Sunday, June 26, 2016

kurzweil ai post on mathematical realism

By that reasoning all art is "discovered".
Animals have a sense of numerosity, and can be tested on numerical competence, their competence is not zero. This suggests evolution happened upon hardware able to handle numerical quantities to some extent, humanity's mathematical abilities rest on biological hardware able to handle numerical concepts and quantities, damage to the tissue performing this function can have profound consequences(as seen in the book The Number Sense: How the Mind Creates Mathematics).
So if numbers and numerical competence are a man made invention on what exactly did evolution happen upon? Were cometh animals competence which predates man?
The answer is that man made symbols, and man made rules to define what can be considered a "number", these rules, iirc, have expanded over time. Like the physical laws, man attempts to define what governs nature, but these rules the physical laws obviously exist and operate independent of 'discovery'. Thus man's definitions tend to be an approximation to the truth, but the truth must obviously underlie reality. Man's abilities rest on biological hardware that provides a basic sense of numerosity and small numerical quantity, this serves as a foundation to all higher numerical thought, even as a baby man's numerical competence is not zero.
As for art, again, afaik, all art can be stored as digital files in a digital system. This being the case, even a procedure as simple as repeated addition will generate ALL POSSIBLE art past present or future(this includes all video, all qualia representations for BCI devices, all sound, all texts, all images, all everything). If we take any finite device of finite resolution, such as a modern TV, this will be the case, also for any finite resolution full brain BCI thus encompassing all possible thought and sensation by a finite brain. The number of images and sounds a modern TV can produce is finite, and this includes all possible past present future or imaginary content as the form of videos, sound or still images(including pictures of all possible events and book and journal pages in all possible languages).
Again numerical relations exist in the outside world, nature developed hardware to perceive these existing relations and behave accordingly. When I see a binary sequence, it doesn't seem sensible to say that it was "invented", the possibility of a system with two types of values likely exists independently of all implementation as a possibility, digital systems also have plenty of naturally occurring implementations(for example using more types of values in dna.). There is something that makes 4 billiard balls similar to 4 legs similar to 4 apples similar to 4 planets, something that makes 3 candies more similar to 3 towers than 4 candies in some aspect, whether a human or animal can perceive this or not, there is a relationship between these, and it can only be seen as numerical in nature.
All one needs is an immortal indestructible machine with infinite computation and a similar body for one's self, which might be one and the same if there's no (hidden) fundamental physical property behind the brain's production of consciousness. Such a machine would allow one to experience all possible experience and have all possible knowledge. If digital physics is true, then that would be equivalent to attaining godhood, the ability to know everything, be everywhere and be all powerful. You wouldn't need to conquer anything or fight anyone, in isolation such a system will make the wielder the absolute embodiment of the law.
An interesting thing is as I mentioned previously, all the content that is in a single 4k(at least one of the 4k definitions if we keep color fidelity the same.) image is already contained in the set of all 1080p images, albeit in 4 different 1080p images, the set of 4k images contains no additional information, also a scaled down single 1080p image exists which provides the gist of the 4k image. The obvious question is what happens with regards to things like journal papers, would adding resolution provide additional content? Again it doesn't seem likely as said all the visible content of a single 4k image is available in the set of 1080 images. All 4k can do is combine a set of 1080p images in different orders, and there's a finite number of 1080p images and a finite number of combinations. So returning to the question again, it seems that eventually the set of images of journal pages will start repeating large quantities of content, the higher the resolution you go, it is still finite but changing to a significantly higher resolution will only provide reorganization of a finite number of pages you would have already seen at a lower resolution.
Can you imagine that entire pages with exactly the same say Billion lines of texts repeating with copies of themselves, in a finite number of combinations of the same blocks of a billion lines of text(or empty space, etc.) for a given resolution. This would give the illusion of infinity, but it would seem in my eyes like a house of mirrors, simply repeating what would seem like an amount of finite content repeated in different orders. Eventually the moment you start repeating not just words, sentences, paragraphs, but entire books worth of unchanged content, well there comes a point where any reader has seemingly already experienced it all.- link to thread

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