Natural laws and how they operate

[nygreenguy]

This is a bit of a question.

In another forum on this board me and another member were discussing the origins of the universe. We started going into the first law, and the whole conservation aspect.

Heres a snippet:

Originally Posted by nygreenguy View Post
I was unaware the two could be separated. Aren't many physics "laws" and "theories" defined mathematically?
The point is that they aren't derivable from mathematics. WRT math, and logic, the laws of physics are essentially arbitrary....

ou said math and physics are inseparable, and that I can't talk about the laws of logic or mathematics separate from the laws of physics. If this were the case, then physics would just be part of mathematics, and we'd be able to derive the laws of physics starting from mathematical assumptions--but we can't. For example, the speed of light is about 1 foot per nanosecond. There's no way you can derive this fact from mathematics; you have to actually observe the movement of light in order to come up with it.

Now, what is the role of math in these laws? How independent are they from each other?

[nygreenguy]

Aww, come on.


SOMEONE has to know the answer!

[espritch]

Natural laws are derived through observation. Math is used to quantify those observations, but the laws are discovered through observation, not math.

For instance, we can define acceleration due to gravity using a simple equation:

a = 32f / s^2

However, the acceleration due to gravity was not determined through mathematics, but through direct observation by Galileo using balls rolling down an inclined plane (http://galileo.rice.edu/lib/student_work/experiment95/inclined_plane.html). So the math is really just a description of the observed behavior.

[dug_down_deep]

Based on my limited understanding, the laws of physics are likely unified at some level, and mathematics may help us to know how to look for that elusive unified theory. But physics is an empirical science -- it can only be confirmed by observation. That's why string theory can be beautifully coherent, and yet possibly imaginary.

[His Noodly Appendage]

Well, the inverse square law is a good example.

The intensity of radiation from a point source is in inverse proportion to the square of the distance from that point.

The reason for this has nothing to do with physics, and everything to do with geometry. If a point is radiating in all directions, then for any given distance, the 3d locus of that point describes the surface of a sphere, across whose surface the entirety of the energy output is distributed.

As the surface area of a sphere is O(r2), the proportion of the total radiation reaching a point on that sphere is therefore O(1/r2).

[Linus]

Now, what is the role of math in these laws? How independent are they from each other?
In posts #48-50 (http://www.talkrational.org/showthread.php?p=15350#post15350) in the same thread I commented on a similar issue, so I'll keep this brief: Mathematics is independent of physics except in that it is easier to motivate research on mathematical problems that are of interest to non-mathematicians. Physics depends entirely on mathematics.

[Preno]

The laws of physics are in large part formulated using mathematics. I don't quite understand what more you are asking about.
The reason for this has nothing to do with physics?

The isotropy of space, for example, has nothing to do with physics?
and everything to do with geometry?

The geometry of our space as nothing to do with physics?

[Ian Nerr]

In posts #48-50 (http://www.talkrational.org/showthread.php?p=15350#post15350) in the same thread I commented on a similar issue, so I'll keep this brief: Mathematics is independent of physics except in that it is easier to motivate research on mathematical problems that are of interest to non-mathematicians. Physics depends entirely on mathematics.

There's some truth to that, but I also think many mathematicians enjoy the esoteric nature of pure math and they get disappointed when physicists find real world applications for their weirdest stuff.

[Ian Nerr]

Well, the inverse square law is a good example.

The intensity of radiation from a point source is in inverse proportion to the square of the distance from that point.

The reason for this has nothing to do with physics, and everything to do with geometry. If a point is radiating in all directions, then for any given distance, the 3d locus of that point describes the surface of a sphere, across whose surface the entirety of the energy output is distributed.

As the surface area of a sphere is O(r2), the proportion of the total radiation reaching a point on that sphere is therefore O(1/r2).

This has a lot to do with physics. There are other possible geometries besides Euclidean. The fact that the inverse square law (and any other assumptions based on Euclidean geometry) works tells us a lot about our universe.

[ravenscape]

This is a little off-topic, but I remember the rush of awe I felt upon learning that equations for defining the geometry of a circle were derivatives of the equations for defining the geometry of a sphere. In my minds eye, I could see a marching progression of integral functions describing geometries of greater and greater dimensionalities.

For me, it was an experience of the numinous.

[Ray Moscow]

Now, what is the role of math in these laws? How independent are they from each other?

Through a lot of incredibly hard work and applied talent, scientists (with a lot of help from mathematicians) found that most phenomena can be described mathematically -- sometimes with simple maths, sometimes very complex maths. Eventually we might be able to describe everything by the same maths and have a "theory of everything".

The maths themselves exist independently -- as intellectual constructs, or depending on how you look at it as realities that we have discovered intellectually.

[Ray Moscow]

This is a little off-topic, but I remember the rush of awe I felt upon learning that equations for defining the geometry of a circle were derivatives of the equations for defining the geometry of a sphere. In my minds eye, I could see a marching progression of integral functions describing geometries of greater and greater dimensionalities.

For me, it was an experience of the numinous.

Now that's Spinoza and why he was so cool!

[llanitedave]

Well, the inverse square law is a good example.

The intensity of radiation from a point source is in inverse proportion to the square of the distance from that point.

The reason for this has nothing to do with physics, and everything to do with geometry. If a point is radiating in all directions, then for any given distance, the 3d locus of that point describes the surface of a sphere, across whose surface the entirety of the energy output is distributed.

As the surface area of a sphere is O(r2), the proportion of the total radiation reaching a point on that sphere is therefore O(1/r2).

This has a lot to do with physics. There are other possible geometries besides Euclidean. The fact that the inverse square law (and any other assumptions based on Euclidean geometry) works tells us a lot about our universe.


Does it? Or does it tell us more about our own hardwired perceptual biases?

[Quizalufagus]

What sort of hardwired perceptual biases are you alluding to? What does it say about us that inverse square laws hold?

[bovie]

Physics is beautiful mathematics (viz. logic/philosophy) which has been screwed-up accounting for mass-energy (viz. observed phenomenon). That's the difference.

[RAFH]

What sort of hardwired perceptual biases are you alluding to? What does it say about us that inverse square laws hold?

That we evolved in a reality where inverse square laws are, for what we evolved into, reasonably accurate and reliable descriptions of that reality.

In other words, why is the ground the puddle lies in shaped exactly like the puddle?

[Preno]

what

[JamesBannon]

The laws of physics are in large part formulated using mathematics. I don't quite understand what more you are asking about.
The reason for this has nothing to do with physics?

The isotropy of space, for example, has nothing to do with physics?
and everything to do with geometry?

The geometry of our space as nothing to do with physics?
Rather the other way round. Maths & Physics are human constructions based on observations.

[Preno]

Well obviously, virtually all uses of language are in part driven by its internal dynamic and in part by our observation, so all of our theories are in part constructions. The fact that there are many equivalent formulations of many laws of physics testifies to the fact that there is some leeway in the building of our theories. But how does that justify the claim that "the reason [why the intensity of radiation from a point source is in inverse proportion to the square of the distance from that point] has nothing to do with physics"? Surely that statement is patently false? Especially in light of the fact that gravitation does not actually follow it.

[JamesBannon]

I don't think that's what HNA was getting at, but I'll let him elaborate.

[Preno]

What he was getting at is irrelevant. He said that the inverse square law has nothing to do with physics, which is absolutely false (and hence doesn't constitute evidence for whatever it was that you are thinking he was "getting at").

ETA: Actually, what he said was partly true - gravitation does, afaik, decrease as O(1/r^2), but that doesn't imply that it follows an inverse square law.

[JamesBannon]

I think HNA was referring to the fact that, in large part, the laws of Physics are formulated using Mathematics rather than a direct reference to the Inverse Square Law. In essence, it need not necessarily be the case that the laws of Physics are required to be formulated using Mathematics, but that they are because it is convenient to do so.

[Preno]

I think HNA was referring to the fact that, in large part, the laws of Physics are formulated using MathematicsI don't think anyone here would disagree with that, so I have no idea why he would want to make that point, but regardless, what he said was false.