6 ms·

While I wouldn't entirely discount the notion that we're living in a simulation, I suspect that this measurement is probably quite problematic, for various reas

by nkoren 14y ago

While I wouldn't entirely discount the notion that we're living in a simulation, I suspect that this measurement is probably quite problematic, for various reasons other people have addressed. Nevertheless, this article got me thinking: Really? Can we actually simulate any part of the universe with 100% quantum accuracy? I hadn't heard about that, and it seems a bit implausible to me. But okay, fine, let's take it as a given that we can in fact simulate a volume a few femtometres in diameter, as the article says. Furthermore, let's say that our universe-simulating capability increases in line with Moore's Law, doubling every 18 months without regards for the limits of silicon or anything else. The question is: how long would it take us to become those universe-simulating gods? This is not a serious question, just a fun little exercise. If all of the above are true, then what will we be able to simulate, and when?: 2019: The nucleus of a single gold atom (8.45 femtometres) 2077: An entire helium atom (62 picometres) 2090: A cesium atom (423 picometres) 2115: A ribosome (20 nanometres) 2152: A red blood cell (7 micrometres) 2192: The smallest vertibrate, Paedophryne amauensis (7.7 millimetres) 2217: A human brain (150 millimetres) 2245: A small apartment and its occupants (10 metres) 2274: A small town (1 kilometre) 2335: Planet Earth (12,742 kilometres) 2407: The earth-moon system (812,000 kilometres) 2454: The inner solar system, inclusive of the asteroid belt (6.6 AU) 2475: The entire solar system, to the extremities of the Kuiper built (200 AU) 2516: Sol's sphere of influence, to the edges of the Oort cloud (100,000 AU) 2589: The Milky Way galaxy (120,000 light years) 2617: The Local Group of galaxies (10,000,000 light years) 2670: The observable universe (29,400,000,000 light years) ...But seeing as none of the initial assumptions are likely to be true, alas for all that. Would be kind of cool, though! (also, a femtometre is really bloody small) [Edit: mixed up radius & diameter for the size of the observable universe. Hate it when that happens!]

ctdonath 14y ago
http://xkcd.com/505/ http://xkcd.com/505/
- nkoren 14y ago
  Bloody hell, that's brilliant. Had missed that one somehow!
- jere 14y ago
  Because I thought for sure it would be 605, here is 605: http://xkcd.com/605/ http://xkcd.com/605/ As acknowledged, this is not a serious answer. Because following Moore's law for 200 more years (the time at which we get a simulated human brain) allows 8e40 times the computing power we currently have.
aqme28 14y ago
You could perhaps simulate two isolated gold nuclei with twice as much computational power as one gold nuclei, but you're forgetting that everything in this universe interacts with everything else. As you get to three, four, five, 1000 gold nuclei, your computational requirements will be O(n^2), and then even the exponential growth of our computational power won't be as big of a deal.
- Retric 14y ago
  That may might not be true. Assuming nothing travels faster than the speed of light. Next assume your calculating all information in some unit of space. Now for small increases in time you can ignore everything further than that time * speed of light. Now, repeat that process for each point in space for 1 tick. Then start over. Think of it like simulating a really large map of 'game of life', you can chunk them into separate threads and only pass information about the overlap after each calculation.
  - ahelwer 14y ago
    We already do this for electromagnetic waves. See: http://en.wikipedia.org/wiki/Finite-difference_time-domain_method http://en.wikipedia.org/wiki/Finite-difference_time-domain_m... Since each field component in the voxel depends only on its immediate neighbours, you can perform massively parallel simulations on GPUs. I've worked on this stuff, it's pretty neat. Discretizing continuous differential equations onto a voxel lattice is how a lot of things these days are done, including seismic and medical imaging.
Daniel_Newby 14y ago
> Really? Can we actually simulate any part of the universe with 100% quantum accuracy? Lattice QCD has been used to simulate an entire proton[1] and derive its mass to an accuracy of a few percent. [1]Popular descriptions of the proton simply call it a triplet of quarks, but it actually contains several virtual quarks too and a bunch of gluons with ever changing bonds and positions. The average amount of crap flying around inside the proton determines its mass, and you can find it by simulation.
- Confusion 14y ago
  An accuracy of a few percent is awesome. It's just that the cumulative accuracy for larger systems becomes lousy pretty fast.
thedufer 14y ago
Its definitely not 100% accurate. We can calculate observables like mass from basic principles to +/- 2-3%. However, there are a few things they didn't mention. First, these things are not simulated at anything approaching realtime. Things are simulated on timescales almost as vanishingly small as the space-scales, and even this takes hours on some of the largest research clusters. Second, these aren't simulations in the sense that you're used to. They involve taking a volume in 4-space (3x space and 1x time) and using Monte Carlo techniques to approximate what happens in that space-time. It is non-trivial to pick up where (in time) one calculation left off and start a new one, and would introduce a lot of error. Third, the calculation time doesn't scale with the volume (or even the 4-space volume). Naively, it scales with volume squared.* We actually do somewhat better than this right now, but again, approximations are required to get there. *Its actually the number of points in the lattice squared, so increasing accuracy by decreasing the space between sites scales as you'd expect. Source: I spent more time than I care to admit writing a very simple version of these simulators as an undergrad.
- guylhem 14y ago
  Why should we have to make it 100% accurate ? I mean, just like with videogames emulators, it can be good to simplify some things. That's how most supernes emulators were made until very recently IIRC. I'm not a physicist, but for exemple if the subatomic particles can't be accurately modeled, couldn't they just be replaced by atomic particles and special case handling?
  - nkoren 14y ago
    (Standard disclaimer: IANAQP, but...) I think you're on to something. Rather than model each quark and gluon explicitly, you could just model probabilistic interactions at much larger scales. Maybe put in some special case handling so that if an observer within our simulated universe were to go looking for quarks and gluons, they'd find them. If they looked hard enough, some gaps might show: since subatomic particles are not actually being simulated in a continuously deterministic fashion, it would never be possible to observe both position and velocity simultaneously. An observer looking at an electron shell in two discrete moments would not be able to track a continuous orbit between them, since they'd actually just be seeing two separate expansions of what is effectively a lossy compression algorithm. Also, it ought to be possible to model only the macroscopic dimensions explicitly, replacing the other seven microscopically enfolded dimensions with a bunch of arbitrary constants that accomplish more or less the same thing. Might drive our observers a bit batty, because those constants would appear to refer to a bunch of microscopic enfolded dimensions, which they'd never actually be able to detect. Right, now I'm starting to freak myself out...

by nkoren 14y ago

ctdonath 14y ago

http://xkcd.com/505/ http://xkcd.com/505/

nkoren 14y ago
Bloody hell, that's brilliant. Had missed that one somehow!
jere 14y ago
Because I thought for sure it would be 605, here is 605: http://xkcd.com/605/ http://xkcd.com/605/ As acknowledged, this is not a serious answer. Because following Moore's law for 200 more years (the time at which we get a simulated human brain) allows 8e40 times the computing power we currently have.

aqme28 14y ago

You could perhaps simulate two isolated gold nuclei with twice as much computational power as one gold nuclei, but you're forgetting that everything in this universe interacts with everything else. As you get to three, four, five, 1000 gold nuclei, your computational requirements will be O(n^2), and then even the exponential growth of our computational power won't be as big of a deal.

Retric 14y ago
That may might not be true. Assuming nothing travels faster than the speed of light. Next assume your calculating all information in some unit of space. Now for small increases in time you can ignore everything further than that time * speed of light. Now, repeat that process for each point in space for 1 tick. Then start over. Think of it like simulating a really large map of 'game of life', you can chunk them into separate threads and only pass information about the overlap after each calculation.
- ahelwer 14y ago
  We already do this for electromagnetic waves. See: http://en.wikipedia.org/wiki/Finite-difference_time-domain_method http://en.wikipedia.org/wiki/Finite-difference_time-domain_m... Since each field component in the voxel depends only on its immediate neighbours, you can perform massively parallel simulations on GPUs. I've worked on this stuff, it's pretty neat. Discretizing continuous differential equations onto a voxel lattice is how a lot of things these days are done, including seismic and medical imaging.

Daniel_Newby 14y ago

> Really? Can we actually simulate any part of the universe with 100% quantum accuracy? Lattice QCD has been used to simulate an entire proton[1] and derive its mass to an accuracy of a few percent. [1]Popular descriptions of the proton simply call it a triplet of quarks, but it actually contains several virtual quarks too and a bunch of gluons with ever changing bonds and positions. The average amount of crap flying around inside the proton determines its mass, and you can find it by simulation.

Confusion 14y ago
An accuracy of a few percent is awesome. It's just that the cumulative accuracy for larger systems becomes lousy pretty fast.

thedufer 14y ago

Its definitely not 100% accurate. We can calculate observables like mass from basic principles to +/- 2-3%. However, there are a few things they didn't mention. First, these things are not simulated at anything approaching realtime. Things are simulated on timescales almost as vanishingly small as the space-scales, and even this takes hours on some of the largest research clusters. Second, these aren't simulations in the sense that you're used to. They involve taking a volume in 4-space (3x space and 1x time) and using Monte Carlo techniques to approximate what happens in that space-time. It is non-trivial to pick up where (in time) one calculation left off and start a new one, and would introduce a lot of error. Third, the calculation time doesn't scale with the volume (or even the 4-space volume). Naively, it scales with volume squared.* We actually do somewhat better than this right now, but again, approximations are required to get there. *Its actually the number of points in the lattice squared, so increasing accuracy by decreasing the space between sites scales as you'd expect. Source: I spent more time than I care to admit writing a very simple version of these simulators as an undergrad.

guylhem 14y ago
Why should we have to make it 100% accurate ? I mean, just like with videogames emulators, it can be good to simplify some things. That's how most supernes emulators were made until very recently IIRC. I'm not a physicist, but for exemple if the subatomic particles can't be accurately modeled, couldn't they just be replaced by atomic particles and special case handling?
- nkoren 14y ago
  (Standard disclaimer: IANAQP, but...) I think you're on to something. Rather than model each quark and gluon explicitly, you could just model probabilistic interactions at much larger scales. Maybe put in some special case handling so that if an observer within our simulated universe were to go looking for quarks and gluons, they'd find them. If they looked hard enough, some gaps might show: since subatomic particles are not actually being simulated in a continuously deterministic fashion, it would never be possible to observe both position and velocity simultaneously. An observer looking at an electron shell in two discrete moments would not be able to track a continuous orbit between them, since they'd actually just be seeing two separate expansions of what is effectively a lossy compression algorithm. Also, it ought to be possible to model only the macroscopic dimensions explicitly, replacing the other seven microscopically enfolded dimensions with a bunch of arbitrary constants that accomplish more or less the same thing. Might drive our observers a bit batty, because those constants would appear to refer to a bunch of microscopic enfolded dimensions, which they'd never actually be able to detect. Right, now I'm starting to freak myself out...