Search found 143 matches

by dosboot
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.
by dosboot
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...
by dosboot
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...
by dosboot
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 ...
by dosboot
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.
by dosboot
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". ...
by dosboot
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.
by dosboot
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 ...
by dosboot
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.
by dosboot
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.
by dosboot
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.
by dosboot
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...
by dosboot
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 ...
by dosboot
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...
by dosboot
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...
by dosboot
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 ...
by dosboot
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.
by dosboot
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.
by dosboot
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.
by dosboot
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...
by dosboot
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.
by dosboot
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...
by dosboot
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?
by dosboot
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 ...
by dosboot
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
by dosboot
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?
by dosboot
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).
by dosboot
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.
by dosboot
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.
by dosboot
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?
by dosboot
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...
by dosboot
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...
by dosboot
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...
by dosboot
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...
by dosboot
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...
by dosboot
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 ...
by dosboot
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.
by dosboot
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 ...
by dosboot
Mon Nov 05, 2007 5:11 am UTC
Forum: Individual XKCD Comic Threads
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.
by dosboot
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.

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