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When I was younger and less of a technophile, I often wished analog computing would somehow overtake digital computing. I suppose from my naïve perspective I fo

When I was younger and less of a technophile, I often wished analog computing would somehow overtake digital computing. I suppose from my naïve perspective I found it unsettling that our model of computing is discrete while the space-time we exist in is continuous. Being much more into technology today than I was 10 years ago (but equally naïve :-), my perspective seems to have flipped. I question whether reality is really continuous or whether it is just our limited perception of it that makes it seem that way. Obviously, my growing interest in digital technology has had a profound impact on how I view the world in which we live. In any case, I'm glad DARPA is looking more seriously into analog computing. I think there is a lot to be learned from revisiting the issue in a field that is still very young.

toolslive 14y ago
Funny, I came to the exact opposite conclusion: It's unsettling our models of physics are based on continuous functions while the space-time we exist in is obviously discrete. Considering them as continuous is a simplification to make the math easier, but not correct.
- ralfd 14y ago
  "Obviously discrete"?
  - vdondeti 14y ago
    From my understanding, the Planck length is the smallest length there can be, and every other length has to be an exact integral multiple of the Planck length [1]. I believe the same applies to the other Planck units [2]- they are fundamental units. Similarly, every charge has to be an exact integral multiple of the charge of the electron. These fundamental units seem to to indicate that our universe is not continuous, but quantized/discrete. With that said, there are some theories stating that these fundamental units only apply to our universe (and even in our own universe, the fundamental units may change over long periods of time), and that other universes may have different fundamental units. So depending on how you define the universe, the answer to whether the universe is continuous or discrete could change. [1] http://en.wikipedia.org/wiki/Planck_length http://en.wikipedia.org/wiki/Planck_length [2] http://en.wikipedia.org/wiki/Planck_units http://en.wikipedia.org/wiki/Planck_units
    - joeyo 14y ago
      Quarks carry fractional charge (e/3) [1]. And Quasiquarks seem to be able to carry any fractional charge with an odd-denominator (e/3, e/5, e/7, ...) [2,3] which would seem to indicate that the universe has quantized space yet has no lower bounds. 1. http://en.wikipedia.org/wiki/Quark#Electric_charge http://en.wikipedia.org/wiki/Quark#Electric_charge 2. http://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect http://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect 3. http://physicsworld.com/cws/article/news/1997/oct/24/fractional-charge-carriers-discovered http://physicsworld.com/cws/article/news/1997/oct/24/fractio...
      - vdondeti 14y ago
        Fair point. Depending on how you define it, all charges are an integral multiple of e or e/3 (see below). Either way, the relevant point to this discussion is that charge is quantized/discrete. As for the Fractional quantum Hall effect, based on a quick glance, it seems that thus far only quasiparticees with charge e/3 have been discovered. So, while the theory could be correct, we will have wait and see if the other predicted fractional charges are detected. ---------------- From the Quark wikipedia page you cited: What is the quantum of charge? All known elementary particles, including quarks, have charges that are integer multiples of 1⁄3 e. Therefore, one can say that the "quantum of charge" is 1⁄3 e. In this case, one says that the "elementary charge" is three times as large as the "quantum of charge". On the other hand, all isolatable particles have charges that are integer multiples of e. (Quarks cannot be isolated, except in combinations like protons that have total charges that are integer multiples of e.) Therefore, one can say that the "quantum of charge" is e, with the proviso that quarks are not to be included. In this case, "elementary charge" would be synonymous with the "quantum of charge".
    - monjaro 14y ago
      Your understanding of the Planck length is incorrect. From the article you linked: "According to the generalized uncertainty principle, the Planck length is in principle, within a factor of order unity, the shortest measurable length - and no improvements in measurement instruments could change that." There is no claim that it is the smallest length possible, and there is certainly no claim that every length has to be an integral multiple of the Planck length.
- cabalamat 14y ago
  > the space-time we exist in is obviously discrete Obviously? It might be obvious to you but it isn't to me.
- co_pl_te 14y ago
  I think I am actually headed in your direction but don't have the means to get there yet. I have intuitions that space-time is discrete, but I don't possess the requisite knowledge or the grasp of physics to corroborate them. Totally agree with how unsettling our model of physics is if we grant that space-time is in fact discrete. I do believe, however, it is not so much about making the math easier as it is about making the universe conform to our perception of beauty. Continuous is just sexier than discrete. :-)
- stordoff 14y ago
  > the space-time we exist in is obviously discrete. Citation? I was under the impression that this wasn't a solved problem, and both discrete and continuous models can be useful in different situations.
- jameskilton 14y ago
  Quantum physicists disagree. Reality is far more weird than we think. http://arstechnica.com/science/2011/11/the-insanely-weird-quantum-wave-function-might-be-real-after-all/ http://arstechnica.com/science/2011/11/the-insanely-weird-qu...
- shenberg 14y ago
  The continuous/analog question is interesting enough that there was a physics essay contest on the matter - the winners are at http://fqxi.org/community/essay/winners/2011.1 http://fqxi.org/community/essay/winners/2011.1 and they were great reads even for a layman such as myself.
FrojoS 14y ago
Reminds me of this: "By the end of that summer of 1983, Richard had completed his analysis of the behavior of the router, and much to our surprise and amusement, he presented his answer in the form of a set of partial differential equations. To a physicist this may seem natural, but to a computer designer, treating a set of boolean circuits as a continuous, differentiable system is a bit strange. Feynman's router equations were in terms of variables representing continuous quantities such as "the average number of 1 bits in a message address." I was much more accustomed to seeing analysis in terms of inductive proof and case analysis than taking the derivative of "the number of 1's" with respect to time. Our discrete analysis said we needed seven buffers per chip; Feynman's equations suggested that we only needed five. We decided to play it safe and ignore Feynman." http://longnow.org/essays/richard-feynman-connection-machine/ http://longnow.org/essays/richard-feynman-connection-machine...
- andreasvc 14y ago
  But it's kind of the opposite. The grandparent was wondering about the fundamental nature of the universe, whereas this quote shows that you can approach a problem both digitally and continuously, calling into question whether the distinction is fundamental.
- pervycreeper 14y ago
  >http://longnow.org/essays/richard-feynman-connection-machine/ http://longnow.org/essays/richard-feynman-connection-machine... Off topic, but thanks for that article. Reading it made my weekend.
sliverstorm 14y ago
I still think it would be cool if analog computing was a thing, but I understand now more than ever why digital computing rules. It's the same as why synchronous computing rules- it is so difficult to design an asynchronous or analog system, that you cannot even hope to catch up, let alone overtake, synchronous digital computing.
- lurker14 14y ago
  Analog is far more energy-efficient than digital, though, because digital is really analog with huge gaps inserted to make the 1s and 0s detectable and not look too much like 0.5s. So there is a theoretical possibility that the efficiency benefits could outweigh the complexity liabilities.

toolslive 14y ago

Funny, I came to the exact opposite conclusion: It's unsettling our models of physics are based on continuous functions while the space-time we exist in is obviously discrete. Considering them as continuous is a simplification to make the math easier, but not correct.

ralfd 14y ago
"Obviously discrete"?
- vdondeti 14y ago
  From my understanding, the Planck length is the smallest length there can be, and every other length has to be an exact integral multiple of the Planck length [1]. I believe the same applies to the other Planck units [2]- they are fundamental units. Similarly, every charge has to be an exact integral multiple of the charge of the electron. These fundamental units seem to to indicate that our universe is not continuous, but quantized/discrete. With that said, there are some theories stating that these fundamental units only apply to our universe (and even in our own universe, the fundamental units may change over long periods of time), and that other universes may have different fundamental units. So depending on how you define the universe, the answer to whether the universe is continuous or discrete could change. [1] http://en.wikipedia.org/wiki/Planck_length http://en.wikipedia.org/wiki/Planck_length [2] http://en.wikipedia.org/wiki/Planck_units http://en.wikipedia.org/wiki/Planck_units
  - joeyo 14y ago
    Quarks carry fractional charge (e/3) [1]. And Quasiquarks seem to be able to carry any fractional charge with an odd-denominator (e/3, e/5, e/7, ...) [2,3] which would seem to indicate that the universe has quantized space yet has no lower bounds. 1. http://en.wikipedia.org/wiki/Quark#Electric_charge http://en.wikipedia.org/wiki/Quark#Electric_charge 2. http://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect http://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect 3. http://physicsworld.com/cws/article/news/1997/oct/24/fractional-charge-carriers-discovered http://physicsworld.com/cws/article/news/1997/oct/24/fractio...
    - vdondeti 14y ago
      Fair point. Depending on how you define it, all charges are an integral multiple of e or e/3 (see below). Either way, the relevant point to this discussion is that charge is quantized/discrete. As for the Fractional quantum Hall effect, based on a quick glance, it seems that thus far only quasiparticees with charge e/3 have been discovered. So, while the theory could be correct, we will have wait and see if the other predicted fractional charges are detected. ---------------- From the Quark wikipedia page you cited: What is the quantum of charge? All known elementary particles, including quarks, have charges that are integer multiples of 1⁄3 e. Therefore, one can say that the "quantum of charge" is 1⁄3 e. In this case, one says that the "elementary charge" is three times as large as the "quantum of charge". On the other hand, all isolatable particles have charges that are integer multiples of e. (Quarks cannot be isolated, except in combinations like protons that have total charges that are integer multiples of e.) Therefore, one can say that the "quantum of charge" is e, with the proviso that quarks are not to be included. In this case, "elementary charge" would be synonymous with the "quantum of charge".
  - monjaro 14y ago
    Your understanding of the Planck length is incorrect. From the article you linked: "According to the generalized uncertainty principle, the Planck length is in principle, within a factor of order unity, the shortest measurable length - and no improvements in measurement instruments could change that." There is no claim that it is the smallest length possible, and there is certainly no claim that every length has to be an integral multiple of the Planck length.
cabalamat 14y ago
> the space-time we exist in is obviously discrete Obviously? It might be obvious to you but it isn't to me.
co_pl_te 14y ago
I think I am actually headed in your direction but don't have the means to get there yet. I have intuitions that space-time is discrete, but I don't possess the requisite knowledge or the grasp of physics to corroborate them. Totally agree with how unsettling our model of physics is if we grant that space-time is in fact discrete. I do believe, however, it is not so much about making the math easier as it is about making the universe conform to our perception of beauty. Continuous is just sexier than discrete. :-)
stordoff 14y ago
> the space-time we exist in is obviously discrete. Citation? I was under the impression that this wasn't a solved problem, and both discrete and continuous models can be useful in different situations.
jameskilton 14y ago
Quantum physicists disagree. Reality is far more weird than we think. http://arstechnica.com/science/2011/11/the-insanely-weird-quantum-wave-function-might-be-real-after-all/ http://arstechnica.com/science/2011/11/the-insanely-weird-qu...
shenberg 14y ago
The continuous/analog question is interesting enough that there was a physics essay contest on the matter - the winners are at http://fqxi.org/community/essay/winners/2011.1 http://fqxi.org/community/essay/winners/2011.1 and they were great reads even for a layman such as myself.

FrojoS 14y ago

Reminds me of this: "By the end of that summer of 1983, Richard had completed his analysis of the behavior of the router, and much to our surprise and amusement, he presented his answer in the form of a set of partial differential equations. To a physicist this may seem natural, but to a computer designer, treating a set of boolean circuits as a continuous, differentiable system is a bit strange. Feynman's router equations were in terms of variables representing continuous quantities such as "the average number of 1 bits in a message address." I was much more accustomed to seeing analysis in terms of inductive proof and case analysis than taking the derivative of "the number of 1's" with respect to time. Our discrete analysis said we needed seven buffers per chip; Feynman's equations suggested that we only needed five. We decided to play it safe and ignore Feynman." http://longnow.org/essays/richard-feynman-connection-machine/ http://longnow.org/essays/richard-feynman-connection-machine...

andreasvc 14y ago
But it's kind of the opposite. The grandparent was wondering about the fundamental nature of the universe, whereas this quote shows that you can approach a problem both digitally and continuously, calling into question whether the distinction is fundamental.
pervycreeper 14y ago
>http://longnow.org/essays/richard-feynman-connection-machine/ http://longnow.org/essays/richard-feynman-connection-machine... Off topic, but thanks for that article. Reading it made my weekend.

sliverstorm 14y ago

I still think it would be cool if analog computing was a thing, but I understand now more than ever why digital computing rules. It's the same as why synchronous computing rules- it is so difficult to design an asynchronous or analog system, that you cannot even hope to catch up, let alone overtake, synchronous digital computing.

lurker14 14y ago
Analog is far more energy-efficient than digital, though, because digital is really analog with huge gaps inserted to make the 1s and 0s detectable and not look too much like 0.5s. So there is a theoretical possibility that the efficiency benefits could outweigh the complexity liabilities.