Math the language of the universe?

[SaganWannaBeWannaBe]

I didn't see an actual Philosophy of Science forum so I'm posting this here in hopes of getting some responses from more "hardcore" science folks.

 

Back in my physics days in college I read all sorts of complex math with terms like Riemann manifolds, gauge invariance, tensors, etc. I was never anywhere near smart enough to understand these. Regardless, I had this notion that if only I *was* smart enough, I'd be able to talk the language of the universe. Most of my hero's are scientists, and I've always revered them partially because they did speak this wonderful language.

 

Then years later, well after leaving college and going on to other things, I was reading about economics. The math was again way over my head BUT it was using the same or similar mathematical things, like tensors, matrixes, etc. I remember it being quite an emotional shock. How could it be that the "creator's language" (and I use that word figuratively) can also be used for such mundane and pedestrian things as cash flow, net cash value, GDP etc.

 

Put another way, I used to think the math of physics corresponded in all actuality to the physical aspects of the world. But now it seems like it doesn't, and is only a highly thought out, but ultimately arbitrary (however useful) human-made framework.

 

 

[ADreamIveDreamt]

I love Math! It's fun when you break down numbers to a single number, the patterns are amazing.

[TrappedLight]

I think math as a tool and a type of language, it is a means of communication by describing physical events under certain procedures and laws. I don't think that the universe is inherently mathematical, like Tegmark, but I do think the universe appreciates symmetry and is bound by it's own laws.

[Delta1212]

Keep in mind, humans are a part of the universe. If the universe runs on a mathematical framework, then anything we do as a part of it will also be describable mathematically, including our economics.

 

The universe isn't a magical place containing the heavens and all the fundamental specs that compose us. The universe is everything, even the mundane stuff of every day life. A language of the universe that couldn't be applied to the mundane wouldn't be a language of the universe.

[studiot]

 

Keep in mind, humans are a part of the universe. If the universe runs on a mathematical framework, then anything we do as a part of it will also be describable mathematically, including our economics.

 

The universe isn't a magical place containing the heavens and all the fundamental specs that compose us. The universe is everything, even the mundane stuff of every day life. A language of the universe that couldn't be applied to the mundane wouldn't be a language of the universe.

 

Good point +1

[Cap'n Refsmmat]

You might be interested in the famous paper "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".

 

I view mathematics as a rigorous but versatile language for expressing rules and relationships between things. When we encounter phenomena that cannot be expressed using mathematics, we invent new rules and new concepts to describe them. (Consider, for example, Newton and Leibniz inventing calculus and using it to express the laws of physics.)

 

If the universe runs on rules, it's no surprise that we can describe it using a system like mathematics, just like anything else that runs on rules (at least approximately).

[Sensei]

Then years later, well after leaving college and going on to other things, I was reading about economics. The math was again way over my head BUT it was using the same or similar mathematical things, like tensors, matrixes, etc. I remember it being quite an emotional shock. How could it be that the "creator's language" (and I use that word figuratively) can also be used for such mundane and pedestrian things as cash flow, net cash value, GDP etc.

 

 

Good that you didn't see any modern computer game source code..

They do more vector/matrix/multiplications/transformations in one second than the all physists did in the whole history of science..

 

If you have 1 million triangles @ 60 fps, object to world transformation will be 180 million multiplications of 3d vector by matrix 4x4. There is needed to multiply it by 2, because each vertex must be projected from 3d world coordinate space to 2d screen coordinate space. And you end up with 360 million vector * matrix calcs per second. These calcs are proportional to quantity of triangles (complexity of geometry).

And that's before any texturing and lighting. For 1920x1080 Full HD resolution it's 2 Mega pixels @ 60 fps = 124 million pixels to process, with 4x anti-aliasing it's 0.5 billions/s.

OpenGL supports up to 8 lights (it can be extended by using pixel-shaders manually), so it's 8 dot products between vector and vector. That gives ~4 billion dot products per second.

 

Math is just a way to simulate thing that we want to simulate, whatever it is.

 

[SaganWannaBeWannaBe]

All great points. I think my thing was, way back I had the notion that math was similar to Plato's forms. Forms are the true and actually existing things "out there" from which all that we see in our little cave of reality is derived. In that sense, a tensor (in my mind) was an actual thing that could only be used to describe spacetime, or whatever. It definitely was NOT something to be used to describe an economy or something so man-made. It doesn't help that the names of things in math are so "physically oriented". Tensor, Spinor, Gauge, Manifold. These sound like in some sense real things (tension like a spring, spin like a spinning top, measuring tool , surface) versus mere analogies or conventions.

[studiot]

Surely there are lots of terms in mathematics, some more cuddly than others.

 

Borromean rings and heexagrams for the occultists

 

Trees and branches for the huggers

 

Pie charts for the.....

 

Cardiod for the medics

 

Napoleon's Theorem (yes the 1812 man) for the military