it is the equivalent of hiding dust under
the carpet (the floor looks clean but it is not).

I think there is not yet a satisfactory solution to this problem. We don't
really understand it. Math works so we use it.

One could write an entire book on this topic, and many books have been
written. Here are some example.


https://www.amazon.com/Pythagorean-World-Mathematics-Unreasonably-Effective/dp/3319409751

https://personal.lse.ac.uk/ROBERT49/teaching/ph201/Week15_xtra_Wigner.pdf

Wigner called the unreasonable effectiveness of mathematics.

Also related problems are how we can know something is true in mathematics
at all, i.e. Godel's theorem.

https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem

Kurt Gödel--Separating Truth from Proof in Mathematics

https://science.sciencemag.org/content/298/5600/1899

https://www.amazon.com/G-C3-B6dels-Theorem-Incomplete-Guide-Abuse-ebook-dp-B08DSH7WYR/dp/B08DSH7WYR/ref=mt_other?_encoding=UTF8&me=&qid=


P.S.
There is a related but somehow different issue with statistics. You can
make precise definitions of probability, distributions, randomness but what
that really means is not understood in my opinion. It is basically a term
for "we don't know what drives this process, so it is random". But the most
exciting places are where dragons live. These are definitely dragon lands.




On Wed, Mar 24, 2021 at 9:39 AM William Flynn Wallace via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> He wanted to know the meaning of this statement:
>
> Mathematics is true, but it doesn't exist."
>
> bill w
> _______________________________________________
> extropy-chat mailing list
> extropy-chat at lists.extropy.org
> http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
>
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