## Search found 399 matches

Fri Jan 04, 2013 10:42 pm UTC
Forum: Computer Science
Topic: What would you do with an infinitely fast computer?
Replies: 818
Views: 228484

### Re: What would you do with an infinitely fast computer?

Even if you could derive a contradiction, this is physical reality, not logic. That just shows that physical reality is inconsistent, or more likely, that your model of physical reality is inconsistent, and you need to get a better one. It doesn't go back and undo one of the premises to maintain va...
Fri Jan 04, 2013 9:48 pm UTC
Forum: Computer Science
Topic: What would you do with an infinitely fast computer?
Replies: 818
Views: 228484

### Re: What would you do with an infinitely fast computer?

I would use it to prove that it isn't infinitely fast. How? There are lots of ways to create paradoxes. If there are components moving infinitely fast inside the computer, you can show relativity is violated. You can also use it to solve the halting problem. In either of those cases, you end up wit...
Thu Jan 03, 2013 11:10 pm UTC
Forum: Computer Science
Topic: What would you do with an infinitely fast computer?
Replies: 818
Views: 228484

### Re: What would you do with an infinitely fast computer?

I would use it to prove that it isn't infinitely fast.
Wed Jan 02, 2013 8:33 pm UTC
Forum: Mathematics
Topic: Question about good derivative operators
Replies: 3
Views: 1713

### Re: Question about good derivative operators

What is your working definition of a "derivative" here?

If you're forced to give a concrete definition for one, you'll probably end up with the notion of a derivation.
Mon Oct 24, 2011 11:05 pm UTC
Forum: Mathematics
Topic: Mathematical Induction
Replies: 47
Views: 6491

### Re: Mathematical Induction

Say you have a ladder. The ladder has rungs. This is a very tall ladder, so it actually has an infinite number of rungs. They are labeled 0, 1, 2, 3, 4, and so on. You want to be able to climb to any rung. Can you find a way to do that? Easy, you climb it! The easiest way to climb a ladder is like t...
Mon Oct 24, 2011 10:00 pm UTC
Forum: Mathematics
Topic: How to practice reading mathematic/logical proof?
Replies: 6
Views: 1499

### Re: How to practice reading mathematic/logical proof?

Learn Coq. It's a theorem-prover. http://www.cis.upenn.edu/~bcpierce/sf/toc.html Theorem-provers are much more limiting than real-life proofs. But the basic techniques they provide are pretty powerful to have in your bag of tricks. Also, the Curry-Howard Correspondence is amazing if you want to do a...
Thu Apr 22, 2010 8:32 pm UTC
Forum: Mathematics
Topic: Where am I on the curve?
Replies: 33
Views: 3895

### Re: Where am I on the curve?

Mathematics as taught in public schools is pretty pathetic. Generally, in an American high school, you will get glancing exposure to calculus. Honestly, it's more than enough for the vast majority of adults. Real math is much more diverse and interesting, but you probably won't learn about it in sch...
Thu Apr 22, 2010 4:56 pm UTC
Forum: Computer Science
Topic: Properties and models of infinitely fast computation
Replies: 46
Views: 8781

### Re: Properties and models of infinitely fast computation

P.S. If I understand correctly, the term "computable" implies computability in a finite number of steps. I wanted a term to describe computability on an infinitely fast computer; I settled on "computably enumerable". Is there a better way to describe this concept? The whole poin...
Thu Apr 22, 2010 4:35 pm UTC
Forum: Computer Science
Topic: Why can't we talk to our computers yet?
Replies: 51
Views: 8547

### Re: Why can't we talk to our computers yet?

Language processing technology is computationally intensive and overall pretty shitty. The problem is that in order to understand human communication, you essentially need software (or hardware) that emulates a human brain. We're still not quite sure how that sucker works. So most research is done t...
Tue Oct 27, 2009 3:47 pm UTC
Forum: Mathematics
Topic: Sum of Subspaces
Replies: 23
Views: 2480

### Re: Sum of Subspaces

What does "A + B" mean when both A and B are sets? Your definition of a subspace seems needlessly complicated for the level you're at. A subspace of a linear space is simply a subset which is closed under addition and scaling. If A and B are both subsets of a common linear space, the set {...
Thu Oct 15, 2009 7:28 pm UTC
Forum: Mathematics
Topic: So, does this work as a prrof that e^pi*i=-1?
Replies: 39
Views: 4228

### Re: So, does this work as a prrof that e^pi*i=-1?

Proof by calculator is a shitty kind of proof.

To prove e^(pi*i) = -1, you first want to prove Euler's theorem. The former is just a special case of the latter.
Tue Oct 13, 2009 2:53 pm UTC
Forum: Science
Topic: Why is it hard to stop cracking knuckles?
Replies: 35
Views: 7858

### Re: Why is it hard to stop cracking knuckles?

Cracking your knuckles doesn't do any harm.

Cracking your knuckles is not an addiction. It's a habit. Habits are hard to break.
Tue Oct 06, 2009 2:48 pm UTC
Forum: Mathematics
Topic: which asshat came up with infix?
Replies: 23
Views: 3409

### Re: which asshat came up with infix?

What is the matter with infix operators? What "precedence issues" are you encountering? I thought most students get a good hold of pemdas by the end of elementary school.

There are so many other ways where math notation is broken. At least the precedence rules are rigid and unambiguous.
Mon Sep 28, 2009 1:51 pm UTC
Forum: Mathematics
Topic: truth and provability
Replies: 17
Views: 1428

### Re: truth and provability

Sure. "Arithmetic is consistent" is a true statement, but is undecidable within the system of Arithmetic. I'm not sure this is quite true. Arithmetic can't be consistent or not. Only a formal system (and the WHOLE system) can be claimed consistent or not. Consistency in logic means that n...
Fri Sep 11, 2009 3:04 pm UTC
Forum: Mathematics
Topic: Why is standard deviation the root mean square? (merged)
Replies: 17
Views: 11166

### Re: Basic statistics question

The reason you square then sum is because you get something that looks almost identical to the 2-norm. If you do much with math, you eventually learn the 2-norm is magical, because it is preserved by rotations. It may not seem like you can rotate data samples, but the world enjoys keeping that kind ...
Tue Sep 01, 2009 8:33 pm UTC
Forum: Mathematics
Topic: Domain of a function.
Replies: 8
Views: 1318

### Re: Domain of a function.

You are on a voyage across an uncharted ocean in search of spices in foreign lands. You are to travel over 4,000 miles west. Once you reach whatever lies beyond, you will return home to live in great wealth. However, your crew is uneasy. No one knows what will become of your fleet. There are two pre...
Fri Aug 28, 2009 8:23 pm UTC
Forum: Mathematics
Topic: I may have actually made a useful function...
Replies: 20
Views: 2658

### Re: I may have actually made a useful function...

it would be quite sad to practically anonymously post it on the Internet and to have someone else publish it by chance. No one cares about your high school level mathematical function. Just like ideas for inventions, companies, or board games, they are a dime a dozen. What matters is the effort you...
Fri Aug 28, 2009 8:09 pm UTC
Forum: Mathematics
Topic: Non-Archimedian field
Replies: 7
Views: 1079

### Re: Non-Archimedian field

I haven't messed around too much with infinitesimal numbers (they aren't useful at all passed explaining derivatives), but I'm pretty sure you're going about this naively. The notion of a limit is dependent on the metric of the real numbers. If M is our metric space (R for real numbers), the metric ...
Mon Aug 24, 2009 7:26 pm UTC
Forum: Mathematics
Topic: A series to represent all information
Replies: 20
Views: 2693

### Re: A series to represent all information

OP, you want to look into these things called formal systems . They are pretty much what you're thinking of. They are a set of rules (like the rules to a game) which generate all true statements given a finite set of axioms (usually the axioms of set theory and arithmetic). These things were supreme...
Wed Aug 19, 2009 6:23 pm UTC
Forum: Mathematics
Topic: Monkeys at typewriters
Replies: 33
Views: 3360

### Re: Monkeys at typewriters

Errr, there are an uncountable number of finite strings. I should have been more precise. But it still works out the same.
Wed Aug 19, 2009 6:13 pm UTC
Forum: Mathematics
Topic: Monkeys at typewriters
Replies: 33
Views: 3360

### Re: Monkeys at typewriters

Shadowfish wrote:There are an uncountable number of strings of letters.

The set of strings is countable.
Wed Aug 19, 2009 6:09 pm UTC
Forum: Mathematics
Topic: Inverse Functions help!
Replies: 19
Views: 2104

### Re: Inverse Functions help!

Someone mentioned the derivative and integral. They are inverses under certain restrictions. For example, if we talk about the set of polynomials {p(x)} where p(0) = 0, the derivative is the inverse of the antiderivative. Except your set isn't closed under the operations, i.e., a polynomial with p(...
Wed Aug 19, 2009 4:22 pm UTC
Forum: Mathematics
Topic: Monkeys at typewriters
Replies: 33
Views: 3360

### Re: Monkeys at typewriters

I realize that the probability for such an occurrence would asymptotically approach one as time approaches infinity, but is that really a guarantee that it'll happen? What do you mean by "happen"? Mathematical probability doesn't correspond very cleanly to the real world. It's useful for ...
Wed Aug 19, 2009 4:05 pm UTC
Forum: Mathematics
Topic: Inverse Functions help!
Replies: 19
Views: 2104

### Re: Inverse Functions help!

The question is: "Name three pairs of types of functions (not specific equations) that are inverses of each other" The identity function is its own inverse. Any set of functions which make up a group. Rotations all have inverses. Translations. Lorentz transformations. Discrete symmetry op...
Mon Aug 17, 2009 8:10 pm UTC
Forum: Science
Topic: Why is there no "center" of the universe?
Replies: 60
Views: 8158

### Re: Why is there no "center" of the universe?

I don't know jack shit about cosmology, but I used to wonder this same thing. After learning some differential geometry, it's clear why it's not absurd. A center is a kind of a average. The midpoint between two points is the "center" between those points: it's the average position of both....
Mon Aug 17, 2009 7:55 pm UTC
Forum: Science
Topic: Is the Lorentz factor messing with our measurements?
Replies: 16
Views: 1566

### Re: Is the Lorentz factor messing with our measurements?

The key word here is "inertial". According to spec. rel. the speed of light is constant in all INERTIAL frames. But if it rotates, its not an inertial frame! The speed of light is locally constant in non-inertial frames. As long as we're make measurements over small distances and times, i...
Mon Aug 17, 2009 7:51 pm UTC
Forum: Mathematics
Topic: Algebra 2?
Replies: 21
Views: 3063

### Re: Algebra 2?

The logarithm is the exponent. The logarithm is the inverse of the exponent..... The process of taking a logarithm is the inverse of taking an exponent. But the resulting logarithm is an exponent. Think about it. That's not the whole story. If you're going to say something like that, word it so you...
Mon Aug 17, 2009 2:23 pm UTC
Forum: Mathematics
Topic: Algebra 2?
Replies: 21
Views: 3063

### Re: Algebra 2?

Qaanol wrote:The logarithm is the exponent.

The logarithm is the inverse of the exponent.....
Fri Aug 14, 2009 6:32 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 161602

### Re: Math: Fleeting Thoughts

Just use whatever notation is best for getting the job done.

If that job is to teach students, consistency is a good thing. If not, then whatever works.
Fri Aug 14, 2009 5:06 pm UTC
Forum: Computer Science
Topic: Non-Algorythmic computing methods
Replies: 13
Views: 3443

### Re: Non-Algorythmic computing methods

I think the most influential book I came across is "The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics" from Roger Penrose Penrose is full of shit. He believes that consciousness cannot be reduced to axiomatic computation and that somehow human thought transcends...
Wed Aug 12, 2009 8:09 pm UTC
Forum: Mathematics
Topic: Algebra 2?
Replies: 21
Views: 3063

### Re: Algebra 2?

Can you also explain what [...] logarithms are? The logarithm takes a number and maps it to its order of magnitude. It's usually denoted "log". Each log has a "base". The most common bases are 2, e, and 10. When the base is e, we call it the "natural" log (and we denot...
Mon Aug 10, 2009 7:17 pm UTC
Forum: Mathematics
Topic: Algebra 2?
Replies: 21
Views: 3063

### Re: Algebra 2?

Algebra 2 doesn't have a universally recognized course guide. It depends on your school. Generally speaking, though, it is a natural continuity after algebra 1. In my second year algebra course, the only thing I remember learning was the complex number system and polar coordinates. Expect lots of po...
Mon Aug 10, 2009 4:09 pm UTC
Forum: Mathematics
Topic: Tvtropes and the halting problem.
Replies: 8
Views: 3064

### Re: Tvtropes and the halting problem.

WarDaft wrote:

It terminates.

It will only be guaranteed to terminate if it is assumed to be done at either infinite speed, or if there are no additional entries being added during the search.

If you are computing lazily, there is no problem here.
Mon Aug 10, 2009 4:07 pm UTC
Forum: Mathematics
Topic: What's the limit of...
Replies: 9
Views: 2018

### Re: What's the limit of...

You can think of h(t) = \lim_{a \to \infty} e^{-tia} geometrically as a rotation in the complex plane of t * a radians. It's pretty easy to show that the limit does not converge. Intuitively, though, rotating an object more and more does not bring it closer and closer to any single state. I ...
Thu Jul 30, 2009 8:33 pm UTC
Forum: Mathematics
Topic: Tvtropes and the halting problem.
Replies: 8
Views: 3064

### Re: Tvtropes and the halting problem.

Thu Jul 30, 2009 8:29 pm UTC
Forum: Mathematics
Topic: Is my calculator wrong?
Replies: 13
Views: 2541

### Re: Is my calculator wrong?

The OP is suffering from DWIMNWIS. The machine does exactly what you tell it to. In this case "you" includes the engineers who designed it as well. Subtraction, division, and exponentiation are all nonassociative. When you are working without parentheses of course you're going to run into ...
Thu Jul 30, 2009 8:22 pm UTC
Forum: Mathematics
Topic: Finding the opperations performed on two numbers
Replies: 2
Views: 818

### Re: Finding the opperations performed on two numbers

I've seen problems like these given as brain teasers. For example x = 3, y = 4 the result is 22. And x = 6, y = 5 the result is 52. And you are supposed to figure out the operation that was performed on those numbers to get those answers. I've started thinking about them more and was wondering if t...
Thu Jul 30, 2009 8:09 pm UTC
Forum: Mathematics
Topic: Proof by Contrapositive
Replies: 14
Views: 2142

### Re: Proof by Contrapositive

Proof by contrapositive is the same thing as proof by contradiction, so you might want to think of it that way for clarity. Whenever you do this kind of proof, it may help to lay everything down in symbolic logical notation: \forall \epsilon > 0: x \leq y + \epsilon \Longrightarrow x \leq y Now, the...
Thu Jul 30, 2009 7:50 pm UTC
Forum: Mathematics
Topic: log x
Replies: 36
Views: 4773

### Re: log x

The three most common bases used in logarithms are 2, e, and 10. Each is useful. Base 2 gives you the number of bits required to encode an integer. Base e is the most natural to define mathematically. Base 10 is useful due to the metric system. Just rely on context. The functions are all equivalent ...
Thu Jun 04, 2009 9:01 pm UTC
Forum: Mathematics
Topic: Real-world examples of -x * -y = +z
Replies: 66
Views: 8364

### Re: Real-world examples of -x * -y = +z

Negation of a number is just swinging the point around to the point on the other side that is equally far away from 0.

When you negate a negative number, you swing it back a second time, back to the positive side of the real line.