The Universe Is Made of Mathematics

> For something to be physical it must be present at some time and place within the universe, and for something to be abstract it must exist outside of space and time.

No. He is redefining words here. 'Physical' is not usually defined as "exists in space and time". Abstract thoughts or concepts do not exist outside of space and time. Abstract thoughts are the results of the modeling capabilities of brains and exist very much in the physical world. It isn't even known whether "existing outside of space and time" is a coherent concept.

> but if the universe is a mathematical object, it needs no creator (on Platonism at least),

Firstly, this is the Kalam argument all over again. It isn't clear at all that the Universe needs a beginning or whether the 'beginning of the Universe' is a coherent concept at all.

Secondly, even assuming mathematical platonism is true, and even if 'creation' was a prerequisite for the universe, mathematical platonism has no construct to go from 'describing a universe' to 'creating a universe'. That seems to be quite an important thing to miss.

> Our universe is fine-tuned because it is one which has the ability to support conscious thought selected from an infinite multitude of mathematical structures, most of which are lifeless.

This is very problematic. Once you start thinking about "different mathematics", you lose all foundations upon which you can reason. Logic does not work anymore. Even if it were true at all, no human could possibly have meaningful thoughts about it. Besides, if we abandon the concept of our 'mathematical structures' in other universes, what do the words true and false itself even mean?

There's lots of handwaving with (very) incoherent concepts and dubious logic in this post to make the argument for a mathematical universe.

The author stresses that all of reality is mathematical in structure, but this is at odds with the fact that all mathematical systems containing self-reference are necessarily incomplete. Physics is a self-referential system.

If the structure of the universe is mathematical, it is probably a very different math than humans are used to. Insert your favorite flavor of metaphysics here!

1. Our nervous system has quite narrow and well defined capability of receiving signals from the outside world. Every of our senses has own limitations. We can't see UV or IR etc.

2. Our body has a specific way of interacting with the world : we have specific size, strength, have to operate as one, undivided entity etc.

3. With such input coming from the above points, our brain creates a specific model of the outside world to function in it, interact, count apples and lions etc.

4. Part of this model is this cool toolset containing math and logic. It's very useful for us to predict and analyze the world and it's so flexible that we can expand and bend it according to our will in face of mismatch between observable reality and math.

So there is no surprise that we keep seeing math around us. We created it as a result of interaction with the world.

But to insist that math is the real way the world works is ridiculous. It's like saying that there's nothing beyond the visible spectrum of light because we can't see it.

I'm quite sure that any creatures with significantly different bodies than ours would come up with different "math" and different view of the universe.

EDIT: I was trying to imagine such creatures but gaps in my knowledge and limitations of my homo sapiens mind are hard to escape and imagine something unimaginable. But I'll give it a try: Think of a creature built of 100 autonomously moving clouds of particles, sharing one consciousness. The clouds can change their sizes in the ping-pong - planet range and communicate by radio waves. I think that just the ability to watch specific event from 100 perspectives would give this alien completely different psychology and approach to the logic, truth etc.

On the "describing reality" to "creating reality". Very few people argue for ex-nihilo creation but far more people tend to project that on the opposing side (ie where did god come from? what was before the big bang?). I don't think the author is arguing that mathematics allows for creating reality from nothing but that anything that resembles reality behaves mathematically and thus can transform into new situations with new mechanics (or realities).

Second nitpick: different mathematics. You don't loose the foundations of reason, rather you are stating that with different assumptions a system behaves differently. You are still computing the logical outcome with the premises given. If you have a universe where true and false mean the same then you have a very small universe that doesn't support any differentiation. Take comfort in knowing this helps solve Gödel’s incompleteness theorem. We can construct an infinite number of consistent mathematical realities but only by comparing their predictions to our reality can we resolve which reality is our own.