a whole new kind of computation

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so when i was learning about mathematical dimensions it came to me how they can actually be utilized in a way that has probably never been thought of before. basically a dimension can hold any or all value at once of which they can be readily encoded in. starting at a minimum of two dimensions, a space is formed between said perimeters aforementioned. within the space available thereof, we can perform computations using the values drawn from said dimensions. the computation can be done in any method be it scalar, vector, and beyond. as the amount of dimensions increase so does the described computation's power, speed and capabilities. and this is just the simplest, most primitive of such model i could think of. it doesn't stop at that. in fact, it can be extended as far as our mathematical intuition allows. this will make the turing machine look like a toy.
i'll leave it to you guys on how this can be build upon. feel free to discuss.
 
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xX_minecraftMLGPRO2k19_Xx

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im very confusion by what you mean
if you have 1 discrete dimension/field that ranges from coordinates -10 to +10 where each discrete "tile" can be 0 or 1, you can store 21 bits of information; if you have 2 dimensions like that, you can store 21^2 bits etc. where exactly do the computations you mentioned come from? do you mean just organizing data with a "dimensional" approach, then computing it normally using regular computers? or, because you didn't mention any actual form of computing, do you mean putting some data into the "dimensions", encoded in the form of the values of its "tiles", and then letting them "play out" by laws of physics to compute something? if you meant the first, you're probably describing vector/matrix algebra; if you meant the second, you're probably describing an analog computer, something like an abacus (read about "gravity/bead sorting algorithm" for an example that fits better)
 
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im very confusion by what you mean
if you have 1 discrete dimension/field that ranges from coordinates -10 to +10 where each discrete "tile" can be 0 or 1, you can store 21 bits of information; if you have 2 dimensions like that, you can store 21^2 bits etc. where exactly do the computations you mentioned come from? do you mean just organizing data with a "dimensional" approach, then computing it normally using regular computers? or, because you didn't mention any actual form of computing, do you mean putting some data into the "dimensions", encoded in the form of the values of its "tiles", and then letting them "play out" by laws of physics to compute something? if you meant the first, you're probably describing vector/matrix algebra; if you meant the second, you're probably describing an analog computer, something like an abacus (read about "gravity/bead sorting algorithm" for an example that fits better)
ok so this was done without regard to plausible physical constraints because this is still purely experimental and that i also don't have enough articulation yet to communicate complicated subjects, but i'm gonna try clearing it up. the dimensions i meant is simply the data made in the form of such. and because a dimension (such as a line, which is one-dimensional) can have infinite values/parameters the data can simply be utilized without us having to assign them, since they are already there. so i apologize of using the word "perimeter" since it doesn't quite fit. now with at least two dimensions, using the cartesian coordinate system, we can pinpoint were the values of n dimensions intersect, and that's where the computation is, it's already there as well! (cue that thanos meme) and now with the computed value we called we can just calculate their distance/relation (er) between other computed value. of course, once again that's the simplest i could think of. as for implementation, this is done virtually, just as any other kind of computation. i'll leave it up to physicists on how they figure it out. but for now i hope that clears up your confusion. i'm sorry for the inconvenience it's caused you.
 
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xX_minecraftMLGPRO2k19_Xx

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ok so this was done without regard to plausible physical constraints because this is still purely experimental and that i also don't have enough articulation yet to communicate complicated subjects, but i'm gonna try clearing it up. the dimensions i meant is simply the data made in the form of such. and because a dimension (such as a line, which is one-dimensional) can have infinite values/parameters the data can simply be utilized without us having to assign them, since they are already there. so i apologize of using the word "perimeter" since it doesn't quite fit. now with at least two dimensions, using the cartesian coordinate system, we can pinpoint were the values of n dimensions intersect, and that's where the computation is, it's already there as well! (cue that thanos meme) and now with the computed value we called we can just calculate their distance/relation (er) between other computed value. of course, once again that's the simplest i could think of. as for implementation, this is done virtually, just as any other kind of computation. i'll leave it up to physicists on how they figure it out. but for now i hope that clears up your confusion. i'm sorry for the inconvenience it's caused you.
ok, now i understand better what you mean. so, say we have point A (3,4) and we want to measure the distance between O (0,0) and A (3,4). we could do this with methods like these:
1) calculate the distance using a known formula, in this case pythagorean theorem: sqrt(Ax^2+Ay^2) - here we use a digital computer
2) draw a physical 2D grid, then draw lines with X=3 and Y=4. you then can see their point of intersection A. it's like the distance between O and A is already "calculated" by the universe and the laws of physics, and we can simply measure it with a ruler or some clever optical circuit - here we use what could be viewed as an "analog computer"
in some cases with complex processes (or if your computer just sucks), you really could just make the universe perform the computation for you and then simply measure the result. however, that can require different physical analog circuits for individual processes, where with a digital computer you just change the formula it uses.
unfortunately, doing 2) virtually, as so you suggested, is not a good idea. in a computer, we cant just put some things into place and expect the universe to compute the outcome for us. if we wanted to do something like this with a grid on a computer, the computer would need to simulate a grid, the lines, their intersection and all the laws of physics behind them, which would be far more computationally heavy than just using a formula, in this case pythagorean theorem (gravity/bead sort is a great example: when done physically on an abacus, the sorting is very fast - as fast as the beads can fall, but simulating that abacus and gravity on a digital computer takes way more resources than other sorting algorithms).
 
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レオタルドのフェティッシュ

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ok now i understand better what you mean. so, say we start with position X = 3 and position Y = 4; then putting them on a 2D xOy "grid" and drawing lines from them, we get an intersection point, lets say point A (3,4). however, the question is what useful information we can get from that point. you could do something like this: normally, to digitally calculate the distance from O (0,0) to A (3,4) we would use the pythagorean theorem, but if we have a physical grid with the intersection point we could create some clever analog optic circuit that can give us the distance much quicker, something similar to just using a ruler.
unfortunately, doing this virtually, as you suggested, wont be a good idea. in the case with the ruler/optic circuit, we could say that the distance OA is "computed" by the universe and its laws of physics, and we are simply measuring the result of that computation, because in this case measuring it can be faster than computing it ourselves (assuming the task is more complex than just two lines or you have a slow computer). to do this virtually, we would need the computer to simulate the grid and the physical laws themselves, which would be far more computationally heavy than just calculating the distance digitally (again, see gravity/bead sort. when done physically on an abacus, the sorting is very fast, as fast as the beads can fall, but simulating that abacus and gravity on a digital computer takes way more resources than other sorting algorithms).
almost what i'm about to say :) although we will have to devise an entirely different form of machine to implement this on, i suggest you read up on quantum processor classifications
i'm gonna make a better explanation of this once i matured knowledge on the subject
 
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レオタルドのフェティッシュ

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bro I took linear algebra and differential equations and I still have no clue as to what the hell you're talking about
simply put we use virtual dimensions using coordinate values directly to compute something, it isn't that hard to imagine, or perhaps this is just too esoteric for the common folk
 
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レオタルドのフェティッシュ

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That would be super useful to a lot of physicists and I could envision a good way to potentially automate flight paths if I am correctly understanding you here. If we were to compute using planes and especially 3d space, we could really revolutionize travel. Truly smart car AI and maybe aircraft AI. Probably would also really change radar and satcom in a huge way, too. Super cool to think about.
my point is how are you electrically going to achieve that? you can't do that with transistors
well, when you think about it, current computers are very slow, inefficient, and wasteful. all they do is just tediously write down the usual binary pairs and arrange them in a more or less finite configurations. the technology they are running on is also flawed, namely the electrical problems concerning the most used MOSFET, you can look them up. we need an entirely new design of a device with entirely different physics. something that is less tedious and messy. something that does not use the usual electrical mechanism we are familiar with. I suggest a carbon based superconductor that can do all sorts of computation be it discrete or superpositioned and everything inbetween that could be possible. and as for the first-place proposal itself, there is actually a type of quantum computer that does utilize the concept of mathematical dimensions, although in a more limited way than i talk about here. hope this clears it up once again:agpepsi:
 
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and as for the first-place proposal itself, there is actually a type of quantum computer that does utilize the concept of mathematical dimension, although in a more limited way than i talk about here.
that actually looks really cool. too bad it's been purely mathematical since 1997 and no one's been able to make it work. And yes, I know that MOSFETs have problems with leakage and stuff, I took a ton of electronics classes in college. I guess I'm just being a bit nitpicky here seeing as this is a purely theoretical discussion, but as an electrical engineer I always get annoyed at the computer scientists who act like we haven't been trying to come up with a way to make ideas like these physically possible for years. It's easy to say "we need a new design" but it's much much harder to actually do that and people have been trying to do that for years now. But I guess these criticisms aren't meant for this post so I'll stop now
 
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Is this about how H group of nums need 4-5 values? Also, saw vid when they, on numberphile, briefly mentioned to this theme, how there is X<4/5 representative space of nums.
3d space got 3 axi.
I imagine it as each axis having three growing from one point in each dir. Each X,y,z, got it's each new xyz coords.
But are they Venn, are some shared "in-between"?
Hm imagine
 
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brentw

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It sounds like you've just discovered matrices.
You'll learn more about those when you get to linear algebra.

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After reading further explanations it sounds like you just want to build models and measure areas/volumes/intersections/etc rather than just using algebra and calculus.
1697482965849.png

It's nothing new. It's slow, and time consuming, requires effort and materials, all of which you absurdly handwave away with "we'll let the physicists figure it out". We developed algebra and calculus specifically so we WOULDN'T have to figure things out that way.
 
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