reality is in material

This is a discussion on reality is in material within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Your problem is you don't understand infinity; there IS a difference between 1/ infinity and 200 / infinity, they both ...

  1. #91
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    Your problem is you don't understand infinity; there IS a difference between 1/ infinity and 200 / infinity, they both give an infinitely small number, BUT those two numbers are different. Yes, you can have two infinite numbers and one can be larger than the other. This scenario arises quite often: consider integrating between 0 and infinity a y = x line, the area will be infinite, now consider integrating between 0 and infinity a y = 2x line, the area will also be infinite but a "larger" infinity than the first one.

    Infinities can cancel out, infinitely large numbers multiplied by infinitely small numbers yield constants. (In some senses that is why light has a mass)
    I think you are the one who does not understand infinity here, Clyde. Infinity can only be considered as existent in the context of topological space or when it used in measuring the "sizes" of sets, as I mentioned earlier. In a topological set, infinity is defined as the object which the set of real numbers converge to. You last statement (the one about how infinities can cancel out) is incorrect, because even in topological space, the infinite object cannot be operated upon in the same fashion as the real set. When someone writes '1/infinity=0' you are not really dividing one by infinity. Instead, it is a statement dealing with the series 1/1,1/2,1/3,1/4...and saying that it converges to 0. Your example 200/infinity is exactly the same.

    Your integration example is also faulty. To the extent that is meaningful to integrate any function with an infinite limit (improper integration), the result of integrating y=x from 0 to infinity is nonexistent, because it is divergent.

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    its a rigidly flat continuum, similar to the rigidly flat space of euclidian geometry. all bodies are moving in space-time, a non moving body is stationary in 3 coordinates but always moving in the 4th, time. the sum of the motions in the 4 dimensions is always constant, so a spacially moving body slows down in the time dimension or its 'clock' slows down. this is time-dilation.the 3 spacial dimensions can be +ve or -ve, but time can only be +ve. as regards the 'clock' - eg a muon particle with a lifetime of 2X10^6 secs at rest may have a lifetime increase of X200 at close to the speed of light.
    Incorrect. Space time is curved overall, alothough it may be flat locally when the Ricci Tensor (I think thats the one) is zero. Basically, the curvature results from mass. However, the word "curved" demonstrates one of the layman's problems (that includes myself) with modern physics in that is impossible to understand fully in any normal, physical sense. The concept of "curved" is rigorously defined in mathematics in a way that human language will never reach.
    In fact, reading pop physics books all the time, as I do, actually can confuse you muchos, even though they are really cool. Trying to visualize a photon, meson, etc is useless. I even think that the word "particles" is rather misleading, because it invites one to attempt to draw an analogy between say, very small sand grains, and electrons, with the sole exception that electrons are much smaller. Of course, this is utterly absurd. Many people also misunderstand the concept of wave, which they relate to a water wave, etc. Many physics contain drawings of waves as little squiggly thingamajigbobbers, which imply that the wave moves like a caterpillar tracing out a sine function. Wave-particle duality cannot be fully explained in words, or even adequately so.
    The best way that I have found is to think of a particle as a sort of bundle of causation. It is caused by collisions, energy fluctuations, etc (which is only partially accurate-the causality is not complete to my knowledge) and it causes other things to happen when it collides with other bundles. All the little bundles of a certain sort can even be said to be the same bundle, and now I am getting very lost.
    To sum up, the only way to understand lots of modern physics is through the mathematics (which is often just a bit difficult ).
    I go to encounter for the millionth time the reality of experience and to forge in the smithy of my soul the uncreated conscience of my race.

    Windows XP consists of 32 bit extensions and a graphical shell for a 16 bit patch to an 8 bit operating system originally coded for a 4 bit microprocessor, written by a 2 bit company, that can't stand 1 bit of competition.

  3. #93
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    >Yes, you can have two infinite numbers and one can be larger than the other.<

    Unless you're talking about infinitely repeating numbers (i.e. 0.1...), how can infinity be larger than itself?

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    from the book i'm reading "the grip of gravity" which is a very in-depth serious book, "Minkowski space-time is rigidly flat", by which they mean 'flat' in the sense of "the sum of the motions in the 4 dimensions is always constant". ie Euclidean.
    "minkowski space-time interval is really an expression of the pythagoras theorem in 4 dimensional euclidean geaometry"

    but thats as far as i'd got, i didn't read far enough into the book !!!

    mass curves the continuum so its not flat, the general theory of relativity maintains the 4 D space-time continuum as the geometrical framework in which the laws of nature are to be stated, like the example of the particles life being altered...all that stuff still is valid, but mass curves the space-time into a non-euclidean form....so as i understand it, u use minkowski model as the framework, then adjust for effects of large mass causing the warping.....

    away from large mass, it would apply, and it still always applies locally(such as small sections of a sphere appear planar). so it applies to experiments taking place on earth, but not say interstellar events.....

    i think...

  5. #95
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    why am i always pooping out lately??????
    that was little me.....

    btw isn't thinking of particles as packets of energy a good way to start ?? i guess thats too simplistic later....

    it also would seem that in fact the warping of space-time is not actually proven yet (i thought it was generally accepted), quantum theory of gravity is explaining graVITY using the graviton particle instead of einsteins theories about the warping of space-time, so in that case wouldn't the flat space-time thing be true ???? can't it be tested experimentally ???

    but up to now experiments are found to agree with Einstein, so i believe him.....its certainly far more elegant and understandable..
    Steve

  6. #96
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    "You last statement (the one about how infinities can cancel out) is incorrect, because even in topological space, the infinite object cannot be operated upon in the same fashion as the real set"

    No Fyodor, it is not incorrect, MANY of my quantum mechanics lecturers have mentioned infinities cancelling out, Stephen Hawking also mentions infinities "cancelling out" several times in BOTH his books.

    "When someone writes '1/infinity=0' you are not really dividing one by infinity. Instead, it is a statement dealing with the series 1/1,1/2,1/3,1/4...and saying that it converges to 0. Your example 200/infinity is exactly the same. "

    I'm well aware of that, both 1/infinity and 200/infinity converge to zero BUT 1/infinity converges faster hence it can be thought of as a "smaller" infinitely small number than 200/infinity. And contrary to your nonsense infinitely small numbers and infinitely large numbers CAN cancel out when multiplied together and yield constants.

    "Your integration example is also faulty. To the extent that is meaningful to integrate any function with an infinite limit (improper integration), the result of integrating y=x from 0 to infinity is nonexistent, because it is divergent."

    You integrate between 0 and infinity ALL the time, what are you talking about? The result of integrating y = x from zero to infinity is infinity; its hardly a difficult calculation.
    Last edited by Clyde; 05-22-2002 at 11:48 AM.

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    MANY of my quantum mechanics lecturers have mentioned infinities cancelling out, Stephen Hawking also mentions infinities "cancelling out" several times in BOTH his books.
    My God. The phrase "cancellation of infinities" is used simply because many can't understand the theory, so physicists try to make it simple. The quantities called "infinities" are really only limits. They can be swept under the rug, so to speak, because we are and must be fairly ignorant of the manner in which the electron interacts with itself. As long as we have some sort of measurement, or regularization, we can toss away the inconveniences pretty easily in most cases. Basically, this is oversimplified renormalization. It is just a way to account for the differences in the properties of electrons as would be found by a simple lagrange and the actual physical properties that we measure. This is a rather confusing topic, and I'm not sure if I can explain it more clearly. Most of the textbooks contain mathematics that is probably too complex for here.

    I'm well aware of that, both 1/infinity and 200/infinity converge to zero BUT 1/infinity converges faster hence it can be thought of as a "smaller" infinitely small number than 200/infinity. And contrary to your nonsense infinitely small numbers and infinitely large numbers CAN cancel out when multiplied together and yield constants
    Actually, 1/inf and 200/inf converge at exactly the same rate. It's very basic calculus. And I repeat, since the limit of both is zero, they are exactly the same value. As a simple test, my calculator returns 'true' to the boolean test '2/inf=200/inf'. Now let me think about how to ram this into your brain. My 'nonsense' is a mathematical fact. Did you even read the point about considering infinity in the context of a number system, cantorian sets, and topological space? You are obviously using it in the sense of a number system, due to your usage of 'multiply.' Read this part carefully, for it is very important: Infinity is nonexistent in the context of number systems. Do you understand that? It is not an object, it is rather a process. Go back a while and look in any precalculus textbook. The above will be in there, for the most part.

    You integrate between 0 and infinity ALL the time, what are you talking about? The result of integrating y = x from zero to infinity is infinity; its hardly a difficult calculation.
    True, one may integrate between 0 and infinity, but there is only a meaningful result when it converges to a number. The result of integrating y=x from 0 to infinity is nonexistent/undefined/null set, whatever notation you care to use. However, for a change you are correct-it is hardly a difficult to calculation (for most peoppe having taken a year of calculus, at least).
    I go to encounter for the millionth time the reality of experience and to forge in the smithy of my soul the uncreated conscience of my race.

    Windows XP consists of 32 bit extensions and a graphical shell for a 16 bit patch to an 8 bit operating system originally coded for a 4 bit microprocessor, written by a 2 bit company, that can't stand 1 bit of competition.

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    *pulls up chair and a bag of popcorn*

    I love these sort of debates...

  9. #99
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    "The phrase "cancellation of infinities" is used simply because many can't understand the theory, so physicists try to make it simple. The quantities called "infinities" are really only limits. They can be swept under the rug, so to speak, because we are and must be fairly ignorant of the manner in which the electron interacts with itself."

    It has nothing to do with simplifications in electron modelling;

    If you multiply an infinitely large number by an infinitely small number you get a constant, hence the infinities "cancel out", you can argue nonsense semantics all you like, but it makes little difference; an infitely large "number" can turn up as the result of a calculation and it can be cancelled out by multiplying it by an infinitely small "number".

    "Actually, 1/inf and 200/inf converge at exactly the same rate"

    That's funny because the physics professor didn't seem to think so, but hey what the hell does he know right?

    "As a simple test, my calculator returns 'true' to the boolean test '2/inf=200/inf'."

    ROFL, it must be true then! Just out of interest how do you input infinity into your calculator?

    "Read this part carefully, for it is very important: Infinity is nonexistent in the context of number systems. Do you understand that? It is not an object, it is rather a process. Go back a while and look in any precalculus textbook. The above will be in there, for the most part. "

    I know full well infinity is infact a series, but you can treat it as if it were a number, physicists do so often. It might well be a simplification but it a valid one, if you are claiming the contrary then I guess all those physicists must be wrong eh?

    "The result of integrating y=x from 0 to infinity is nonexistent/undefined/null set"

    It's infinity. The area under a 1/x^2 curve is a constant, the area under a y = x line is infinite, but a "different" infinity to the area under a y = 2x line.
    Last edited by Clyde; 05-23-2002 at 11:46 AM.

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    It has nothing to do with simplifications in electron modelling;
    Do you know anything at all? Renormailzation is an essential technique in QED.

    If you multiply an infinitely large number by an infinitely small number you get a constant, hence the infinities "cancel out", you can argue nonsense semantics all you like, but it makes little difference; an infitely large "number" can turn up as the result of a calculation and it can be cancelled out by multiplying it by an infinitely small "number".
    So inf/2 multiplied by 2/inf is equal to 1? And that is a good way of replying, Clyde. Just call it nonsense semantics. I suppose they are nonsense to someone totally incapable of understanding.

    That's funny because the physics professor didn't seem to think so, but hey what the hell does he know right?
    What exactly did your physics professor say? In a fairly rigorous course, the term convergence rate would not even be used for the mentioned description. It is likely that you are ignorant, he mispoke, or you are simply fabricating.

    ROFL, it must be true then! Just out of interest how do you input infinity into your calculator?
    Let me think of how to explain this-it's a very complex process. Try and understand this: you press the key combination represents infinity. Symbolic computation, anyone?

    I know full well infinity is infact a series, but you can treat it as if it were a number, physicists do so often. It might well be a simplification but it a valid one, if you are claiming the contrary then I guess all those physicists must be wrong eh?
    It is not a series. It simply means "this function increases for [a,b] and does not have a max on [a,b]. You are obviously ignorant of the basic tenets of mathematics. The physicists are not wrong-you are.
    It's infinity. The area under a 1/x^2 curve is a constant, the area under a y = x line is infinite, but a "different" infinity to the area under a y = 2x line.
    The concept of area does not work very well when the function to be integrated is infinite and divergent. A difficult fact.
    I go to encounter for the millionth time the reality of experience and to forge in the smithy of my soul the uncreated conscience of my race.

    Windows XP consists of 32 bit extensions and a graphical shell for a 16 bit patch to an 8 bit operating system originally coded for a 4 bit microprocessor, written by a 2 bit company, that can't stand 1 bit of competition.

  11. #101
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    "Do you know anything at all? Renormailzation is an essential technique in QED. "

    Renormalisation? Do you mean Normalisation? As in normalising the wavefunction, because i've done that plenty of times, in lab, and in workshops and I can tell you none of my calculations have involved infinity. Tell me what "renormalisation" is.

    I'm not saying that whatever this process is it doesnt involve infinity, i'm saying there are plenty of times when my lecturers have mentioned infinities "cancelling out" when they were clearly not reffering to your "renormalisation"

    "So inf/2 multiplied by 2/inf is equal to 1"

    If both inf's are equal then yes.

    "Just call it nonsense semantics. I suppose they are nonsense to someone totally incapable of understanding"

    Yea, i'm totally incapable of understanding, thats why i came top of my year in quantum mechanics, and hell both my physics flat mates (who both came in the top ten of their year) they must be "totally incapable" too, oh yea and my professors, they are an "incapable" bunch, thank God we have you Fyodor......

    "What exactly did your physics professor say?"

    My physics professor said you had "different" infinities, and that you could think of them as approaching limits faster, I don't remember word for word, but that was the gist of it.

    It's very easy to understand fyodor, take my y = x line, integrate it between 0 and infinity, the answer is infinity, take y = 2x integrate it between 0 and infinity, the answer is also infinity but the second one is getting larger "quicker", for any value of X, the area under y = 2x is larger.

    "Try and understand this: you press the key combination represents infinity. Symbolic computation, anyone? "

    And how exactly does the calculator compute infinity?

    "It is not a series. It simply means "this function increases for [a,b] and does not have a max on [a,b]. You are obviously ignorant of the basic tenets of mathematics. The physicists are not wrong-you are. "

    I was merely reffering to your:

    "Instead, it is a statement dealing with the series 1/1,1/2,1/3,1/4...and saying that it converges to 0"

    The point remains that you can treat it as if it were a number, thats what i've been repeatedly told. IE. you can imagine there is a real number at which y = 0, that number is infinity.

    "The concept of area does not work very well when the function to be integrated is infinite and divergent"

    You're having problems with the concept of area!!? .... The concept of area is so simple most people understand it by the age of about 9.... most people....

    This whole debate sprung from your idiotic statement claiming you could not apply probability given an infinite number of possiblilities, let me help you:

    The probability of picking one sock at random from 2, is 1/2, the probability of picking one sock at random from 5 is 1/5, the probability of picking one sock at random from 200 is 1/200,

    Getting the picture here? As you increase the number of possiblities you decrease the probability, in fact its a simple 1/x curve! At an infinite value of X, Y = 0, too hard to grasp? Are ya struggling there with this concept? Or perhaps you disagree, perhaps you don't think that y = 0 at an infinite value of x...... lol.

    This whole debate over your inability to grasp a simple 1/x curve, *sigh*.
    Last edited by Clyde; 05-24-2002 at 05:04 PM.

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