Yes, I've seen it mentioned; no, I haven't visited it. If I am ever to go to Christmas Island's domain, or Tokelau or the like, first I'll make sure there is good reason for it.
I don't want to hear a word from anybody... in Los Angeles our judges are hip! So there.
I believe the judge is novelist Jerzy Kozinski's son...and I seem to recall novels by the latter where women's lust reached new (for adolescent me, then) extremes:-)
With all the clamor of protest I hear, though, I cannot help wondering: just WHO, then, visit by the thousands all those extreme-porn sites, or buy Master Baiter Ira's videos?!:-P
Actually, there is validated parking next to the Los Angeles Courthouse... and travel expenses, some fraction of a dollar per mile. So the $15 go to cover lunch:-)
Justice is a spare, Spartan affair:-O
If you want to get off duty, you can get creative. When asked whether you are able to fairly assess the evidence presented, you reply: "No need. I'm PSYCHIC. I already KNOW who is guilty and who isn't!"
Corner Bakery's WiFi is not slow where I use it, and the coffee is OK (not to mention much less expensive than Starbucks, as they offer free refills). The only quaint thing is that they attempt to "block pornography", i.e. what they think might be pornography:)
I do not consider it proper nowadays to pay for WiFi at a coffeeshop -- your business ought to be enough. If I find myself at a Starbucks, now that the Safari User Agent trick no longer works:) I hook up my Blackberry and use it as a modem. So there!
There IS a reason to ask the question; the answer matters, be it to a few.
It has nothing to do with physical applications -- more than half the posts here are irrelevant, because Math not only is not physics; it is not a physical science at all.
If Math is "discovered", i.e. if mathematical objects lead a charmed life of their own and are not artifacts of ours, if the notions of "real numbers", "set of real numbers", "the set of sets of real numbers" are meaningful and well-defined, then it DOES maker sense, for example, to look for an answer to the Continuum problem (Cantor's Continuum Hypothesis, "CH")...beyond the current axiomatic framework (ZFC), which is known not to imply CH, nor not-CH.
If Math is not, one might retreat into formalism, or formalism of sorts, where CH (among other things) is a consequence of this and its negation is a consequence of that, and so on and so forth...without commitment to, or maybe even a notion of, what is ultimately true. About the real numbers, if you will -- this is no abstruse question regarding large cardinals or something.
Some mathematicians are formalists on Sundays; not always, though, when they are grappling
with a problem:-P
[ Compare: "there are few atheists in the trenches". ]
My answer, if you haven't guessed yet: Math is discovered.
It would be a blessing were the gPhone to stir up a field mired in lack of purpose and direction. I'm tired of seeing phone companies busy building elaborate business models instead of better phones. Almost the opposite -- consider AT&T's attempt to kill GPS in its Blackberries.
I wouldn't worry about UI... There is precedent for having both a robust, no-frills terminal interface for jocks AND elaborate KDE, Gnome or what have you GUI interfaces for the spoiled:-)
The gPhone might even use [L-word]. How fitting for a Windows Mobile killer.
>If there is no clear definition is because there is no clear-cut, established procedure to determine when an initial condition is computationally simple enough to be acceptable. Some would wish universal computation stick to a finite initial condition with an unbounded tape filled with "blanks", because that's the only case where the theory is entirely clear.
Uh, no -- THAT is THE case envisioned by ordinary recursion theory. That is the meaning the TECHNICAL TERM "universal Turing machine" has. If "something else" is "universal" in some other sense, fine -- but please, CALL IT SOMETHING ELSE! (Whether it helps sell a book or not:-P )
How do I explain this?! Example: it might be reasonable to call a function from the reals to the reals "continuous" if it assumes "all the in-between values" -- that is, for any a and b, for any t between f(a) and f(b) there is an s between a and b such that f(s) = t. Unfortunately, there already exists a familiar, epsilon-delta definition of "continuous" that turns out to be non-equivalent to the previous one (indeed, stronger). You cannot, then, say "continuous" and mean the _former_ definition... just because it "sounds reasonable"! OK? "Continuous" is a technical term. So is "universal Turing machine"!
>However, others accept generalizations such as periodic "blank" words as long as they remain computationally simple enough (possibly generated in the same fashion as an unbounded "blank" tape).
You don't have to "generate" an unbounded blank tape, you simply assume it contains "blanks", in other words, anything BUT your symbols for "0" and for "1". And you don't have to prepare anything infinite -- "unbounded" means at any step you might have to make available one more tape square. If the machine "never halts", it will be using longer and longer finite stretches of tape, forever. At no moment will it have "used up infinitely much tape".
Preparing an infinite tape, with whatever contents, is beyond the pale of ORT (ordinary recursion theory). I myself said, it IS done, itself and other, more complex things -- but when we do it we do not call it ORT. It is something else.
>So Alex Smith's use of a non-periodic but still sufficiently computationally simple background is a natural generalization of this sort.
Fine -- so call the result "a due generalization of so-and-so"! Something universal in a certain specified sense, "W-universal" or something.
>The key point is that the background can be set up without doing universal computation, so the 2,3 machine itself actually carries out the computation. One could fairly argue that two non-universal coupled automata can reach universality, but it would require the couple to interact at every step, as in Margenstern's nice example [1], but that's very different from a non-universal second automaton intervening only once at the first step.
What do you mean by "not doing universal computation"... or similarly for the coupled automata? Let me discuss the latter -- it IS known that any Turing machine can be simulated by two appropriate PDAs (Pushdown automata)...quite obvious; two stacks simulate a tape, i.e. moving the TM head one square along the tape becomes popping a symbol off one stack and pushing it onto the other. In particular, any universal TM M can be simulated by an appropriate pair of PDAs, A and B. But there is no sense in "dividing up universality"; neither A nor B is universal...since no PDA can be a universal TM. It sounds like you are treating universality as if it were mass, or a measure of sorts, as if A + B being of measure 1 and A of measure 0 means B is of measure 1. Where is this coming from?! It makes no sense!
The definitions and results of ORT are precise...but also hair-thin. Even a seemingly innocuous change can have drastic effects. [Quick example: suppose you impose on TM's that their input be read-only... the rest of the tape is available for read-write as usua
I confess I can't wait to read FOM in the next few days and see the reception Wolfram's letter receives... Don't get me wrong, Stephen W. has done a lot of good for Mathematics, but this is different. It is deceitful to hijack terminology with a settled, fixed meaning... and the term "universal Turing machine" is just that. And, may I add, lots of members of FOM have worked on these matters for a lifetime. Indeed, the moderator, Martin Davis, has written well-known textbooks in the field, has done research...and WAS a member of the Committee...and WAS NOT consulted about the decision!
Turing machines with infinite initial conditions, or maybe operating on infinite tape-contents, possibly for an infinite number of steps, ARE interesting -- you can find some information already in the Rogers textbook, and there has been a lot of work in these and similar matters, generalizations to hyperarithmetical sets, Pi-1-1 sets, recursion on admissible sets etc... catch-all term: "higher recursion theory". BUT, this does not alter the standard meaning of universal Turing machine, for plain, standard recursion theory - and THAT is a finite control, operating on a TM description, finite of course, and a finite TM input, on an otherwise blank tape.
Wolfram is free, to be sure, to define a notion of "Wolfram universality", and prove things about it; but it is misleading to claim that the results have something to do with universal TMs.
Barring a _proof_ that they do!:-)
I haven't priced laxative lately, but do you suppose if they cut the coke to 50% Merck purity and put the hookers on double duty, we can have half-price CDs ?!
"Easter Island's Weather Forecasting Service believes operation of the NEC SX-9 would realize a 53% savings under Windows Server 2008 compared to under UNIX"
"Created today" is not the point -- wouldn't YOU opt for secrecy if you were getting mixed up in this sort of thing? The 5 lone hits in Google for "Tolstokozhev", though, make me pause. One could come up with a scenario: T. conducted business using other names, he crossed up his police protectors, they did him in and now they will cover up! But this needs some support to qualify as plausible...
Ah, yes...Quantum Mechanics has strangeness and charm, entanglements, hadrons for the odd dyslexic pornographer... and bras all around.
What next? Mathematical Logic, maybe; V^kappa/mu , Ultrapower of the Universe, seems just right to sell videogames.
Rumor has it that "Undersea Transatlantic Cable" will be embedded in and inextricably intertwined [ouch!] with the next MS Windows release. VeryLongHorn indeed.
ALL things can tempt me from this craft of verse:
One time it was a woman's face, or worse--
The seeming needs of my fool-driven land;
Now nothing but comes readier to the hand
Than this accustomed toil. When I was young,
I had not given a penny for a song
Did not the poet sing it with such airs
That one believed he had a sword upstairs;
Yet would be now, could I but have my wish,
Colder and dumber and deafer than a fish.:-)
They don't have diminished profits now; they had excessive profits before. Good luck to Ms Lindor!
Slashdot Mirror
I can live with scars in my soul, but I want none in my Operating System :-X
Yes, I've seen it mentioned; no, I haven't visited it. If I am ever to go to Christmas Island's domain, or Tokelau or the like, first I'll make sure there is good reason for it.
I believe the judge is novelist Jerzy Kozinski's son...and I seem to recall novels by the latter where women's lust reached new (for adolescent me, then) extremes :-)
With all the clamor of protest I hear, though, I cannot help wondering: just WHO, then, visit by the thousands all those extreme-porn sites, or buy Master Baiter Ira's videos?! :-P
Justice is a spare, Spartan affair :-O
If you want to get off duty, you can get creative. When asked whether you are able to fairly assess the evidence presented, you reply: "No need. I'm PSYCHIC. I already KNOW who is guilty and who isn't!"
I do not consider it proper nowadays to pay for WiFi at a coffeeshop -- your business ought to be enough. If I find myself at a Starbucks, now that the Safari User Agent trick no longer works :) I hook up my Blackberry and use it as a modem. So there!
Note: The Paul principle. You rise to your level of incontinence
Whereas Spinal Tap is just fine?! :-P
What I've felt/ what I've known/ Never shines through in what I've shown :)
(obtained over other P2P, of course :-P )
They are "unforgiven" :-))
There IS a reason to ask the question; the answer matters, be it to a few. It has nothing to do with physical applications -- more than half the posts here are irrelevant, because Math not only is not physics; it is not a physical science at all. If Math is "discovered", i.e. if mathematical objects lead a charmed life of their own and are not artifacts of ours, if the notions of "real numbers", "set of real numbers", "the set of sets of real numbers" are meaningful and well-defined, then it DOES maker sense, for example, to look for an answer to the Continuum problem (Cantor's Continuum Hypothesis, "CH")...beyond the current axiomatic framework (ZFC), which is known not to imply CH, nor not-CH. If Math is not, one might retreat into formalism, or formalism of sorts, where CH (among other things) is a consequence of this and its negation is a consequence of that, and so on and so forth...without commitment to, or maybe even a notion of, what is ultimately true. About the real numbers, if you will -- this is no abstruse question regarding large cardinals or something. Some mathematicians are formalists on Sundays; not always, though, when they are grappling with a problem :-P
[ Compare: "there are few atheists in the trenches". ]
My answer, if you haven't guessed yet: Math is discovered.
Aw, you're just jealous the Voices are speaking to ME.
Wherever Shahi does?! (She's gorgeous).
Ah, the vagaries of marketing!...
It would be a blessing were the gPhone to stir up a field mired in lack of purpose and direction. I'm tired of seeing phone companies busy building elaborate business models instead of better phones. Almost the opposite -- consider AT&T's attempt to kill GPS in its Blackberries. I wouldn't worry about UI... There is precedent for having both a robust, no-frills terminal interface for jocks AND elaborate KDE, Gnome or what have you GUI interfaces for the spoiled :-)
The gPhone might even use [L-word]. How fitting for a Windows Mobile killer.
>If there is no clear definition is because there is no clear-cut, established procedure to determine when an initial condition is computationally simple enough to be acceptable. Some would wish universal computation stick to a finite initial condition with an unbounded tape filled with "blanks", because that's the only case where the theory is entirely clear.
Uh, no -- THAT is THE case envisioned by ordinary recursion theory. That is the meaning the TECHNICAL TERM "universal Turing machine" has. If "something else" is "universal" in some other sense, fine -- but please, CALL IT SOMETHING ELSE! (Whether it helps sell a book or not :-P )
...quite obvious; two stacks simulate a tape, i.e. moving the TM head one square along the tape becomes popping a symbol off one stack and pushing it onto the other. In particular, any universal TM M can be simulated by an appropriate pair of PDAs, A and B. But there is no sense in "dividing up universality"; neither A nor B is universal...since no PDA can be a universal TM. It sounds like you are treating universality as if it were mass, or a measure of sorts, as if A + B being of measure 1 and A of measure 0 means B is of measure 1. Where is this coming from?! It makes no sense!
How do I explain this?! Example: it might be reasonable to call a function from the reals to the reals "continuous" if it assumes "all the in-between values" -- that is, for any a and b, for any t between f(a) and f(b) there is an s between a and b such that f(s) = t. Unfortunately, there already exists a familiar, epsilon-delta definition of "continuous" that turns out to be non-equivalent to the previous one (indeed, stronger). You cannot, then, say "continuous" and mean the _former_ definition... just because it "sounds reasonable"! OK? "Continuous" is a technical term. So is "universal Turing machine"!
>However, others accept generalizations such as periodic "blank" words as long as they remain computationally simple enough (possibly generated in the same fashion as an unbounded "blank" tape).
You don't have to "generate" an unbounded blank tape, you simply assume it contains "blanks", in other words, anything BUT your symbols for "0" and for "1". And you don't have to prepare anything infinite -- "unbounded" means at any step you might have to make available one more tape square. If the machine "never halts", it will be using longer and longer finite stretches of tape, forever. At no moment will it have "used up infinitely much tape".
Preparing an infinite tape, with whatever contents, is beyond the pale of ORT (ordinary recursion theory). I myself said, it IS done, itself and other, more complex things -- but when we do it we do not call it ORT. It is something else.
>So Alex Smith's use of a non-periodic but still sufficiently computationally simple background is a natural generalization of this sort.
Fine -- so call the result "a due generalization of so-and-so"! Something universal in a certain specified sense, "W-universal" or something.
>The key point is that the background can be set up without doing universal computation, so the 2,3 machine itself actually carries out the computation. One could fairly argue that two non-universal coupled automata can reach universality, but it would require the couple to interact at every step, as in Margenstern's nice example [1], but that's very different from a non-universal second automaton intervening only once at the first step.
What do you mean by "not doing universal computation"... or similarly for the coupled automata? Let me discuss the latter -- it IS known that any Turing machine can be simulated by two appropriate PDAs (Pushdown automata)
The definitions and results of ORT are precise...but also hair-thin. Even a seemingly innocuous change can have drastic effects. [Quick example: suppose you impose on TM's that their input be read-only... the rest of the tape is available for read-write as usua
I confess I can't wait to read FOM in the next few days and see the reception Wolfram's letter receives... Don't get me wrong, Stephen W. has done a lot of good for Mathematics, but this is different. It is deceitful to hijack terminology with a settled, fixed meaning... and the term "universal Turing machine" is just that. And, may I add, lots of members of FOM have worked on these matters for a lifetime. Indeed, the moderator, Martin Davis, has written well-known textbooks in the field, has done research...and WAS a member of the Committee...and WAS NOT consulted about the decision! Turing machines with infinite initial conditions, or maybe operating on infinite tape-contents, possibly for an infinite number of steps, ARE interesting -- you can find some information already in the Rogers textbook, and there has been a lot of work in these and similar matters, generalizations to hyperarithmetical sets, Pi-1-1 sets, recursion on admissible sets etc... catch-all term: "higher recursion theory". BUT, this does not alter the standard meaning of universal Turing machine, for plain, standard recursion theory - and THAT is a finite control, operating on a TM description, finite of course, and a finite TM input, on an otherwise blank tape. Wolfram is free, to be sure, to define a notion of "Wolfram universality", and prove things about it; but it is misleading to claim that the results have something to do with universal TMs. Barring a _proof_ that they do! :-)
I haven't priced laxative lately, but do you suppose if they cut the coke to 50% Merck purity and put the hookers on double duty, we can have half-price CDs ?!
Exactly! :-)
"Easter Island's Weather Forecasting Service believes operation of the NEC SX-9 would realize a 53% savings under Windows Server 2008 compared to under UNIX"
The fact that the Jaegermeister is going to work ON Giselle?! :-)
"Created today" is not the point -- wouldn't YOU opt for secrecy if you were getting mixed up in this sort of thing? The 5 lone hits in Google for "Tolstokozhev", though, make me pause. One could come up with a scenario: T. conducted business using other names, he crossed up his police protectors, they did him in and now they will cover up! But this needs some support to qualify as plausible...
Ah, yes...Quantum Mechanics has strangeness and charm, entanglements, hadrons for the odd dyslexic pornographer... and bras all around. What next? Mathematical Logic, maybe; V^kappa /mu , Ultrapower of the Universe, seems just right to sell videogames.
Rumor has it that "Undersea Transatlantic Cable" will be embedded in and inextricably intertwined [ouch!] with the next MS Windows release. VeryLongHorn indeed.
ALL things can tempt me from this craft of verse: One time it was a woman's face, or worse-- The seeming needs of my fool-driven land; Now nothing but comes readier to the hand Than this accustomed toil. When I was young, I had not given a penny for a song Did not the poet sing it with such airs That one believed he had a sword upstairs; Yet would be now, could I but have my wish, Colder and dumber and deafer than a fish. :-)
They don't have diminished profits now; they had excessive profits before. Good luck to Ms Lindor!