Mathematics ?

[vlaiv]

38 minutes ago, Kishen20 said:

I didn't get about half of this thread (blame me, not this thread) and therefore skipped (so I may missed something important), but isn't Mathematics used to explain the Universe, technically?
We humans need metres for distance, degree Celsius/Kelvin for temperature, seconds, minutes and hours for time (and angles) etc etc, so why not Maths is used to explain the Universe?
Some other intelligent being out there in space may use another method to explain what's going on around it, and it may be correct too, at least in their way.

Not all mathematical concepts are related to physical universe in a way that units are. Some of them are quite strange, and discovered before there were real use for them in explaining the universe. For example - imaginary unit and complex numbers, all kind of infinities, even some concepts that we thought relate to physical world turned out to have no real meaning at the deepest level - some definite values (precise position, precise time) for example.

What this thread is about is the following idea: No matter what "language" and "units" you invent to describe things, a perfect circle, no matter its size, will always have same ratio of its diameter to its circumference. Now, one could argue that we humans made up the concepts of circle and circumference and it has nothing to do with universe, or that that ratio is consequence of properties of universe that we are discovering. Or even at higher level, the idea that I presented in previous post, universe has these properties because of mathematics and we are just discovering the rules.

[Kishen20]

On 26/01/2016 at 23:14, vlaiv said:

Not all mathematical concepts are related to physical universe in a way that units are. Some of them are quite strange, and discovered before there were real use for them in explaining the universe. For example - imaginary unit and complex numbers, all kind of infinities, even some concepts that we thought relate to physical world turned out to have no real meaning at the deepest level - some definite values (precise position, precise time) for example.

What this thread is about is the following idea: No matter what "language" and "units" you invent to describe things, a perfect circle, no matter its size, will always have same ratio of its diameter to its circumference. Now, one could argue that we humans made up the concepts of circle and circumference and it has nothing to do with universe, or that that ratio is consequence of properties of universe that we are discovering. Or even at higher level, the idea that I presented in previous post, universe has these properties because of mathematics and we are just discovering the rules.

Well I got carried away with the space-maths theme of this topic and this very forum...
Of course I didn't actually mean that Maths is used only to explain the universe lol...
Sorry.

[ollypenrice]

On 26/1/2016 at 16:14, vlaiv said:

Or even at higher level, the idea that I presented in previous post, universe has these properties because of mathematics and we are just discovering the rules.

I see this as a step too far. In order for us to exist at all as observers and for the universe to exist in an observable form it has to be systematic. (If the laws of physics changed rapidly and randomly, if the strong nuclear force increased in range or vanished altogether several times per second, if gravity suddenly increased by a foactor of 10,000, etc etc, then neither we nor the present universe would exist at all. It can exist and we can observe it because it is highly systematic (even if only at a probablistic level as in quantum theory.)

And mathematics is systematic as well. It therefore follows that mathematics should be, and is, good at describing the universe. That is, good at desciribing the systems which underpin the universe. But is there no other way of describing these systems? Are these systems mathematics? Or are they just describable by mathematics? A six inch diameter ball will not pass through a five inch diameter hole. Is that because mathematics won't allow it or because the hole won't allow it?

Olly

[vlaiv]

Well, yes, I understand such point of view, and question is if my idea is arguable at all.

Sometimes I just like to think about abstractions, and that can lead to some interesting insights.

For example, let's consider following: There are some entities, and some relations. One can assert that entity can be in relation to itself (reflexive relation). One entity can be in relation to another but not vice versa (anti symmetry). And if we look at three or more entities we can imagine following: first entity is in relation to second and second is in relation to third - implies that first is in relation to third (such is relation - and let us call this transitivity). From these three rules (only entities and relations) we can conclude that there is something that we can call relation of order. Which in turn implies different sizes (you can always put sizes in order) which leads to smaller ball will fit larger hole, but larger ball will not. So there you go, if you take entities and relationships you assert that there might be something (there is grounds for its existence) that will behave in such a way as balls and holes. Granted balls and holes probably have much more mathematical concepts needed to be combined to facilitate their existence and behavior as we perceive it.

 

[Tiki]

On ‎1‎/‎19‎/‎2016 at 21:27, topdude said:

But how the hell do you " do the maths " first then make the observations to prove or disprove the calculations ?

Firstly guess, secondly you scrutinize. If the initial guess stands up to sufficient scrutiny then it becomes science. Eg. General relativity.

 

https://www.youtube.com/watch?v=5v8habYTfHU  (60 seconds of Feynman)

[ollypenrice]

My idle musings on the systematic nature of the universe, and the fact that it couldn't be what we call a universe without stable physical laws, made me wonder if that was what happened in the beginning. For some reason the fundamental forces stabilized and, when they did so, begain to play out the interactions which led to what we now see.

I can't be the first person to have considered this!

Olly

[vlaiv]

We are now entering seriously brain-twisting territory

I often hear scientists contemplate "underlying mechanism" for this or that. Olly's post reminded me of that. In the early beginning everything was chaotic and then it stabilized over some period of time. Things began to function "normally". But people seek "the mechanism" by which that occurred. We as humans are always seeking scheme/pattern/underlying mechanism by which something happened. Question now becomes: can something exist/happen without underlying pattern/template/mechanism, call it whatever you like (and use language of mathematics to try to describe it ). Is our brain able to comprehend and accept the following: something happened with no reason, no cause, no causality, no underlying mechanism, but just did happen - like that. No answer to how and why (and not because there is no way to find out, but in general because there is no how and why).

Going back to early universe, although we think of it as chaotic, I believe that it was highly structured in how and why. Therefore systematicity of universe does not lie in present day stability of fundamental physics, but rather that there is underlying pattern that defines existence (there is always answer to how or why, albeit not always knowable).