[ExI] favor for a friend

Thu Mar 25 05:07:31 UTC 2021

I actually like this book at lot:

https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From

It is an undervalued book and I think they are into something big.
Their main idea is mathematics is not the language of nature but the
language humans develop to understand nature.
It is an approximation of what really is going on in nature because like
all languages is just made of abstractions and metaphors.
It works but like all metaphors, it breaks at a point.
It is a powerful language because it does allow us to explain each other
operations and procedures that allow us to be effective in the natural
world (i.e. shoot very precisely, for all practical purposes, with a cannon
an enemy base for example) but real world knows nothing of mathematics. If
one day we will discover how the physical world really does its things (for
example a ball falling in a gravitational field) we will find out that is
not really mathematics but something else that mathematics only
approximates as a metaphor.
My gut feeling says there is Truth in this idea.

On Wed, Mar 24, 2021 at 9:57 PM Giovanni Santostasi <gsantostasi at gmail.com>
wrote:

> 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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