I remember, at the turn of the millennium, when lava lamps were actually used to produce entropy. An SGI project called lavarand had a battery of the things bubbling up and down, used low-end digital cameras to capture images and, after some postprocessing, hashed the results to get what was effectively a fairly good PRNG.
Still, I'd say that it's "close enough" to be considered a real RNG. There's almost no way to see a pattern in it, and I'm pretty sure that it would be completely impractical to simulate the contents inside, even if you knew all the initial conditions.
Technically, it's only "deterministic" if you can fully establish the initial state. That's not possible, if for no other reason than the Uncertainty Principle [1] prevents you from measuring the initial conditions carefully enough. Plus you're not really dealing with a closed system, so basically the entire Universe can influence your system going forward. Chaos theory [2] says that you're fighting a losing game if you think it's deterministic.
That's a really good question. I'd love to hear the answer from a physicist in the know.
Assume you could overcome the uncertainty principle or observer effect and you could fully determine the initial conditions of the entire system. You knew the position and momentum of every atom. You knew the spin of every electron. Etc. Etc. Etc.
Doesn't the inherent nature of quantum mechanics say that it's stillimpossible to predict the state of that system at some future time? Interactions only occur probabilistically, and there is no way to predict them a priori.
In terms of predicting the "future state", it depends on what you want to call the "state".
If I know the complete wave function of the system, then knowing the wave function at a future point in time is trivial. Just apply the time evolution operator.
However, knowing the wave function at a given point in time doesn't tell me the position or momentum - it just tells me the probability with which I'll measure a given position or momentum. So knowing the "state" still means that my measurements will have random components.
On a slightly different note, when you talk about knowing the exact position and momentum of every particle, you're not talking about overcoming a physical limitation, but a mathematical one. To put it differently, if I know that the momentum is exactly zero, I do know that the position is. The problem is that the position is NaN. If the position isn't NaN, then I know longer know the momentum isn't precisely defined.
> If I know the complete wave function of the system, then knowing the wave function at a future point in time is trivial. Just apply the time evolution operator.
But wouldn't the regular measurement cause a collapse onto a randomly-chosen eigenstate of the measured operator? That is, if we have a PRNG based on a regularly measuring the lava lamp, then to predict the state after N steps, we not only have the issue of the randomly chosen N-th measurement but also have to take into account the random results of the N-1 previous measurements, which can potentially evolve into entirely new directions.
Overall, it's difficult to place a lava lamp over human time scales, as both are far from the usual quantum/classical limits: We know that even in thousands of years’ time, Earth will still revolve mostly deterministically (in the classical sense) around the sun. Similarly, electrons will hardly ever behave deterministically. Lava lamps and a couple of years are oddly in between.
You're a couple of abstraction levels lower than where I aimed my post :-)
You're absolutely right that everything breaks down after a measurement. However, I'd begun my hypothetical by assuming that we had some magical technique for getting the complete wave function. If our measurements again give us the complete wave function, then we just use the time evolution operator on that again.
I guess what I'm trying to say is that we should be okay after N-1 measurements, as long as we're allowed to see the result of that final measurement. You're right, though, that we rapidly lose the ability to make any predictions if some jerk keeps measuring the system. I think that there's also an Everettian argument that, if you haven't given me the complete wave function for the jerk making the measurements, then you didn't really give me the the complete wave function of the system. However, that's pushing outside my area of expertise.
>If I know the complete wave function of the system, then knowing the wave function at a future point in time is trivial. Just apply the time evolution operator.
I was under the impression that the Bell experiments indicated that there was randomness not accounted for by our inability to measure with 100% accuracy (because of the uncertainty principle). Doesn't the falsity of hidden variable theory mean that actual randomness is present in quantum events, and we can't predict the future state perfectly even if we had the exact wave function of the system?
I could be totally off base here; please set me on the right track!
That's a good question and you're actually pretty close to the right track. The catch is the difference between the wave function and the actual measurement. Quantum mechanics and Schrodinger's equation gives us the wave function. If you know the current wave function, there's a well established way to calculate the wave function at a future point in time.
The catch is that the wave function doesn't tell us values - only probabilities. So knowing the probability distribution at any given point in time doesn't make anything less random because it's all still probability and not actual measurements.
As an analogy, imagine a casino where the roulette wheel has an LCD label for each number. Each round, they change the layout of the wheel. Sometime, they make all the labels black. Other times, it's 2/3rds red and all the numbers are primes. They also have a big book in the corner that tells you what the layout of the roulette wheel will be each round. As a result, if I put down a bet, you can tell me the odds of my bet coming up each round. However, you still can't actually tell me what will WIN the round.
The layout of the labels is like the wave function, the pages of the book are the time evolution operator, and the roulette ball is the fundamental randomness of quantum mechanics. The results are still random, just as Bell said that they must be, but we are at least allowed to know the odds.
Yeah, I meant "deterministic" as in "generated using standard computations starting from a simple seed." Whether the lava lamp itself is deterministic, or the Universe moreover, is another issue.
Didn't it turn out to be the case that SGI discovered that they got the same amount of randomness from the CCD from just taking a picture with the lens cap on?
It's hard to quantify randomness. It's possible that whatever test(s) they were using reported similar results, even though the data from a lens-capped camera might be somewhat predictable if you know the physical properties of the device.
I know individual models of camera frequently have very similar thermal and electrical noise profiles, so that wouldn't be too surprising to me.
I have a lava lamp on my desk at work- not only does it attract attention (more so than the more boring plasma globes), it's also very relaxing to watch when thinking about some bug or implementation detail.
Unfortunately, the quality of the ones you find today is pretty dismal, and they're easily ruined if you leave them on for too long or if they stay in sub-optimal temperatures (e.g. an office building that gets cold over the weekend). Collectors seem to favor the Lava Lite from the 80s for durability.
I also do. And - funnily enough, once I got mine on my desk, one of the others in the office brought his in from home, and a third engineer asked his wife for one for Christmas so now he has one on his desk as well...
Oh, re. reliability, I turn mine on every morning, and off when I leave each night. I wouldn't leave it on overnight. One of the other guys has his on a timer, I believe.
Sadly, the article didn't mention one big problem that will become worse and worse going forward: incandescent bulbs are on the way out.
I have a lava lamp that uses a 40 W "appliance light bulb" as a light and heat source. I haven't been able to buy a "frosted" appliance bulb in a number of years. I was able to buy a "clear" bulb a while ago, but the light isn't quite as pleasant from it. And in a few years I'm sure all incandescent bulbs will go the way of the Dodo bird.
This was my immediate thought a few paragraphs in. In my head, I was thinking, "That wastes a lot of energy, and you have to pick your color at purchase time." Why not formulate a combination of fluids that requires less heat to operate, and use a multicolor LED for infinite colors?
Thanks for the pointer. I see that the bulborama website (the actual seller on Amazon) has lots of obscure bulbs. I love LED lightbulbs, e.g. the Philips 60 W equivalents I've been buying. But for some applications the older incandescents and halogens are better.
I've had a rough design for something like this in my notes for a while now, under the heading "what do to when you can't buy incandescent bulbs anymore?" It's a serious concern for me as my collection of 30 or so Lava Lamps (from the 70s through modern ones) are far less interesting when they're cold.
That is the fault of the EU, they banned sales of incandesent lightbulbs in order to be green. Meanwhile the retards move back and fourth between two cities every 6 months and fly all over Europe.
Is the word "retard" really a necessary or useful addition to this sentence? It is roughly the equivalent of calling someone "nigger" or "faggot" as an insult. When used in this way it is demeaning to the developmentally disabled.
I understand that this is somewhat common usage on the Internet at large, but I believe we'd all like to see Hacker News be better than the Internet at large. And, I'm sure you don't intend harm or insult anyway (other than the "people who move back and fourth between two cities"); but, the harm is there, whether intended or not.
So, I can't call out racism when I see it? Can't call out misogyny in a conversation with only men in it? Can't call out oppressive language in any circumstance unless I am directly effected by it? No, I don't think that's the way it works, and it's not the way it should work. I hit the privilege lottery: I'm white, male, able-bodied, middle class, American. If I'm unwilling to call oppression what it is, I'm empowering the oppressive behavior.
I believe my request was polite and stated without malice or (much) judgment. I would ask you to consider where your desire to argue with that request comes from.
Given that Mathmos is in the UK, which is still part of the EU, at least last time I checked, how would they still be in business if bulbs suitable for lava-lamps were banned?
There was an EU law on incandescent bulbs, but it only applies to general purpose lighting bulbs without reflectors, not special purpose bulbs, heat lamps, industrial or automotive.
" Bottles are still filled by hand (one employee is able to get through about 400 per day); as a result, Mathmos lamps start at $80 while cheaper, mass-produced lamps sell for as little as $15. "
Let's do a little math. Assuming the person doing that makes $20/h, so $160/day. That makes the cost of the employee per lamp $0.4.
I dont think the $65 price difference to China can be explained this way.
Add on the cost of premises, power, distribution. Then factor in the costs of the components. And realise the wholesale price will be half the retail if they are selling through shops. Direct sales could be full value.
DIY is still a pretty big pain, I've tried several different kinds from those pages. I have to give Mathmos and/or Lava-Lite credit, they /do/ have the chemistry down pretty well. The commercial ones are far more reliable than homebrew.
Funnily enough, my lava lite quite very reliably after a couple hours. It will run normally for a while, and then it will just have a big blob in the bottom.
I suspect that there somehow is not enough heat being dissipated at the top. I had toyed with the idea of 3D printing a heat sink, but my design would have cost about $100 USD.
I actually have a USB temperature probe, it would be simple enough to just plot the temp over time and see what's going on.
[0]http://en.wikipedia.org/wiki/Lavarand