[ExI] favor for a friend

[Giovanni Santostasi]

Another angle that is not explored much (but it is a fundamental piece of
the puzzle) is where the human (or even other species) brains and nervous
systems fit in this story (relationship between mathematical truth and
physical reality).

*Where Mathematics Comes From*
https://www.amazon.com/Where-Mathematics-Come-Embodied-Brings/dp/0465037712

Origins of the brain networks for advanced mathematics in expert
mathematicianshttps://www.pnas.org/content/113/18/4909



On Wed, Mar 24, 2021 at 9:37 PM Giovanni Santostasi <gsantostasi at gmail.com>
wrote:

> 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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