Mathematics as a way of knowing?

**Follow-up to:**

*Knowing beyond science and mathematics?*

I think I have to clarify why I mentioned mathematics in my recent post —

*Knowing beyond science and mathematics?*— as a

*way of knowing*in addition to science and separated from other logical systems.

First of all, I'm only at the beginning of my long journey towards a decent education, as I've only started as recently as a year ago to seriously get into mathematics and other important fields. I'm still struggling with the basics.

My posts here at SpaceCollective.org are merely mental outpourings,

*so well-thought-out musings and problems that haunt my mind. What I write does not necessarily reflect my opinion.*

**NOT**So let me explain...

There seem to be quite a few arguments in favor of the Mathematical universe hypothesis and that math is timeless and being discovered, not invented.

…there’s still sometimes a tendency to think as though turning on a sufficiently advanced calculator causes something to mysteriously blink into existence or awareness, when all it is doing is reporting facts about some very large numbers that would be true one way or the other.

— The mathematical universe: the map that is the territory

I recently started to read

*The Big Questions*, a book by Steven Landsburg. The basic tenet seems to be that

*mind is biology, biology is chemistry, chemistry is physics, physics being math. Mind perceives math, thus the universe exists physically. Erase the “baggage” and all that’s left is math.*

If we can feel real inside a non-magical computer simulation, then our feeling of reality must be due to necessary properties of the information being computed, because such properties do not exist in the abstract process of computing, and those properties will not cease to be true about the underlying information if the simulation is stopped or is never created in the first place. This is identically true about every other possible reality.

— The mathematical universe: the map that is the territory

There has been a really nice plain English description of this idea being posted on lesswrong.com recently. Though everybody who has read Greg Egan’s Permutation City might already be unknowingly familiar with it.

Existence is what mathematical possibility feels like from the inside. Turn off G.O.D., and we’ll go on with our lives, not noticing that anything has changed. Because the only thing that has changed is that the people who were running the simulation won’t get to find out what happens next.

— The mathematical universe: the map that is the territory

Mathematics is the basis of all of science and even seems to play a large role in our thinking, as it may be probabilistic. When it comes to quantum mechanics it all seems to be about probability as well, and therefore math. But in what sense do mathematical structures exist? Well, as Steven Landsburg puts it, mathematics is a kind of extrasensory perception. It's all

*out*there, 1+1=2 has always been there and true, even before anybody ever thought about it. And yet you won't find perfect circles anywhere

*"out" there*. Does that mean math has no influence, that it is not tangible, that math doesn't exist? It is subject to inquiry. I think you can make predictions that are falsifiable. It even bears fruit by providing accurate descriptions of the physical world that can be tested. So yes, I believe mathematics, as science, is a way of knowing.

There is something almost mystical about this: any sequence of digits, for example, randomly conceived in the mind, must correspond to a sequence of digits in the unknowable expansion of Pi (in that realm over 10^1000 digits into the expansion), based on the laws of probability.

— Garth Kroeker, Irrational Numbers Metaphor

What about other logical structures? They are ultimately part of mathematics, as they are describable by pure math, and in the case of a Mathematical universe are timeless structures. But the difference between World of Warcraft or a programming language like Haskell is that these systems are not subject to induction, as you cannot arrive at general, much less specific conclusions and facts about reality by a sole examination of these structures. They do not imply everything that exists. Whereas mathematics can be used to deduce even the most abstract fact about our world, about reality. Mathematics does specify everything that is possible and thus includes everything that exists.

Anyway, I'll likely need a long time to see if this makes sense, if the idea of a mathematical universe might be likely, or even worthy of consideration. Thus I just put it out there into that post, for that otherwise I couldn't have posted it for a long time. And I believe it might be a good idea to first make your own thoughts, come up with your own ideas and conclusions about a subject, before you go listen and learn what other people have to say about it. What I think may or may not turn out to be

*completely*wrong, but this way I might be able to learn how to think, how to be less wrong the next time I encounter something new that I'll have to reason about myself.