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Relativity and the Counting Process

  1. Oct 27, 2004 #1
    I refer you to a proposal about the finiteness of the integers: http://paulandellen.com/essays/essay089.htm

    How could this be? Everyone has assumed that the integers are infinite, yet a proof can be give to illustrate otherwise. Firstly we will use the characters necessary for expression of the integers in various ways: we will use the 26 letters of the alphabet along with the 10 numerals and will also throw in commas, spaces, !,^,etc, to get a collection of 50 or less characters.

    Ramanujan of whom it was said, "Every positive integer was his personal friend," was asked how he arrived at a hospital, and he answered that he came by cab #65. He was told that 65 was a "very ordinary number," but Ramanujan, said that this was not true:

    "65 is the smallest number that can be express as the sum of two squares in two different ways."

    That, of course, illustrates that 65 has more than one name, just as 2 could be referred to as, "The smallest even integer, " or "The largest integer less than three."

    Now, it has been assumed that the integers are infinite, but we will show there is an upper limit to counting, which indicates that the counting process slows down and finally reaches an upper limit, similar to that for velocity as shown by Dr. Einstein. (This is actually not all that surprising, since Relativity prevades the physical world, there is no reason not to suppose it would also effect counting, which is extrapolated from physical objects.)

    Theorem: Every integer is expressible is less than 50^37 characters. Proof, by contradiction: If there is a integer that can not so be expressed, then there is a least such integer, that number is:

    "The least integer not expressible in 50^53 characters."

    But the number is so expressed! Thus the matter is proven and the only way to reconcile this with our process of counting is to realize that as we near 50^53, the counting processes continually slow down and eventually even stop. But this is not realizable to the counter, who is mislead by a process now classified as "number dilation." This process has frequently been confused with the fact that as the digits grow, the number takes more and more time, in general, to utter; but "number dilation" is now realized to be an entirely distinct phenomena.
    Last edited: Oct 27, 2004
  2. jcsd
  3. Oct 27, 2004 #2


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    I have a better bound. :smile: Every positive integer can be expressed in 9 words! Assume otherwise; the smallest such counterexample would then be expressed as:

    "The smallest positive integer not expressable in nine words."

    Which, of course, is an expression of that integer in 9 words!

    The fallacy here is similar to the liar's paradox: "This statement is false". Freedom of self-reference is bad for logic, and mathematical logic is strictly tiered so that it is not possible.
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