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 10:35 PM, Michael Swan ms...@voyagergaming.comwrote: 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. Sorry, I meant unnecessary to demonstrate that particular point. There's no need to say you have no innate ability to know what 3456/6 is when you are unlikely to have an innate concept of the number 3456 or any other arbitrary number greater than a few hundred to begin with, you can get by with a few lookup tables upon which you get a vague idea what 3456 of something would be, but if I were to show you a sheet of paper with 3000-4000 dots on it, you would be unlikely to be able to tell me whether it was greater or less than 3456. I don't see any way an evaluator of some sort wouldn't be completely necessary for an AGI, sorry for the confusion. Though, you do bring to mind the point that while can be an extremely useful tool for composing other concepts, our internal comparisons do seem to tend more towards the analog than towards the binary, and while you can compose those analog outputs with and - easily enough, you probably want concepts supported as close to natively as is possible. Remember, there are turing-complete one-dimensional systems of cellular automata, but that doesn't make it feasible to port the Linux kernel to them. --- 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 ?
And yet you dream dreams wh. are broad-ranging in subject matter, unlike all programs wh. are extremely narrow-ranging. -- From: Michael Swan ms...@voyagergaming.com Sent: Thursday, July 15, 2010 5:16 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 ? I watched a brain experiment last night that proved that connections between major parts of the brain stop when you are asleep. They put electricity at different brain points, and it went everywhere when the person was a awake, and dissipated when they were asleep. On Thu, 2010-07-15 at 02:13 +0100, Mike Tintner wrote: 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/?; 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/?; 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 ?
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
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
Re: [agi] What is the smallest set of operations that can potentially define everything and how do you combine them ?
Well, if you want a simple but complete operator set, you can go with
-- Schonfinkel combinator plus two parentheses
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
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...
A better question IMO is what set of operators and structures has the
property that the compact expressions tend to be the ones that are useful
for survival and problem-solving in the environments that humans and human-
like AIs need to cope with...
-- Ben G
On Tue, Jul 13, 2010 at 1:43 AM, Michael Swan ms...@voyagergaming.com wrote:
Hi,
I'm interested in combining the simplest, most derivable operations
( eg operations that cannot be defined by other operations) for creating
seed AGI's. The simplest operations combined in a multitude ways can
form extremely complex patterns, but the underlying logic may be
simple.
I wonder if varying combinations of the smallest set of operations:
{ , memory (= for memory assignment), ==, (a logical way to
combine them), (input, output), () brackets }
can potentially learn and define everything.
Assume all input is from numbers.
We want the smallest set of elements, because less elements mean less
combinations which mean less chance of hitting combinatorial explosion.
helps for generalisation, reducing combinations.
memory(=) is for hash look ups, what should one remember? What can be
discarded?
== This does a comparison between 2 values x == y is 1 if x and y are
exactly the same. Returns 0 if they are not the same.
(a logical way to combine them) Any non-narrow algorithm that reduces
the raw data into a simpler state will do. Philosophically like
Solomonoff Induction. This is the hardest part. What is the most optimal
way of combining the above set of operations?
() brackets are used to order operations.
Conditionals (only if statements) + memory assignment are the only valid
form of logic - ie no loops. Just repeat code if you want loops.
If you think that the set above cannot define everything, then what is
the smallest set of operations that can potentially define everything?
--
Some proofs / Thought experiments :
1) Can , ==, (), and memory define other logical operations like
(AND gate) ?
I propose that x==y==1 defines xy
xy x==y==1
00 = 0 0==0==1 = 0
10 = 0 1==0==1 = 0
01 = 0 0==1==1 = 0
11 = 1 1==1==1 = 1
It means can be completely defined using == therefore is not
one of the smallest possible general concepts. can be potentially
learnt from ==.
-
2) Write a algorithm that can define 1 using only ,==, ().
Multiple answers
a) discrete 1 could use
x == 1
b) continuous 1.0 could use this rule
For those not familiar with C++, ! means not
(x 0.9) !(x 1.1) expanding gives ( getting rid of ! and )
(x 0.9) == ((x 1.1) == 0) == 1 note !x can be defined in terms
of == like so x == 0.
(b) is a generalisation, and expansion of the definition of (a) and can
be scaled by changing the values 0.9 and 1.1 to fit what others
would generally define as being 1.
---
agi
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--
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
CTO, Genescient Corp
Vice Chairman, Humanity+
Advisor, Singularity University and Singularity Institute
External Research Professor, Xiamen University, China
b...@goertzel.org
I admit that two times two makes four is an excellent thing, but if
we are to give everything its due, two times two makes five is
sometimes a very charming thing too. -- Fyodor Dostoevsky
---
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 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 anywhere and it can
potentially kill every other process, not just itself. This is why
computers die all the time.
for (int x = 0; x 2; x++)
{
for (int y = 0; y 2; y++)
{
put_pixel(x,y);
}
}
opposed to
/* The below is faster (even on single step instructions), and can be
run in parallel, damage resistant ( ie destroy put_pixel(0,1); and the
rest of the code will still run), is less scalable ( more code is
required for larger operations)
put_pixel(0,0);
put_pixel(0,1);
put_pixel(1,0);
put_pixel(1,1);
The lack of loops in the brain is a fundamental difference between
computers and brains. Think about it. 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.
A better question IMO is what set of operators and structures has the
property that the compact expressions tend to be the ones that are useful
for survival and problem-solving in the environments that humans and human-
like AIs need to cope with...
For me that is stage 2.
-- Ben G
On Tue, Jul 13, 2010 at 1:43 AM, Michael Swan ms...@voyagergaming.com wrote:
Hi,
I'm interested in combining the simplest, most derivable operations
( eg operations that cannot be defined by other operations) for creating
seed AGI's. The simplest operations combined in a multitude ways can
form extremely complex patterns, but the underlying logic may be
simple.
I wonder if varying combinations of the smallest set of operations:
{ , memory (= for memory assignment), ==, (a logical way to
combine them), (input, output), () brackets }
can potentially learn and define everything.
Assume all input is from numbers.
We want the smallest set of elements, because less elements mean less
combinations which mean less chance of hitting combinatorial explosion.
helps for generalisation, reducing combinations.
memory(=) is for hash look ups, what should one remember? What can be
discarded?
== This does a comparison between 2 values x == y is 1 if x and y are
exactly the same. Returns 0 if they are not the same.
(a logical way to combine them) Any non-narrow algorithm that reduces
the raw data into a simpler state will do. Philosophically like
Solomonoff Induction. This is the hardest part. What is the most optimal
way of combining the above set of operations?
() brackets are used to order operations.
Conditionals (only if statements) + memory assignment are the only valid
form of logic - ie no loops. Just repeat code if you want loops.
If you think that the set above cannot define everything, then what is
the smallest set of operations that can potentially define everything?
--
Some proofs / Thought experiments :
1) Can , ==, (), and memory define other logical operations like
(AND gate) ?
I propose that x==y==1 defines xy
xy x==y==1
00 = 0 0==0==1 = 0
10 = 0 1==0==1 = 0
01 = 0 0==1==1 = 0
11 = 1 1==1==1
Re: [agi] What is the smallest set of operations that can potentially define everything and how do you combine them ?
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 anywhere and it can
potentially kill every other process, not just itself. This is why
computers die all the time.
for (int x = 0; x 2; x++)
{
for (int y = 0; y 2; y++)
{
put_pixel(x,y);
}
}
opposed to
/* The below is faster (even on single step instructions), and can be
run in parallel, damage resistant ( ie destroy put_pixel(0,1); and the
rest of the code will still run), is less scalable ( more code is
required for larger operations)
put_pixel(0,0);
put_pixel(0,1);
put_pixel(1,0);
put_pixel(1,1);
The lack of loops in the brain is a fundamental difference between
computers and brains. Think about it. 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.
A better question IMO is what set of operators and structures has the
property that the compact expressions tend to be the ones that are useful
for survival and problem-solving in the environments that humans and
human-
like AIs need to cope with...
For me that is stage 2.
-- Ben G
On Tue, Jul 13, 2010 at 1:43 AM, Michael Swan ms...@voyagergaming.com
wrote:
Hi,
I'm interested in combining the simplest, most derivable operations
( eg operations that cannot be defined by other operations) for
creating
seed AGI's. The simplest operations combined in a multitude ways can
form extremely complex patterns, but the underlying logic may be
simple.
I wonder if varying combinations of the smallest set of operations:
{ , memory (= for memory assignment), ==, (a logical way to
combine them), (input, output), () brackets }
can potentially learn and define everything.
Assume all input is from numbers.
We want the smallest set of elements, because less elements mean less
combinations which mean less chance of hitting combinatorial explosion.
helps for generalisation, reducing combinations.
memory(=) is for hash look ups, what should one remember? What can be
discarded?
== This does a comparison between 2 values x == y is 1 if x and y are
exactly the same. Returns 0 if they are not the same.
(a logical way to combine them) Any non-narrow algorithm that reduces
the raw data into a simpler state
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 anywhere and it can
potentially kill every other process, not just itself. This is why
computers die all the time.
for (int x = 0; x 2; x++)
{
for (int y = 0; y 2; y++)
{
put_pixel(x,y);
}
}
opposed to
/* The below is faster (even on single step instructions), and can be
run in parallel, damage resistant ( ie destroy put_pixel(0,1); and the
rest of the code will still run), is less scalable ( more code is
required for larger operations)
put_pixel(0,0);
put_pixel(0,1);
put_pixel(1,0);
put_pixel(1,1);
The lack of loops in the brain is a fundamental difference between
computers and brains. Think about it. We can't do operations that
require 1,000,000 loop iterations. I wish someone would give me a PHD
for
[agi] What is the smallest set of operations that can potentially define everything and how do you combine them ?
Hi,
I'm interested in combining the simplest, most derivable operations
( eg operations that cannot be defined by other operations) for creating
seed AGI's. The simplest operations combined in a multitude ways can
form extremely complex patterns, but the underlying logic may be
simple.
I wonder if varying combinations of the smallest set of operations:
{ , memory (= for memory assignment), ==, (a logical way to
combine them), (input, output), () brackets }
can potentially learn and define everything.
Assume all input is from numbers.
We want the smallest set of elements, because less elements mean less
combinations which mean less chance of hitting combinatorial explosion.
helps for generalisation, reducing combinations.
memory(=) is for hash look ups, what should one remember? What can be
discarded?
== This does a comparison between 2 values x == y is 1 if x and y are
exactly the same. Returns 0 if they are not the same.
(a logical way to combine them) Any non-narrow algorithm that reduces
the raw data into a simpler state will do. Philosophically like
Solomonoff Induction. This is the hardest part. What is the most optimal
way of combining the above set of operations?
() brackets are used to order operations.
Conditionals (only if statements) + memory assignment are the only valid
form of logic - ie no loops. Just repeat code if you want loops.
If you think that the set above cannot define everything, then what is
the smallest set of operations that can potentially define everything?
--
Some proofs / Thought experiments :
1) Can , ==, (), and memory define other logical operations like
(AND gate) ?
I propose that x==y==1 defines xy
xy x==y==1
00 = 0 0==0==1 = 0
10 = 0 1==0==1 = 0
01 = 0 0==1==1 = 0
11 = 1 1==1==1 = 1
It means can be completely defined using == therefore is not
one of the smallest possible general concepts. can be potentially
learnt from ==.
-
2) Write a algorithm that can define 1 using only ,==, ().
Multiple answers
a) discrete 1 could use
x == 1
b) continuous 1.0 could use this rule
For those not familiar with C++, ! means not
(x 0.9) !(x 1.1) expanding gives ( getting rid of ! and )
(x 0.9) == ((x 1.1) == 0) == 1note !x can be defined in terms
of == like so x == 0.
(b) is a generalisation, and expansion of the definition of (a) and can
be scaled by changing the values 0.9 and 1.1 to fit what others
would generally define as being 1.
---
agi
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