I meant transfinite. Thank you for correcting me on that. However,
your suggestion to post when I actually solve the problem is one of the most
absurd comments I have ever seen in these groups given the absolute
necessity of posting about AI-related ideas that have yet to be solved, and
especially given your own history of posting about unverifiable conjectures
as if they were absolute truths.
I thought that it would be impossible to use a single computer program to
iterate every irrational number even if given infinite resources because the
irrationals are considered to be transfinite. However, I found a way to do
it. What really surprised me was that I also found an abbreviated method to
do it. (And there may also be a super-abbreviated method that would look
humorously absurd.) However, there are four issues. One is that the
algorithm obviously will not make much progress, two is that the algorithm
can only output an infinity of finite representations, three the algorithm
has no known use and four is that the algorithm has one error. It cannot
recognize that all binary numbers that have a fractional part .111(followed
by infinite ones) is equal to 1, or .999 (followed by infinite 9s) in for
decimal numbers is equal to 1.
However, the theoretical problem, while not directly related to AGI, is
interesting enough to make it worthwhile. And I believe that there is a
chance that I might be able to use it to solve an important problem, but
that is purely speculative.
Jim Bromer
On Mon, Aug 2, 2010 at 4:12 PM, Matt Mahoney matmaho...@yahoo.com wrote:
Jim, you are thinking out loud. There is no such thing as
trans-infinite. How about posting when you actually solve the problem.
-- Matt Mahoney, matmaho...@yahoo.com
--
*From:* Jim Bromer jimbro...@gmail.com
*To:* agi agi@v2.listbox.com
*Sent:* Mon, August 2, 2010 9:06:53 AM
*Subject:* [agi] Re: Shhh!
I think I can write an abbreviated version, but there would only be a few
people in the world who would both believe me and understand why it would
work.
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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