Dunno about the cat, but the horse is. Quit floggin’ it.
Yes it is.
No it isn’t.
Spiritus:
::raises hand::
Do I have to? I’m getting really hungry.
Mmmm… you boys were at it all night, weren’t you?
And Tuckerfan, sure, but keep that damn girly poofy thing away from me. Hands only!
Sexy…
Now, now, now – look here, it’s all really quite simple. Define a modified universal Turing machine U’ as follows: [ul] [li]On unary input x[sub]1[/sub] in L, U’ converts it to the corresponding binary representation x[sub]2[/sub] = 1[sup]k[/sup]0y. This should take no more than |x[sub]1[/sub]| log |x[sub]1[/sub]| steps. Note that the conversion can be performed by repeatedly decrementing the unary number and incrementing a corresponding binary counter. Using a carry-lookahead adder, binary addition can be performed in time Theta(log n). Since we are simply incrementing, however, it may take even less time–possibly O(1). []U’ simulates M[sub]y[/sub] on x[sub]2[/sub] for at most t[sub]2/sub steps. We can do this by using an extra worktape for a unary counter which is decremented for each step of M[sub]y[/sub]. []U’ rejects if M[sub]y[/sub] accepts within the alotted time; otherwise U’ accepts.[/ul]From the second point above, we have that L is in DTIME(t[sub]2[/sub]), provided that t[sub]2/sub is greater than or equal to n log n. Therefore if we take our modified UTM U’ as applied to the task of emulating an alternating Turing machine computing the graph clique problem, we find, without loss of generality, that any integer (a)[sub]2[/sub] can be uniquely expressed as a product of the form (a)[sub]2[/sub] = (p[sub]1[/sub])[sub]2[/sub] (p[sub]2[/sub])[sub]2[/sub] … (p[sub]r[/sub])[sub]2[/sub], where the (p[sub]i[/sub])[sub]2[/sub] are prime and (p[sub]1[/sub])[sub]2[/sub] <= (p[sub]2[/sub])[sub]2[/sub] <= … <= (p[sub]r[/sub])[sub]2[/sub]. In this case, y is a binary encoding of the list of (x)[sub]2[/sub]'s prime factors and their associated certificates. (Because PRIME is in NP, each encoded prime has a certificate which can be used to verify its primality in polynomial time.) In the worst case, there will be log (x)[sub]2[/sub] such factors, so the list of factors is polynomial to |x|. Furthermore, the certificates are polynomial to their respective primes, and since polynomials are closed under addition and multiplication, it follows that all of y must be polynomial to |x|.[/li]
From this it is clear that even when not operating under constraints of Gödel’s Incompleteness Theorem in a Frinkian-partitioned feature space, our modified UTM would have to reduce the graph-clique theorem (or any isomorphic diagonalizable NP-optimized procedure) to a non-time-constructible phlogistonizable linear-time algorithm before it would be able to reliably compute the probability of finding the third English word ending in -gry. (For further references, see “Non-monotonic defeasible complexity classes as applied to a temporal rectangular prism” by Ray et al. (1998), available on the author’s website.).
God, I love complexity theory.
Tease!
< Oprah on Complexity theory >
This doesn’t seem like the basis of a healthy relationship.
U’ should do whatever she feels is right for her future growth, regardless of the actions of M[sub]y[/sub]. What she’s essentially saying is "I’ll accept L, but only if M[sub]y[/sub] rejects him first.
As it is, by handing control of decisions about her future to M[sub]y[/sub], she’s avoiding responsiblity and will never be the independant, free-spirited variable that we all know that U’ is capable of being. She should weight the pros and cons of being with L and if she thinks that’s a good future path for her, she should go after L and th’ hell with M[sub]y[/sub]'s acceptance or rejections! You GO girl!
< /Oprah on Complexity theory >
psycho, I’m afraid you can’t resolve this by oversimplifying.
OK, this thread has ispired me to A)crack open my copy of Jan Gilberg’s Mathematics* to refresh the whole Godel/Peano thing and then to the public biblio to check out Rudy Rucker’s take on Godel’s Incompleteness Theorem.
(See, this is the stuff Mensa promises to deliver and no dues required at the Dope!)
So, psychonaut, if I can further simplify your simplification, Gödel’s Incompleteness Theorem is itself incomplete because it can’t determine what happened to the bellhop’s extra dollar (at least in a Frinkian-partitioned feature space).
Am I right.
TVAA, since you’ve done us the favour of opening this Pit thread, let me join in ultrafilter and Spiritus’s chorus: you’re an idiot.
Specifically, you’re an obtuse chowderhead. You respond to valid arguments by rephrasing your original claims ad nauseam. I gave up posting to your thread around page 3, when this became painfully obvious, because I have better things to do than pound my head against a wall. (Although I applaud ultrafilter and Spiritus Mundi’s patience in this matter, which clearly exceeds mine.) You bring to mind the missing and unlamented Archimedes Plutonium, web kook extraordinaire, who had a similar inability to examine the misconceptions so near and dear to him.
Your argument is an pathetic case of hand-waving, and when this is pointed out you berate your accusers for…gasp!..demanding rigour in a mathematical argument. You make gradiose universal claims about computers and number theory and yet evidently did not know what a Turing Machine was at the beginning of the thread. You have no cites to support your case, and no evidence.
And after all of that, when we refuse to bow down before your pathetic bleating, you resort to crap-slinging like this:
The FUCK??? This, just because someone had the temerity to argue the facts with you? And you call them “self-agrandizing”?
For the record, you ego-maniacal self-aggrandizing little twit: I have a bachelor’s degree in Pure Mathematics and Computer Science. I have worked as a software developer, and taken electives in philosophy and the philosophy of science in particular. And this Thursday I am defending my Ph.D. thesis in topology, concerning research which included a computer-aided attempt to prove an outstanding mathematical conjecture. I think I know a damned thing or two about mathematics and computer science.
And I think you’re full of shit, you offensive little turd.
You’re all making the baby Spock cry.
:dubious:
I’m not one to roll up my sleeves for a math debate, but now you’re trespassing onto my territory. So, not only have you outwitted every last math expert on this board, but you have unraveled the philosophical mysteries of the universe and existence as well?
You know how the human mind works? Who clued you in, your anonymous cadre of specialists? Why do I get the sinking suspicion they are studying cock-eyed assholes and hence specializing in you?
In a nutshell, yes. Moreover, the assumption of completeness would violate the well-known principles of the so-called Scarecrow Theorem from elementary geometry, i.e., that the sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.
If you all could get over yourselves for just a moment…
No one ever actually DEALS WITH THE POINTS I BRING UP.
Spiritus does nothing but demand more mathematical rigor and reiterate his claims that I’m wrong. The rest of you never did anything more than that, either.
Additionally, many of you have made obvious mistakes when discussing what GIT says – when you actually use normal English instead of mathematical terminology, you screw everything up.
Orbitfold, with your vast and deep knowledge of mathematics and computer science: was Spiritus’ explanation about what GIT implies (on page 5 of the GIT thread) correct or not?
I’ve checked. It isn’t. And you couldn’t tell this why, exactly?
The evolution of a physical system is the same as the generation of new statements in an axiomatic system. Are you really telling me that you storied sages can’t understand how that’s true?
Just take the description of the initial condition and apply the operations that describe the interactions between the things in the system. The resulting statements will describe the new configuration of the system.
I don’t claim to understand the mechanism of the brain, but from a cognitive perspective, we use the same strategies to determine theorems as electronic computers do.
Oh, okay. I get it now. That really is quite obvious isn’t it?
I’m sure we can all agree that TVAA has made an excellent point and proven his case.
Here’s a thought, the mind is not a physical entity, its abstract. You can’t sense it physically. When you ‘hear’ your thoughts or ‘see’ a dream you aren’t using your eyes or your ears, you aren’t picking up a physical stimuli from the world. 5,000 years of great thinkers haven’t figured out how the mind works, and you KNOW that it MUST be explainable within the same framework of a system that we invented.
The best we have done is sketch out some extremely rough foundational ideas, fuck that, we barely know how the brain works let alone the mind. I can’t speak to your math skills, but you are unquestionably the leading asshole in the field of philosophy.
But TVAA has already explained his point, which I will restate for those of you too stupid to have read it.
How much more SIMPLE can it be? Why can you not grasp the clear implications for GIT, the universe, and the mind?
Calling Spiritus Mundi an idiot is rather like pissing in a hurricane. But I guess when you gotta go, you gotta go. Tell us, Vorlon, does it really taste like warm beer?