The last is not really an assertion one can make in the same way as the other two...that's just a stated Lagrangian for a set of Standard Model Interactions, whereas the other two are provable in some system.

But the dance is awesome.

One of my favorite quotes about math comes from that Einstein dude. Math and the sciences are pretty pivotal on how people see the world by and large. Which is why, when one of the greatest contributors to the shaping of that idea said this,

"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."

I was taken back a little. Later, as I started to learn more and more, I came across the same type of though in my own education. Math can be perfectly consistent when talking about itself, but when you start to translate that over to the real world you have to consider you are mapping one system onto another and some things might be lost in translation. For example, calculus is beautiful, but does it actually answer the question how finite objects move through infinitely divisible space in a time that is finite? Drat you maths! You bring us beautiful proofs and no understanding!

(ohh hey maths, I know I was just talking some mess, but can you help me see if the tensile strength of this cable is enough to support this bridge...hey thanks man, I'll buy you a drink...(as x tends to infinity..eheheh sucker))

(edited 4 times for spelling, I fail at life!)

Meh.

I disagree with the last four words of that statement. The rest is great. >> ^GeeSussFreeK:

(edited 4 times for spelling, I fail at life!)

Maths*

@GeeSussFreeK:

Why do you think that space is infinitely divisible?

Actually I don't, but scientists still think it is. I think everything has to be granular to be logically consistent. I think it is interesting that the realm of the small is starting to show this as true. The state changes of atoms resemble this granular nature, like when light changes phases, it does it in desecrate steps. And the "noise" these very sensitive probes are getting can be leveled at space actually being discrete instead of infinitely reducible. My epistemology concerning science and math holds them in very high re-guard. But what they don't get us is "Truth" or certainty. Science deals with how humans understand the universe, I usually like to deal with how the universe must actually be; a subtle but completely different paradigm than most people concern themselves with.

I remember this popular science article where they had mathematicians asking philosophers about the implications of a formula he derived. The mathematician had time to the 4th power and didn't really understand what that would even mean in the real world. It was a funny read but adds to the notion that math is a beautiful castle, but in some ways it is a castle in the sky that lays un-anchored to reality. And that isn't to smack talk it, I use math and science rigorously. However, when talking of epistemology it is important to know the limits of a line of questioning.

But now I am babbling on.

GeeSussFreek. You are right in that everything can be broken into quanta...

Except for space...you could, for example have a unit of space smaller than an electron, correct?

But for everything else, there is a some sort of "granule" LCD. Or so it seems.

There is no logical reason to suppose that any piece of matter is "the smallest unit"; it would always be logically possible to see something smaller. The smallest unit of space would be a point, it would have no real dimension to speak of, it is what defines dimension; it is not measurable by any other means, it is that base of all measure. A smallest unit of space is logically necessary for motion and many other things. Without it, Zeno's paradox is maintained. Calculus tries to help us out and estimate things based on an ever shrinking delta, but ultimately, this is still just an estimation. This would also mean that all notions of dimensionality could be flawed. IE, there is no real dimension except for what a brain perceives. 3-d (or 4-d or whatever science calls it next) isn't logically a condition of the universe but a condition of the human mind. This isn't to say that the rules of Euclidean geometry are voided, but it does bring some interesting questions as to how objects exist. Waves would not be contiguous in the strictest scene, nor would circles be true circles. At the smallest level, everything would be aliased like a monitor screen, or even more so contain no "space" and just be a formula. In other words, one of the base principles of matter, that it is extended in space would be voided as the idea of extension in what is a non-dimensional reality is meaningless.

What the smallest unit of space does for us is something magical though. Logically speaking, there has to be a smallest unit of time. The smallest unit of time would be the amount of time an entity can transition itself from one space to another space. With this, a logical "fastest speed in the universe" is created; and as evidence would have it there seems to be just such a phenomena! Without a smallest unit of space or time, it means that logically matter is jumping over entire segments of space because it is the only way one could end up moving. As such, there would be no real understanding of how motion really works. If objects are just jumping from one set of spaces to another motion becomes a great mystery. Anyway, I am rambling again. Once again, I usually don't think about the universe like a scientist. I care little for how things appear, and want to understand how things must actually be. So for me, for things to move, for time to progress, for thing to happen they have to be discrete.