Surely math is not just about numbers, it's about concepts and abstraction.

https://www.quantamagazine.org/

The science of patterns. Numerical patterns or quantitative aspects
are an important part of that, but so are other aspects, like qualitative
aspects (like the difference between a rotation and a reflection, that
has little to do with numbers but is clearly related to the concept
of symmetry).

On Friday, January 7, 2022 at 3:41:09 AM UTC+1, sobriquet wrote:
> Surely math is not just about numbers, it's about concepts and abstraction.
>
> https://www.quantamagazine.org/
That link should actually be this one instead:
https://www.quantamagazine.org/the-map-of-mathematics-20200213/

>
> The science of patterns. Numerical patterns or quantitative aspects
> are an important part of that, but so are other aspects, like qualitative
> aspects (like the difference between a rotation and a reflection, that
> has little to do with numbers but is clearly related to the concept
> of symmetry).

On Thursday, January 6, 2022 at 6:43:44 PM UTC-8, sobriquet wrote:
> On Friday, January 7, 2022 at 3:41:09 AM UTC+1, sobriquet wrote:
> > Surely math is not just about numbers, it's about concepts and abstraction.
> >
> > https://www.quantamagazine.org/
> That link should actually be this one instead:
> https://www.quantamagazine.org/the-map-of-mathematics-20200213/
> >
> > The science of patterns. Numerical patterns or quantitative aspects
> > are an important part of that, but so are other aspects, like qualitative
> > aspects (like the difference between a rotation and a reflection, that
> > has little to do with numbers but is clearly related to the concept
> > of symmetry).

One way to look at mathematics is a diamond. It is an infinite tree
into the diamond, also from the other side, a diamond. Then, there
is even that the platonist's numbers, really do exist, calling them metal
and concrete numbers, is really about what mathematics is substance.

(Inverting the tree, completing the diamond, type inversion.)

Here these metal and concrete numbers speak to any notion that
the numbers are real and concrete in units and metal in quantities,
these are the hardest numbers.

You mention substance and of course the substance of the matter,
means that after the translation or state of being, nature of being -
the substance here after perception there are empiricist's that agree,
scientists of sorts, quantitative perception, mathematical platonists,
then strong mathematical platonists - that some strong mathematical
platonists have as metal and concrete numbers, a diamond.

Then, it is the diamond that is perspective, it's the hologram and
it's to be sure - The Fourth Dimension this way is out side of time,
perspective - while yet of course time as fourth dimension is meter.

The hypercomplex, though, rest assured, all possible theory lives
in it - if only in "theory" - mostly for mathematical platonism then
actually strong mathematical platonism, a concrete realism of a sort,
then in that there are theories that it organizes itself of course "naturally".

Fundamental complement of sorts seems the same theory as symmetry.
In a sense they are, that the "fundamental theory" would have to so
reflect in itself its own terms, why the _same_ theorems, altogether and
overall, result from whatever path or principle was chosen as elementary,
like sets in set theory, as about the complement in symmetry, here for
example theories where parts instead of sets are elementary, though that
the theories have the same theorems about all the objects what result,
overall, and altogether.

Then these null and universal theories usually with "let all standard
theory result in the theories which are the same in result if not outset",
is for assorting why the nonstandards in universals are so, and if usually
fundamentally, a usual mode of a sort.

I.e. this "complement in null and universal theories as universal theories",
is really not so complicated when in concerns it results as "and that's it".

So, that perspective is free, that the diamond is hard for that the concrete
is strong, then concrete breaks while the metal bends.

This way as an analogy in materials, it's as direct as elementary -
an abstract formalism for the strength of mathematics.

On Friday, January 7, 2022 at 6:45:14 AM UTC+1, Ross A. Finlayson wrote:
> On Thursday, January 6, 2022 at 6:43:44 PM UTC-8, sobriquet wrote:
> > On Friday, January 7, 2022 at 3:41:09 AM UTC+1, sobriquet wrote:
> > > Surely math is not just about numbers, it's about concepts and abstraction.
> > >
> > > https://www.quantamagazine.org/
> > That link should actually be this one instead:
> > https://www.quantamagazine.org/the-map-of-mathematics-20200213/
> > >
> > > The science of patterns. Numerical patterns or quantitative aspects
> > > are an important part of that, but so are other aspects, like qualitative
> > > aspects (like the difference between a rotation and a reflection, that
> > > has little to do with numbers but is clearly related to the concept
> > > of symmetry).
> One way to look at mathematics is a diamond. It is an infinite tree
> into the diamond, also from the other side, a diamond. Then, there
> is even that the platonist's numbers, really do exist, calling them metal
> and concrete numbers, is really about what mathematics is substance.
>
> (Inverting the tree, completing the diamond, type inversion.)
>
>
> Here these metal and concrete numbers speak to any notion that
> the numbers are real and concrete in units and metal in quantities,
> these are the hardest numbers.
>
> You mention substance and of course the substance of the matter,
> means that after the translation or state of being, nature of being -
> the substance here after perception there are empiricist's that agree,
> scientists of sorts, quantitative perception, mathematical platonists,
> then strong mathematical platonists - that some strong mathematical
> platonists have as metal and concrete numbers, a diamond.
>
> Then, it is the diamond that is perspective, it's the hologram and
> it's to be sure - The Fourth Dimension this way is out side of time,
> perspective - while yet of course time as fourth dimension is meter.
>
> The hypercomplex, though, rest assured, all possible theory lives
> in it - if only in "theory" - mostly for mathematical platonism then
> actually strong mathematical platonism, a concrete realism of a sort,
> then in that there are theories that it organizes itself of course "naturally".
>
> Fundamental complement of sorts seems the same theory as symmetry.
> In a sense they are, that the "fundamental theory" would have to so
> reflect in itself its own terms, why the _same_ theorems, altogether and
> overall, result from whatever path or principle was chosen as elementary,
> like sets in set theory, as about the complement in symmetry, here for
> example theories where parts instead of sets are elementary, though that
> the theories have the same theorems about all the objects what result,
> overall, and altogether.
>
> Then these null and universal theories usually with "let all standard
> theory result in the theories which are the same in result if not outset",
> is for assorting why the nonstandards in universals are so, and if usually
> fundamentally, a usual mode of a sort.
>
> I.e. this "complement in null and universal theories as universal theories",
> is really not so complicated when in concerns it results as "and that's it".
>
> So, that perspective is free, that the diamond is hard for that the concrete
> is strong, then concrete breaks while the metal bends.
>
> This way as an analogy in materials, it's as direct as elementary -
> an abstract formalism for the strength of mathematics.

I like the interplay between math and physics, where developments in math
give rise to new physics and vice versa.
https://www.youtube.com/watch?v=Dz6nqXItDQE

At the most basic level the difference between the conceptual realm and
the physical realm seems to be that the physical realm is discrete while the
conceptual realm is continuous.
You can take a piece of gold and divide it into smaller pieces of gold and you
can keep doing that until you end up with individual gold atoms. At that point
you can further subdivide those, but the smaller parts will no longer be gold.
With a rational number like 1/2, you can subdivide it into smaller rational numbers
like 1/4 and you can keep doing that and you will never end up with the atoms
of rational numbers.
Now most scientists will argue that monism is the ultimate outlook of the
hardcore materialist or the hardcore idealist, but it's curious that even in the
physical realm, as you break things down to their fundamental components,
things seems to end up into neatly divided categories of bosons and fermions
that are collectively exhaustive and mutually exclusive (very reminiscent of
a categorical perspective where the fermions are the objects and the
bosons are the arrows). Though perhaps we can have things that behave
as superpositions of these two possibilities under certain circumstances.