## Search found 143 matches

Sat Mar 01, 2008 1:14 am UTC
Forum: Computer Science
Topic: Non-deterministic Turing machine
Replies: 13
Views: 4163

### Re: Non-deterministic Turing machine

Thanks, that makes more sense than what I was thinking.
Fri Feb 29, 2008 9:22 pm UTC
Forum: Computer Science
Topic: Non-deterministic Turing machine
Replies: 13
Views: 4163

### Non-deterministic Turing machine

What does it mean for a ND Turing machine to be capable of solving a decision problem, such as in the statement "subset sum can be solved in poly time with a ND Turing machine"? Solving a decision problem requires that that the Turing machine both halts and gives a yes/no answer. By defini...
Tue Feb 19, 2008 4:46 pm UTC
Forum: Mathematics
Topic: Realism?
Replies: 18
Views: 1901

### Re: Realism?

I admit it feels sensible to have sets running in the background for model theory. And yet if we are doing model theory with a bonafide set theory running in the background, why use ZFC? I don't think one needs the axiom of choice or cardinalities bigger than the naturals to define the notion of fir...
Tue Feb 19, 2008 5:27 am UTC
Forum: Mathematics
Topic: Realism?
Replies: 18
Views: 1901

### Re: Realism?

Who says you need ZFC in the background to construct complicated things like ZFC to use them as models? Here: the ontological notions of my theory are: "theories, sentences, languages, n-ary operations, and ontological notions." Add whatever else I should have added and add in some axioms ...
Tue Feb 19, 2008 2:43 am UTC
Forum: Mathematics
Topic: Realism?
Replies: 18
Views: 1901

### Re: Realism?

I don't know if that is true. You could be working in a different system used (just) for model theory. The system need not even bear resemblance to any set theory.
Mon Feb 18, 2008 11:10 pm UTC
Forum: Mathematics
Topic: Realism?
Replies: 18
Views: 1901

### Re: Realism?

For example, if the sentence is "(for all x)(there exists y) [xRy]", (where R is the relation symbol in your language) and your structure is the reals with R being <, the structure allows you to interpret the sentence as "for any real number x, there is real number y with y<x". ...
Mon Feb 18, 2008 4:17 pm UTC
Forum: Mathematics
Topic: Pure Maths - putting it all together
Replies: 33
Views: 3515

### Re: Pure Maths - putting it all together

From List of statements undecidable in ZFC:

The Whitehead problem ("is every abelian group A with Ext1(A, Z) = 0 a free abelian group?") is independent of ZFC.

Stuff like this is the only time that not worrying about foundations bothers me.
Mon Feb 18, 2008 7:12 am UTC
Forum: Mathematics
Topic: Realism?
Replies: 18
Views: 1901
Say I have a theory which is 'like' ZFC. The only objects in this theory are sets, the only binary relation is set membership, and the theory has no axioms. In a certain sense everything is a model of my theory, but what is that sense? Is this all taking place on a foundation that I should be aware ...
Sun Feb 17, 2008 5:31 am UTC
Forum: Mathematics
Topic: Propositional calculus: proves vs implies
Replies: 4
Views: 1314

### Propositional calculus: proves vs implies

What is the difference between "a proves b" and "a implies b" in propositional calculus? Also what are the inference rules that say you can ever introduce the "proves" symbol in the first place? Wikipedia is doing a poor job of trying to explain this.
Sat Feb 16, 2008 4:05 am UTC
Forum: Mathematics
Topic: Eigenvalues of a special case matrix help
Replies: 20
Views: 2786

### Re: Eigenvalues of a special case matrix help

Yikes, yea I'm mistaken.
Sat Feb 16, 2008 3:55 am UTC
Forum: Mathematics
Topic: Eigenvalues of a special case matrix help
Replies: 20
Views: 2786

### Re: Eigenvalues of a special case matrix help

The square of the matrix is almost diagonal. There is one 2x2 submatrix that isn't diagonal, and it has two linearly independent eigenvectors. Using Jordan canonical form it is easy to prove the relationship between the eigenvalues of a matrix and its square.
Sat Feb 16, 2008 3:32 am UTC
Forum: Mathematics
Topic: A Fifth of Euclid....or...Trading Spaces..
Replies: 3
Views: 1103

### Re: A Fifth of Euclid....or...Trading Spaces..

Under standard mathematical definitions, it doesn't make sense to say any of Euclid's postulates hold or do not hold in a vector space. In a finite dimensional real vector space, lines and angles do have definitions so the statement makes more sense. What he was probably trying to explain is that Eu...
Mon Feb 11, 2008 4:15 am UTC
Forum: Mathematics
Topic: Notation
Replies: 18
Views: 2046

### Re: Notation

I use single bars for the length of a vector. If I'm writing my vectors with arrows over them then I also just write the letter of the vector without an arrow as a shorthand for its length. In general, I prefer to notate things so that meaning can be implied without explicitly saying it. Whenever I ...
Mon Feb 11, 2008 3:59 am UTC
Forum: Mathematics
Topic: Galois Group basic question
Replies: 2
Views: 960

### Re: Galois Group basic question

That's very odd that no proof is given; that's a pretty important result! What's the name/ISBN of the book? I remember my book being great when it came to proofs(even the difficult ones like Sylow's). Yea, tell me about it. It is an undergraduate level textbook called 'Algebra' by Michael Artin. Th...
Sun Feb 10, 2008 11:53 pm UTC
Forum: Mathematics
Topic: Galois Group basic question
Replies: 2
Views: 960

### Galois Group basic question

I'm looking through this book and it says that the Galois group of a finite extension divides the degree of the extension, but it doesn't provide a proof. This chapter always assumes characteristic zero, essentially as a way to avoid defining separability, so I suspect it is true for at least any fi...
Mon Jan 28, 2008 3:46 am UTC
Forum: Science
Topic: Physics of Car Tires...
Replies: 61
Views: 7563

### Re: Physics of Car Tires...

I think I see now. I was thinking of the car and the semi as being identically braked (either both vehicles with their wheels locked, or both with the same slipping ratio, or whatever), at which point the larger frictional force of the semi's tires against the road evens out its larger inertia. The ...
Sun Jan 27, 2008 7:29 pm UTC
Forum: Science
Topic: Physics of Car Tires...
Replies: 61
Views: 7563

### Re: Physics of Car Tires...

The mass cancels out though. f = friction = uN = umg. f = ma = umg -> a = ug.
Sun Jan 27, 2008 4:17 am UTC
Forum: Science
Topic: Physics of Car Tires...
Replies: 61
Views: 7563

### Re: Physics of Car Tires...

I hope I may ask a slightly OT question:

What's the simplest explanation as to why a semi-truck will take a longer distance to stop than a normal car under identical braking conditions? If the frictional force is proportional to the normal force then the two should have the same deceleration.
Fri Jan 18, 2008 2:28 am UTC
Forum: Science
Topic: Miscellaneous Science Questions
Replies: 2958
Views: 711176

### Re: Common Questions

Am I missing something? The thread about a plane on a treadmill did not reach a consensus.
Thu Jan 17, 2008 1:55 am UTC
Forum: Mathematics
Topic: Assigning Personality to Numbers
Replies: 51
Views: 6255

### Re: Assigning Personality to Numbers

I have a relatively noticeable grapheme → color synesthesia for variable and function names (e, pi, f(x), etc.). For numbers I have no color synesthesia but possibly a very weak personality type of synesthesia. I cannot assign any descriptive personalities, all I can say is how closely related certa...
Wed Jan 16, 2008 6:03 am UTC
Forum: Science
Topic: Growing organs and other stuff
Replies: 29
Views: 2352

### Re: Growing organs and other stuff

Sir_Elderberry wrote:
dosboot wrote:Why isn't there an advantage to living longer? If I live for 500 years won't I have a lot more offspring than everyone else?

Old men aren't very fertile.

Aha.. but you see my statement is a refutation of the idea that it isn't evolutionarily beneficial to stay younger and live longer.
Wed Jan 16, 2008 3:40 am UTC
Forum: Science
Topic: The ethics of PGD (and 'Designer Babies')
Replies: 11
Views: 1553

### Re: The ethics of PGD (and 'Designer Babies')

You can't fault someone for not having children at all, so we shouldn't fault someone for having a child with chosen genes. In the first case the person contributes zero population and zero genetic variation, and in the second case the person contributes one population and some variation. The differ...
Wed Jan 16, 2008 3:22 am UTC
Forum: Science
Topic: Growing organs and other stuff
Replies: 29
Views: 2352

### Re: Growing organs and other stuff

Why isn't there an advantage to living longer? If I live for 500 years won't I have a lot more offspring than everyone else?
Fri Jan 04, 2008 7:03 am UTC
Forum: Mathematics
Topic: On raptors and running away:
Replies: 33
Views: 3067

### Re: On raptors and running away:

You know, in the year or so since I read the comic I never thought about the problem this way before. The way I was imagining the problem in my head was much simpler: the human selects an angle of escape, and then the two adjacent raptors select an angle of attack (which will be a forced choice, at ...
Sat Dec 15, 2007 3:14 pm UTC
Forum: Mathematics
Topic: when should e day be?
Replies: 22
Views: 2423

### Re: when should e day be?

One day Europeans and Americans will set aside their differences and finally agree on a date system.

and that day will be January 1st, ha! - LTB
Thu Dec 13, 2007 3:30 am UTC
Forum: Mathematics
Topic: Discrete probability distributions on dense sets
Replies: 9
Views: 1877

### Re: Discrete probability distributions on dense sets

Surely if one drops choice then the existence of non-measurable sets should at most be undecidable. Are you saying the negation of the axiom of choice implies there is a measure in which every set is measurable?
Fri Dec 07, 2007 8:06 am UTC
Forum: Mathematics
Topic: Some advanced number theory help
Replies: 6
Views: 1169

### Re: Some advanced number theory help

The first equality is the way that products work for Dirichlet Series. Think about

sum(an/ns) * sum(bn/ns) = sum(cn/ns)

and ask yourself what should cn be in terms of an and bn? In your question an=1 and bn=phi(n).
Thu Nov 29, 2007 4:14 am UTC
Forum: News & Articles
Topic: What if schools taught English the way they taught maths?
Replies: 59
Views: 9034

### Re: What if schools taught English the way they taught maths?

Most people just won't care that a theorem is true or why it is true even if they could appreciate what an abstract proof is. Maybe there is a better way to teach Math, but that is the reason basic Math is taught using lots of problems and not lots of proofs.
Sat Nov 24, 2007 6:02 am UTC
Forum: Logic Puzzles
Topic: Left/Right
Replies: 38
Views: 4250

### Re: Left/Right

Spoiler:
That's only a tricky question if you are thinking in terms of coordinates. All you have to do is provide a unique description of the object. "The star your planet orbits around", for example.
Fri Nov 23, 2007 6:08 am UTC
Forum: Mathematics
Topic: TI-86 vs TI-89 Titanium
Replies: 30
Views: 10784

### Re: TI-86 vs TI-89 Titanium

Don't forget that the TI-89 has pretty print. If you already have the 89, why go back?
Wed Nov 21, 2007 4:46 am UTC
Forum: Mathematics
Topic: Fluency with mathematical proofs.
Replies: 18
Views: 3045

### Re: Fluency with mathematical proofs.

If your university is anything like the ones I've been too just head down to your college bookstore right now. They'll have the textbooks for next semester on the shelves by now and you can buy it and start reading. You probably have a long weekend for Thanksgiving, so it'll give you something fun t...
Thu Nov 08, 2007 9:46 am UTC
Forum: Mathematics
Topic: On Linear Algebra
Replies: 35
Views: 4184

### Re: On Linear Algebra

Correct me if I'm wrong, but isn't this just a system of equations in a matrix? Reduced Row Echelon Form, etc? What else do I get into? What purpose does Linear Algebra serve in the real world? I've never taken a pure linear algebra course, but I'm fairly sure there isn't a whole lot to linear alge...
Wed Nov 07, 2007 9:45 pm UTC
Forum: Science
Topic: Are physical constants rational?
Replies: 158
Views: 14078

### Re: Are physical constants rational?

In mathematics, there is no way to express the notion that something is right or wrong in the sense that it does or does not represent a real world system. It is not something that is supposed to be surprising either. There are only a handful of axioms for set theory - the conventional basis for mat...
Wed Nov 07, 2007 8:36 am UTC
Forum: Science
Topic: Are physical constants rational?
Replies: 158
Views: 14078

### Re: Are physical constants rational?

The constant is divorced from measurement, and math is divorced from reality: I'll give you a theory right now which determines all the physical constants. Just don't complain when they fail spectacularly to agree with observation (and are all equal to substrings of my drivers license #). That's pre...
Wed Nov 07, 2007 7:56 am UTC
Forum: Science
Topic: Are physical constants rational?
Replies: 158
Views: 14078

### Re: Are physical constants rational?

Yes, but this is only because our theories are not good enough. There's no reason why a theory can't predict them (and, in fact, they can predict some constants). Yea, there are constants that theories can predict. That's fine then. The theory implies (mathematically) that the constant has a partic...
Wed Nov 07, 2007 7:27 am UTC
Forum: Science
Topic: Are physical constants rational?
Replies: 158
Views: 14078

### Re: Are physical constants rational?

NO. This is totally wrong. Uncertainty only applies to operators in hilbert space acting on wave functions. Constants are NOT operators... They have absolutely no uncertainty associated with them. edit: To emphasize, since people have posted wrong things several times: - Physical constants have no ...
Wed Nov 07, 2007 3:12 am UTC
Forum: Science
Topic: Are physical constants rational?
Replies: 158
Views: 14078

### Re: Are physical constants rational?

Blatm wrote:Take 3 numbers that are mutually irrational: 1, pi and root2. In no base are all three of these rational.

My question is: are physical constants mutually irrational?

There is still the problem that a constant defined experimentally does not define a number to a mathematician.
Wed Nov 07, 2007 2:53 am UTC
Forum: Mathematics
Topic: when am I ever going to use this (help me choose a class)
Replies: 17
Views: 1844

### Re: when am I ever going to use this (help me choose a class)

The applications of math are not focused enough that you should make your decision based on what math course is applicable to what field. What is more significant for a non-math major, I think, is the effect that taking a theoretical math course has on your analytical thinking skills. Real analysis ...
Mon Nov 05, 2007 5:11 am UTC
Topic: 0338: "Future"
Replies: 140
Views: 21773

### Re: "Future" Discussion

I can't decide if this comic is supposed to be inexplicable things that don't normally happen or a metaphor for being stuck in a past relationship. I guess it is both? Well done Randall.
Sat Nov 03, 2007 3:37 am UTC
Forum: Mathematics
Topic: Geodesics: Donuts are Delicious
Replies: 10
Views: 1776

### Re: Geodesics: Donuts are Delicious

Would the shortest path still have to be one of those 9 segments, even though their arc lengths are not what we expect? That would reduce the problem to calculations.