Nullity?

[simplethinker]

I just read this thing on another post here Nullity. This guy has got to be crazy.
When he's talking about a 'Super-Turing Machine' and defines his axioms, isn't he contradicting himself? A Turing machine is a computer that can tell when any program will halt, which Turing himself has explained is impossible (there's probably something on wikipedia if you don't know what I'm talking about). Godels Incompleteness theorem and the Hilbert/Turing/Post FAS prove that one is impossible. The basis for this guy's work is based on the possibility of a Turing Machine. The most disturbing part about his work is that he defines a set of axioms to use on a Turing Machine. Turing's halting problem along with Hilbert's 10th implies that for there to be a machine like that, that there must be only one, complete, set of axioms. The backbone of this guy's argument is contradicting the definitions of what he uses to prove his point, while he assumes they are true. Am I missing something or should my head be exploding right now?

[leofox]

Nullity is kinda weird. I like the idea of it though, I always think that infinity stands for an infinity amount of numbers, each with a different value, but all infinity. Like the limit of 2X is a different infinity than the limit of X or the limit of Sin(X) for X to infinity or the limit of 1/X for X to zero (the second and the last seem to be the same though..) but they're all infinities or nullities.

But for most mathematical problems, treating infinity as an actual number seems kinda weird.

[Weregoose]

1. James Anderson had been trying for years to get this concept to gain recognition, yet it only became relevant in that it was an overly-hyped story by the BBC that was, unfortunately, swallowed up by the ignorant public.
   
2. The inclusion of transreal objects in a statement involving real numbers is not dissimilar to adding a duck to a scallop and calling it a tuna sandwich. There are no lives being saved here; it's just a classroom with a teacher who is beside himself with the notion that he solved a one thousand-year-old "dilemma" and who now should be fired for corrupting young minds with erroneous details that can only impede their progress in so many areas of mathematics.
   
3. James Anderson's Wikipedia entry for [url="http://en.wikipedia.org/wiki/Nullity_(transreal)"]Transreal number[/url] is already [s]marked for deletion[/s] gone. Perspex machine is also marked for deletion.
   
4. The term Nullity is already taken.
   
5. IEEE 754
   
6. Chuck Norris
   

[simplethinker]

Refer to Goose's point 6, RESOLUTION PROVEN

But, in case you still don't believe:
1. Sadly, I only found out about this from DarkerLine's post, so like kill him for encouraging stupidness and crimes against humanity (nothing personal).
2. What's his name uses the methods he's trying to disprove to prove he's right, and then his (false) axioms to prove that the rest of his theory is right.
3. For a theory that very few people understand to be taken off of Wikipedia it has to suck
4. What part of his research wasn't plagerized? (and isn't /phi/ already used as one of the most well-known transcendental numbers).
5. So even if nullity is true ( which it's not) then it's pointless

Am I right in everything so far?

[AlienCC]

The amount of monetary damage this would cause to existing software and hardware to implement a value for 0 which could be divided by is astronomical.

I for one vote against this, and instead suggest we continue educating the value of programming divide by zero checks in the code.

--AlienCC

[thornahawk]

Mathematical crankery, I say. Mathematical crankery. The fact that it made this much of a splash puzzles me to no end...

thornahawk

[benryves]

[Weregoose]

[JoeImp]

[simplethinker]

[Rezek]

[DarkerLine]

[quote name='"simplethinker"']When he's talking about a 'Super-Turing Machine' and defines his axioms, isn't he contradicting himself? A Turing machine is a computer that can tell when any program will halt...[/quote]Not quite; in fact, in "solving the halting problem", Turing proved that a Turing machine cannot be designed that will tell if any program will halt.

The utility of a Turing machine is that, apart from having infinite memory (which doesn't do you any more good than a really large amount of finite memory), it is roughly equal in terms of computing power to currently available computers, but is much easier to deal with mathematically. So, for example, a proof that a Turing machine can't factor a number in polynomial time would also imply that computers can't factor numbers in polynomial time.

Note that if, say, quantum computers become widely used, we'll have to modify our definition of Turing machine to one that mirrors the goings-on of a quantum computer. These would (most likely) be more powerful (in fact, google says we don't know if quantum Turing machines can solve the halting problem).

But to the best of my knowledge "Perspex machines" are still ridiculous.

[simplethinker]

OK, here's a quote from Gregory Chaitin's Meta Math:
"If there were such an algorithm to prove the halting problem , we could use it to find all the elegant programs. You'd do this by checking in turn every program to see if it halts, and then running the ones that halt to see what they produce, and then keeping only the first program you find that produces a given output. If you look at ll the programs in size order, this will give you precisely all the elegant programs (barring ties.....)... In fact, we've actually just shown that if our halting problem algorithm in N bits in size, then there's got to be a program that never halts, and that's at most just a few bits larger than N bits in size, but we can't decide that this program never halts using out N-bit halting problem algorithm. (This assumes that the halting problem algorithm prefers never to give an answer rather than to give the wrong answer....)"

Complexity is best measured in the size it takes to program something, not the speed, which is dependent on computing power. So a Turing machine is never achievable because nothing we will ever make can have infinite complexity, so only theoretically are they useful.

Four of the most influential number/set theorists (Emil Post, Hilbert, Godel, Turing) each have different, un-flawed, proofs that the halting problem is impossible (I'm not sure what google says about the other 3, but I'm too lazy to type them, the books I have are long. This is the most straight forward one.) Logically and theoretically the Halting problem (along with Hilbert's 10th) are impossible, proven in multiple ways.

[Tiberious726]

If you want evidence against it just look into Georg [sic] Cantor's work.

He showed that there are different degrees of infinity. This being the case the whole concept of "nullity" (which was stupid in the first place, as inderteminate forms are so much more powerful) falls apart

[DarkerLine]

[benryves]

[elfprince13]