What are the alternative initiatives that you mentioned. Would you please share more?

[1] http://research.microsoft.com/en-us/um/people/lamport/pubs/proof.pdf

]]>I was browsing on TiddlySpace just now, and I saw an announcement that they are shutting down in December. I do not know if you are aware of this. You might want to back up all that you have written about the P vs NP approach.

]]>this is an amusing blog by lipton & have cited it myself in my own blog. however, the ref to P vs NP as a “disease” imho while obviously facetiously intended is imho somewhat, to some degree, in poor taste. yes I know this is a joke. but if it really is a joke, Id like to ask a question on tcs stackexchange, which am sure would probably get voted down– what are cases of complexity theorists referring to their own field in disparaging and near-derogatory terms?

have seen this in multiple cases. of course its due to frustration of lack of progress/results (in many ways not all that much better than those found by shannon 1/2 century ago).

yes, obviously this is “inside baseball” and experts need to have some leeway to talk about it informally/casually esp in blogs & informal communication etc. but on the other hand, lots of ppl are listening to these blog including students and possible future researchers.

another point is that P vs NP is not an abstract problem like many others lipton cites as “diseases”. it has huge practical implications, possibly almost more so than almost any other math problem. can anyone think of a math problem with greater practical implications? maybe a theorem in thermodynamics? to me P vs NP actually has a lot of analogies to thermodynamics theorems on work/energy/information– ie almost an as-yet undiscovered law of physics.

in short its an elite/superb problem of highest calibre. a better analogy for public purposes would be Everest in its pre-summitted state. we can all agree on that, right? doesnt that sound much better? or say, if you are really pessimistic, Olympus Mons on Mars. but even NASA is planning to visit mars one day.

]]>It is questionable however whether it is worth doing, because to start one need first read my book. I realize that not many people will go read it.

I spend some time attempting to prove this conjecture, but failed.

Dear Gowers, what you advise on this? Should I make a tiddler for this my problem? If yes, in your tiddler or to create my own?

]]>There’s the permalink into a TiddlyWiki that you’re familiar with.

There’s also a first class link to that tiddler directly, outside of TiddlyWiki. For your use you may never need to use that link, but it is one that search index systems might stumble upon so may get exposed via searches. So having it render the math might be worthwhile.

With regard to viewing the tiddler while editing it’s likely you could include what’s in the ViewTemplate in the EditTemplate. That’s the sort of thing that the the tiddlywiki google group could probably provide a good answer for. The boring but workable way to accomplish the same thing without additional code would be to put to browser windows side by side.

]]>One reason that would be nice is that at the moment if I make a mistake in the LaTeX, I have to hold in my head what and roughly where the mistake was when I click on “edit”. It can sometimes be a bit tedious to do that in a way that it would not be tedious if I could see the compiled text at the same time as the edited text.

]]>In the meantime I figured out how to make the mathjax show up properly from outside TiddlyWiki when viewing a single tiddler.

]]>I’m one of the maintainers and primary developers of TiddlySpace. I’m extremely happy to see the value you are getting out of it. It would be fantastic to start a conversation to figure out ways of making TiddlySpace more useful for you and people who would like to do similar things. There are a lot of features that don’t make themselves immediately obvious and functionality which needs a push to take it from prototype to useful.

I’m personally very interested in opening up academic publishing and discourse to a wider audience, especially using web based tools.

Please contact me if you have the time and interest to talk about it more.

]]>Let the payoff set include:

(Condition A) all sequences where .

(Condition B) out of the sequences where , sequences where .

(Condition C) out of the sequences where and , sequences where and .

Player I starts at . Condition A will force to be a non-parity changing mood. Condition B also indicates neither nor can change parity. Hence Player II has no parity control after the first move.

If Player II continues at so Player I can use his or her turns to make the parity the opposite of what Player II chose. (This is Player II’s “out” which will allow the set to be winning in the unmodified version of the game.)

If Player II continues at , following condition C Player I matches at . If Player II continues at , then Player I matches at and wins. If Player II continues at , then Player I continues at such that , forcing Player II to make and being defeated by condition B.

If Player II instead continues at , a similar argument applies.

]]>Let the payoff set include:

(Condition A) all sequences where .

(Condition B) out of the sequences where , sequences where .

If Player I starts at , condition A forces Player II to play at and make a parity choice. Now condition B means that Player II no longer has any control over the parity (since Player II’s only chance to win now is for ) so Player I can use his or her turns to make the parity the opposite of what Player II chose. If it wasn’t for the parity choice, Player II would have won.

]]>Suppose your subsets can be described by the set of polynomial equations of degree d. write down all monomials up to degree d . expand the set of polynomial equations describing the constraints by multiplying by monomials from and taking them modulo the current set of equations. After few steps you get saturated system.

The complexity measure is the ratio between the size of null space of saturated system and the size of .

The linear system is easy: the ratio is close to 0.

The simple NP-complete problems can be encoded as and say partition problem for saturation. The complexity is .

The complexity of the subset is the minimum simplicity across all possible encoding. It is also possible to define measure with respect to d+1, so that non-linearity of the system appears in the problem, and use as the measure the size of null-space itself, without normalization.

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