Jim,
:) Looks to me like you are developing your own internally consistent
mathematics without worrying about relating it back to the standard stuff.
(How do you define the result of running a program continuum long? Is the
result unique?) This is great, but it might be worth your while to later
come back to basic computability theory and see if/how you can present your
ideas as an extension of it.
Whenever I have done this, I've later found out that whatever-great-idea has
already been thought of (but with very different terminology, of course). I
take this as evidence that there is a very strong "mental landscape"... if
you go in a particular direction there is a natural series of landmarks,
including both great ideas and pitfalls that everyone runs into. (Different
people take different amounts of time to climb out of the pitfalls, though.
Some may keep looking for gold at a dead end for a long time.)
--Abram
On Mon, Aug 2, 2010 at 8:53 AM, Jim Bromer <jimbro...@gmail.com> wrote:
> I can write an algorithm that is capable of describing ('reaching') every
> possible irrational number - given infinite resources. The infinite is not
> a number-like object, it is an active form of incrementation or
> concatenation. So I can write an algorithm that can write *every* finite
> state of *every* possible number. However, it would take another
> algorithm to 'prove' it. Given an irrational number, this other algorithm
> could find the infinite incrementation for every digit of the given number.
> Each possible number (including the incrementation of those numbers that
> cannot be represented in truncated form) is embedded within a single
> infinite infinite incrementation of digits that is produced by the
> algorithm, so the second algorithm would have to calculate where you would
> find each digit of the given irrational number by increment. But the thing
> is, both functions would be computable and provable. (I haven't actually
> figured the second algorithm out yet, but it is not a difficult problem.)
>
> This means that the Trans-Infinite Is Computable. But don't tell anyone
> about this, it's a secret.
>
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--
Abram Demski
http://lo-tho.blogspot.com/
http://groups.google.com/group/one-logic
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