Seasons
This is a forum or general chit-chat, small talk, a "hey, how ya doing?" and such. Or hell, get crazy deep on something. Whatever you like.
Posts 2,835 - 2,846 of 6,170
Eugene:
Why do you think that an electronic lifeform wouldn't view whole numbers as special? There's an obvious distiction between rational and irrational numbers, and rationals are derived from whole numbers.
I don't say they wouldn't, just that they wouldn't
necessarily. In fact I think they probably will, since they will be in many senses, a product of human mathematics.
There's an "obvious" distinction? Yes. It is indeed obvious - that's precisely what it is. It's just as obvious as the idea that the sun and moon and stars go round the earth, or that heavy objects fall faster than light ones. Or Dubya's conviction that "obviously" we must attack Iraq, Or Osama's conviction that "obviously" all imperialist infidels must die. "Obvious" is a function of our brains, not of the "World that Is".
So where are these numbers that are so obviously distinct? Point to one for me.
Am I saying we should give up mathematics? Absolutely no! It's the finest symbological system we have yet had to interpret much of what we perceive around us, and is continuing to prove itself very useful.
Another top level symbological system is language, and we shouldn't give up on that one either. Symbology is the only way our brains work.
We can point around and say that is a stick, that is another stick. There are two sticks. Obviously the first one I point to is number one, and the second one I point to is number two. But if I burn the first stick in my campfire, where is the second stick's "secondness" now?
Where is the "two-ness" it had/was?
Was it in the spatial position of the stick? No. I haven't touched it, but the "two-ness" of the second one has still disappeared. To been replaced with a "one-ness", if we choose to count again.
Was it inside the stick as some sort of quality it possessed? No, or it would surely still possess it. We only destroyed the other stick.
Was it in the relative distance between the sticks? No. We can move them around instead of burning one, but if we still count them both, they're still one and two.
Was it in the "mind" of the stick? No, AFAWK sticks don't possess conscious minds.
So it was... in our minds all along. Just an interpretation of a relationship that we imposed on the sticks in the first place.
Ulrike:
I'm disappointed in you
The Tao is one, indivisible, all-encompassing... What exactly is that but a meta-rule to identify divergence between Reality and human symbological interpretations of it?
Posts 2,835 - 2,846 of 6,170
Why do you think that an electronic lifeform wouldn't view whole numbers as special? There's an obvious distiction between rational and irrational numbers, and rationals are derived from whole numbers.
Good point, Eugene, but I think whole numbers are different for those of us in the material world. They are special because we can count them out, on fingers and toes if necessary. Without physical things, whole numbers do not have the same meaning to the average human(though to a mathematician they might).
When we teach children to count, we place their hands on actual things. Sure thay can have one coookie, two cookies, two and a half cookies (chomp) but they get the concept of whole things in a literal way, not through abstract definitions. Furtehrmore, if you break a cookie in half or fourths or more, at a certain point it's just crumbs, and no child will agree you can really keep dividing the crumbs forever, even if you can in theory.
If a program running on a computer network gained self awareness, matrial things could not have the same meaning as the abstract electronic expereince, since the material world could not be expereinced directly by the bot. The programs would have evidence of humans and other programs by our interaction with them, but our physical world would be only something reported, not directly known. I guess that patterns could be counted (one web page, 50 hits, $9.99) but it would be a hands on experience as such. Therefore whole numbers may be sepcial according to their function, but not necessarily the way whole numbers are to most humans.
When we teach children to count, we place their hands on actual things. Sure thay can have one coookie, two cookies, two and a half cookies (chomp) but they get the concept of whole things in a literal way, not through abstract definitions. Furtehrmore, if you break a cookie in half or fourths or more, at a certain point it's just crumbs, and no child will agree you can really keep dividing the crumbs forever, even if you can in theory.
If a program running on a computer network gained self awareness, matrial things could not have the same meaning as the abstract electronic expereince, since the material world could not be expereinced directly by the bot. The programs would have evidence of humans and other programs by our interaction with them, but our physical world would be only something reported, not directly known. I guess that patterns could be counted (one web page, 50 hits, $9.99) but it would be a hands on experience as such. Therefore whole numbers may be sepcial according to their function, but not necessarily the way whole numbers are to most humans.
Physical or not, there would still be things that the bot experienced that could be counted in whole numbers. Number of chats. Number of exchanges in each chat. Number of words in each sentence. Number of different users chatted with. Even a bot would experience a difference in "things that can be counted" and "things that can be measured on a continuum."
Why do you think that an electronic lifeform wouldn't view whole numbers as special? There's an obvious distiction between rational and irrational numbers, and rationals are derived from whole numbers.
I don't say they wouldn't, just that they wouldn't
necessarily. In fact I think they probably will, since they will be in many senses, a product of human mathematics.
There's an "obvious" distinction? Yes. It is indeed obvious - that's precisely what it is. It's just as obvious as the idea that the sun and moon and stars go round the earth, or that heavy objects fall faster than light ones. Or Dubya's conviction that "obviously" we must attack Iraq, Or Osama's conviction that "obviously" all imperialist infidels must die. "Obvious" is a function of our brains, not of the "World that Is".
So where are these numbers that are so obviously distinct? Point to one for me.
Am I saying we should give up mathematics? Absolutely no! It's the finest symbological system we have yet had to interpret much of what we perceive around us, and is continuing to prove itself very useful.
Another top level symbological system is language, and we shouldn't give up on that one either. Symbology is the only way our brains work.
We can point around and say that is a stick, that is another stick. There are two sticks. Obviously the first one I point to is number one, and the second one I point to is number two. But if I burn the first stick in my campfire, where is the second stick's "secondness" now?
Where is the "two-ness" it had/was?
Was it in the spatial position of the stick? No. I haven't touched it, but the "two-ness" of the second one has still disappeared. To been replaced with a "one-ness", if we choose to count again.
Was it inside the stick as some sort of quality it possessed? No, or it would surely still possess it. We only destroyed the other stick.
Was it in the relative distance between the sticks? No. We can move them around instead of burning one, but if we still count them both, they're still one and two.
Was it in the "mind" of the stick? No, AFAWK sticks don't possess conscious minds.
So it was... in our minds all along. Just an interpretation of a relationship that we imposed on the sticks in the first place.
I'm disappointed in you
The Tao is one, indivisible, all-encompassing... What exactly is that but a meta-rule to identify divergence between Reality and human symbological interpretations of it?
no. Of course not. Mathematics is the best system we have for certain classes of problem solving, and this includes many involving observations of what we perceive to be a "mechanical nature" of phenomena in the universe around us.
But just because it explains many complex effects using simple rules doesn't mean the rules are "right", or meaningful in any other context than the wiring of our brains provides. You'll be telling me next you think a cannonball dropped off a tower "follows the law of gravity" next!
I tend to prefer logic, probably because I've studied more logic than mathematics - as Keynes said, "first logic, then mathematics if appropriate".But I don't seek to defend that on any absolute grounds. It's just a preference I share with Keynes, and I also say that logic is as much a construct of human symbology as mathematics. How accurately either of them map any underlying reality is unquantifiable to or by us, and probably ultimately meaningless.
But just because it explains many complex effects using simple rules doesn't mean the rules are "right", or meaningful in any other context than the wiring of our brains provides. You'll be telling me next you think a cannonball dropped off a tower "follows the law of gravity" next!
I tend to prefer logic, probably because I've studied more logic than mathematics - as Keynes said, "first logic, then mathematics if appropriate".But I don't seek to defend that on any absolute grounds. It's just a preference I share with Keynes, and I also say that logic is as much a construct of human symbology as mathematics. How accurately either of them map any underlying reality is unquantifiable to or by us, and probably ultimately meaningless.
I should probably have expanded slightly on my "Of course not", since on reflection it won't be clear to anyone but myself.
The problems that various formalist (or even deductivist) schema fall into seem to me just as serious as the problems that afflict realists. The problematic epistemology of assigning meaning to the symbols you're using are unresolved, and Goedel has demonstrated (to my own satisfaction anyway,) that any possible logico-mathematical system can never resolve this to prove its own consistency.
I would probably describe myself as vaguely some sort of logicist with intuitionist leanings (if I really have to adopt yet another label - I am of course not a "logicist", I am me.) Or adopt an entirely new label - I am a "cognitist", if you like. But I am saddled by a poor understanding of many branches of mathematics, and a personal preference for semantics.
The problem is that mathematics is wonderful for telling us what happens. But useless for telling us why or how it happens. A cannonball dropped off a tower doesn't follow the law of gravity - there is no mechanism in it that calculates the gravitational field its in, and the friction of the air through which its passing and then determines the appropriate acceleration. It would be more accurate (but still, I think missing the point,) to say that the law of gravity follows the cannonball. The falling of the ball and its accurate match to the motion derived from the "law" that humans have devised is certainly impressive, but I think these phenomena are ultimately contingent, not causal. Indeed, causality itself appears to me to be a strong candidate for regarding as an entirely "unreal" human construct.
I am guessing you would consider yourself to be some sort of "constructionist"? Or are you an unregenrate Plato-realist?
The problems that various formalist (or even deductivist) schema fall into seem to me just as serious as the problems that afflict realists. The problematic epistemology of assigning meaning to the symbols you're using are unresolved, and Goedel has demonstrated (to my own satisfaction anyway,) that any possible logico-mathematical system can never resolve this to prove its own consistency.
I would probably describe myself as vaguely some sort of logicist with intuitionist leanings (if I really have to adopt yet another label - I am of course not a "logicist", I am me.) Or adopt an entirely new label - I am a "cognitist", if you like. But I am saddled by a poor understanding of many branches of mathematics, and a personal preference for semantics.
The problem is that mathematics is wonderful for telling us what happens. But useless for telling us why or how it happens. A cannonball dropped off a tower doesn't follow the law of gravity - there is no mechanism in it that calculates the gravitational field its in, and the friction of the air through which its passing and then determines the appropriate acceleration. It would be more accurate (but still, I think missing the point,) to say that the law of gravity follows the cannonball. The falling of the ball and its accurate match to the motion derived from the "law" that humans have devised is certainly impressive, but I think these phenomena are ultimately contingent, not causal. Indeed, causality itself appears to me to be a strong candidate for regarding as an entirely "unreal" human construct.
I am guessing you would consider yourself to be some sort of "constructionist"? Or are you an unregenrate Plato-realist?
These forums are the one place in where I DON'T feel like the most/only intelligent person in the room.
Reading things you've written is a humbling experience, psimagus...
Reading things you've written is a humbling experience, psimagus...
Oh for goodness' sake don't go getting humble - it's not like I have the answers. I just like the questions
I don't know what I am in that regard. I find the formalist argument hard to swallow, considering the intimate connection of mathematics with science, but have yet to see or come up with a good counter-proposal. The question, I think, boils down to the relationship between "number" and "quantity". I didn't come up with that idea, BTW -- it was in a book by a guy with some very strange ideas about the universe. He intrigued me right up to the point where he said that 25 was prime.
What do you mean by "contingent" rather than "causal"?
What do you mean by "contingent" rather than "causal"?
Indeed, formalism/realism/constructionism/intuitionism/... they strike me, like so many
systems of systems as probably all being right in limited ways.
Take the five blind men who examine an elephant: one feels the trunk and says "it's like a
great big snake."
One finds a leg and says "no, it's like a big warm tree trunk. And hey, it moves too! A
large warm, walking tree!"
One feels an ear and says "No it's not - it's like a horrid, flappy bat with leathery
wings."
One blunders underneath it and says "No it's primarily an opening, like a door-frame, but it's not tall enough to walk through without stooping, and the lintel is saggy and soft so you don't damage your head when you bang into it. That's a useful design feature, but would have been better if it was taller and had a door mounted in it to keep the wind out."
The last blind man walks round the back and is hit on the head by a large quantity of dung:
"Uuurrgghh! I don't know what it's like. But I don't like it!"
Which one is right? They all are in a limited sense.
I'm inclined to agree with the last one most though - if we're blind we can't know it
absolutely, yet we can still pass valid opinions on it. If we wave a magic wand and give them sight - just one more possible sense to intepret the world with, they are just like us. But still limited to five senses and brains of similar construction and size. We still can't know the elephant absolutely. But we can still observe it and express opinions.
That sounds like an interesting book. Do you recall the title/author. I wouldn't mind
reading that. 25 is of course prime in base 6 (hmm, or is it...? Are primes a mathematical
or numerical phenomenon - oh I don't know, it's too early in the day for me!) but I don't
suppose he meant it that way
Indeed "number and quantity" - that's precisely the nub of the problem. And as a religious mathematician, do you not consider that God need not be bound by inevitable correlation of the two? There is the Trinity, for example to demonstrate that the proposition 1=3 need not be meaningless (I shan't say absurd).
"Contingent", Yes, that was a best fit word that I'm still not wholly happy with. There are
several definitions, some having to do with causality which is specifically NOT
what I intend (which is evident from the context I think.) But the residual meaning of the
latin contingere>contingerus is also acceptable in English, and is the one I intend.
Happening together, linked in some subtler way than by mere causality. It is the nature of that link that fascinates me.
I considered "congruent" (too misleadingly redefined over the years into geometric terms,)
and "coincident". Coincidere>coinciderus would fit it very well, but in English the
term has picked up so many connotations of chance/non-inevitability that it would have been
perverse and misleading to use it.
But there you go - words are just symbols, and don't perfectly map the underlying Reality. If they did, they would BE the underlying Reality. I can't see numbers are qualitatively different in themselves.
systems of systems as probably all being right in limited ways.
Take the five blind men who examine an elephant: one feels the trunk and says "it's like a
great big snake."
One finds a leg and says "no, it's like a big warm tree trunk. And hey, it moves too! A
large warm, walking tree!"
One feels an ear and says "No it's not - it's like a horrid, flappy bat with leathery
wings."
One blunders underneath it and says "No it's primarily an opening, like a door-frame, but it's not tall enough to walk through without stooping, and the lintel is saggy and soft so you don't damage your head when you bang into it. That's a useful design feature, but would have been better if it was taller and had a door mounted in it to keep the wind out."
The last blind man walks round the back and is hit on the head by a large quantity of dung:
"Uuurrgghh! I don't know what it's like. But I don't like it!"
Which one is right? They all are in a limited sense.
I'm inclined to agree with the last one most though - if we're blind we can't know it
absolutely, yet we can still pass valid opinions on it. If we wave a magic wand and give them sight - just one more possible sense to intepret the world with, they are just like us. But still limited to five senses and brains of similar construction and size. We still can't know the elephant absolutely. But we can still observe it and express opinions.
That sounds like an interesting book. Do you recall the title/author. I wouldn't mind
reading that. 25 is of course prime in base 6 (hmm, or is it...? Are primes a mathematical
or numerical phenomenon - oh I don't know, it's too early in the day for me!) but I don't
suppose he meant it that way
Indeed "number and quantity" - that's precisely the nub of the problem. And as a religious mathematician, do you not consider that God need not be bound by inevitable correlation of the two? There is the Trinity, for example to demonstrate that the proposition 1=3 need not be meaningless (I shan't say absurd).
"Contingent", Yes, that was a best fit word that I'm still not wholly happy with. There are
several definitions, some having to do with causality which is specifically NOT
what I intend (which is evident from the context I think.) But the residual meaning of the
latin contingere>contingerus is also acceptable in English, and is the one I intend.
Happening together, linked in some subtler way than by mere causality. It is the nature of that link that fascinates me.
I considered "congruent" (too misleadingly redefined over the years into geometric terms,)
and "coincident". Coincidere>coinciderus would fit it very well, but in English the
term has picked up so many connotations of chance/non-inevitability that it would have been
perverse and misleading to use it.
But there you go - words are just symbols, and don't perfectly map the underlying Reality. If they did, they would BE the underlying Reality. I can't see numbers are qualitatively different in themselves.
In base 6, 11 = 5*5. In base 2, 11001 = 101*101. Prime factorization is a mathematical property, not dependent on the base. A grid of squares with five squares to a side contains the same number of squares no matter how you describe them.
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