[ExI] Gemini on Mathematical Realism

[Jason Resch]

On Thu, Oct 8, 2026 at 2:54 PM Ben Zaiboc via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On 08/10/2026 16:19, John K Clark wrote:
> > Mathematics is the language of physics but like any language it is
> capable of writing both fiction and non-fiction, I have often wondered if
> some of the more esoteric areas of higher mathematics might be the
> mathematical equivalent of a Harry Potter novel.
>
>
> A very good point. Any language worthy of the name must be capable of
> making untrue statements, not to mention total gibberish, as well as true
> and useful statements.
>

You can make an untrue statement, like "1 + 1 = 5" but then a useful and
consistent mathematical theory would enable you to identify that as an
untrue statement.
It's no different from someone saying "on earth, g = 2.3 m/s^2", but then
applying our physical theories (concerning gravity and acceleration)
reveals that statement is untrue.


>
> Ha, that gives me hope! I always thought it was my fault that maths often
> seems to make no sense (only half joking. I've still never seen any
> sensible reason for 1 not being a prime number).
>

I sympathize with this, and there are many reasons 1 could be considered a
prime number, but for definitional reasons mathematicians settled on the
convention that it was not (mainly so that every integer has a unique prime
decomposition in the fundamental theorem of arithmetic
<https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic> ). It
would not surprise me if alien civilizations went the other way and chose
to instead consider 1 prime. I think most alien civilizations treat 2*Pi
(6.28...) as the important constant, rather than our bizarre definition as
the ratio between circumference and diameter (circumference to radius is
what makes the most sense, and many physical and mathematical
equations are much
cleaner <https://www.tauday.com/tau_manifesto.pdf>).


>
> Personally, I don't think it's even necessary to get into 'esoteric areas
> of higher mathematics' to find oneself in the fiction section.
>

You could write false physical equations all day using the language of
physics, but that doesn't mean the field concerns fictional entities.

Jason
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