Comment author: thomblake 13 March 2009 08:11:30PM 3 points [-]

But you don't reject the hypothesis that "Barack Obama is a wooly mammoth" because it's absurd - nobody has seriously presented it. If someone had a reason to seriously present it, then I'd not dismiss it out of hand - if only because I was interested enough to hear it in the first place, so would want to see if the speaker was making a clever joke, or perhaps needed immediate medical care. As EY might say, noticing a hypothesis is unlikely enough in the first place that you should probably pay some attention to it, if the speaker was one of the people you listen to. cf. Einstein's Arrogance

Comment author: flexive 04 January 2016 08:21:58PM 1 point [-]

But you don't reject the hypothesis that "Barack Obama is a wooly mammoth" because it's absurd - nobody has seriously presented it.

Funny thing is that someone actually did.

In response to Tell Culture
Comment author: flexive 28 December 2015 10:07:06PM 0 points [-]

I definitely want to thank you for putting all of this in clear words and introducing these abstractions.

However out of my personal experience I find the advocacy of Tell-mode to be a terrible practical advice. Especially for people who haven't yet figured out some sort of a model on these and how to interact productively with people in their environment. I suppose a lot of my younger self social hardships came from using sort of Tell/Ask way too often and utterly failing at Guess.

There are areas where people seem to use Guess almost universally. The whole flirting thing is based on slowly converging Guesses. Noticing when someone does Guess because she just doesn't know how to respond and helping them out [or using their confusion to sway them in a direction you want] also seems an important social skill to me.

I think Tell mode should be attempted only after you grasped some minimal level of Guess [or whatever it is the norm in your environment] if at all.

Comment author: flexive 05 December 2015 10:17:02AM *  5 points [-]

"Direct action is not always the best way. It is a far greater victory to make another see through your eyes than to close theirs forever."

Kreia, KOTOR 2

Comment author: RichardKennaway 24 August 2015 11:15:45PM 1 point [-]

Probably the full formulation by Scott would help. Does anybody have a link?

This.

Comment author: flexive 27 August 2015 07:37:50PM 0 points [-]

Thank you.

Nice paper. Signs are treated accurately there of course. However call to "formal functions" in the end of the proof seems wacky at best. Formalizing it looks harder to me than the initial statement. At this point it should be easier to just look at the smoothness degrees of the norm on x_i = 0 hyperplanes.

If anybody knows what was meant, however, please clarify.

Comment author: Stephen 01 May 2008 07:08:37PM 1 point [-]

"Given the Born rule, it seems rather obvious, but the Born rule itself is what is currently appears to be suspiciously out of place. So, if that arises out of something more basic, then why the unitary rule in the first place?"

While not an answer, I know of a relevant comment. Suppose you assume that a theory is linear and preserves some norm. What norm might it be? Before addressing this, let's say what a norm is. In mathematics a norm is defined to be some function on vectors that is only zero for the all zeros vector, and obeys the triangle inequality: the norm of a+b is no more than the norm of a plus the norm of b. The functions satisfying these axioms seem to capture everything that we would intuitively regard as some sort of length or magnitude.

The Euclidian norm is obtained by summing the squares of the absolute values of the vector components, and then taking the square root of the result. The other norms that arise in mathematics are usually of the type where you raise the each of the absolute values of the vector components to some power p, then sum them up, and then take the pth root. The corresponding norm is called the p-norm. (Does somebody know: are all the norms invariant under permutation of the indices p-norms?) Scott Aaronson proved that for any p other than 1 or 2, the only norm-preserving linear transformations are the permutations of the components. If you choose the 1-norm, then the sum of the absolute values of the components are preserved, and the norm preserving transformations correspond to the stochastic matrices. This is essentially probability theory. If you choose the 2-norm then the Euclidean length of the vectors is preserved, and the allowed linear transformations correspond to the unitary matrices. This is essentially quantum mechanics. (Scott always hastens to add that his theorem about p-norms and permutations was probably known by mathematicians for a long time. The new part is the application to foundations of QM.)

Comment author: flexive 24 August 2015 10:43:31PM 1 point [-]

Scott Aaronson proved that for any p other than 1 or 2, the only norm-preserving linear transformations are the permutations of the components.

This seems to be true, but with the small note that you should add multipication of the coordinates by -1 [by any number from unit circle if the space is taken over complex numbers] and their compositions with permutations to the allowed isomorphisms. Never heard about this though, interesting.

However this does not generalize to all the norms. As Douglas noted below one can imagine norm simply as a central-symmetric convex body. And there are plenty of those. Now if we can fix a finite subgroup of space rotations and symmetries that strictly contains all the coordinate permutations and central-symmetry then we are done, since one can simply take convex hull of the orbit of some point as your desired norm. Symmetries and rotations of regular 100-gon on the plane would work for example.

If you choose the 1-norm, then the sum of the absolute values of the components are preserved, and the norm preserving transformations correspond to the stochastic matrices.

Hmm, something fishy is going with signs in the whole argument and here I am completely lost. What if I take 2x2 matrix with all entries equal to 1/2 and a vector (1/2, -1/2)? Probably the full formulation by Scott would help. Does anybody have a link?

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