In the Beginning...which one are you?

[Max Byzantium]

1. God created the Universe in 6, 24 hour days. (Young Earth view)

2. God created the Universe over billions of years. (Old Earth view)

3. God is behind the Big Bang, but allows the Universe to evolve based on the laws of physics and biology. (Theistic Evolution).

4. There is no God, he is construct of man. The Universe is a mathimatical probability. (Athiestic view).

Personally, I am number 3 guy.

[Amphigorey]

Which only increases the weight of the question, if simple mathematical functions can depict nature in terms of fractals, chaotic attractors, self-similarity, other related concepts, then doesn't it makes sense to say that mathematical equations actually cause the evolutionary patterns of our world? In other words, doesn't it seem compelling that our material realm is acting in response to some kind of mathematical realm?

Mathematics is an incredible modeling tool, it is a language. But I don’t think you can take that leap and say therefore that the Universe is mathematical. Some people would argue that mathematics is a product of evolution, not the other way around. Some people expect to find a nice neat “language” in the Genome also. But natural systems are always fuzzy. There’s all that talk about “junk DNA” now. There are probably lots of patterns in the white noise that we don’t see yet.

[harvey1]

In other words, doesn't it seem compelling that our material realm is acting in response to some kind of mathematical realm?

No!Mathematics is used only to model the physical phenomena. The math may reveal something deeper about the underlying causes, but then again it may not.

If it doesn't, then you should be able to explain why the world can be understood in short, concise mathematical equations (e.g., e=mc^2). For example, Pythagorean's theorem which is used to calculate distances of a hypotenuse (etc) is extremely precise. In fact, it is used in special relativity as well. You can prove the theorem from simple axioms of math. Now, are you saying that there it is a matter of pure chance that some of our most accurate and wide-encompassing theories of science which use some of these equations just happen to be simple and concise?

To the physicist it doesn't matter whether the math reveals a fundemental reality, only whether the math gives a correct solution. A good way to see this is to consider complex numbers. The imaginary component is a real number multiplied by the square root of negative one, or i.

It might not matter to the physicist, but it should matter to the materialist who takes on a position which rejects the metaphysical element to the universe. If one takes such a position, then they should be able to offer a sound explanation showing why the Pythagorean theorem is no more true than comparing the universe to the results of numerology (which is Pythagoras' discipline, btw).

Now, i doesn't exist. It is a meaningless expression. You might as well talk about the square root of the color blue. But in the realm of pure math, the concept of i has certain properties that are useful in representing things like electromagnetic waves. So imaginary numbers are commonly used in many areas. But in terms of the underlying fundemental physical reality, the use of imaginary numbers is a nonsense. They really are imaginary, in the philosophical sense.

I disagree. The term 'imaginary number' is just the square root of -1. The term is indeed useful if combined into a complex number (real times imaginary), but complex numbers can be shown to be real by representing them as two 2 x 2 real matrices. It is just tricky math is what it amounts to. Some tricky math is forbidden (e.g., dividing by zero), but it just so happens that square roots of negative numbers is allowed within mathematics. The representation of the real world comes from equating the variables (e.g., real matrices) with the world. So, in those cases, a little reduction shows that nothing is imaginary in the philosophical sense.

In sum, math has a utilitarian function, in representing reality, but does not necessarily have any existential relationship to reality.

Well, logic does not necessarily have any existential relationship to reality. Our thoughts do not necessarily have any existential relationship to reality. The people you know do not necessarily have any existential relationship to reality. The question is what is reasonable to believe. I'd like to hear your argument which shows how you can remove mathematical tendencies of the universe as a causal basis for the universe. You'd have to either show how different formal systems have almost the same effectiveness at constructing physical theories (i.e., which stay consistent and do not reduce to the same mathematics just using different terms), or, you'd have to show how science can be done without mathematics (i.e., staying consistent and does not reduce to the same mathematics). You can start with Pythagorean's theorem.

[harvey1]

Which only increases the weight of the question, if simple mathematical functions can depict nature in terms of fractals, chaotic attractors, self-similarity, other related concepts, then doesn't it makes sense to say that mathematical equations actually cause the evolutionary patterns of our world? In other words, doesn't it seem compelling that our material realm is acting in response to some kind of mathematical realm?

Mathematics is an incredible modeling tool, it is a language. But I don’t think you can take that leap and say therefore that the Universe is mathematical. Some people would argue that mathematics is a product of evolution, not the other way around. Some people expect to find a nice neat “language” in the Genome also. But natural systems are always fuzzy. There’s all that talk about “junk DNA” now. There are probably lots of patterns in the white noise that we don’t see yet.

I have no disagreement that evolution is responsible for making us adept at mathematics. Where I disagree is that it made us so adept that the equations of the physical sciences turn out to be so concise and simple, not to mention the symmetry in those equations is profound. To discount these equations as mere inventions does not do justice to rational thinking, I'm afraid.

It is of course conceivable that we invent equations to match reality, but it is not conceivable that in such a case that a majority of our equations (and certainly the most universal and wide-reaching ones) can fit on a post-it note. In addition, appealing to things "we don't see yet" is an appeal to faith. Spetey will get upset with you (I don't because I know that people naturally appeal to their intuitive judgement of the nature of the world on things like this).

[Amphigorey]

I have no disagreement that evolution is responsible for making us adept at mathematics. Where I disagree is that it made us so adept that the equations of the physical sciences turn out to be so concise and simple, not to mention the symmetry in those equations is profound. To discount these equations as mere inventions does not do justice to rational thinking, I'm afraid.

I'm not discounting anything. Is faith rational?

It is of course conceivable that we invent equations to match reality, but it is not conceivable that in such a case that a majority of our equations (and certainly the most universal and wide-reaching ones) can fit on a post-it note. In addition, appealing to things "we don't see yet" is an appeal to faith.

Atheists and Scientists work on faith all the time.
Among other things, they have faith that the universe is understandable.

In Fractal Geometry, Mandelbrot was pretty quiet about causes. His whole approach was to describe consequences and maybe work up to an overarching theory … if he felt like it. But he works from reality.
http://www.edge.org/q2005/q05_2.html#mandelbrot

[harvey1]

I'm not discounting anything. Is faith rational?

Aren't you discounting the existence of God? And, yes, faith is rational.

It is of course conceivable that we invent equations to match reality, but it is not conceivable that in such a case that a majority of our equations (and certainly the most universal and wide-reaching ones) can fit on a post-it note. In addition, appealing to things "we don't see yet" is an appeal to faith.

Atheists and Scientists work on faith all the time. Among other things, they have faith that the universe is understandable. In Fractal Geometry, Mandelbrot was pretty quiet about causes. His whole approach was to describe consequences and maybe work up to an overarching theory … if he felt like it. But he works from reality.

But, you didn't reply to my point about how equations produce a similar world and they describe our world with conciseness that would not be expected of something that is invented.

[Amphigorey]

Aren't you discounting the existence of God? And, yes, faith is rational.

I am tempted to believe that people are hardwired to have faith. People who don't believe in dieties still have faith in political systems, people they love, in themselves, etc.
http://www.edge.org/q2005/q05_2.html#norretranders

But, you didn't reply to my point about how equations produce a similar world and they describe our world with conciseness that would not be expected of something that is invented.

harvey1, if you're an engineer, you know your circuit design or building materials design source books are full of ugly nasty unweildy equations that are utterly essential tools that you can't live without. Was Einstein merely lucky that he happened upon E=MC^2 or are you? The mathematical appeal to "elegance" is aesthetic and somehow inherently not mathematical. But its always a goal and is celebrated when achieved.

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality". - Einstein

[harvey1]

But, you didn't reply to my point about how equations produce a similar world and they describe our world with conciseness that would not be expected of something that is invented.

harvey1, if you're an engineer, you know your circuit design or building materials design source books are full of ugly nasty unweildy equations that are utterly essential tools that you can't live without.

That's exactly what I'm saying! If you look at equations of engineering designs, you would see the equations that are very messy. However, if you look at major scientific theories, you see that most of the main equations inevitably reduce to some pretty simply stated equations that everyone can at least understand to some point (e.g., "energy is equal to..."). This would seem to go against a case where mathematics is invented. How do you respond?

Was Einstein merely lucky that he happened upon E=MC^2 or are you? The mathematical appeal to "elegance" is aesthetic and somehow inherently not mathematical. But its always a goal and is celebrated when achieved. "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality". - Einstein

Einstein isn't saying, and I am not saying, that we have a total description of the world. However, the description that we have, which is a pretty indepth one, can be all printed on a few pages as simple equations. This is the challenge for the materialist. My argument is that if you kick the leg of materialism from under the atheist belief, then the whole structure topples. It's easy enough to do if the obviousness of our mathematical universe is acknowledged.

[mrmufin]

Hi, harvey1... man, I like reading your posts.

In other words, doesn't it seem compelling that our material realm is acting in response to some kind of mathematical realm?

No!Mathematics is used only to model the physical phenomena. The math may reveal something deeper about the underlying causes, but then again it may not.

If it doesn't, then you should be able to explain why the world can be understood in short, concise mathematical equations (e.g., e=mc^2). For example, Pythagorean's theorem which is used to calculate distances of a hypotenuse (etc) is extremely precise.

Not all of the world can be described in short, concise mathematical statements. We still struggle with accurate weather forecasts beyond a few days... In the planar realm, the Pythagorean theorem does serve us quite well. In non-Euclidean geometry, things can get much trickier.

In fact, it is used in special relativity as well. You can prove the theorem from simple axioms of math.

While the Pythagorean theorem can be proven using simple axioms, confirming special relativity was, again, a bit trickier.

Now, are you saying that there it is a matter of pure chance that some of our most accurate and wide-encompassing theories of science which use some of these equations just happen to be simple and concise?

Chance or not, it certainly is convenient that we can understand and predict several aspects of nature with some physics that uses not-so-difficult mathematics. On the other hand, I doubt that we'll ever be able to summarize some aspects of nature so tersely. In fact, I'd probably feel a bit shortchanged if my emotional attraction to the very lovely msmufin, for example, could be reduced to a handful of equations.

Ultimately, I don't think nature has any obligation to adhere to our best theoretical or mathematical models. That so many things are predictable, however, suggests to me that we're on the right track in understanding our universe. That many things still confound us should help to keep us all humble.

Regards,
mrmufin

[Amphigorey]

If you look at equations of engineering designs, you would see the equations that are very messy. However, if you look at major scientific theories, you see that most of the main equations inevitably reduce to some pretty simply stated equations that everyone can at least understand to some point (e.g., "energy is equal to..."). This would seem to go against a case where mathematics is invented.

Mathematics at its root is not "invented" because enumerating or counting things is what intelligent beings do. We have fingers, toes, sheep, bananas, and we count them. Euclid didn't have computers, he drew pictures in the mud with sticks. His achievements are not metaphysical, they're intelligent. And if we ever come in contact with extra-terrestrials we will undoubtedly communicate via mathematics. Doesn't this say more about intelligence than it does about the universe? But as a language Mathematics is invented.

With no disrespect, harvey1 if you want to ascribe the mathematical nature of the universe to any religion I would think you would be espousing Dionysian Mysteries. Aren't you on the wrong bulletin board for this?

edited for clarity

[juliod]

If it doesn't, then you should be able to explain why the world can be understood in short, concise mathematical equations (e.g., e=mc^2).

The simple elegance you admire is in fact an illusion. The equation you note is a simple one, showing only that energy and mass are proportional (E~M).

Direct proportionality is one of the ways things can relate to each other. (Others being a=b^2, a= b^3, etc; trigonometric function, a=sin(b); exponenets, a=2^b, a=e^b; and several others.) All relationships between two things are simple when expressed in bare mathematical terms.

In order to declare this a fundementally simple and concise relationship you need to examine the value of the constant (c^2). That's where you will see order and regularity. The relationship E=M is simple. The relationship E=2M is simple.

What do you make of the relationship E=M*2.99792458e8^2 (approximately)?

Is there any order, simplicity, or regularity in the universe, as significed by the fundemental constants? No.

The permittivity of the vacuum is 8.85418782e-12, approximately.
The permeability of the vacuum is 12.5663706144e-7, approximately.

Faraday Constant? 9.648456e4, approximately.

Gas Constant? 8.31441, approximately.

Gravitational Constant? 6.67204e-11, approximately.

Pi, famously, is an irrational number.

What these constant reveal is an absolute absense of order or regularity in the construction of the universe.

DanZ