posted 05-02-2001 19:45         

quote:

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Originally posted by BaldGhoti:
Plus, as a scientist, how can one base one's entire LIFE around something based so entirely on blind faith?

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posted 05-02-2001 20:14            

Firstly, infinity is a number. For all practical purposes, anyway, just a weird number, much like pi or the square root of negative 1. The fact that it has odd properties doesn't make it a non-number. And, from the perspective of light wavelengths, a few centimeters is not infinite - it's just rather large, which is to say it approaches infinity, which is not the same thing.

Secondly - Yes, it is possible to predict the outcome of a complex system without modeling it (necessarily) - just difficult. The "butterfly flaps its wings in X and causes a hurricane in Y" hypothesis is supposed to demonstrate the difference between chaotic (hard to predict) systems and non-chaotic (easy to predict) systems. They're both still predictable, much like a RNG, if you have perfectly accurate knowledge of the starting conditions. The only difference between chaotic and non-chaotic is how wildly your results diverge across small changes in start values.

Aside from this, there are such things as "truly" random events that aren't predictable, to us- quantum events. It's unclear whether God would be able to predict quantum events or not. On the one hand, if quantum mechanics is correct, such events aren't predictable in any way (unless you count "50% chance of A and a 50% chance of B" as a prediction), regardless of how much knowledge you have before hand. On the other hand, God may have evolved better theories than QM. In any event, its always seemed likely to me that our "free will" (to the extent that such a thing exists) is a rersult of the quantum events in our brains.

To expand upon that: the electrical interactions between axons are small enough in scale to have quantum components. This, according to QM, makes at least some part of our brain's functioning un-predictable. On top of that, the geometry of the brain dictates the percentage chances of a particular neural interaction, which would vary from person to person (and be influenced by past thoughts, among other things). Hence, we have a random system that is weighted by past experience and bias, which is a pretty close approximation of human behavior. Unfortunately, that hypothesis doesn't make "free" will very free, but them's the breaks; I don't think you can postulate real free will without stipulating a soul, or some metaphysical equivalent thereof. Which is probably why so many people believe in God.

posted 05-02-2001 20:16            

quote:

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Originally posted by deeznuts:
were you referring to science or religion? or both?

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Science is verifiable within its own constraints, religion is not. Guess.

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Reverend Rob

posted 05-02-2001 21:35         

weis - about infinity you're probably right. i was using it in a scientific sense which i felt i clarified at the beginning. as in my light wave example i was using infinity to mean "without measure" rather than "without limit". it's a common simplification, so i don't really feel i was abusing the word that badly.

regarding the knowing of a complex system: it is entirely possible to get the exact output from the input - by running the system. there is no faster way to get the output. there are plenty of other ways, but the only way you could get it done faster is basically to cheat. for instance having a faster version of the same system and arranging for the difference in state caused by the accelerated operation to be negligable. you could also get it done slower through careful simulation.

posted 05-02-2001 23:27            

Oh...

IRON MAIDEN!!!

posted 05-02-2001 23:37            

quote:

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Originally posted by weis:
Damn you all. Just because you're knee-deep
in a theological discussion doesn't mean you can go misusing mathematical terms and get away with it, not on my watch ... The only difference between chaotic and non-chaotic is how wildly your results diverge across small changes in start values.

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posted 05-03-2001 09:48            

I'm going to guess that you do, in fact, think of pi as a number. If you do, just think of infinity as pi with the decimal point shifted... well, infinitely far to the right.

posted 05-03-2001 09:53            

[fades back into background and hides in the darkness]

posted 05-03-2001 10:31            

uh-huh.

posted 05-03-2001 11:36            

This is quite consistent with the concept of God espoused in organized religion: God is everywhere, God is in everything, God can do everything, God knows everything. ("God is in the details." -Ludwig Mies van der Rohe)

Which is how and why this whole hoo-rah about "infinity" came about to start with.

I think where we were getting off on the wrong foot is sloppily referring to "an infinitely large number" as infinity itself.

posted 05-03-2001 13:58            

an infinitly large number doesnt really make sense. we can either talk about a very very large number, or infinity, or perhaps the limit of x as x approaches infinity.

one cannot consider an infinitly large value to be an irrational number. first of all, for any large number X, we can express X as X/1 and have perfect accuracy. an irrational number is not defined by its ability or inability to be defined as a fraction. in fact, most irrational numbers are better expressed as fractions, or using some other notation such as sqrt (2). pi is irrational however because of its infinitly long and non-repeating decimal expansion. pi can also be perfectly expressed using the circumfrence and radius of a circle.

posted 05-03-2001 15:13            

No Cyd-ness required. Infinity is, properly speaking, a set - not a number. It is the set which contains all possible subsets. Since it is itself a set, that means it is a possible subset - therefore the set infinity can be considered a subset of itself. Recursive, and all that.

posted 05-04-2001 04:06            

"infinity is not a number. it is a relative measure of anything which is superlative compared to anything else."

Unless we're talking about Jimbo's definition. Jimbo, I'm sure what you mentioned is a valid definition of something infinite, but scalar numbers and sets are two different things, and they could both be infinitely large. But, the concept of infinity can be applied to various realms of mthematics, so it doesn't have to have a definition that narrow.

Think about it; let's say I draw a graph of the equation y=1/x, which happens to be vertically asymptotic to the line x=0; and I ask you, "at what point on the y axis will x equal zero?" Infinity would be a valid answer; a set that contains all possible subsets would not.

Also, I like pi. I once worked with a guy that could recite pi to 200 decimal places. Of course, he was a 22-year old virgin. Not that that should be taken to besmirch pi, though. Sure beats the shit outta cake.

posted 05-04-2001 11:36            

quote:

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Originally posted by weis:
Think about it; let's say I draw a graph of the equation y=1/x, which happens to be vertically asymptotic to the line x=0; and I ask you, "at what point on the y axis will x equal zero?" Infinity would be a valid answer; a set that contains all possible subsets would not.

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Not quite - it is, however, correct to say that for the asymptotic curve y=1/x, y=0 for infinite values of x. The problem is that infinity ISN'T a "point" on a line, it really is a set that contains all subsets. I didn't pick that definition spuriously.

You are perfectly correct that there's a big difference between scalar numbers and sets, I won't argue that for a minute. But if you get nitpicky about it, infinity isn't a scalar number and cannot be described as a single point on a graph.

Assume we are graphing the asymptotic curve you described with "infinity" as the left hand side of the graphed portion of the x axis, thus conveniently avoiding the problem of actually getting there. Begin plotting curve points on the graph, with major intervals on the x axis being units of 1.

if x = infinity, y = 1 / ¥ = 0.

Now we graph the point on the curve at the next major interval of x - our original value of x was ¥, so our next major interval occurs at ¥ + 1, which is still ¥.

So at our second major interval, y = 1 / ¥ = 0.

Y is still going to be 0 at every further interval we care to plot, because where n is any natural number, ¥ + n = ¥.

Ergo, infinity is a set, not a scalar, and therefore a scalar can be described as being "infinitely large", but not as being "infinity" itself. I didn't just pull that one out of my ass.

(edited to note that ¥ is the mathematical symbol which denotes infinity.)

posted 05-04-2001 15:33            

weis: ""at what point on the y axis will x equal zero?" Infinity would be a valid answer;"

this is wrong. x never ever equals zero in y = 1/x. it is, however, proper to say that x approaches zero as y approaches infinity, or rather, the limit of x as y approaches infinity is zero. but x never ever equals zero.

jimbo: "it is, however, correct to say that for the asymptotic curve y=1/x, y=0 for infinite values of x. " is also not correct.

x cannot take on infinite values. inifinity is not a value, nor is it a measure of a value. real numbers cannot be assigned a property of inifinitness, whereby one number is more infinite than another. also, a number cannot be closer to infinity than another number for the same reason. both 1 and 1*10^200 are equally close to infinity. the function y = 1/x will never evaluate to zero. however, again, as we take the limit of y as x approaches infinity, y will approach zero, but NEVER equal zero.

posted 05-04-2001 17:17            

quote:

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i know this sounds like nitpicking, but it is of the utmost importance to agree that infinity cannot be treated as a number in such a callous manner. this is the first thing we're taught in first year calculus. unless you're an engineer. engineers seem to disregard these rules for some reason without caring. it's all the same to them. damn engineers with their baby math.

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I actually think we're agreeing here zippy - if you look back at what I was doing, you'll note that I stated outright that infinity is NOT a scalar, it's a set - and was attempting to demonstrate this by showing what would happen if you tried to plot points on a curve which involved an infinitely large value.

posted 05-04-2001 22:16            

Pie beats Cake!

cuz pie comes sooooo much closer to being infenitely good than cake could ever,
and you can you pi on circles and can use pi to figure radians ect.... cake just sits there while pie can be your best friend and run with you and walk your dog then come home and snuggle up against you and then watch a movie and maybe if its a bad movie fool around with you a little and then when the movie is done you can sit with it and talk and laugh with it and cuddle with it and love her..... it i mean pie that is

not my girlfriend,
pie
yeah
pie