Is Math Real, or is Math Reality

I came across this YouTube video by Sabine Hossenfelder {who was born in Frankfurt at the same time I was living there - ah the connections we can make :-)} I’ve learned to respect her opinion, I’ve looked into her bona fides and they stand up, and I do like the touch of Germanic hard-ass about her.
The video is a year old, but arrived on my laptop right on time, and not a day too soon. It makes wonderful bookend to my own past week’s intellectual adventures.
Listening to this video felt like coming home - she does a superb job of explaining things I can only flail at. Not to mention she knows lights years more than I do.

Are we made of math?
Sabine Hossenfelder

Jul 31, 2021

What is space-time? What is a particle? I get these questions a lot. My best answer is “math”. But does this mean that mathematics is real? Are we maybe even made of math? Or could it even be, as Max Tegmark has argued in his “mathematical universe Hypothesis”, that all of math is real? In this video I go through what we know and what we don’t know.


“Math is real because it correctly describes our observation”

What is space-time, what is an object? …

I don’t know what to do with questions like that.

Space-time is a mathematical structure that we use in our theories,

This structure is defined by its properties. … it’s a math thing.

We call it real, because it describes reality.

{S.H.:Correction to what I say at 4 mins 7 seconds: That should have been “irreducible representations of the Poincare group”.}

0:00 Intro
0:25 Which math is real?
2:52 Are particles and space-time real?
4:19 Is there more to reality than math?
5:20 Is all math real?

But should you believe Tegmark? Well, as we have seen earlier, the justification we have for calling some mathematical structures real is that they describe what we observe.
This means we have no rationale for talking about the reality of mathematics that does not describe what we observe, therefore the mathematical universe hypothesis isn’t scientific.
This is generally the case for all types of the multiverse. The physicists who believe in this argue that unobservable universes are real because they are in their math. But just because you have math for something doesn’t mean it’s real.

You can just assume it’s real, but this is unnecessary to describe what we observe and therefore unscientific.

Let me be clear that this doesn’t mean it’s wrong. It isn’t wrong to say the exponential function exists, or there are infinitely many other universes that we can’t see. It’s just that this is a belief-based statement, not supported by evidence. What’s wrong is to claim that science says so. …

I really like Sabine Hossenfelder. She is a top-notch teacher.
And she is correct that it isn’t science that says so, it’s nature that says so.

This is the way I interpret Tegmark.
Science says that certain specific “patterns” self-organize from chaos (Chaos theory) and those patterns can be studied for their properties.
Examples can be found in crystals.

It clearly shows that these patters contain mathematical relational values and that suggests that these pattern during their self-assembly followed a mathematical “guiding equation”. Their self-assembly just follow certain generic mathematical functions.

Mathematics is not a thing, it is a language. It is the way certain relational values must interact, just like certain words create sentences with specific meanings.

Functions (or words) cannot be called physical in and of themselves, but logically guide the way their meaning becomes expressed in physical reality.

“For every action there is an equal and opposite reaction” is a mathematical equation that guides the relationship and function between physical forces.

In some research about quantum I ran across a claim that quantum only uses certain discreet values and immediately I thought about fractals and CDT (Causal Dynamical Triangulation) as somehow being connected with quantum function .

Then I ran across this amazing video of quantum fractals that I had never even imagined. Yet here is the proof and this relationship is even applicable to brain function at a certain level.