Math & Science: Can Theories be Proven with Math?

[Universe_Man]

Since Mathematics is tied so closley to nature, and our observation of nature, wouldn't it be reasonable to believe that anything we develop in mathematics to explain a phenomenon or derive a theory be really close to reality? Could theories be proven with mathematics?

 

[matt grime]

Your first sentence is not gramatically correct: it does not make sense.

 

[selfAdjoint]

Since Mathematics is tied so closley to nature, and our observation of nature, wouldn't it be reasonable to believe that anything we develop in mathematics to explain a phenomenon or derive a theory be really close to reality? Could theories be proven with mathematics?

So you would say that if we develop a mathematical model of something - I assume that it agrees with observations - it must be "really close to reality"? Consider Ptolemy's epicycles, deferents, and equants; they were as mathematical as you could want, and agreed with the state of observation at the time (with a few small problems), so were they really close to the reality of planetary motion?

 

[kmarinas86]

[Universe_Man]Your first sentence is not gramatically correct: it does not make sense.

Since Mathematics is tied so closley to

nature
and our observation of nature​

wouldn't it be reasonable to believe that

anything we develop in mathematics to explain

a phenomenon
or derive a theory​

be really close to reality?​

Could theories be proven with mathematics?

Seems ok to me.

selfAdjoint gave a good answer to this question, so I better not give my own.

 

[Universe_Man]

Hey, thanks for replying, I suppose I did not ask a question coherently, I just went with some random thought, my apologies. I will take the time to think about what I want to say from now on.

 

[HallsofIvy]

Mathematical theories are really theories about how we think. In any study (not necesarily one that has to do with nature) humans tend to "classify". Mathematics gives us many different ways to classify and then methods of changing from one classification to another. It isn't that mathematics is somehow "natural"- it's that mathematics is so flexible.

You can find mathematical models for "wrong" theories as easily as for "true" theories!

 

[octelcogopod]

Here's just a random thought..
What if we can classify the universe, logic and math, as existing in different emergent levels.

For instance, the universe exists on the most fundamental emergent level, at the very deepest, there will be only one ultimate answer for every and any problem.
Logic exists as a higher emergent pattern, as we all know, something can be very logical, but very wrong when compared to a problem in the universe(a physical one), and so can math.
So if math and logic exists as higher emergent logic, that we simply aren't seeing deep enough.

Here's a small analogy on the thesis;

It is an ultimate truth and fact that there exists only two types of fundamental particles in the universe.
1. The Kwakk
2. The Kwikk

It is also a fundamental truth that there exists only 2 types of objects made with those particles in the universe.
1. An apple
2. An orange

It is also a fundamental truth and fact that each object can only be made up of one type of fundamental particle, the problem; We don't know which particle makes up which object.

At this point, it is completely logical to assume that the Kwikks makes up the orange, and the Kwakks makes up the apple, but this isn't necessarily true.
The deeper we dig into how the apple is made, or the orange, the closer we get to eliminating different options.

That's as close as I can get to emergent levels.
If anyone has any problems with this thought, I'd be happy to hear it and learn from it..

 

[HallsofIvy]

Here's just a random thought..
What if we can classify the universe, logic and math, as existing in different emergent levels.

For instance, the universe exists on the most fundamental emergent level, at the very deepest, there will be only one ultimate answer for every and any problem.
Logic exists as a higher emergent pattern, as we all know, something can be very logical, but very wrong when compared to a problem in the universe(a physical one), and so can math.
So if math and logic exists as higher emergent logic, that we simply aren't seeing deep enough.

Here's a small analogy on the thesis;

It is an ultimate truth and fact that there exists only two types of fundamental particles in the universe.
1. The Kwakk
2. The Kwikk

It is also a fundamental truth that there exists only 2 types of objects made with those particles in the universe.
1. An apple
2. An orange

It is also a fundamental truth and fact that each object can only be made up of one type of fundamental particle, the problem; We don't know which particle makes up which object.

At this point, it is completely logical to assume that the Kwikks makes up the orange, and the Kwakks makes up the apple, but this isn't necessarily true.
The deeper we dig into how the apple is made, or the orange, the closer we get to eliminating different options.

That's as close as I can get to emergent levels.
If anyone has any problems with this thought, I'd be happy to hear it and learn from it..

You understand, do you not, that this makes no sense at all? For one thing, although every thing seems to be based on "emergent levels" you haven't bother to define "emergent levels"!

 

[octelcogopod]

Hmmm, ok fair enough.
I'll try to explain what I mean.

If the universe started out as one single most fundamental particle, then there are no emergent levels.
The only thing that exists is that one particle.
If suddenly there existed two particles in the entire universe, emergence comes forth.
There is now a unity between the two particles, either abstract, physically, technically or metaphysically, regardless of how these two particles are bound, they are indeed bound together.
So now there are two emergent levels, one level is where the two particles exist individually and isolated from each other, and the other is when they co-exist in unity.

The more particles you have, the more layers of emergence you get.

So basically my point was in regards to the OP, that while math can be accurate, it may or may not be even close to the reality of the situation, depending on how deep the emergent layers are before we reach "rock bottom", or should I say, the most fundamental particle.

 

[HallsofIvy]

Unfortunately, you still haven't told us what you mean by "emergent levels" so there is no way for any of us to make sense of what you said.

 

[octelcogopod]

Ah, so you're one of those who need every little detail so there's no room for misinterpretation..

Well, how's this;
An emergent level is when the most fundamental particles bind in such a way that weakly emergent patterns arise and create a function that transcends the individual functions of each particle consisting of that object.

 

[matt grime]

But that only introduces more undefined terms. If you want someone else to understand you then you need to use terms that are either known or that you define in terms of known things.

 

[octelcogopod]

Ah, so you're one of those who need every little detail so there's no room for misinterpretation..

Well, how's this;
An emergent level is when the most fundamental particles bind in such a way that weakly emergent patterns arise and create a function that transcends the individual functions of each particle consisting of that object.

Okay, let's try again then.

Fundamental particle = the smallest physical entity, a string perhaps.

Bind = create a unity, melt into one, become a new object from 2 or more individual objects.

Weakly emergent = An advanced form of binding, where a new type of object comes into existence by the physics of the smaller objects working together as a whole.

Transcends = Emergence in a prettier word, something transcends when it becomes more than the sum of its parts.


Does that help any then?
Or shall I continue to define stuff.