half of a half of a half of a philosophic problem

Factual Questions
21

I really don’t get Zeno’s paradox. Okay, so an infinite number of events must occur. So what? Why is there anything paradoxical about moving through an infinite number of points in a finite amount of time? That doesn’t require infinite velocity. Velocity is space per time, not points per time. Anyway, you move through an infinite number of time points as well, so the two infinities cancel out.

As for quantinization, there is no quantinization of energy. For a particular frequency, the energy of photon is quantized, but photons can have any frequency at all, so their energy can be anything at all.

22

Are you sure about this? Could you direct me to a reference, because this is nothing I’ve ever heard before.

23

Ding ding ding, we have a winner! Ryan that’s precisely the answer.

The Greeks, while amazingly advanced given the era, lacked many of the mathematical developments we take for granted today.

Zeno extrapolated the current theories on geometry to reach an obviously false statement. Logically, he said, something must be wrong with the theories.

It wasn’t until calculus with Leibniz and Newton that good mathematical answer was formulated.

Their answer? Basically what you said above. When the tortoise travels have the distance, he does it in half the time. When he goes the next quarter, he does it in a quarter of the time. As the distance travelled approaches zero, so does the time period. The ratio, however, is constant. This is the concept of the infinitessimal and the derivative, which didn’t exist in Euclid’s day.

24

Who is this new alonicist showing up on the boards all of a sudden? Have I left information around somewhere allowing somebody to hijack my identity, or is there a technical screwup? None of the previous posts in this thread are mine- I cannot take responsibility for any intelligent or stupid remarks made by the poster identified as me.

25

Oh, okay, it looks like that’s my younger, smarter brother. I am now looking into ways of letting us have different identities on this board.

26

Well, in fact, Zeno’s paradox is correct. It is not possible for a philosopher to get that can of beverage. Most philsophers starve to death, unable to reach the food that their housekeeper has set nearby. It’s a tragic sacrifice in the name of philosophy.

27

Well, you could try finding a frequency within 90 and 100 MHz that your radio doesn’t receive. Not simply receives static at, but doesn’t receive at all. All frequencies between 90 and 100 exist, because frequency is not quantized.

28

I’m still a little confused. Could you explain yourself better The Ryan?

29

To back up The Ryan’s contention that energy is not quantized, consider the kinetic energy in an object travelling X feet per second. As long as space is not quantized, energy cannot be - X can be indefinitely small, driving kinetic energy to similar extents of smallness.

30

I was under the impression that the results of the black body problem require energy to be quantized. Otherwise, there are interesting (read: impossible) implications.

31

Well, this thread has certianly drifted a bit, but it’s drifted to somewhere where I can help out. First of all, energy typically is quantized, but not in the same way as, say, electric charge or angular momentum. Any charge you have on an object will be an integer multiple of q[sub]e[/sub] (the charge of the electron), or q[sub]e[/sub]/3 , if you’re dealing with quarks. Similarly, any angular momentum you’ll ever have will be an integer multiple of hbar/2. It’s easy to see that those are quantized. With energy, it’s a bit more complicated: It usually is quantized, but the quantization depends on the system, and isn’t even necessarily constant, then. For instance, a hydrogen atom has certain discreet energy levels. You can be in the ground state, or you can be at 10.2 eV (a unit of energy) above the ground state, but you can’t be at any energy in between. This is quantization, in a sense. However, 10.2 eV isn’t some sort of absolutely idivisible quantity: The next higher energy is not at 20.4 eV, but at 12.09 eV, then at 12.75, etc. There is a mathematical relationship, but it’s quadratic, not linear (E[sub]n[/sub] = 13.6eV *(1-n[sup]2[/sup]) ). Then, if you take some atom other than hydrogen, you’ll see energy levels in completely different places.

Not so much is known about the quantization of spacetime. Nobody knows if it’s quantized in the same sense as energy (with particular discreet values allowed, depending on the system). If you can prove that one way or the other, you’ll receive fame, fortune, and adulation for the rest of your life. However, it’s pretty safe to say that it’s not quantized in the same way as charge, with some fundamental distance such that all other distances are an integer multiple of that distance. Think of it this way: Suppose that you had a triangle, with two sides equal to that fundamental distance. What’s the third side? It can’t be zero, because that’s not a triangle, it’s a doubled-up line segment. It can’t be two or greater, because the sum of any two sides of a triangle is always greater than the third side. If all distances must be integers, we’re stuck with saying that it’s one. OK, so at the smallest level, the only triangles we’re allowed to draw are equilateral ones. Now, what if you take two of those triangles, and match their bases together, to make a rhombus. What’s the distance between the points? That’s easy, according to Pythagoras, it’s the square root of three… But that’s not only not an integer, it’s irrational. Looks like everything’s not a multiple of that fundamental distance, after all.

32

You all are so short sighted.

When I reach for my drink, I set my hand in motion and aim for the thin air an inch beyond where the drink lies. And my hand can’t help but run into the bottle.

Works every time.

[sub]I should have been an engineer.[/sub]

33

I just have to quote my original sig line:
“Tell Zeno I’m willing to meet him halfway.”

34

The obvious solution, is that whenever we’re going somewhere, our destination is the other end of the universe. So you hit the can early in the first half of your journey. Simplifying that, if you want to reach the can, move for the space 2 feet on the other side…you’ll hit the can in the first half. (Looking now, this theory was proposed in a way by honkytonkwillie…didn’t see it till now).

Jman

35

Everyone seems to be missing the obvious fact that your hand can never even leave for it’s journey in the first place. I mean consider the first half distance…how is it possible to cover that first half considering it too has a half, half, half etc. problem? And then that also has the same problem. And so on. So you can see how working back your hand can never even get started. Therefore your hand never moves in the first place…and I never typed this.

36

Actually, the joke was about the misapplication of statistics. The stat: the Mississippi is getting shorter every year (due to erosion, but let’s ignore that). The application–extrapolating backwards, in prehistoric times the Miss. was 5,000 miles long and “stuck out over the Gulf of Mexico like a fishing rod.” Extrapolating forwards, pretty soon the Miss. will be 100 yards long, and the cities of New Orleans and Cairo, Ill. will need to merge, and “plod along under a mutual board of aldermen.”

37

Re Arthur’s post of quantised energy and matter, see the March issue of Discover magazine, “very dark energy.” I quote from it: “Gravity is the only one of the four known forces that has eluded description in terms of energy bundles called quanta. Physicists hav already managed to bring the other three - the strong force, the electromagnetic force, and the weak force - into the quantum field.”

So, it appears to my simple mind (that equates things that have quanta with quantised), that energy and matter are both quantised, or quantisized, or quantized.

38

Reach out and grab your beer. How long did it take? Let’s say it took exactly one second.

Zeno’s paradox says that it took one-half second to get halfway to your beer, one-quarter second to get halfway through the remaining distance, one-eighth second to get half of the still remaining distance, etc.

So Zeno says that we have an infinite series of time intervals. Like this:

1/2 + 1/4 + 1/8 + 1/16 + 1/32…

The series goes on forever! So how can your hand ever reach the beer—the time must be infinite if the series is infinite, right?

Wrong, because an infinite series can have a finite sum, an insight provided by, ta-da!, calculus. This particular series has a sum of one (second). So at the end of one second your hand will grab the beer, having passed through, yes, an infinite series of incremental distances.

Thank Newton and Leibniz for this insight.