Re: [agi] How do we Score Hypotheses?
On Tue, Jul 13, 2010 at 9:05 PM, Jim Bromer jimbro...@gmail.com wrote: Even if you refined your model until it was just right, you would have only caught up to everyone else with a solution to a narrow AI problem. I did not mean that you would just have a solution to a narrow AI problem, but that your solution, if put in the form of scoring of points on the basis of the observation *of definitive* events, would constitute a narrow AI method. The central unsolved problem, in my view, is: How can hypotheses be conceptually integrated along with the observable definitive events of the problem to form good explanatory connections that can mesh well with other knowledge about the problem that is considered to be reliable. The second problem is finding efficient ways to represent this complexity of knowledge so that the program can utilize it efficiently. --- 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] How do we Score Hypotheses?
What do you mean by definitive events? I guess the first problem I see with my approach is that the movement of the window is also a hypothesis. I need to analyze it in more detail and see how the tree of hypotheses affects the hypotheses regarding the es on the windows. What I believe is that these problems can be broken down into types of hypotheses, types of events and types of relationships. then those types can be reasoned about in a general way. If possible, then you have a method for reasoning about any object that is covered by the types of hypotheses, events and relationships that you have defined. How to reason about specific objects should not be preprogrammed. But, I think the solution to this part of AGI is to find general ways to reason about a small set of concepts that can be combined to describe specific objects and situations. There are other parts to AGI that I am not considering yet. I believe the problem has to be broken down into separate pieces and understood before putting it back together into a complete system. I have not covered inductive learning for example, which would be an important part of AGI. I have also not yet incorporated learned experience into the algorithm, which is also important. The general AI problem is way too complicated to consider all at once. I simply can't solve hypothesis generation, comparison and disambiguation while at the same time solving induction and experience-based reasoning. It becomes unwieldly. So, I'm starting where I can and I'll work my way up to the full complexity of the problem. I don't really understand what you mean here: The central unsolved problem, in my view, is: How can hypotheses be conceptually integrated along with the observable definitive events of the problem to form good explanatory connections that can mesh well with other knowledge about the problem that is considered to be reliable. The second problem is finding efficient ways to represent this complexity of knowledge so that the program can utilize it efficiently. You also might want to include concrete problems to analyze for your central problem suggestions. That would help define the problem a bit better for analysis. Dave On Wed, Jul 14, 2010 at 8:30 AM, Jim Bromer jimbro...@gmail.com wrote: On Tue, Jul 13, 2010 at 9:05 PM, Jim Bromer jimbro...@gmail.com wrote: Even if you refined your model until it was just right, you would have only caught up to everyone else with a solution to a narrow AI problem. I did not mean that you would just have a solution to a narrow AI problem, but that your solution, if put in the form of scoring of points on the basis of the observation *of definitive* events, would constitute a narrow AI method. The central unsolved problem, in my view, is: How can hypotheses be conceptually integrated along with the observable definitive events of the problem to form good explanatory connections that can mesh well with other knowledge about the problem that is considered to be reliable. The second problem is finding efficient ways to represent this complexity of knowledge so that the program can utilize it efficiently. *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 --- 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] What is the smallest set of operations that can potentially define everything and how do you combine them ?
Actually, Fibonacci numbers can be computed without loops or recursion.
int fib(int x) {
return round(pow((1+sqrt(5))/2, x)/sqrt(5));
}
unless you argue that loops are needed to compute sqrt() and pow().
The brain and DNA use redundancy and parallelism and don't use loops because
their operations are slow and unreliable. This is not necessarily the best
strategy for computers because computers are fast and reliable but don't have a
lot of parallelism.
-- Matt Mahoney, matmaho...@yahoo.com
- Original Message
From: Michael Swan ms...@voyagergaming.com
To: agi agi@v2.listbox.com
Sent: Wed, July 14, 2010 12:18:40 AM
Subject: Re: [agi] What is the smallest set of operations that can potentially
define everything and how do you combine them ?
Brain loops:
Premise:
Biological brain code does not contain looping constructs, or the
ability to creating looping code, (due to the fact they are extremely
dangerous on unreliable hardware) except for 1 global loop that fires
about 200 times a second.
Hypothesis:
Brains cannot calculate iterative problems quickly, where calculations
in the previous iteration are needed for the next iteration and, where
brute force operations are the only valid option.
Proof:
Take as an example, Fibonacci numbers
http://en.wikipedia.org/wiki/Fibonacci_number
What are the first 100 Fibonacci numbers?
int Fibonacci[102];
Fibonacci[0] = 0;
Fibonacci[1] = 1;
for(int i = 0; i 100; i++)
{
// Getting the next Fibonacci number relies on the previous values
Fibonacci[i+2] = Fibonacci[i] + Fibonacci[i+1];
}
My brain knows the process to solve this problem but it can't directly
write a looping construct into itself. And so it solves it very slowly
compared to a computer.
The brain probably consists of vast repeating look-up tables. Of course,
run in parallel these seem fast.
DNA has vast tracks of repeating data. Why would DNA contain repeating
data, instead of just having the data once and the number of times it's
repeated like in a loop? One explanation is that DNA can't do looping
construct either.
On Wed, 2010-07-14 at 02:43 +0100, Mike Tintner wrote:
Michael: We can't do operations that
require 1,000,000 loop iterations. I wish someone would give me a PHD
for discovering this ;) It far better describes our differences than any
other theory.
Michael,
This isn't a competitive point - but I think I've made that point several
times (and so of course has Hawkins). Quite obviously, (unless you think the
brain has fabulous hidden powers), it conducts searches and other operations
with extremely few limited steps, and nothing remotely like the routine
millions to billions of current computers. It must therefore work v.
fundamentally differently.
Are you saying anything significantly different to that?
--
From: Michael Swan ms...@voyagergaming.com
Sent: Wednesday, July 14, 2010 1:34 AM
To: agi agi@v2.listbox.com
Subject: Re: [agi] What is the smallest set of operations that can
potentially define everything and how do you combine them ?
On Tue, 2010-07-13 at 07:00 -0400, Ben Goertzel wrote:
Well, if you want a simple but complete operator set, you can go with
-- Schonfinkel combinator plus two parentheses
I'll check this out soon.
or
-- S and K combinator plus two parentheses
and I suppose you could add
-- input
-- output
-- forget
statements to this, but I'm not sure what this gets you...
Actually, adding other operators doesn't necessarily
increase the search space your AI faces -- rather, it
**decreases** the search space **if** you choose the right operators,
that
encapsulate regularities in the environment faced by the AI
Unfortunately, an AGI needs to be absolutely general. You are right that
higher level concepts reduce combinations, however, using them, will
increase combinations for simpler operator combinations, and if you
miss a necessary operator, then some concepts will be impossible to
achieve. The smallest set can define higher level concepts, these
concepts can be later integrated as single operations, which means
using operators than can be understood in terms of smaller operators
in the beginning, will definitely increase you combinations later on.
The smallest operator set is like absolute zero. It has a defined end. A
defined way of finding out what they are.
Exemplifying this, writing programs doing humanly simple things
using S and K is a pain and involves piling a lot of S and K and
parentheses
on top of each other, whereas if we introduce loops and conditionals and
such, these programs get shorter. Because loops and conditionals happen
to match the stuff that our human-written programs need to do...
Loops are evil in most situations.
Let me show you why:
Draw a square using put_pixel(x,y)
// loops are more scalable, but, damage this code
[agi] Comments On My Skepticism of Solomonoff Induction
Last week I came up with a sketch that I felt showed that Solomonoff Induction was incomputable *in practice* using a variation of Cantor's Diagonal Argument. I wondered if my argument made sense or not. I will explain why I think it did. First of all, I should have started out by saying something like, Suppose Solomonoff Induction was computable, since there is some reason why people feel that it isn't. Secondly I don't think I needed to use Cantor's Diagonal Argument (for the *in practice* case), because it would be sufficient to point out that since it was impossible to say whether or not the probabilities ever approached any sustained (collared) limits due to the lack of adequate mathematical definition of the concept all programs, it would be impossible to make the claim that they were actual representations of the probabilities of all programs that could produce certain strings. But before I start to explain why I think my variation of the Diagonal Argument was valid, I would like to make another comment about what was being claimed. Take a look at the n-ary expansion of the square root of 2 (such as the decimal expansion or the binary expansion). The decimal expansion or the binary expansion of the square root of 2 is an infinite string. To say that the algorithm that produces the value is predicting the value is a torturous use of meaning of the word 'prediction'. Now I have less than perfect grammar, but the idea of prediction is so important in the field of intelligence that I do not feel that this kind of reduction of the concept of prediction is illuminating. Incidentally, There are infinite ways to produce the square root of 2 (sqrt 2 +1-1, sqrt2 +2-2, sqrt2 +3-3,...). So the idea that the square root of 2 is unlikely is another stretch of conventional thinking. But since there are an infinite ways for a program to produce any number (that can be produced by a program) we would imagine that the probability that one of the infinite ways to produce the square root of 2 approaches 0 but never reaches it. We can imagine it, but we cannot prove that this occurs in Solomonoff Induction because Solomonoff Induction is not limited to just this class of programs (which could be proven to approach a limit). For example, we could make a similar argument for any number, including a 0 or a 1 which would mean that the infinite string of digits for the square root of 2 is just as likely as the string 0. But the reason why I think a variation of the diagonal argument can work in my argument is that since we cannot prove that the infinite computations of the probabilities that a -program will produce a string- will ever approach a limit, to use the probabilities reliably (even as an infinite theoretical method) we would have to find some way to rearrange the computations of the probabilities so that they could. While the number of ways to rearrange the ordering of a finite number of things is finite no matter how large the number is, the number of possible ways to rearrange an infinite number of things is infinite. I believe that this problem of finding the right rearrangement of an infinite list of computations of values after the calculation of the list is finished qualifies for an infinite to infinite diagonal argument. I want to add one more thing to this in a few days. 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] Comments On My Skepticism of Solomonoff Induction
Jim Bromer wrote: Last week I came up with a sketch that I felt showed that Solomonoff Induction was incomputable in practice using a variation of Cantor's Diagonal Argument. Cantor proved that there are more sequences (infinite length strings) than there are (finite length) strings, even though both sets are infinite. This means that some, but not all, sequences have finite length descriptions or are the output of finite length programs (which is the same thing in a more formal sense). For example, the digits of pi or sqrt(2) are infinite length sequences that have finite descriptions (or finite programs that output them). There are many more sequences that don't have finite length descriptions, but unfortunately I can't describe any of them except to say they contain infinite amounts of random data. Cantor does not prove that Solomonoff induction is not computable. That was proved by Kolmogorov (and also by Solomonoff). Solomonoff induction says to use the shortest program that outputs the observed sequence to predict the next symbol. However, there is no procedure for finding the length of the shortest description. The proof sketch is that if there were, then I could describe the first string that cannot be described in less than a million bits even though I just did. The formal proof is http://en.wikipedia.org/wiki/Kolmogorov_complexity#Incomputability_of_Kolmogorov_complexity I think your confusion is using the uncomputability of Solomonoff induction to question its applicability. That is an experimental question, not one of mathematics. The validity of using the shortest or simplest explanation of the past to predict the future was first observed by William of Ockham in the 1400's. It is standard practice in all fields of science. The minimum description length principle is applicable to all branches of machine learning. However, in the conclusion of http://mattmahoney.net/dc/dce.html#Section_Conclusion I argue for Solomonoff induction on the basis of physics. Solomonoff induction supposes that all observable strings are finite prefixes of computable sequences. Occam's Razor might not hold if it were possible for the universe to produce uncomputable sequences, i.e. infinite sources of random data. I argue that is not possible because the observable universe if finitely computable according to the laws of physics as they are now understood. -- Matt Mahoney, matmaho...@yahoo.com From: Jim Bromer jimbro...@gmail.com To: agi agi@v2.listbox.com Sent: Wed, July 14, 2010 11:29:13 AM Subject: [agi] Comments On My Skepticism of Solomonoff Induction Last week I came up with a sketch that I felt showed that Solomonoff Induction was incomputable in practice using a variation of Cantor's Diagonal Argument. I wondered if my argument made sense or not. I will explain why I think it did. First of all, I should have started out by saying something like, Suppose Solomonoff Induction was computable, since there is some reason why people feel that it isn't. Secondly I don't think I needed to use Cantor's Diagonal Argument (for the in practice case), because it would be sufficient to point out that since it was impossible to say whether or not the probabilities ever approached any sustained (collared) limits due to the lack of adequate mathematical definition of the concept all programs, it would be impossible to make the claim that they were actual representations of the probabilities of all programs that could produce certain strings. But before I start to explain why I think my variation of the Diagonal Argument was valid, I would like to make another comment about what was being claimed. Take a look at the n-ary expansion of the square root of 2 (such as the decimal expansion or the binary expansion). The decimal expansion or the binary expansion of the square root of 2 is an infinite string. To say that the algorithm that produces the value is predicting the value is a torturous use of meaning of the word 'prediction'. Now I have less than perfect grammar, but the idea of prediction is so important in the field of intelligence that I do not feel that this kind of reduction of the concept of prediction is illuminating. Incidentally, There are infinite ways to produce the square root of 2 (sqrt 2 +1-1, sqrt2 +2-2, sqrt2 +3-3,...). So the idea that the square root of 2 is unlikely is another stretch of conventional thinking. But since there are an infinite ways for a program to produce any number (that can be produced by a program) we would imagine that the probability that one of the infinite ways to produce the square root of 2 approaches 0 but never reaches it. We can imagine it, but we cannot prove that this occurs in Solomonoff Induction because Solomonoff Induction is not limited to just this class of programs (which could be proven to approach a limit). For example, we could make a
Re: [agi] How do we Score Hypotheses?
Actually, I just realized that there is a way to included inductive knowledge and experience into this algorithm. Inductive knowledge and experience about a specific object or object type can be exploited to know which hypotheses in the past were successful, and therefore which hypothesis is most likely. By choosing the most likely hypothesis first, we skip a lot of messy hypothesis comparison processing and analysis. If we choose the right hypothesis first, all we really have to do is verify that this hypothesis reveals in the data what we expect to be there. If we confirm what we expect, that is reason enough not to look for other hypotheses because the data is explained by what we originally believed to be likely. We only look for additional hypotheses when we find something unexplained. And even then, we don't look at the whole problem. We only look at what we have to to explain the unexplained data. In fact, we could even ignore the unexplained data if we believe, from experience, that it isn't pertinent. I discovered this because I'm analyzing how a series of hypotheses are navigated when analyzing images. It seems to me that it is done very similarly to way we do it. We sort of confirm what we expect and try to explain what we don't expect. We try out hypotheses in a sort of trial and error manor and see how each hypothesis affects what we find in the image. If we confirm things because of the hypothesis, we are likely to keep it. We keep going, navigating the tree of hypotheses, conflicts and unexpected observations until we find a good hypothesis. Something like that. I'm attempting to construct an algorithm for doing this as I analyze specific problems. Dave On Wed, Jul 14, 2010 at 10:22 AM, David Jones davidher...@gmail.com wrote: What do you mean by definitive events? I guess the first problem I see with my approach is that the movement of the window is also a hypothesis. I need to analyze it in more detail and see how the tree of hypotheses affects the hypotheses regarding the es on the windows. What I believe is that these problems can be broken down into types of hypotheses, types of events and types of relationships. then those types can be reasoned about in a general way. If possible, then you have a method for reasoning about any object that is covered by the types of hypotheses, events and relationships that you have defined. How to reason about specific objects should not be preprogrammed. But, I think the solution to this part of AGI is to find general ways to reason about a small set of concepts that can be combined to describe specific objects and situations. There are other parts to AGI that I am not considering yet. I believe the problem has to be broken down into separate pieces and understood before putting it back together into a complete system. I have not covered inductive learning for example, which would be an important part of AGI. I have also not yet incorporated learned experience into the algorithm, which is also important. The general AI problem is way too complicated to consider all at once. I simply can't solve hypothesis generation, comparison and disambiguation while at the same time solving induction and experience-based reasoning. It becomes unwieldly. So, I'm starting where I can and I'll work my way up to the full complexity of the problem. I don't really understand what you mean here: The central unsolved problem, in my view, is: How can hypotheses be conceptually integrated along with the observable definitive events of the problem to form good explanatory connections that can mesh well with other knowledge about the problem that is considered to be reliable. The second problem is finding efficient ways to represent this complexity of knowledge so that the program can utilize it efficiently. You also might want to include concrete problems to analyze for your central problem suggestions. That would help define the problem a bit better for analysis. Dave On Wed, Jul 14, 2010 at 8:30 AM, Jim Bromer jimbro...@gmail.com wrote: On Tue, Jul 13, 2010 at 9:05 PM, Jim Bromer jimbro...@gmail.com wrote: Even if you refined your model until it was just right, you would have only caught up to everyone else with a solution to a narrow AI problem. I did not mean that you would just have a solution to a narrow AI problem, but that your solution, if put in the form of scoring of points on the basis of the observation *of definitive* events, would constitute a narrow AI method. The central unsolved problem, in my view, is: How can hypotheses be conceptually integrated along with the observable definitive events of the problem to form good explanatory connections that can mesh well with other knowledge about the problem that is considered to be reliable. The second problem is finding efficient ways to represent this complexity of knowledge so that the program can utilize it efficiently. *agi* |
Re: [agi] Comments On My Skepticism of Solomonoff Induction
Jim, There is a simple proof of convergence for the sum involved in defining the probability of a given string in the Solomonoff distribution: At its greatest, a particular string would be output by *all* programs. In this case, its sum would come to 1. This puts an upper bound on the sum. Since there is no subtraction, there is a lower bound at 0 and the sum monotonically increases as we take the limit. Knowing these facts, suppose it *didn't* converge. It must then increase without bound, since it cannot fluctuate back and forth (it can only go up). But this contradicts the upper bound of 1. So, the sum must stop at 1 or below (and in fact we can prove it stops below 1, though we can't say where precisely without the infinite computing power required to compute the limit). --Abram On Wed, Jul 14, 2010 at 11:29 AM, Jim Bromer jimbro...@gmail.com wrote: Last week I came up with a sketch that I felt showed that Solomonoff Induction was incomputable *in practice* using a variation of Cantor's Diagonal Argument. I wondered if my argument made sense or not. I will explain why I think it did. First of all, I should have started out by saying something like, Suppose Solomonoff Induction was computable, since there is some reason why people feel that it isn't. Secondly I don't think I needed to use Cantor's Diagonal Argument (for the *in practice* case), because it would be sufficient to point out that since it was impossible to say whether or not the probabilities ever approached any sustained (collared) limits due to the lack of adequate mathematical definition of the concept all programs, it would be impossible to make the claim that they were actual representations of the probabilities of all programs that could produce certain strings. But before I start to explain why I think my variation of the Diagonal Argument was valid, I would like to make another comment about what was being claimed. Take a look at the n-ary expansion of the square root of 2 (such as the decimal expansion or the binary expansion). The decimal expansion or the binary expansion of the square root of 2 is an infinite string. To say that the algorithm that produces the value is predicting the value is a torturous use of meaning of the word 'prediction'. Now I have less than perfect grammar, but the idea of prediction is so important in the field of intelligence that I do not feel that this kind of reduction of the concept of prediction is illuminating. Incidentally, There are infinite ways to produce the square root of 2 (sqrt 2 +1-1, sqrt2 +2-2, sqrt2 +3-3,...). So the idea that the square root of 2 is unlikely is another stretch of conventional thinking. But since there are an infinite ways for a program to produce any number (that can be produced by a program) we would imagine that the probability that one of the infinite ways to produce the square root of 2 approaches 0 but never reaches it. We can imagine it, but we cannot prove that this occurs in Solomonoff Induction because Solomonoff Induction is not limited to just this class of programs (which could be proven to approach a limit). For example, we could make a similar argument for any number, including a 0 or a 1 which would mean that the infinite string of digits for the square root of 2 is just as likely as the string 0. But the reason why I think a variation of the diagonal argument can work in my argument is that since we cannot prove that the infinite computations of the probabilities that a -program will produce a string- will ever approach a limit, to use the probabilities reliably (even as an infinite theoretical method) we would have to find some way to rearrange the computations of the probabilities so that they could. While the number of ways to rearrange the ordering of a finite number of things is finite no matter how large the number is, the number of possible ways to rearrange an infinite number of things is infinite. I believe that this problem of finding the right rearrangement of an infinite list of computations of values after the calculation of the list is finished qualifies for an infinite to infinite diagonal argument. I want to add one more thing to this in a few days. Jim Bromer *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] What is the smallest set of operations that can potentially define everything and how do you combine them ?
On Wed, 2010-07-14 at 07:48 -0700, Matt Mahoney wrote:
Actually, Fibonacci numbers can be computed without loops or recursion.
int fib(int x) {
return round(pow((1+sqrt(5))/2, x)/sqrt(5));
}
;) I know. I was wondering if someone would pick up on it. This won't
prove that brains have loops though, so I wasn't concerned about the
shortcuts.
unless you argue that loops are needed to compute sqrt() and pow().
I would find it extremely unlikely that brains have *, /, and even more
unlikely to have sqrt and pow inbuilt. Even more unlikely, even if it
did have them, to figure out how to combine them to round(pow((1
+sqrt(5))/2, x)/sqrt(5)).
Does this mean we should discount all maths that use any complex
operations ?
I suspect the brain is full of look-up tables mainly, with some fairly
primitive methods of combining the data.
eg What's 6 / 3 ?
ans = 2 most people would get that because it's been wrote learnt, a
common problem.
What 3456/6 ?
we don't know, at least not from the top of our head.
The brain and DNA use redundancy and parallelism and don't use loops because
their operations are slow and unreliable. This is not necessarily the best
strategy for computers because computers are fast and reliable but don't have
a
lot of parallelism.
The brains slow and unreliable methods I think are the price paid for
generality and innately unreliable hardware. Imagine writing a computer
program that runs for 120 years without crashing and surviving damage
like a brain can. I suspect the perfect AGI program is a rigorous
combination of the 2.
-- Matt Mahoney, matmaho...@yahoo.com
- Original Message
From: Michael Swan ms...@voyagergaming.com
To: agi agi@v2.listbox.com
Sent: Wed, July 14, 2010 12:18:40 AM
Subject: Re: [agi] What is the smallest set of operations that can
potentially
define everything and how do you combine them ?
Brain loops:
Premise:
Biological brain code does not contain looping constructs, or the
ability to creating looping code, (due to the fact they are extremely
dangerous on unreliable hardware) except for 1 global loop that fires
about 200 times a second.
Hypothesis:
Brains cannot calculate iterative problems quickly, where calculations
in the previous iteration are needed for the next iteration and, where
brute force operations are the only valid option.
Proof:
Take as an example, Fibonacci numbers
http://en.wikipedia.org/wiki/Fibonacci_number
What are the first 100 Fibonacci numbers?
int Fibonacci[102];
Fibonacci[0] = 0;
Fibonacci[1] = 1;
for(int i = 0; i 100; i++)
{
// Getting the next Fibonacci number relies on the previous values
Fibonacci[i+2] = Fibonacci[i] + Fibonacci[i+1];
}
My brain knows the process to solve this problem but it can't directly
write a looping construct into itself. And so it solves it very slowly
compared to a computer.
The brain probably consists of vast repeating look-up tables. Of course,
run in parallel these seem fast.
DNA has vast tracks of repeating data. Why would DNA contain repeating
data, instead of just having the data once and the number of times it's
repeated like in a loop? One explanation is that DNA can't do looping
construct either.
On Wed, 2010-07-14 at 02:43 +0100, Mike Tintner wrote:
Michael: We can't do operations that
require 1,000,000 loop iterations. I wish someone would give me a PHD
for discovering this ;) It far better describes our differences than any
other theory.
Michael,
This isn't a competitive point - but I think I've made that point several
times (and so of course has Hawkins). Quite obviously, (unless you think
the
brain has fabulous hidden powers), it conducts searches and other
operations
with extremely few limited steps, and nothing remotely like the routine
millions to billions of current computers. It must therefore work v.
fundamentally differently.
Are you saying anything significantly different to that?
--
From: Michael Swan ms...@voyagergaming.com
Sent: Wednesday, July 14, 2010 1:34 AM
To: agi agi@v2.listbox.com
Subject: Re: [agi] What is the smallest set of operations that can
potentially define everything and how do you combine them ?
On Tue, 2010-07-13 at 07:00 -0400, Ben Goertzel wrote:
Well, if you want a simple but complete operator set, you can go with
-- Schonfinkel combinator plus two parentheses
I'll check this out soon.
or
-- S and K combinator plus two parentheses
and I suppose you could add
-- input
-- output
-- forget
statements to this, but I'm not sure what this gets you...
Actually, adding other operators doesn't necessarily
increase the search space your AI faces -- rather, it
**decreases** the search space **if** you choose the right operators,
that
encapsulate regularities in the
Re: [agi] What is the smallest set of operations that can potentially define everything and how do you combine them ?
Michael Swan wrote:
What 3456/6 ?
we don't know, at least not from the top of our head.
No, it took me about 10 or 20 seconds to get 576. Starting with the first
digit,
3/6 = 1/2 (from long term memory) and 3 is in the thousands place, so 1/2 of
1000 is 500 (1/2 = .5 from LTM). I write 500 into short term memory (STM),
which
only has enough space to hold about 7 digits. Then to divide 45/6 I get 42/6 =
7
with a remainder of 3, or 7.5, but since this is in the tens place I get 75. I
put 75 in STM, add to 500 to get 575, put the result back in STM replacing 500
and 75 for which there is no longer room. Finally, 6/6 = 1, which I add to 575
to get 576. I hold this number in STM long enough to check with a calculator.
One could argue that this calculation in my head uses a loop iterator (in STM)
to keep track of which digit I am working on. It definitely involves a sequence
of instructions with intermediate results being stored temporarily. The brain
can only execute 2 or 3 sequential instructions per second and has very limited
short term memory, so it needs to draw from a large database of rules to
perform
calculations like this. A calculator, being faster and having more RAM, is able
to use simpler but more tedious algorithms such as converting to binary,
division by shift and subtract, and converting back to decimal. Doing this with
a carbon based computer would require pencil and paper to make up for lack of
STM, and it would require enough steps to have a high probability of making a
mistake.
Intelligence = knowledge + computing power. The human brain has a lot of
knowledge. The calculator has less knowledge, but makes up for it in speed and
memory.
-- Matt Mahoney, matmaho...@yahoo.com
- Original Message
From: Michael Swan ms...@voyagergaming.com
To: agi agi@v2.listbox.com
Sent: Wed, July 14, 2010 7:53:33 PM
Subject: Re: [agi] What is the smallest set of operations that can potentially
define everything and how do you combine them ?
On Wed, 2010-07-14 at 07:48 -0700, Matt Mahoney wrote:
Actually, Fibonacci numbers can be computed without loops or recursion.
int fib(int x) {
return round(pow((1+sqrt(5))/2, x)/sqrt(5));
}
;) I know. I was wondering if someone would pick up on it. This won't
prove that brains have loops though, so I wasn't concerned about the
shortcuts.
unless you argue that loops are needed to compute sqrt() and pow().
I would find it extremely unlikely that brains have *, /, and even more
unlikely to have sqrt and pow inbuilt. Even more unlikely, even if it
did have them, to figure out how to combine them to round(pow((1
+sqrt(5))/2, x)/sqrt(5)).
Does this mean we should discount all maths that use any complex
operations ?
I suspect the brain is full of look-up tables mainly, with some fairly
primitive methods of combining the data.
eg What's 6 / 3 ?
ans = 2 most people would get that because it's been wrote learnt, a
common problem.
What 3456/6 ?
we don't know, at least not from the top of our head.
The brain and DNA use redundancy and parallelism and don't use loops because
their operations are slow and unreliable. This is not necessarily the best
strategy for computers because computers are fast and reliable but don't have
a
lot of parallelism.
The brains slow and unreliable methods I think are the price paid for
generality and innately unreliable hardware. Imagine writing a computer
program that runs for 120 years without crashing and surviving damage
like a brain can. I suspect the perfect AGI program is a rigorous
combination of the 2.
-- Matt Mahoney, matmaho...@yahoo.com
- Original Message
From: Michael Swan ms...@voyagergaming.com
To: agi agi@v2.listbox.com
Sent: Wed, July 14, 2010 12:18:40 AM
Subject: Re: [agi] What is the smallest set of operations that can
potentially
define everything and how do you combine them ?
Brain loops:
Premise:
Biological brain code does not contain looping constructs, or the
ability to creating looping code, (due to the fact they are extremely
dangerous on unreliable hardware) except for 1 global loop that fires
about 200 times a second.
Hypothesis:
Brains cannot calculate iterative problems quickly, where calculations
in the previous iteration are needed for the next iteration and, where
brute force operations are the only valid option.
Proof:
Take as an example, Fibonacci numbers
http://en.wikipedia.org/wiki/Fibonacci_number
What are the first 100 Fibonacci numbers?
int Fibonacci[102];
Fibonacci[0] = 0;
Fibonacci[1] = 1;
for(int i = 0; i 100; i++)
{
// Getting the next Fibonacci number relies on the previous values
Fibonacci[i+2] = Fibonacci[i] + Fibonacci[i+1];
}
My brain knows the process to solve this problem but it can't directly
write a looping construct into itself. And so it solves it very slowly
compared to a computer.
The brain probably consists of vast repeating look-up
Re: [agi] What is the smallest set of operations that can potentially define everything and how do you combine them ?
Michael :The brains slow and unreliable methods I think are the price paid for generality and innately unreliable hardware Yes to one - nice to see an AGI-er finally starting to join up the dots, instead of simply dismissing the brain's massive difficulties in maintaining a train of thought. No to two -innately unreliable hardware is the price of innately *adaptable* hardware - that can radically grow and rewire (wh. is the other advantage the brain has over computers). Any thoughts about that and what in more detail are the advantages of an organic computer? In addition, the unreliable hardware is also a price of global ardware - that has the basic capacity to connect more or less any bit of information in any part of the brain with any bit of information in any other part of the brain - as distinct from the local hardware of computers wh. have to go through limited local channels to limited local stores of information to make v. limited local kinds of connections. Well, that's my tech-ignorant take on it - but perhaps you can expand on the idea. I would imagine v. broadly the brain is globally connected vs the computer wh. is locally connected. --- 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] What is the smallest set of operations that can potentially define everything and how do you combine them ?
A demonstration of global connectedness is - associate with anO I get: number, sun, dish, disk, ball, letter, mouth, two fingers, oh, circle, wheel, wire coil, outline, station on metro, hole, Kenneth Noland painting, ring, coin, roundabout connecting among other things - language, numbers, geometry, food, cartoons, paintings, speech, sports, science, technology, art, transport, transportation system, money. Note though the other crucial weakness of the brain wh. impairs global connections - fatigue. To maintain any piece of information in consciousness for long is a strain, (unless it's sexual?). But the above demonstrates IMO why the brain is and has to be an image processor. --- 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] What is the smallest set of operations that can potentially define everything and how do you combine them ?
On Wed, 2010-07-14 at 17:51 -0700, Matt Mahoney wrote:
Michael Swan wrote:
What 3456/6 ?
we don't know, at least not from the top of our head.
No, it took me about 10 or 20 seconds to get 576. Starting with the first
digit,
3/6 = 1/2 (from long term memory) and 3 is in the thousands place, so 1/2 of
1000 is 500 (1/2 = .5 from LTM). I write 500 into short term memory (STM),
which
only has enough space to hold about 7 digits. Then to divide 45/6 I get 42/6
= 7
with a remainder of 3, or 7.5, but since this is in the tens place I get 75.
I
put 75 in STM, add to 500 to get 575, put the result back in STM replacing
500
and 75 for which there is no longer room. Finally, 6/6 = 1, which I add to
575
to get 576. I hold this number in STM long enough to check with a calculator.
The brain does have one global loop, which I think goes at about 100~200
hertz. I would argue that your using that. Also note, brain are unlikely
to use RAM. Memory is most likely stored very locally to the process, as
the brain prob. can't access memory frivolously like in a computer. So,
the processes that require going backwards have to wait for the next
global loop to get the data, causing massive loss in time.
So about (~10sec * ~100hertz)= 1000+ loops I suspect is about right.
One could argue that this calculation in my head uses a loop iterator (in
STM)
to keep track of which digit I am working on. It definitely involves a
sequence
of instructions with intermediate results being stored temporarily. The brain
can only execute 2 or 3 sequential instructions per second and has very
limited
short term memory, so it needs to draw from a large database of rules to
perform
calculations like this. A calculator, being faster and having more RAM, is
able
to use simpler but more tedious algorithms such as converting to binary,
division by shift and subtract, and converting back to decimal. Doing this
with
a carbon based computer would require pencil and paper to make up for lack of
STM, and it would require enough steps to have a high probability of making a
mistake.
Intelligence = knowledge + computing power.
+ an clever way of using that computing power
The human brain has a lot of
knowledge. The calculator has less knowledge, but makes up for it in speed
and
memory.
-- Matt Mahoney, matmaho...@yahoo.com
- Original Message
From: Michael Swan ms...@voyagergaming.com
To: agi agi@v2.listbox.com
Sent: Wed, July 14, 2010 7:53:33 PM
Subject: Re: [agi] What is the smallest set of operations that can
potentially
define everything and how do you combine them ?
On Wed, 2010-07-14 at 07:48 -0700, Matt Mahoney wrote:
Actually, Fibonacci numbers can be computed without loops or recursion.
int fib(int x) {
return round(pow((1+sqrt(5))/2, x)/sqrt(5));
}
;) I know. I was wondering if someone would pick up on it. This won't
prove that brains have loops though, so I wasn't concerned about the
shortcuts.
unless you argue that loops are needed to compute sqrt() and pow().
I would find it extremely unlikely that brains have *, /, and even more
unlikely to have sqrt and pow inbuilt. Even more unlikely, even if it
did have them, to figure out how to combine them to round(pow((1
+sqrt(5))/2, x)/sqrt(5)).
Does this mean we should discount all maths that use any complex
operations ?
I suspect the brain is full of look-up tables mainly, with some fairly
primitive methods of combining the data.
eg What's 6 / 3 ?
ans = 2 most people would get that because it's been wrote learnt, a
common problem.
What 3456/6 ?
we don't know, at least not from the top of our head.
The brain and DNA use redundancy and parallelism and don't use loops
because
their operations are slow and unreliable. This is not necessarily the best
strategy for computers because computers are fast and reliable but don't
have a
lot of parallelism.
The brains slow and unreliable methods I think are the price paid for
generality and innately unreliable hardware. Imagine writing a computer
program that runs for 120 years without crashing and surviving damage
like a brain can. I suspect the perfect AGI program is a rigorous
combination of the 2.
-- Matt Mahoney, matmaho...@yahoo.com
- Original Message
From: Michael Swan ms...@voyagergaming.com
To: agi agi@v2.listbox.com
Sent: Wed, July 14, 2010 12:18:40 AM
Subject: Re: [agi] What is the smallest set of operations that can
potentially
define everything and how do you combine them ?
Brain loops:
Premise:
Biological brain code does not contain looping constructs, or the
ability to creating looping code, (due to the fact they are extremely
dangerous on unreliable hardware) except for 1 global loop that fires
about 200 times a second.
Hypothesis:
Brains cannot calculate iterative problems quickly, where
Re: [agi] What is the smallest set of operations that can potentially define everything and how do you combine them ?
On Wed, Jul 14, 2010 at 4:53 PM, Michael Swan ms...@voyagergaming.comwrote:
On Wed, 2010-07-14 at 07:48 -0700, Matt Mahoney wrote:
Actually, Fibonacci numbers can be computed without loops or recursion.
int fib(int x) {
return round(pow((1+sqrt(5))/2, x)/sqrt(5));
}
;) I know. I was wondering if someone would pick up on it. This won't
prove that brains have loops though, so I wasn't concerned about the
shortcuts.
unless you argue that loops are needed to compute sqrt() and pow().
I would find it extremely unlikely that brains have *, /, and even more
unlikely to have sqrt and pow inbuilt. Even more unlikely, even if it
did have them, to figure out how to combine them to round(pow((1
+sqrt(5))/2, x)/sqrt(5)).
Does this mean we should discount all maths that use any complex
operations ?
I suspect the brain is full of look-up tables mainly, with some fairly
primitive methods of combining the data.
eg What's 6 / 3 ?
ans = 2 most people would get that because it's been wrote learnt, a
common problem.
What 3456/6 ?
we don't know, at least not from the top of our head.
I'd argue that mathematical operations are unnecesary, we don't even have
integer support inbuilt. The number meme is a bit of a hack on top of
language that has been modified throughout the years. We have a peripheral
that allows us decent support for the numbers 1-10, but beyond that numbers
are basically words to which several different finicky grammars can be
applied as far as our brains are concerned.
---
agi
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Re: [agi] What is the smallest set of operations that can potentially define everything and how do you combine them ?
On Thu, 2010-07-15 at 01:37 +0100, Mike Tintner wrote: Michael :The brains slow and unreliable methods I think are the price paid for generality and innately unreliable hardware Yes to one - nice to see an AGI-er finally starting to join up the dots, instead of simply dismissing the brain's massive difficulties in maintaining a train of thought. No to two -innately unreliable hardware is the price of innately *adaptable* hardware - that can radically grow and rewire (wh. is the other advantage the brain has over computers). Any thoughts about that and what in more detail are the advantages of an organic computer? Program software can rewire themselves in some senses, one creates virtual hardware inside the program as though it was real hardware. But it's extremely rare to find ones that are purely general, so much so I doubt purely general ones even exist. Are NN's purely general? Are GA's purely general? I thought perhaps code that writes code could potentially reach such a lofty goal (as it can turn into a GA or NN or , well, anything). Then I thought the code writing the code restricts what the written code can be. So, then I made some simple experiments of the code modifying itself. The end result was surprisingly ( at least I suspect it was) similar to DNA. I still had a large section of code, whose purpose was to read part itself, and modify it, and this large piece of code had no bearing in what the modified code actually did. DNA has 2 sections, a coding section, which actually most of the hard work, and poorly named junk DNA (or non-coding DNA), which most biologist thought did nothing, until they discovered it doing stuff all over the place but in a somewhat discrete, subtle fashion. So, is my experiment 6 http://codegenerationdesign.webs.com/index.htm the first ever program to roughly mimic the programming of DNA ? I find this really hard to prove, but I think it remains a possibility. Apparently, Biologists don't think much my degree in biology from the University of Wikipedia, nature docs, and other random stuff you read from the internet. In addition, the unreliable hardware is also a price of global ardware - that has the basic capacity to connect more or less any bit of information in any part of the brain with any bit of information in any other part of the brain - as distinct from the local hardware of computers wh. have to go through limited local channels to limited local stores of information to make v. limited local kinds of connections. Well, that's my tech-ignorant take on it - but perhaps you can expand on the idea. I would imagine v. broadly the brain is globally connected vs the computer wh. is locally connected. Yep, the ability to grab memory from anywhere is called RAM - Random Access Memory. A single neurons can only access data from it's 25,000 connections, which sounds like a lot, but isn't because computers can access a theoretical infinite set of data. Being that the program in a brain can only go forward, how does it tell other neurons that it wants data about X that is behind it ? One theory, is that certain neurons detect that they need more data, and create a greater positive charge to attract more of negatively charged data. So in a sense they sux more data into themselves, effectively sending a different, non-dangerous backward running signal. (Author note: that I can't prove this at all, and is just a possibility) --- 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/?; Powered by Listbox: http://www.listbox.com --- 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] What is the smallest set of operations that can potentially define everything and how do you combine them ?
I'd argue that mathematical operations are unnecesary, we don't even have integer support inbuilt. I'd disagree. is a mathematical operation, and in combination can become an enormous number of concepts. Sure, I think the brain is more sensibly understood in a programattical sense than mathematical. I say programattical because it probably has 100 billion or so conditional statements, a difficult thing to represent mathematically. Even so, each conditional is going to have maths constructs in it. The number meme is a bit of a hack on top of language that has been modified throughout the years. We have a peripheral that allows us decent support for the numbers 1-10, but beyond that numbers are basically words to which several different finicky grammars can be applied as far as our brains are concerned. True, but numbers awesomeness lies it there power to represent relative differences between any concepts. With this power, numbers are a universal language, a language that can represent any other language, and hence, the ideal language and probably only real choice for an AGI. agi | Archives | Modify Your Subscription --- 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
