8 ms·

My hunch agrees with the paper. Because computers operate on the rational numbers instead of the real numbers, they can never be embodied. They are always in a

My hunch agrees with the paper. Because computers operate on the rational numbers instead of the real numbers, they can never be embodied. They are always in a simulation...

mattnewton 6y ago
Maybe I don’t understand your point, but our senses are also compressed to some extent. Your synapses fire or don’t fire, providing digitized input for some of your senses like hearing. At any point there is a discrete amount of hormones in your body. etc etc. That doesn’t seem categorically different from any man made sensor.
- jchrisa 6y ago
  Our sensorium could be indistinguishable from how it'd be in a simulation without impacting my point. Software can hop from host to host (all Turing machines can simulate each other) but living intelligence is embodied. Because of this, no matter how "smart" computers get, we can't trust them not to do stupid stuff. They are smart like that kid in high school who comes up with a formula to turn the world into silly putty, and is stupid enough to use it. There is more than one kind of intelligence, here the argument is that some kinds of intelligence require having skin in the game.
  - sgillen 6y ago
    But would it be impossible to have artificial “skin in the game”? Is there no robot body that could serve this purpose?
    - selestify 6y ago
      Why isn’t computer hardware already as “embodied” in the physical world as our brain matter is?
  - mcguire 6y ago
    We can't trust people not to do stupid stuff.
  - D-Coder 6y ago
    > They are smart like that kid in high school who comes up with a formula to turn the world into silly putty, and is stupid enough to use it. So that kid isn't intelligent?
credit_guy 6y ago
This is like saying CD players will never be as good as vinyl record players because the first use digital signals (rational numbers) and the second analogue (real numbers).
- grogenaut 6y ago
  if you want to be pedantic record players are also digital because they can't represent anything tighter than an atom or the molecule of vinyl
  - mindcrime 6y ago
    Isn't everything digital to a point, since we can't ever measure anything smaller than the Planck length?
- jchrisa 6y ago
  I'm on record saying heterodox things about the Nyquist theorem and SACD 1-bit DAC, so you are on topic. :)
  - credit_guy 6y ago
    In that case, since we are here and it's Friday and everyone needs to take it easy from time to time, here's my proof that we don't live in a simulation: according to [1], ray tracing is computationally undecidable. For example, say you are in a museum at night, and a light bulb turns on in a room on the third floor, is it still dark in some room on the first floor? This problem is undecidable using the axioms of geometric optics. Of course, geometric optics is like real numbers, and the actual world is discrete: light is a finite collection of photons. So, you can do the simulation by simply emitting a number of photons from each light source and tracing them all the way until they are all absorbed. We can still live in a simulation, but one without algorithmic shortcuts, a simulation where you simulate every single photon. Now, I'm sure you can come up with your own version of proof that we can't live in a simulation using Nyquist's theorem. If you do, and your Friday is not too busy, please share. [1] https://users.cs.duke.edu/~reif/paper/tygar/raytracing.pdf https://users.cs.duke.edu/~reif/paper/tygar/raytracing.pdf
cowboysauce 6y ago
> Because computers operate on the rational numbers instead of the real numbers, Computers are just devices that perform computations. It's perfectly possible to construct computers that operate on values that are continuous and not discrete. In fact, such computers have been constructed before. They are know as analog computers and were used for things like numerically solving differential equations.
- karmakaze 6y ago
  This is not even true. We have symbolic processing that can manipulate and formulate with non-rational expressions. This article is so worthless.
- ogogmad 6y ago
  You don't need analog computation. The theory of Computable Real Analysis still assumes a digital computer: https://en.wikipedia.org/wiki/Computable_analysis https://en.wikipedia.org/wiki/Computable_analysis See here for a concrete application of the theory: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound-and-robust-solid-modeling-via-exact-real-arithmetic-and-continuity https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound... Another application is the Android calculator, which computes over exact real numbers in the sense described by Computable Analysis. Finally, it's debatable whether analog computation achieves true computation over the real numbers. The presence of physical noise, and the fact that many physical quantities (like electrical charge) are ultimately discrete at the quantum level, implies that it doesn't really work AFAICT.
  - caymanjim 6y ago
    It seems likely that absolutely nothing is analog. The best theories about physics are all quantized. The only things that we don't have strong quantum theories about are things we barely understand, like time and gravity. And that's just because we haven't found the quanta yet.
ethanwillis 6y ago
It has been a minute since I picked up my information theory book. However if I remember correctly continuous signals (that is functions of the reals) can be represented without loss with a finite (but sufficient number of) discrete samples.
- sgillen 6y ago
  As long as all those reals are computable ;) https://en.m.wikipedia.org/wiki/Computable_number https://en.m.wikipedia.org/wiki/Computable_number
  - ggggtez 6y ago
    It's fully possible for a computer to do symbolic math without reducing the symbols to a decimal.
    - sgillen 6y ago
      Of course! I meant my comment to be tongue in cheek, but saying that some numbers are uncomputable is not incompatible with symbolic math on a computer. Note that for example Pi is computable, despite having an infinite decimal expansion.
airstrike 6y ago
> Because computers operate on the rational numbers instead of the real numbers, they can never be embodied. They are always in a simulation... I read the exact opposite argument yesterday but not from an AGI perspective: https://getpocket.com/explore/item/a-new-theory-explains-how-consciousness-evolved https://getpocket.com/explore/item/a-new-theory-explains-how...
vidarh 6y ago
The counter-point to this: Brains. Brains are computational devices that are embodied.
guhayun 6y ago
Camera pixels are pretty real to me
ogogmad 6y ago
Actually, digital computers can compute over the real numbers. They can compute quite a lot over the real numbers, even. See https://en.wikipedia.org/wiki/Computable_analysis#Basic_results https://en.wikipedia.org/wiki/Computable_analysis#Basic_resu... This even has some concrete applications. See this: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound-and-robust-solid-modeling-via-exact-real-arithmetic-and-continuity https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound... Finally, saying that digital computers can't compute functions of the form Real -> Real is like saying that a computer can't compute functions of the form (Int -> Int) -> (Int -> Int). In other words, it's like saying that higher order functions are impossible.
Der_Einzige 6y ago
This actually makes sense to me, but for those who aren't familiar with set theory, you may want to link this for context: https://en.wikipedia.org/wiki/Continuum_hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis
mcguire 6y ago
"Real numbers" have some problems. Information density, for one. Imagine a real number, say 0.27777..., represented as a point on a piece of string, with zero being one end and 1.0 being the other. That point represents infinite information density. It also would seem to run afoul of some of quantum mechanics.

My hunch agrees with the paper. Because computers operate on the rational numbers instead of the real numbers, they can never be embodied. They are always in a simulation...

mattnewton 6y ago

Maybe I don’t understand your point, but our senses are also compressed to some extent. Your synapses fire or don’t fire, providing digitized input for some of your senses like hearing. At any point there is a discrete amount of hormones in your body. etc etc. That doesn’t seem categorically different from any man made sensor.

jchrisa 6y ago
Our sensorium could be indistinguishable from how it'd be in a simulation without impacting my point. Software can hop from host to host (all Turing machines can simulate each other) but living intelligence is embodied. Because of this, no matter how "smart" computers get, we can't trust them not to do stupid stuff. They are smart like that kid in high school who comes up with a formula to turn the world into silly putty, and is stupid enough to use it. There is more than one kind of intelligence, here the argument is that some kinds of intelligence require having skin in the game.
- sgillen 6y ago
  But would it be impossible to have artificial “skin in the game”? Is there no robot body that could serve this purpose?
  - selestify 6y ago
    Why isn’t computer hardware already as “embodied” in the physical world as our brain matter is?
- mcguire 6y ago
  We can't trust people not to do stupid stuff.
- D-Coder 6y ago
  > They are smart like that kid in high school who comes up with a formula to turn the world into silly putty, and is stupid enough to use it. So that kid isn't intelligent?

credit_guy 6y ago

This is like saying CD players will never be as good as vinyl record players because the first use digital signals (rational numbers) and the second analogue (real numbers).

grogenaut 6y ago
if you want to be pedantic record players are also digital because they can't represent anything tighter than an atom or the molecule of vinyl
- mindcrime 6y ago
  Isn't everything digital to a point, since we can't ever measure anything smaller than the Planck length?
jchrisa 6y ago
I'm on record saying heterodox things about the Nyquist theorem and SACD 1-bit DAC, so you are on topic. :)
- credit_guy 6y ago
  In that case, since we are here and it's Friday and everyone needs to take it easy from time to time, here's my proof that we don't live in a simulation: according to [1], ray tracing is computationally undecidable. For example, say you are in a museum at night, and a light bulb turns on in a room on the third floor, is it still dark in some room on the first floor? This problem is undecidable using the axioms of geometric optics. Of course, geometric optics is like real numbers, and the actual world is discrete: light is a finite collection of photons. So, you can do the simulation by simply emitting a number of photons from each light source and tracing them all the way until they are all absorbed. We can still live in a simulation, but one without algorithmic shortcuts, a simulation where you simulate every single photon. Now, I'm sure you can come up with your own version of proof that we can't live in a simulation using Nyquist's theorem. If you do, and your Friday is not too busy, please share. [1] https://users.cs.duke.edu/~reif/paper/tygar/raytracing.pdf https://users.cs.duke.edu/~reif/paper/tygar/raytracing.pdf

cowboysauce 6y ago

> Because computers operate on the rational numbers instead of the real numbers, Computers are just devices that perform computations. It's perfectly possible to construct computers that operate on values that are continuous and not discrete. In fact, such computers have been constructed before. They are know as analog computers and were used for things like numerically solving differential equations.

karmakaze 6y ago
This is not even true. We have symbolic processing that can manipulate and formulate with non-rational expressions. This article is so worthless.
ogogmad 6y ago
You don't need analog computation. The theory of Computable Real Analysis still assumes a digital computer: https://en.wikipedia.org/wiki/Computable_analysis https://en.wikipedia.org/wiki/Computable_analysis See here for a concrete application of the theory: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound-and-robust-solid-modeling-via-exact-real-arithmetic-and-continuity https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound... Another application is the Android calculator, which computes over exact real numbers in the sense described by Computable Analysis. Finally, it's debatable whether analog computation achieves true computation over the real numbers. The presence of physical noise, and the fact that many physical quantities (like electrical charge) are ultimately discrete at the quantum level, implies that it doesn't really work AFAICT.
- caymanjim 6y ago
  It seems likely that absolutely nothing is analog. The best theories about physics are all quantized. The only things that we don't have strong quantum theories about are things we barely understand, like time and gravity. And that's just because we haven't found the quanta yet.

ethanwillis 6y ago

It has been a minute since I picked up my information theory book. However if I remember correctly continuous signals (that is functions of the reals) can be represented without loss with a finite (but sufficient number of) discrete samples.

sgillen 6y ago
As long as all those reals are computable ;) https://en.m.wikipedia.org/wiki/Computable_number https://en.m.wikipedia.org/wiki/Computable_number
- ggggtez 6y ago
  It's fully possible for a computer to do symbolic math without reducing the symbols to a decimal.
  - sgillen 6y ago
    Of course! I meant my comment to be tongue in cheek, but saying that some numbers are uncomputable is not incompatible with symbolic math on a computer. Note that for example Pi is computable, despite having an infinite decimal expansion.

airstrike 6y ago

> Because computers operate on the rational numbers instead of the real numbers, they can never be embodied. They are always in a simulation... I read the exact opposite argument yesterday but not from an AGI perspective: https://getpocket.com/explore/item/a-new-theory-explains-how-consciousness-evolved https://getpocket.com/explore/item/a-new-theory-explains-how...

vidarh 6y ago

The counter-point to this: Brains. Brains are computational devices that are embodied.

guhayun 6y ago

Camera pixels are pretty real to me

ogogmad 6y ago

Actually, digital computers can compute over the real numbers. They can compute quite a lot over the real numbers, even. See https://en.wikipedia.org/wiki/Computable_analysis#Basic_results https://en.wikipedia.org/wiki/Computable_analysis#Basic_resu... This even has some concrete applications. See this: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound-and-robust-solid-modeling-via-exact-real-arithmetic-and-continuity https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound... Finally, saying that digital computers can't compute functions of the form Real -> Real is like saying that a computer can't compute functions of the form (Int -> Int) -> (Int -> Int). In other words, it's like saying that higher order functions are impossible.

Der_Einzige 6y ago

This actually makes sense to me, but for those who aren't familiar with set theory, you may want to link this for context: https://en.wikipedia.org/wiki/Continuum_hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis

mcguire 6y ago

"Real numbers" have some problems. Information density, for one. Imagine a real number, say 0.27777..., represented as a point on a piece of string, with zero being one end and 1.0 being the other. That point represents infinite information density. It also would seem to run afoul of some of quantum mechanics.