I make the following prediction : the transfiguration exercise of ch. 104 foreshadows the possibility of safely transfiguring a certain kind of explosive, that relies on containing several components that will explode upon contact. The ch. 104 exercise tells us that containment chambers can be formed first, and their contents afterwards, such that the bomb will not accidentally explode during transfiguration.
Plasmon
Karma: 865
binding constraint that you absolutely must make sure he doesn’t say certain words at school
What would happen if he did say those words at school? Would they expel him? Does he know what the consequences of saying those words at school are, and does he think these consequences are insufficiently bad to act as an effective deterrent?
There are other options. Especially in cases where requiring this is illegal, forging such a proof may be an option. Or, answer “If I give you proof that my previous salary was X, I will precommit to only accept this job if you pay at least X + 20%”.
Why would anyone be able to sell an item with a given pricing scheme like 1/n?
On downloaded, digital goods, this would be simple.
If their competitor is undercutting them on the first item, they’ll never get a chance to sell the latter ones. And besides there’s no reason such a scheme would be profit-maximizing.
Please see the numerical example in this comment
I imagine the following:
Suppose 2 movies have been produced, movie A by company A and movie B by company B. Suppose further that these movies target the same audience and are fungible, at least according to a large fraction of the audience. Both movies cost 500 000 dollars to make.
Company A sells tickets for 10 dollars each, and hopes to get at least 100 000 customers in the first week, thereby getting 1000 000 dollars, thus making a net gain of 500 000 dollars.
Company B precommits to selling tickets priced as 10 f(n) dollars, with f(n) defined as 1 / ( 1 + (n-1)/150000 ) , a slowly decreasing function. If they manage to sell 100 000 tickets, they get 766 240 dollars. Note that the first ticket also costs 10 dollars, the same as for company A.
200 000 undecided customers hear about this.
If both movies had been 10 dollars, 100 000 would have gone to see movie A and 100 000 would have seen movie B.
However, now, thanks to B’s sublinear pricing, they all decide to see movie B. B gets 1270 000 dollars, A gets nothing.
Sublinear pricing.
Many products are being sold that have substantial total production costs but very small marginal production costs, e.g. virtually all forms of digital entertainment, software, books (especially digital ones) etc.
Sellers of these products could set the product price such that the price for the (n+1)th instance of the product sold is cheaper than the price for the (n)th instance of the product sold.
They could choose a convergent series such that the total gains converge as the number of products sold grows large (e.g. price for nth item = exp(-n) + marginal costs )
They could choose a divergent series such that the total gains diverge (sublinearly) as the number of products sold grows large (e.g. price for nth item = 1/n + marginal costs )
Certainly, this reduces the total gains, but any seller who does it would outcompete sellers who don’t. And yet, it doesn’t seem to exist.
True, many sellers do reduce prices after a certain amount of time has passed, and the product is no longer as new or as popular as it once was, but that is a function of time passed, not of items sold.
I was unclear, of course it is real physics. By “real” I mean simply something that occurs in reality, which quantum nonlocality certainly does.
Quantum nonlocality—despite being named “nonlocality”- is actually local in a very important sense, just like the rest of physics : information never moves faster than c.
Every single physical theory that is currently considered fundamental is local, from general relativity to quantum mechanics.
I dislike the wikipedia article on the subject, it gives far to much credence to the fringe notion that maybe there is a way to exploit entanglement to get faster-than-light information transfer.
The quantum nonlocality article is much better, it correctly points out that
it (quantum nonlocality) does not allow for faster-than-light communication, and hence is compatible with special relativity.
Real physics is local. The graphs, to the extent that there are any, are embedded in metric spaces, have small upper bounds on the number of edges per vertex, are planar, …. generally there is plenty of exploitable structure beyond the pure graph-theoretical problem. This is why I do not think hardness results on abstract graph-theoretical problems will be a great obstacle for practical problems.
Recently, there has been talk of outlawing or greatly limiting encryption in Britain. Many people hypothesize that this is a deliberate attempt at shifting the overton window, in order to get a more reasonable sounding but still quite extreme law passed.
For anyone who would want to shift the overton window in the other direction, is there a position that is more extreme than “we should encrypt everything all the time” ?
What you mean is there’s no way to write Pi with finitely many digits, in any basis.”
pi=1 in base pi
… but that’s not what you meant :)
doctors, who know jack shit about statistical and causal inference
Another is an asymmetry in the average temperatures on opposite hemispheres of the sky. This runs counter to the prediction made by the standard model that the Universe should be broadly similar in any direction we look.
Why doesn’t this just mean that we are moving w.r.t. the rest frame of the CMB? The signal is redshifted in the hemisphere we’re moving away from, and blueshifted in the hemisphere we’re moving towards, so it would look hotter in the hemisphere we’re moving towards.
The prior distribution over hypotheses is distribution over programs, which are bit strings, which are integers. The distribution must be normalizable (its sum over all hypotheses must be 1). All distributions on the integers go to 0 for large integers, which corresponds to having lower probability for longer / more complex programs. Thus, all prior distributions over hypotheses have a complexity penalty.
You could conceivably use a criterion like “pick the simplest program that is longer than 100 bits” or “pick the simplest program that starts with 101101″, or things like that, but I don’t think you can get rid of the complexity penalty altogether.
Solomonoff induction justifies this : optimal induction uses a prior which weights hypotheses by their simplicity.
Two is an odd prime number, because two isn’t odd.
Languages : what’s a syllable?
what happens if we find all these biologically feasible exoplanets that just don’t have any life on them?
That would be evidence for an early filter over a late filter, so it would probably be good news.
The fact that quantum mechanics conserves energy is stronger evidence for the hypothesis that reality conserves energy than the fact that classical mechanics conserves energy. He is saying “our best model of reality conserves energy” which is very relevant.