Re: [agi] Shhh!
I meant I am able to construct an algorithm that is capable of reaching every expansion of a real number given infinite resources. However, the algorithm is never able to write any of them completely since they are all infinite. So in one sense, no computation is able to write any real number, but in the other sense, the program will, given enough time, eventually start writing out any real number. Since the infinite must be an ongoing process I can say that the algorithm is capable of reaching any real number although it will never complete any of them. Jim Bromer --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
Re: [agi] Shhh!
for {set i 0} {$i infinity} {incr i} {
print $i
}
On Mon, Aug 2, 2010 at 6:23 PM, Jim Bromer jimbro...@gmail.com wrote:
I can write an algorithm that is capable of describing ('reaching') every
possible irrational number - given infinite resources. The infinite is not
a number-like object, it is an active form of incrementation or
concatenation. So I can write an algorithm that can write *every* finite
state of *every* possible number. However, it would take another
algorithm to 'prove' it. Given an irrational number, this other algorithm
could find the infinite incrementation for every digit of the given number.
Each possible number (including the incrementation of those numbers that
cannot be represented in truncated form) is embedded within a single
infinite infinite incrementation of digits that is produced by the
algorithm, so the second algorithm would have to calculate where you would
find each digit of the given irrational number by increment. But the thing
is, both functions would be computable and provable. (I haven't actually
figured the second algorithm out yet, but it is not a difficult problem.)
This means that the Trans-Infinite Is Computable. But don't tell anyone
about this, it's a secret.
*agi* | Archives https://www.listbox.com/member/archive/303/=now
https://www.listbox.com/member/archive/rss/303/ |
Modifyhttps://www.listbox.com/member/?;Your Subscription
http://www.listbox.com
--
cheers,
Deepak
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
RSS Feed: https://www.listbox.com/member/archive/rss/303/
Modify Your Subscription:
https://www.listbox.com/member/?member_id=8660244id_secret=8660244-6e7fb59c
Powered by Listbox: http://www.listbox.com
Re: [agi] Shhh!
On Tue, Aug 3, 2010 at 3:34 AM, deepakjnath deepakjn...@gmail.com wrote:
for {set i 0} {$i infinity} {incr i} {
print $i
}
That's the basic idea, except there are one and a half axes, positive
integers, negative integers and fractional parts for all possible irrational
numbers. (Well it is two axes but two parts one from one of the axes can be
joined together. Positive increments of integers with positive increments
of fractional parts, and then just take the negative of each value to output
negative increments with negative increments of the fractional parts.
So it's not rocket science but it was a little more difficult than counting
to infinity (which is of course is itself impossible!)
Jim Bromer
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
RSS Feed: https://www.listbox.com/member/archive/rss/303/
Modify Your Subscription:
https://www.listbox.com/member/?member_id=8660244id_secret=8660244-6e7fb59c
Powered by Listbox: http://www.listbox.com
[agi] Shhh!
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.
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
RSS Feed: https://www.listbox.com/member/archive/rss/303/
Modify Your Subscription:
https://www.listbox.com/member/?member_id=8660244id_secret=8660244-6e7fb59c
Powered by Listbox: http://www.listbox.com
Re: [agi] Shhh!
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.
*agi* | Archives https://www.listbox.com/member/archive/303/=now
https://www.listbox.com/member/archive/rss/303/ |
Modifyhttps://www.listbox.com/member/?;Your Subscription
http://www.listbox.com
--
Abram Demski
http://lo-tho.blogspot.com/
http://groups.google.com/group/one-logic
---
agi
Archives: https://www.listbox.com/member/archive/303/=now
RSS Feed: https://www.listbox.com/member/archive/rss/303/
Modify Your Subscription:
https://www.listbox.com/member/?member_id=8660244id_secret=8660244-6e7fb59c
Powered by Listbox: http://www.listbox.com
Re: [agi] Shhh!
Abram Wrote: 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.) That is a very nice description of AI research and the pitfalls we come across in our quest. :) Dave --- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
