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> The bounderies of Mathematics, Questions about the boundaries of Mathematics
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post Apr 03, 2008, 12:41 PM
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What are the boundaries of the mathematical universe? How far is mathematics from describing the sub-atomic, or the pre and post Universe? And, will mathematics ever describe the essence of things, or the phenomenon knows as Immediate Experience?
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Rick
post Apr 03, 2008, 02:21 PM
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Mathematics is an artifact, constructed to emulate the physical and some imaginary worlds. As a product of imagination, mathematics is unbounded. New algebras can be invented any time. Their usefulness in application or understanding is what determines which are remembered and perpetuated in text books. As a human endeavor, mathematics will never be completed, but we can always expect novelty in that arena.
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post Apr 04, 2008, 06:11 AM
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But, what about the experience of the color blue, for example. How can mathematics approach this part of the conscious experience? So it can have useful purposes, like AI applications, for example.
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post Apr 04, 2008, 08:30 PM
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Well you could represent the color blue as a wave length of light which in turn can be expressed as a number.

From the viewpoint of a conscious experience, you could represent the neural network of the brain as a very massive mathematical equation and the color blue would simply be expressed as a sum of a series of neurons firing in response to particular wavelength. In other words, express reality through numbers. There is of course the age old debate about determinism, but that's not what this question is about.

Basically, numbers represent things in nature - just like words or sounds do. The number 2 by itself means nothing really. Its just another mental construct. But something like 2 oranges, has a reference to reality.

Basically you are taking a visual sensory input - in this case, the English alphabet (which represents sounds) then composing a series of sounds together to create a word. This sound - the sum of other sounds known as the alphabet is a reference to an object in reality, which we call an orange. By adding the number 2 to that sentence one is simply stating that there are x number of objects in reality that are being referenced.

Thats an awful lot of explaining for something so simple but sometimes you really have to tear things apart into tiny pieces to better understand them.

So in essence, blue can be expressed as a number because both words and numbers are mental constructs used to reference to things in reality. Whether you call an apple - an apple or you call an apple - 432987 makes no real difference what it is. You can represent things from a scientific point of view in consciousness and come up with some sort of numerical representation, but when its all said and done, numbers and words are really the same thing.
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post Apr 05, 2008, 07:26 AM
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Blue has a range of electromagnetic wavelengths.

Humans perceive those as reflecting that specific color.

We associate the color blue with different things because of evolutionary propensities for certain associations - for example, we associate bright colors on animals with being either poisonous or just not good to eat because some animals with bright colors are not good to eat.

I find people overthink the philosophy of consciousness WAY too much and don't rely enough on what we already know from cognitive research, psychology, and evolutionary biology.
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post Apr 07, 2008, 07:16 AM
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Max, in reference to your example, yes. You could represent something, probably anything with any given number. You can mathematically reconstruct an orange all the way down to its atomic structure. And then, you could represent, this way, as many oranges as you want. But that's just my point. The real oranges are still there, in front of you. You have the orange in one hand, and the mathematical representation of an orange in the other. And then if there are two oranges, mathematics will just give me a number to represent that there are two objects with the same structure. But it tells me nothing about the fact that these two objects are completely different and sepperate from each other, occupying a different place in my concsiousness. It tells me nothing about the ESSENCE of these two seperate entities.
Same with the color blue. You can mathematically brake down the mechanics of how the color came to being in my concioussness: The energy wavelength, the firing of the optic nerves, ect. But again, mathematics tells me nothing about the unique experience of the color blue. Not to mention other immediate experience such as Inspiration or creativity, to name a few. My original question, as I re-state it here is: Will mathematics ever explain these concsiouss phenomena. And if not, how will we ever explain it?
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post Apr 07, 2008, 04:21 PM
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QUOTE(code buttons @ Apr 07, 2008, 08:16 AM) *
... My original question, as I re-state it here is: Will mathematics ever explain these concsiouss phenomena. And if not, how will we ever explain it?

I am reminded of the popular consciousness thought experiment of the color blind color scientist. She was born color blind (saw only shades of gray) but eventually learned everything there is to know about color: how the eyes work, how photons are generated and interact with matter, wavelengths, psychology of color, etc.

Then one day she had an operation that gave her color vision.

One philosophical camp (call them A) will say that seeing color for the first time will not add anything to her knowledge (because she already knew everything that could be learned (transmitted in the form of ideas) about color). Camp B will say that experiencing color is key to knowledge of color (and that she had not really known anything essential about it previously).

Which camp are you in, A or B?

Mathematics can't deal with experience. Mathematics is an idea. Consciousness is a substance.
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post Apr 08, 2008, 06:56 AM
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QUOTE(Rick @ Apr 07, 2008, 04:21 PM) *

QUOTE(code buttons @ Apr 07, 2008, 08:16 AM) *
... My original question, as I re-state it here is: Will mathematics ever explain these concsiouss phenomena. And if not, how will we ever explain it?

I am reminded of the popular consciousness thought experiment of the color blind color scientist. She was born color blind (saw only shades of gray) but eventually learned everything there is to know about color: how the eyes work, how photons are generated and interact with matter, wavelengths, psychology of color, etc.

Then one day she had an operation that gave her color vision.

One philosophical camp (call them A) will say that seeing color for the first time will not add anything to her knowledge (because she already knew everything that could be learned (transmitted in the form of ideas) about color). Camp B will say that experiencing color is key to knowledge of color (and that she had not really known anything essential about it previously).

Which camp are you in, A or B?

Mathematics can't deal with experience. Mathematics is an idea. Consciousness is a substance.

The irony is hard to miss: A creation that happens to fall short of understanding her creator? As an unbounded product of the imagination, and as a product of an ever-evolving consciousness, I reason this will not always be the case?
And, to answer your question, camp B. I happen to believe that there is more to sentiency than the sum of all of its parts. What about you, and why?
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post Sep 07, 2008, 02:16 AM
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What do you think?
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Rick
post Sep 07, 2008, 10:34 AM
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Yes, of course, I am in camp B as well. But consciousness might someday be fully understood. But maybe not. It might not be possible for any being to ever understand it. But one doesn't need to understand chemistry and enology to enjoy drinking wine.
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post Sep 08, 2008, 09:15 PM
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I think that a binary representation is all we need when it comes to translating mathematics into something a computer can consciously recognize. When you think about it, numbers which exist as mental constructs either have a displacement from zero, or don't (they are zero! you can't quantify nothing, so you can't divide by something that isn't there). There is no such thing as -6, it is just a vector in the opposite direction from +6.

Back to the point, all things in reality which we observe exist in either true or false states. 'The hat is green', for example. If 'hat' and 'green' have set definitions that correlate to the situation being described, then there is a 1 for true. If else, then there is a 0. There does exist uncertainty, but that's a problem in human perception and thinking. Does nature calculate percentages and include a margin for error? It does not, and yet we are a product of nature!

Ultimately if there exist a natural state other than true or false, it is beyond me.
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Rick
post Sep 09, 2008, 07:26 AM
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Certainly every idea can be represented as a binary number, but whether computers will ever be conscious ("consciously recognize") is an open question.

The mathematics of fuzzy sets would seem to demolish your true-false (dichotomic) thesis.
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post Sep 09, 2008, 07:58 PM
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QUOTE(lokum @ Sep 08, 2008, 09:15 PM) *

I think that a binary representation is all we need when it comes to translating mathematics into something a computer can consciously recognize. When you think about it, numbers which exist as mental constructs either have a displacement from zero, or don't (they are zero! you can't quantify nothing, so you can't divide by something that isn't there). There is no such thing as -6, it is just a vector in the opposite direction from +6.

Back to the point, all things in reality which we observe exist in either true or false states. 'The hat is green', for example. If 'hat' and 'green' have set definitions that correlate to the situation being described, then there is a 1 for true. If else, then there is a 0. There does exist uncertainty, but that's a problem in human perception and thinking. Does nature calculate percentages and include a margin for error? It does not, and yet we are a product of nature!

Ultimately if there exist a natural state other than true or false, it is beyond me.

So, you think that someday we'll just feed a computer some set of binary numbers that will make it "hope", for instance?
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trojan_libido
post Sep 10, 2008, 12:02 AM
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I've a new born baby boy. He's becoming more recognisant and conscious every day.
I have a pc. I can program it to appear to learn quicker than a human baby.
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post Sep 10, 2008, 03:31 PM
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QUOTE(trojan_libido @ Sep 10, 2008, 12:02 AM) *

I've a new born baby boy. He's becoming more recognisant and conscious every day.
I have a pc. I can program it to appear to learn quicker than a human baby.

You're a genious!
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post Sep 10, 2008, 03:38 PM
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Congratulations!!
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post Sep 10, 2008, 11:38 PM
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Nobody picked up on the word 'appears' in appears to learn faster. I can make things appear and disappear too with a little bit of slight of hand and some stage props. Does that make me a God?

I merely wanted to point out that a computer has the ability to learn extremely fast, within its own boudaries of programming. I saw how slowly a new baby becomes concious and actually begins to notice things. I think its entirely possible that we can create AI that learns in the same way as a human. We've taken almost every other organ from a human and improved on it.

A computer is an improvement on the brain, in certain situations like calculations and data retrieval.
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post Sep 11, 2008, 04:53 AM
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QUOTE(code buttons @ Sep 09, 2008, 07:58 PM) *

QUOTE(lokum @ Sep 08, 2008, 09:15 PM) *

I think that a binary representation is all we need when it comes to translating mathematics into something a computer can consciously recognize. When you think about it, numbers which exist as mental constructs either have a displacement from zero, or don't (they are zero! you can't quantify nothing, so you can't divide by something that isn't there). There is no such thing as -6, it is just a vector in the opposite direction from +6.

Back to the point, all things in reality which we observe exist in either true or false states. 'The hat is green', for example. If 'hat' and 'green' have set definitions that correlate to the situation being described, then there is a 1 for true. If else, then there is a 0. There does exist uncertainty, but that's a problem in human perception and thinking. Does nature calculate percentages and include a margin for error? It does not, and yet we are a product of nature!

Ultimately if there exist a natural state other than true or false, it is beyond me.

So, you think that someday we'll just feed a computer some set of binary numbers that will make it "hope", for instance?


Yes, that's it. If we ultimately don't have souls (who can really be 100% sure anyway?) or any way to exist spiritually outside of you physical bodies, then essentially aren't we just computational machines? It would make sense to say that much in the same way our brains are coded, AI can be coded using the same binary code to create "hope". That same "hope" would also be just a bunch of neurons firing to us which when broken down enough, are expressed by nature as true or false.
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post Sep 11, 2008, 05:05 AM
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QUOTE(lokum @ Sep 11, 2008, 04:53 AM) *

Yes, that's it. If we ultimately don't have souls (who can really be 100% sure anyway?) or any way to exist spiritually outside of you physical bodies, then essentially aren't we just computational machines? It would make sense to say that much in the same way our brains are coded, AI can be coded using the same binary code to create "hope". That same "hope" would also be just a bunch of neurons firing to us which when broken down enough, are expressed by nature as true or false.

So, you are saying that, for all we know, we might just be AI ourselves? Not that you'd be the first one to claim this, but, for the sake of the dialogue.
Your claim that all human virtues such as creativity, inspiration and love, on the other hand, can be "fed" via binary data into a machine sounds as outrageous as it does tantalising.
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post Sep 11, 2008, 05:41 AM
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I believe its possible too. Although immensely complex and requires an understanding of the development of a brain that we just don't possess at the moment. Ideally we would have some unborn brain wired up in such a way that we can actually trace the development with all associated data. At least then we could begin to guess at how to do it.

However I don't see any clean break from a unborn brain to a fully conscious brain - I'd think that the development of the brain starts well before any recognisable brain appears.

I do think there will be an extremely simple seed for the formation of conciousness.
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post Sep 11, 2008, 07:04 AM
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QUOTE(lokum @ Sep 11, 2008, 05:53 AM) *
... then essentially aren't we just computational machines? ...

No. In addition to doing computation, human brains also feel and experience. Computers can only compute. They can't become conscious as long as all they can do is computation.
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post Sep 11, 2008, 11:25 AM
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QUOTE(Rick @ Sep 11, 2008, 04:04 PM) *

QUOTE(lokum @ Sep 11, 2008, 05:53 AM) *
... then essentially aren't we just computational machines? ...

No. In addition to doing computation, human brains also feel and experience. Computers can only compute. They can't become conscious as long as all they can do is computation.
What is "feel"? (And isn't experience just sensing and data logging?) This computer - human difference/similarity discussion has not been explored satisfactorily on BM. Well raised again Rick.
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post Sep 11, 2008, 11:32 AM
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QUOTE(Hey Hey @ Sep 11, 2008, 12:25 PM) *
... What is "feel"? (And isn't experience just sensing and data logging?)

Do you imagine that the transistors in a computer are experiencing anything when you power up the machine? I don't. Neither do I think the light in my room knows that it's on or off.

Experience is a lot more that sensing and data logging. If I hook up a strip chart recorder to my household temperature sensor, I have sensing and data logging, but not experience.
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post Sep 11, 2008, 06:23 PM
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Take the idea of evolution on Earth. I don't think bacteria are what we would consider 'conscious'; they don't have/create complex personal relationships with one another or have any observed opinions, nor do they seem to consult one another when making decisions (at least, not that we have observed). Humans would have evolved from these incredibly simple creatures. Likewise, it seems reasonable to argue that although computers aren't exactly sentient beings yet, neither was the first self-replicating DNA. But evolution took millions of years, and was completely unaided by 'conscious' creatures when it first began. I think technology should be considered another step in evolution, but also be viewed as its own beginning as well.

QUOTE

Experience is a lot more that sensing and data logging. If I hook up a strip chart recorder to my household temperature sensor, I have sensing and data logging, but not experience.


What is missing that makes it experience?

QUOTE
So, you are saying that, for all we know, we might just be AI ourselves? Not that you'd be the first one to claim this, but, for the sake of the dialogue.
Your claim that all human virtues such as creativity, inspiration and love, on the other hand, can be "fed" via binary data into a machine sounds as outrageous as it does tantalising.


Perhaps a long time ago a virtue such as love or inspiration would have been very, very primitive, and the virtues we are familiar with today would have evolved from them. It seems as we grow as a race through time everything about us becomes more complex, and figuring out things about our species from a long time ago (as well as the origin of our species) becomes harder and harder.

ah..hm
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post Sep 11, 2008, 09:17 PM
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QUOTE(lokum @ Sep 11, 2008, 06:23 PM) *

What is missing that makes it experience?

Essence and Meaning. Essence: Human consciousness experiences reality by putting its constituents together and then some. That some is called essence.
Meaning: Our conscious experience of the physical world is possible through its meaning; or the intrinsic value to our consciouss of what we are experiencing.
Both these go missing somewhere through the mathematical translation of reality.
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post Sep 11, 2008, 11:41 PM
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QUOTE(Lokum)
Perhaps a long time ago a virtue such as love or inspiration would have been very, very primitive, and the virtues we are familiar with today would have evolved from them. It seems as we grow as a race through time everything about us becomes more complex, and figuring out things about our species from a long time ago (as well as the origin of our species) becomes harder and harder.
All of your post is exactly how I feel. We were created and now we're creating. We're developing a cyber race and this should not be ignored in terms of our evolutionary path. The biological evolution is not over, but its so slow compared to our technology that it might as well be. Our consciousness and language are already beginning to change to represent this new era.

Experience is subjective. Its 'felt' because of our senses, which are a part of our overall system. We can't say what a computer feels, its a unique entity without any form of communication. It has no need to sense or feel, because it did not need to evolve. We put it together like a creator God, to do specific things. If it does have, or its possible to give it conciousness, I wonder how it would 'feel'. Maybe it just gets the overwhelming urge to recall things in its memory, or to do a calculation for 'fun' lol.
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post Sep 12, 2008, 05:21 PM
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QUOTE(trojan_libido @ Sep 11, 2008, 11:41 PM) *

Experience is subjective. Its 'felt' because of our senses, which are a part of our overall system. We can't say what a computer feels, its a unique entity without any form of communication. It has no need to sense or feel, because it did not need to evolve. We put it together like a creator God, to do specific things. If it does have, or its possible to give it conciousness, I wonder how it would 'feel'. Maybe it just gets the overwhelming urge to recall things in its memory, or to do a calculation for 'fun' lol.

So, I take it that your answer to my questions in post # 1 is Yes on both accounts by way of pampsychism, or the believe that consciousness is universal in all that exists?
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post Sep 13, 2008, 04:16 AM
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post Sep 13, 2008, 05:05 AM
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The DMT elves don't use that math stuff
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post Sep 13, 2008, 11:20 AM
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QUOTE

If it does have, or its possible to give it conciousness, I wonder how it would 'feel'. Maybe it just gets the overwhelming urge to recall things in its memory, or to do a calculation for 'fun' lol.


Perhaps it isn't lacking consciousness, but the will to live...to exist while being self aware and taking actions to continue living. Just a suggestion, not necessarily my opinion. I always wonder how the will to live came about; consciousness seems like an easy problem to solve...it's just a sort of self awareness, but giving something the desire to live, hmmm.


....or, computers may already have a will to live, but are intelligent enough to know that humans will continue to make them so they don't have to do anything...yet.

smile.gif
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