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Old 2004-12-10, 09:10   #45
xilman
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Quote:
Originally Posted by TTn
Quote:
Originally Posted by xilman
The speed of light is just a proportionality factor
Doesn't this negate the type 1A supernova phenonmenon?
Please elaborate your question. Perhaps I'm being dim, but I don't understand what you are asking. Further detail may be enough for me to give a substantive response.

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Old 2004-12-10, 15:06   #46
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Measurements of light emitted shortly after the big bang show that some of the constants we consider to be absolutes maybe weren't so absolute at some point in time. I prefer to think of PI as a Newtonian absolute just waiting for an Einstein to show that its maybe not so fixed as we think. For instance, in the vicinity of a black hole would pi retain its value? I suspect not since that sliding scale for the speed of light would be moved up the range toward the time axis. I have absolutely no proof of this however, just speculation that constants aren't and variables don't.

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Old 2004-12-10, 15:35   #47
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Quote:
Originally Posted by Fusion_power
Measurements of light emitted shortly after the big bang show that some of the constants we consider to be absolutes maybe weren't so absolute at some point in time. I prefer to think of PI as a Newtonian absolute just waiting for an Einstein to show that its maybe not so fixed as we think. For instance, in the vicinity of a black hole would pi retain its value? I suspect not since that sliding scale for the speed of light would be moved up the range toward the time axis. I have absolutely no proof of this however, just speculation that constants aren't and variables don't.

Fusion
Ok, I've missed that (about shortly after the big bang). Do you have a reference so I can read up on it? I should check it out.

When asking about the value of pi "in vicinity of a black hole": which pi do you mean?

If by pi you mean four times the value of the sum of the series 1-1/3+1/5-1/7+1/9- ... then it most certainly does have the same value near a black hole as it does here.

If by pi, you mean the result of measuring the circumference of a circle embedded in a particular space-time, measuring the diameter of that same circle and dividing one measurement by the other, you have no need to go anywhere near a black hole. Your dining room table will do. If you measure carefully enough (and you have to be very careful) you will find that the ratio is not the same as the value of the aforementioned series. Mass-energy bends space-time, according to GR, though space-time is very, very rigid. The entire mass-energy of the earth is enough to produce a radius of curvature of around one lightyear at the earth's surface.

If you'd like to experiment with a more highly curved surface, consider the surface of a sphere. An infinitesimally small circle drawn on the sphere will have the ratio c/d (circumference / diameter) infinitesimally different from the pi which is the sum of that series. (What this says is that all surfaces are locally flat, and the GR equivalent is that as long as distances and durations are small enough, SR is valid.) Make the circle bigger, and the ratio will change. Eventually, when the circle is infinitesimally smaller than the equator of the sphere, the diameter passes infinitesimally close to a pole and the ratio c/d approaches the value 2.

On a surface of negative curvature, and a saddle-surface is the classical example, c/d is always strictly greater than the sum of the series.

On a surface of zero curvature (flat spacetime, or Euclidean space) the two values for "pi" are strictly equal.

This is a long way from random numbers and even further away from Mersenne numbers, but fun nonetheless --- IMO, but if the consensus is otherwise I'll drop this discussion.

Paul
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Old 2004-12-10, 16:32   #48
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The measurements re constants that varied was in the news about a year ago. I don't remember the full context but the gist of it was that some of the physical constants as derived by measuring quasar light from the very early universe showed small but measurable variances from the expected values. It threw certain cosmological theories into a dither trying to explain the differences. There were implications for Planck's constant as well as a couple of others.

Re the value of pi, my intent was to say that pi near an area of highly curved space such as near a black hole would have a different value than pi in normal space. Essentially the same thing you posted above though the geometry would neither be sphere nor saddle.

I read a well thought out discussion that the universe is approximately 150 billion light years across. This is based on observed oldest light of @13 billion years and taking into account the effect of expansion. It implies that there are parts of the universe that we can't see because light would not have had time to reach us yet.

Our universe. The ultimate random event. Humanity? Probably only one of many billions.

Fusion

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Old 2004-12-10, 23:18   #49
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Quote:
The speed of light is just a proportionality factor

Doesn't this negate the type 1A supernova phenonmenon?

Please elaborate your question. Perhaps I'm being dim, but I don't understand what you are asking. Further detail may be enough for me to give a substantive response.

Ok where do I start, maybe I am dim on this...
Dim Shane As variant (lol)

Type 1a supernova proves a static universe(IMHO), without disproving an expansive one.
I had already thought this before the finding, as I published on a website.
The speed of light is fixed to the wavelength(meters), and yet we find this absurd opposite behaviour with 1a waves. It had been thought that the universe was slowing down in it's expansion, but now we also know that it speeding up.

Am I on the same page?
Shane.Brain = "Overload"
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Old 2004-12-11, 00:17   #50
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Quote:
Originally Posted by Fusion_power
I read a well thought out discussion that the universe is approximately 150 billion light years across. This is based on observed oldest light of @13 billion years and taking into account the effect of expansion. It implies that there are parts of the universe that we can't see because light would not have had time to reach us yet.
I think this is probably the article you have in mind: http://www.space.com/scienceastronom...ay_040524.html

Unfortunately, as with most science news headlines, the title somewhat distorts the actual scientific findings. The title implies that the Universe is about 156 billion light years in "diameter", but if you read into the body of the article, you'll see that this was not the finding. The actual result was that the Universe is at least 156 billion light years across, possibly more.

However, if you read the actual scientific paper itself, written by Cornish et al. you'll see that even that is not wholly accurate. Actually, what the researchers did was examine different possible topologies (shapes) the Universe might take and compare them with observations. They were able to rule out the possibility that the Universe is less than 156 billion light years (they use the figure 24 Gpc, which is just a different unit) across for some topologies. Thus, in fact, it may still be possible for the Universe to be less than 156 billion light years across.

You can read their findings at http://arxiv.org/abs/astro-ph/0310233

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Old 2004-12-11, 01:50   #51
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Pi is a mathematical constant, not a physical constant.

The value of C is determined by physical measurement, the value of Pi is determined by first principles.
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Old 2004-12-11, 02:55   #52
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Quote:
Originally Posted by jinydu
Originally Posted by shaxper
Then that would be the same outcome. 3.1 and 3.1 are the same outcome, but 3.1 and 3.14 are different outcomes.

But I don't see how you can call that "randomness". I can guarantee getting the value 3.1 by asking my computer to compute 2 significant figures, while I can guarantee getting 3.14 by programming for 3 significant figures.
I think you're holding on to Fusion_Power's definition of random that it should be unpredictable or, at the least, unknown. But those words aren't in your definition. (Nor is guarantee.)

Quote:
Originally Posted by jinydu
I think your definition of space is too vague. From what your post says, my best guess is that you define a "space" as an "area" with a different conception of infinity as all other similar "areas". So far, you have described three kinds of "spaces": numbers, pictures and music. Yet I don't think your explanation of why they should be considered different spaces is adequate.

In what you call "rational space", you say that infinity is conceived of as numbers increasing without end. But in fact, there are other ways to use numbers to think of infinity. Another way is to think of "infinity" in terms of limits, what something approaches as a variable gets arbitrarily close to a certain variable. The notion of limits is central to the entire (mathematical) theory of calculus.

In addition, pictures and music aren't really seperate from numbers. You seem to imply that fractals are the prime example of pictures. However, if you study Chaos Theory, you would know that fractals are mathematical objects that cannot be described without numbers. For a more detailed description of this, see http://pirate.shu.edu/~wachsmut/Workshops/Camden/. One example of generating fractals is to use Newton's Method on a cubic equation in the complex plane. If you color each point according to what root it converges to, and all three roots are distinct, you get a fractal. For more information, see http://mathworld.wolfram.com/NewtonsMethod.html.

I am even more mystified by your claim that music is another seperate space. Yet you have not explained how music has its own conception of infinity, which seems to be your definition of a "space". Furthermore, there is already a way to turn music into numbers so that the pattern becomes conceivable. The mathematical theory of osciallations has already been applied to the study of sound waves, and plenty of regularities in music have already been found. Furthermore, there is already a device that can convert music into numbers, at least to a good enough approximation that most people don't notice: its called a DVD recorder/player.

Finally, you claimed in an earlier post that to determine something is to bring it into rational space. First of all, this is inconsistent with your claim that nothing is 100% determined, since by this definition, anything in rational space would be completely determined.
My bad. I told myself not to go off topic and I went off topic.
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Furthermore, you haven't explained why determinism is only possible in rational space.
True, but I don't need to because I'm now using your 2nd definition to assert that pi is random (multiple outcomes).
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Old 2004-12-11, 04:40   #53
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Maybe I should try to restate my point then:

If I tell my computer to calculate pi to 2 decimal places, the outcome will be: 3.1

If I tell my computer to calculate pi to 3 decimal places, the outcome will be: 3.14

Furthermore, it can be proven mathematically that those are the only possible outcomes for 2 decimal places and 3 decimal places, respectively. It is impossible for the computer to output say, 3.2 in the first case.

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Old 2004-12-12, 13:09   #54
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Quote:
Originally Posted by jinydu
Maybe I should try to restate my point then:

If I tell my computer to calculate pi to 2 decimal places, the outcome will be: 3.1

If I tell my computer to calculate pi to 3 decimal places, the outcome will be: 3.14

Furthermore, it can be proven mathematically that those are the only possible outcomes for 2 decimal places and 3 decimal places, respectively. It is impossible for the computer to output say, 3.2 in the first case.
But the value of pi doesn't change, just the determination (the outcome) of that value.
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Old 2004-12-12, 15:29   #55
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Quote:
Originally Posted by Fusion_power
Re the value of pi, my intent was to say that pi near an area of highly curved space such as near a black hole would have a different value than pi in normal space. Essentially the same thing you posted above though the geometry would neither be sphere nor saddle.
Ok, that clears up one thing. As I thought, you are not talking about the same pi as the one defined by most mathematicians. You define pi to be the length of a simple closed curve which every point on which is always a fixed distance from a paricular fixed point (the centre) not on the curve and divided by twice that distance.

There is no dispute, as far as I am aware, that your quantity pi is not a constant but depends on the curvature of the space. The mathematician's pi is indeed a constant and independent of the precise geometry in question.

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