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This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick! Just encode the text
by air7 5y ago
This reminds me of a joke idea I read somewhere: You can encode the entire Encyclopaedia Britannica using a single mark on a simple stick!
Just encode the text as a ascii codes after the decimal dot of a zero. (0.656168.. etc). Then just mark that ratio of the sticks length and you're done...
- thehappypm 5y agoYou can do it easier than that -- just make a stick of length .65168 meters. (Same idea, just the "full 1 meter stick" is defined elsewhere, not by the length of the stick).
- tshaddox 5y agoThat’s way harder, because you have to cut a stick to write and have a meter ruler to read.
- gh02t 5y agoAnd of course in a footnote of the documentation for this encoding "Sufficiently precise measurement of this mark left as an exercise to the reader."
- mjburgess 5y agoI don't see this as a joke, but a radical and important point. Reality, in being geometrical, is infinitely informationally dense (with a discrete conception of information). This distinction between geometrical space and time, and discrete algorithmic computability is unbridgeable. And hence there is an extemely firm footing on which to reject: AI, brain scanning readers, teleporters, etc and most sci-fi computationalim. Almost nothing can be simulated, as in, realised by a merely computational system.
- idiotsecant 5y agoReality isn't quite infinitely dense though, it's hard to imagine how you could encode data geometrically over a distance smaller than the planck length, for example. Reality just has a very, very fine resolution.
- Rapzid 5y agoA quick Google shows 6.25e+34 plank lengths in a meter. So, seems impossible to measure and make the mark. Edit: As a fraction of appended ascii codes.
- petercooper 5y agoAnd if the mark were instead the removal of a single atom in a 40cm length, the resolution would be even poorer.. able to encode a single 30 bit number by my very rough calculation.
- deleted 5y ago[deleted]
- WithinReason 5y agoHow do you know reality is not computational?
- joshgrib 5y agoI just wanted to add that reality being a non-discrete geometric thing is still an assumption - we don't know for sure that it isn't discrete and a lot of quantum stuff points more toward a discrete reality than a continuous one. So assuming continuous space/time and discrete information then I'd agree, but as far as we know space/time aren't continuous, but just appear that way to us. It doesn't seem like we know for sure that it is discrete, but at the least I'd say it's solid evidence that stuff like brain scanning is definitely in the realm of possibility. This answer from the Physics StackExchange nicely covers how time/space could appear continuous to us even if they are in fact discrete at lower levels. Also some interesting discussion in the other answers https://physics.stackexchange.com/a/35676 https://physics.stackexchange.com/a/35676
- mjburgess 5y agoI think for my purposes defining continuous = unmeasurably discrete produces the same results. Ie., there is an irreducible geometrical continuity in the sense that no discontinuity can ever appear. The state density is maximal. via this route we reporduce the same point: computationalism/simulation'ism' is then just the thesis that computers qua measurably discrete systems can realise dense unmeasurable discrete systems. This can be shown to be impossible with much the same argument: spatial and temporal geometrical properties obtain in virtue of dense discreteness; and fail to obtain at measureable levels. The key property of continuity is its irreducibility to measurably discrete systems. That irreducibility isn't, however , limited to continuity . Wolfram makes this point about the failures of reductionism in a perfectly discrete context, ie., that no CA can compute a CA whose complexity is greater than it can summarise. I prefer to press a continuous angle: our best theories of all of reality are continuous and geometrical . That energy levels are discrete in bounded quantum systems has almost nothing to do with the indispensability of contintuous mathemtatjcs in every known physical system -- including that very bounded wavefn
- drdeca 5y agoI agree that we can’t reject the hypothesis that reality is continuous (and, even if spacetime turns out to be discrete, it seems hard to imagine that the amplitudes of the wavefunction(s) have finitely many possible complex values, though I suppose we can’t rule it out) I disagree that this necessarily implies any difficulty for the possibility of brain scanning and AI. Just as things sampled faster than the nyquist frequency (or twice it or whatever) of a uh, band limited thing, can be perfectly recovered, (I mean there’s still discritization of the amplitudes but I hear this can also be handled), I don’t see why uh, arbitrarily high frequency (in space and time) should be necessary in order to model the behavior of a brain to the point of long-term indistinguishability. (That being said, I don’t particularly expect whole brain emulation to ever be achieved, I just don’t see “spacetime is continuous (or well approximated as continuous)” as being a strong argument for it being impossible.) I’m not sure what you mean by computationalism. If you mean the idea that the way the world works is computable in the abstract sense (not requiring any practical bounds on the computational resources needed), then the idea that the world is discrete and finite, merely with extremely fine grains, then this poses no issue for computation in that abstract sense (just make the imaginary computer even bigger). If you mean like, an accurate simulation of the past of the world being run within the world, yeah that doesn’t work.
- whatshisface 5y agoIt's computational again when you allow the computation to be precise enough for any practical purpose, which is not infinitely precise.
- wallacoloo 5y agoThese are weird conclusions. Any attempt to measure “reality” gives some amount of uncertainty. The only way for this to lead to the relatively stable experience you perceive is if those small variations in measurement lead to relatively small differences in perception. In which case, you can truncate the resolution of your simulation and still get plausible results. I assure you there are plenty of groups out there simulating systems that operate with similar densities (but lower volume) to the brain.
- mgraczyk 5y agoI wouldn't say that the distinction is "unbridgeable". Keep in mind that we send packets over plenty of "geometrical" and seemingly infinitely dense analog channels all the time, like electricity over a copper wire or EM waves over the air. The "mark on a stick" channel has a capacity like any other channel. If you're sending just one symbol, you could easily calculate the information capacity given a desired probability of bit-error. Assuming you can put the mark in exactly the right spot, you can model the "noise" as a distribution over the values that the reader will measure. If you model this as `mark + zero-mean normal distribution` with a known variance, then your stick is just an AWGN channel.
- dtagames 5y agoThe gentleman is not suggesting that quantized information cannot be fully represented in a continuous function, but the opposite. That the continuous functions of life (his muscle example) and consciousness (AI example) cannot be simulated in any meaningful way by a discrete nomenclature or algorithm. The idea is impossible by definition and can be dismissed immediately.
- dlivingston 5y agoEven if space and time were continuous (which things like the Planck length would discredit), there are still discrete objects in that continuum. Elementary particles, for example, are discrete. You could argue that they have continuous effects vis a vis the EM field and spatial positioning, but ensemble effects usually render that irrelevant at large enough scales.
- tsimionescu 5y agoI will note that even in QM, both space and time are considered continuous - the Planck length is just a smallest measurable distance, but nothing in QM currently assumes that particles must be separated by an integer multiple of the Planck length (unlike spins, for example). I believe there are some theories of quantum gravity that do rely on the idea that space-time is quantized in integer multiples of Planck's length, but these are far from definitive theories. A much more relevant limit in terms of possible information density is Heisenberg's uncertainty principle, which essentially puts a limit on the maximum possible precision for any measurement.
- Ginden 5y agoExistence of analog reality is quite problematic, because it opens can of worms - eg. hypercomputation is possible.
- dnautics 5y ago> And hence there is an extemely firm footing on which to reject: AI This is like saying it's impossible to build a water pump without solving the quantum mechanical interactions that govern water flow.
- gnramires 5y agoI used to think there must be something 'special' to brains to distinguish us from computers. There isn't. Brains encode finite amounts of information (quantum mechanics seems to imply bounded local information). We are a huge information network ourselves -- that's what consciousness is (with some added bits like self-identity and various particulars structures that dictate the character of our experience). But that doesn't mean brains aren't special -- it means brains are special and computers are special. Even more: it seems to imply computers, AI, etc. can be as special as ourselves, sentient, and perhaps even more special in ways we haven't realized yet. It's difficult to even imagine a physical theory with unbounded local information. It seems to open the possibility to crazy things like hypercomputation, which do not seem very well defined. (For example: every 1-1/n seconds, (n>1) from now, flip a switch ON/OFF. At what state will the switch be at t>1s? An at exactly t=1s?) Note: while information and information flow itself bounded (hence no hypercomputation), I don't know of any obvious objections to continuous time. (I'm not sure the continuity of time has any profound implications)
- mjburgess 5y agothe issue isn't brains no algorithm running on a cpu can move a muscle -- it is precisely that movement is a spatiotemporal property which means no turing machine can realise it movement isn't a symbolic operation
- tsimionescu 5y agoThis is such a strange claim to make, I can't even tell what you could have meant. We are surrounded by simplistic mechanical computations moving muscles , and have been for more than a hundred years, since the industrial revolution at least.
- gnramires 5y agoWhat do you suppose those computers are doing, then? ;) https://www.youtube.com/watch?v=tF4DML7FIWk https://www.youtube.com/watch?v=tF4DML7FIWk https://www.youtube.com/watch?v=tfb6aEUMC04&t=115s https://www.youtube.com/watch?v=tfb6aEUMC04&t=115s
- tsimionescu 5y agoThis is not just a false idea, but an obviously false one, contradicted by all the laws of physics. If you were right, then any finite volume would contain an infinite amount of information, which would mean it has infinite entropy, temperature, and energy. Also, by the same logic you apply to space, you could say that time is infinitely divisible, so you could create a computer which finishes an infinite amount of steps in a finite amount of time.
- mjburgess 5y agoinformation here, ie log of a probability, is a continuous notion -- it is real-valued, as not least, log is a transcendental fn -- i specifically said with a /discrete/ conception , geometry is infinitely dense (of discrete states)
- tsimionescu 5y agoIn all physical theories, any finite system has a finite number of distinguishable states. So it is not infinitely informationally dense, especially when working with discrete bits of information. Not to mention, the finer the distinctions between two states of a system, the more energy you need to distinguish them. So, the less impact these differences can have, unless the system is extraordinarily energetic (and even then, you end up in fundamental limits of energy per volume, like the Schwarzschild radius). So again, there is no sense in which a finite part of the universe is universally dense. Even worse for your argument, all currently known laws of physics use computable functions (the randomness in QM notwithstanding). So, by definition, all known laws of physics can be simulated by an ideal Turing machine (again, give or take some randomness in QM, depending on the interpretation you chose to believe in and on how you chose to simulate the QM system).
- eru 5y agoQM is even linear!
- rnhmjoj 5y agoThere's an interesting paper[1] that argues that real numbers aren't physical, for the precise reasons you stated. That is, only the subset of real numbers that contain a finite amount of information (like constructive real numbers) are physically meaningful. A consequence of this is that classical physics is not really deterministic: this is because, in general (ie. including chaotic systems), the evolution of a system depends on a set of initial conditions that are specified by full real numbers, impossible to measure with finite precision. So, the use of real numbers is hiding the indeterminism in the initial conditions, much like the function in this article encodes a dataset in a single parameter. [1]: https://arxiv.org/abs/1803.06824 https://arxiv.org/abs/1803.06824
- deleted 5y ago[deleted]
- yongjik 5y agoIn theory, pi has infinite digits. You could publish a book of a trillion digits of pi, and you have barely scratched the surface: in fact you published a precisely 0.00000% of all digits of pi. In practice, you "only" need ~42 digits of pi to draw a circle spanning the entire known universe (diameter of 8.8 * 10^26 m) and it will deviate from the ideal circle by less than the size of a proton (0.8 * 10^−15 m). Having a theoretically infinite precision does not mean that it makes a measurable difference.
- Kranar 5y agoEvery number has infinite digits or can be made to have infinite digits for a given representation, but that's not the same as a number having an infinite amount of information. PI represents a finite amount of information, as opposed to say a number like Chaitin's constant which represents an infinite and irreducible amount of information: https://en.wikipedia.org/wiki/Chaitin%27s_constant https://en.wikipedia.org/wiki/Chaitin%27s_constant
- eru 5y agoYou are right about information, but the comment you replied to is still right about precision.
- tbabb 5y agoI think there are at least two things wrong with this take: One is that I don't think it follows from the premise that the continuity of the physical world precludes AI, brain scanning, etc. Even if the physical world were continuous (likely not, see below), an arbitrary degree of approximation could be attained, in principle. At the very least I would not call the footing "firm". The second is that the universe is very likely not continuous anyway. The Beckenstein bound[1] puts an upper limit on the number of bits of information a region of space may contain. If the ruler tickmark were either measured or localized to the precision required to encode the information, the information density would cause it to collapse into a black hole. This would happen once your measurement needs to be about as precise as a Planck length, which would allow you to encode about 115 bits of information with your tickmark. (This in of itself is independent of the fact that you would need to construct the ruler out of objects that the universe permits; your ruler tickmark would need to be made of and measured with discrete fundamental particles, which by their very nature are quantized). [1] https://en.wikipedia.org/wiki/Bekenstein_bound https://en.wikipedia.org/wiki/Bekenstein_bound
- oever 5y agoOr use a larger stick. Every doubling of the stick length gives another bit of information. A stick of one light-year length would add about 53 bits.
- tbabb 5y agoThe main point I'm making is that the information density of the physical world is not unlimited as GP suggests. But I think that example just shows how few bits you can really get out the exercise!
- deleted 5y ago[deleted]
- naasking 5y ago> Reality, in being geometrical, Prove it.
- robbedpeter 5y agoPlanck length and the speed of light define the limits. It's also a resolution of Xeno's Paradox.
- macrolocal 5y agoAs an aside, this idea that reality is "geometrical" leads to all kinds of fascinating paradoxes[1]. [1] https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421
- hammock 5y agoWhat you are saying is P/=NP
- eru 5y agoHuh? What does that have to do with anything here?
- potatoman22 5y agoTo your last point: "All models are wrong, but some are useful."
- somewhereoutth 5y agoIndeed! I term it the 'Cardinality Barrier'. It is gratifying to know that the mathematician Georg Cantor demolished AI some hundred odd years before any engineer had thought seriously of it.
- NavinF 5y ago> Cantor demolished AI Citation needed. Btw nothing in this thread has anything to do with AI. Perhaps you are using a very unusual definition of AI that programmers don't use? Or maybe I just fell for satire. It's really hard to tell on this site.
- perl4ever 5y ago>infinitely informationally dense That can't possibly be true, because then there would be no point to space and time. If a single location could hold an infinite amount of information, then the rest of reality would be redundant. >hence there is an extemely firm footing on which to reject [the Matrix] This seems to be the opposite of the conclusion that your premise implies. I'm the one that doesn't believe in matryoshka simulated universes, but infinite information density is what would make it possible, no? If we lived in a non-discrete universe, why would computation be unable to exploit it?
- dtagames 5y agoSpace time is something that appears to you, the obsever, and only to you. There is no universal shared perception of anything or any event and therfore no common "reality" to try and suss out. It is quite likely (rather obvious, really) that what we call reality is continuous in design, infinite in abstractions, relationships, and descriptions, yet at the same time cohesive in a single entity. Those type of systems are not representable in computers.
- perl4ever 5y ago>therefore no common "reality" to try and suss out. You or I may be wrong about any specific aspect of reality, or fail to be aware of it. However, we can be sure there is such a thing. "Reality is that which, when you stop believing in it, doesn't go away." (Philip K. Dick) It's kind of like the concept of agnosticism.
- eru 5y agoHow do you know that reality is 'being geometrical, is infinitely informationally dense'? You might be interested in the Bekenstein bound (https://en.wikipedia.org/wiki/Bekenstein_bound https://en.wikipedia.org/wiki/Bekenstein_bound): > In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level.[1] It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. In computer science, this implies that there is a maximal information-processing rate (Bremermann's limit) for a physical system that has a finite size and energy, and that a Turing machine with finite physical dimensions and unbounded memory is not physically possible. Lots of math works out well that as a continuous approximation, eg the Navier-Stokes differential equations seem to describe fluids well on everyday scales. But we know very well that water is made of molecules, so we know that this particular continuous approximation will fail at small enough scales. By the way, the closest thing we have come to for teleportation is cutting-and-pasting of quantum states. So no classical, digital computers involved there.
- still_grokking 5y agoOnly if real numbers are a "real" thing.
- vidarh 5y agoDepends how you define simulation. There's no reason to assume that you need, or even that it's desirable, to simulate more than "almost nothing" in order to simulate what you'd want to simulate - even a whole universe can be simulated with ease if your required fidelity is low enough. So, if you want to simulate every possible interaction in realtime, sure. But you can increase overall capabilities by making sacrifices along several axes: duration, speed, precision, persistence of changes from a generative baseline and lots more. In other words it depends entirely of your purpose for simulation.
- nathancahill 5y agoSomething that I love about analog cameras and film: the "resolution" of film is infinite. Infinitely informationally dense as you say.
- rhn_mk1 5y agoThat's not really true in any sense. Film has grain size, and optics have a diffraction limit.
- Radim 5y agoOthers already noted how shaky your assertion "Reality, in being geometrical, is infinitely informationally dense" is. Instead, let me throw out another extreme (but fun) view in the opposite direction: Finitism [0]. These guys not only reject the existence of the continuum; they reject all infinities altogether! In finitism, even discrete things exist only as finite objects (that is further constructable – Ultrafinitism [1]). So no infinite universe, no "set of all natural numbers", no "limits" and other ideals over infinite domains. Screw Platonism. Hello Wittgenstein (and Wolfram). I don't know how far that theory can be taken in a practical sense – most body of science is built on Platonism [2] – but I have to say finitism does appeal to my CS heart and my earthly experience. [0] https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Finitism [1] https://en.wikipedia.org/wiki/Ultrafinitism https://en.wikipedia.org/wiki/Ultrafinitism [2] https://en.wikipedia.org/wiki/Primitive_recursive_arithmetic https://en.wikipedia.org/wiki/Primitive_recursive_arithmetic
- mjburgess 5y agoMy view is indeed the opposite. It seems trivial to me that reality has actual infinities as seen from a discrete pov. A trivial example: you can partition the environment into an infinite number of objects. And which partition scheme you choose is, in some sense, abitary. Eg., "object: the edge of the glass", "composite: edges of glasses on the table", etc. Reality admits an infinite number of such schemes, and also forcloses an infinite number (eg., if "pen"=pen, then "paper"!=pen). I dont think one can meaningfully speak "of reality", ie., provide a discrete linguistic/propositional account, which avoids these infinities. I also think there is no meta-scheme, so one cannot even order (in terms of fundamentality) which scheme is 'the really real' one. It's my view that the reason for this issue is that cognition is discrete but reality continuous. Since discrete aggregations arent enough, likewise "aggregative models of atoms" arent enough for chemistry. An aqueous solution, just like a society, is much more than merely the sum of the properties of its members. When we partition the world with a discrete scheme, we introduce "emergent properties" which are only the "leftovers from our reductive failure". The only problem infinity poses is to being realised by a discrete sequential process. That can never be actually infinite. But everything else can!
- an1sotropy 5y agoI remember reading about this as a kid in one of Martin Gardner's books, either "aha!" or "aha! Gotcha"
- meowphius 5y agoThat is from the novel "Hard-Boiled Wonderland and the End of the World" by Haruki Murakami[0]. [0]: https://everything2.com/title/Encyclopedia+on+a+toothpick https://everything2.com/title/Encyclopedia+on+a+toothpick
- optimalsolver 5y agoMartin Gardner illustrated this principle in "Paradoxes to Puzzle and Delight" back in 1982, and I'm sure he wasn't the first to think of the concept.
- joiguru 5y agoOne theoretical objection to this idea is that distances measured have an accuracy limit of Planck length (1.616e-35 meters). So if your number needs more precision then "just mark" step can't be done.
- pveierland 5y agoMy shot at the calculation for fun :-) Stick encoding with graphite resolution (0.335 * 10^-9 meter) [1]: "Uti" (31 bits -> 3 UTF8 characters) Stick encoding with Planck resolution (1.616255 * 10^-35 meter) [2]: "Utility ought " (115 bits -> 14 UTF8 characters) Complete first sentence: "Utility ought to be the principal intention of every publication." [3] It appears that this storage scheme may not be suited towards the safekeeping of literature. [1] https://www.wolframalpha.com/input/?i=floor%28floor%28log_2%281+meter+%2F+%280.335+nanometer%29%29%29+%2F+8%29 https://www.wolframalpha.com/input/?i=floor%28floor%28log_2%... [2] https://www.wolframalpha.com/input/?i=floor%28floor%28log_2%281+meter+%2F+1.616255*10%5E-35+meter%29%29%2F8%29 https://www.wolframalpha.com/input/?i=floor%28floor%28log_2%... [3] https://digital.nls.uk/encyclopaedia-britannica/archive/144133901 https://digital.nls.uk/encyclopaedia-britannica/archive/1441...
- alittlesalami 5y agoThis is Arithmetic Coding: https://en.wikipedia.org/wiki/Arithmetic_coding https://en.wikipedia.org/wiki/Arithmetic_coding
- ohazi 5y agoYou jest, but this is almost exactly how arithmetic coding works. If you arrange your symbols and contexts carefully, you can even use this as a technique for progressive or lossy compression -- i.e. the more accurately you specify the ratio, the higher fidelity your result.
- signa11 5y agohow big of a stick are we talking about here ?
- alisonkisk 5y agoThat's πfs https://github.com/philipl/pifs https://github.com/philipl/pifs
- fouc 5y agoYou reminded me of https://en.wikipedia.org/wiki/Gödel_numbering https://en.wikipedia.org/wiki/Gödel_numbering > Each letter of the message is represented in order by the natural order of prime numbers—that is, the first letter is represented by the base 2, the second by the base 3, the third by the base 5, then by 7, 11, 13, 17, etc. The identity of the letter occupying that position in the message is given by the exponent, simply: the exponent 1 meaning that the letter in that position is an A, the exponent 2 meaning that it is a B, 3 a C, 4 a D, up to 26 as the exponent for a Z. The message as a whole is then rendered as the product of all the bases and exponents. Examples. The word 'cab' can thus be represented as 2^3 x 3^1 x 5^2, or 600. Excerpt From: Frederik Pohl. “Starburst.”