Search found 156 matches

by afarnen
Sat Jul 10, 2010 10:48 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 159592

Re: Math: Fleeting Thoughts

It hasn't been said yet, but I hate it when people say "timesing" or "minusing" instead of "multiplying" or "subtracting". But it's overly ridiculous when people say "plussing" instead of "adding". It makes me want to scream. Although I ha...
by afarnen
Sat May 29, 2010 5:50 am UTC
Forum: Mathematics
Topic: Math discovered or invented?
Replies: 110
Views: 18003

Re: Math discovered or invented?

Except that triangles don't exist in the real world, they're merely simplifications of nature we're capable of articulating. Mathematical objects are in general defined , their dependency on language should be obvious from that alone. I'd say that mathematical objects are more like unicorns, they b...
by afarnen
Fri Mar 26, 2010 6:07 am UTC
Forum: Logic Puzzles
Topic: My Hobby: Simplifying Sentences
Replies: 16
Views: 7635

Re: My Hobby: Simplifying Sentences

Are the spaces placed randomly? if they are, the possibilities are too many... As far as I understand, word order, spaces and punctuation are preserved. But ignoring this, they are still solvable. Since the first-of-each-letter order is preserved, they are always easier than anagrams, which are sti...
by afarnen
Mon Mar 22, 2010 6:58 am UTC
Forum: Mathematics
Topic: So, my dad sent me 30 dollars
Replies: 17
Views: 3098

Re: So, my dad sent me 30 dollars

God Created the Integers: The Mathematical Breakthroughs That Changed History by Stephen Hawking is perhaps the thickest and densest book within your budget. Pros: Lots of math. Definitely does NOT follow the "for every math formula, half the sales..." philosophy. This book is not trying ...
by afarnen
Mon Mar 22, 2010 6:04 am UTC
Forum: Logic Puzzles
Topic: Bear Puzzle
Replies: 23
Views: 17551

Re: Bear Puzzle

My thought (which didn't go anywhere): Newtonian mechanics tells us what the bear's acceleration was (assuming no initial velocity, and constant acceleration): \begin{eqnarray*}d &=& \frac{a}{2}t^2\\ -19.617\:\textrm{m} &=& \frac{a}{2}(2\:\textrm{s})^2\\ a &=...
by afarnen
Sat Mar 20, 2010 7:50 am UTC
Forum: Logic Puzzles
Topic: Bear Puzzle
Replies: 23
Views: 17551

Re: Bear Puzzle

My thought (which didn't go anywhere): Newtonian mechanics tells us what the bear's acceleration was (assuming no initial velocity, and constant acceleration): \begin{eqnarray*}d &=& \frac{a}{2}t^2\\ -19.617\:\textrm{m} &=& \frac{a}{2}(2\:\textrm{s})^2\\ a &=&...
by afarnen
Thu Mar 18, 2010 5:41 am UTC
Forum: Mathematics
Topic: Happy Pi Day!
Replies: 12
Views: 1764

Re: Happy Pi Day!

BlackSails wrote:My favorite approximation to pi:

3! (thats an exclamation point, not a factorial)


No, 4 is a better approximation.



... for very square circles.
by afarnen
Wed Mar 17, 2010 6:37 am UTC
Forum: Mathematics
Topic: Prime modulo prime triangle
Replies: 1
Views: 475

Prime modulo prime triangle

I couldn't find this anywhere else, so here it goes. Please excuse my possibly strange terminology. I do lots of math without any formal instruction, so I don't always know the correct terminology. First of all, I'm using P(n) to mean the nth prime, where P(0)=2. The entry at row m and column n is P...
by afarnen
Sun Mar 14, 2010 9:56 pm UTC
Forum: Mathematics
Topic: Happy Pi Day!
Replies: 12
Views: 1764

Re: Happy Pi Day!

Here's one of my favorite definitions of pi, as it's very easy to compute (though probabilistic):
[math]\frac{\pi}{4}=P(x^{2}+y^{2}\le1)[/math] where x and y are randomly chosen points in the unit interval.
by afarnen
Wed Mar 10, 2010 2:01 am UTC
Forum: Science
Topic: Are all universes Turing-complete?
Replies: 20
Views: 2542

Are all universes Turing-complete?

Following the analogy that the universe is essentially an automaton, it can easily be shown that we live in a Turing-complete universe, because we are able to implement Turing-complete systems within its rules. My question is, must all universes in the multiverse (ones with twerked fundamental const...
by afarnen
Wed Feb 24, 2010 2:20 am UTC
Forum: Mathematics
Topic: An interesting numeral system
Replies: 28
Views: 7972

Re: An interesting numeral system

Here's a way to solve the problem/redundancy of every number except for zero starting with a 1. Here f is the function that encodes a number as a string, and + is string concatenation: f(n)=\begin{cases} \textrm{"0"} & n=0\\ \textrm{"1"} & n=1\\ \textrm{"[&qu...
by afarnen
Wed Feb 17, 2010 9:21 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 2010369

Re: Coding: Fleeting Thoughts

Today in french class, we were given some Mardi gras vocabulary, and to my humor, I saw that the french word "char" means "float". Of course, it means a carnival float and not a floating-point number, but I thought it was neat nonetheless. And I was the only person in the room wh...
by afarnen
Wed Feb 17, 2010 9:08 am UTC
Forum: Mathematics
Topic: Significant Figures
Replies: 9
Views: 1785

Re: Significant Figures

I give the answers in the most exact form I can. However, in IB math, you must give either exact answers, or inexact answers to three significant figures. Significant figure "rules" only apply in operations with measurements whose precisions are not explicitly given, as a rough way of pres...
by afarnen
Tue Feb 16, 2010 9:13 am UTC
Forum: Mathematics
Topic: An interesting numeral system
Replies: 28
Views: 7972

Re: An interesting numeral system

jestingrabbit wrote:
afarnen wrote:* This uses only three symbols,


for large values of three.

Yeah, I guess I meant five.
by afarnen
Tue Feb 16, 2010 7:17 am UTC
Forum: Serious Business
Topic: December 21st 2012
Replies: 77
Views: 12117

Re: December 21st 2012

Voice of reason wrote:And I don't think it will be the appocalpse I think it will begining of the end or the halfway point.

Oh, okay. It's one of those compromise theories.

From comic 690: "I believe the truth always lies halfway between the most extreme claims."
by afarnen
Tue Feb 16, 2010 3:09 am UTC
Forum: Mathematics
Topic: An interesting numeral system
Replies: 28
Views: 7972

Re: An interesting numeral system

http://en.wikipedia.org/wiki/Mixed_radix#Primorial_based_radix This is sometimes known as the "Primoradic" numbering system. Thanks for the link. Yes, they're similar in appearance... as they are both numeral systems, and both refer to the prime numbers, but they are fundamentally complet...
by afarnen
Tue Feb 16, 2010 1:33 am UTC
Forum: Mathematics
Topic: An interesting numeral system
Replies: 28
Views: 7972

An interesting numeral system

The other day I discovered a neat notation for uniquely representing numbers (I'm not sure what numbers... at least all rational numbers). I have searched, but have not come across such a notation--if something at least similar exists, please point it out. Its basis is the fundamental theorem of ari...
by afarnen
Thu Feb 11, 2010 3:02 pm UTC
Forum: Religious Wars
Topic: The Turing Machine vs. Lambda Calculus
Replies: 32
Views: 21451

Re: The Turing Machine vs. Lambda Calculus

My vote is with the Lambda Calculus. First of all, I just find this to be pretty: (\lambda mnfx.mf(nfx))(\lambda fx.f(f(fx)))\lambda fx.(f(f(f(f(fx))))) Second, the entire state of, and everything you need to know about ...
by afarnen
Tue Jan 12, 2010 11:06 pm UTC
Forum: Logic Puzzles
Topic: A kind of "The Lady or the tiger" puzzle machine.
Replies: 63
Views: 13446

Re: A kind of "The Lady or the tiger" puzzle machine.

This is really fun! I like the idea of the wizards, humans and vampires. I have two questions. If a liar said, for example, "At least one human is telling the truth," does this guarantee the existence of a human? Does "All the humans are lying" guarantee the existence of at least...
by afarnen
Wed Jan 06, 2010 5:25 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 2010369

Re: Coding: Fleeting Thoughts

python does it too, of course.... Anyway, customizable syntax is great until you want to collaborate in any way, or use someone else's code from the web. True. It seems like more of a gimmick than useful. It'd be difficult to standardize. However, some sort of language-independent preprocessor coul...
by afarnen
Tue Jan 05, 2010 9:12 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 2010369

Re: Coding: Fleeting Thoughts

I've been wishing recently that there was a language with an easily customizable syntax. Like, if you could change the name of keywords. Or change the position (infix/prefix/postfix), precedence or associativity of operators, or the code-blocking style (curly-brackets vs. python-style), etc. That w...
by afarnen
Tue Jan 05, 2010 1:56 pm UTC
Forum: School
Topic: ACT scores
Replies: 81
Views: 10877

Re: ACT scores

I took it once without really knowing what I was getting into--that science section was a surprise. And I didn't get much sleep (excuses, excuses).

Well, I'm happy about 35 in math and 33 in english. Not so happy about my (identical) reading and science scores which made my composite a 30.
by afarnen
Tue Jan 05, 2010 12:28 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 2010369

Re: Coding: Fleeting Thoughts

I've come up with a minimally "typed" variant of combinatory logic/programming language. It's very inspired by Haskell, ML and Miranda but it aims to be much more minimal. First of all, types are defined by 'constructors', which are like functions that never reduce or evaluate (by default)...
by afarnen
Thu Dec 10, 2009 7:55 pm UTC
Forum: Mathematics
Topic: Why is standard deviation the root mean square? (merged)
Replies: 17
Views: 11050

Re: Why is standard deviation the root mean square? (merged)

Wow, I didn't expect to get so many replies. Thanks, I understand better now. One thing, I forgot that absolute value also applies to higher dimensions when I first read the "mean absolute deviation is complicated" argument, and was thinking "what's so hard about dropping a negative s...
by afarnen
Wed Dec 09, 2009 10:24 pm UTC
Forum: Mathematics
Topic: Why is standard deviation the root mean square? (merged)
Replies: 17
Views: 11050

Standard deviation is awful

Today in math class, I looked at the arbitrary definition of standard deviation, and (not for the first time during a stats lesson) thought, why ? So I tried making sense of it, and eventually came up with a seemingly much better formula (called the mean deviation, which I didn't know at the time) w...
by afarnen
Sat Dec 05, 2009 8:44 pm UTC
Forum: Computer Science
Topic: Discrete Structures
Replies: 12
Views: 3220

Re: Discrete Structures

If anybody needs an example of something taught in a discrete structures class, I visited one the other day, and the lesson was public-key cryptography, which included proving how RSA works, in detail, citing group theory, complexity theory, etc.
by afarnen
Sun Nov 22, 2009 11:48 am UTC
Forum: Coding
Topic: B is cool!
Replies: 3
Views: 983

Re: B is cool!

Hmm.. B is a bit more interesting than I first thought.. Couldn't really image doing any "real" programming in it even as hobby work.. Right. I think it would have to be able to communicate with C libraries to do useful things (it can communicate with a Unix environment, however). Since t...
by afarnen
Sat Nov 21, 2009 8:29 pm UTC
Forum: Coding
Topic: B is cool!
Replies: 3
Views: 983

B is cool!

I'd always heard of B (being the predecessor to C) and had seen its Hello World program: main( ) { extrn a, b, c; putchar(a); putchar(b); putchar(c); putchar('!*n'); } a 'hell'; b 'o, w'; c 'orld'; which would turn anybody off, right? That whole splitting up the string thing... However, this is perf...
by afarnen
Sun Sep 27, 2009 1:27 am UTC
Forum: Coding
Topic: Fake Programming Language
Replies: 210
Views: 31329

Re: Fake Programming Language

You, sir, name? wrote:Congratulations. You have invented the abbacus.

Yes, my method of addition of peano numbers is similar, but this language can do so many other things, things that your abacus could only dream of doing :twisted:. For instance, I bet I could write a lambda calculus interpreter.
by afarnen
Sat Sep 26, 2009 11:56 pm UTC
Forum: Coding
Topic: Fake Programming Language
Replies: 210
Views: 31329

Re: Fake Programming Language

There's this simple language for which I've had the general idea in my mind for maybe a year. Anyway, it's a data-structured language, though I'm not sure if I want it to be string-based (e.g. a program could look like '2+2') or list-of-strings-based (e.g. a program could look like '2 plus 2', repre...
by afarnen
Tue Sep 22, 2009 9:05 pm UTC
Forum: Computer Science
Topic: Making a 3D model from images
Replies: 4
Views: 1565

Re: Making a 3D model from images

The easiest way to do this would be to use pixel-perfect, bitmap stereogram (as computers aren't good at recognizing visual patterns, only patterns in bits). This would be done by taking two bitmap images (representing the left and right parts of a stereogram), and returning a single grayscale bitma...
by afarnen
Fri Sep 18, 2009 4:41 am UTC
Forum: Serious Business
Topic: Instance of consciousness: A series of thought experiments
Replies: 65
Views: 10155

Re: Instance of consciousness: A series of thought experiments

First of all, I'm assuming that by the atoms in the person's body when disassembling/reassembling them you mean all particles, including atoms, free electrons, and photons, etc. And that you mean not only position, but momentum of these particles as well. In other words, the complete physical config...
by afarnen
Fri Sep 18, 2009 3:21 am UTC
Forum: Serious Business
Topic: God is... or ____ is
Replies: 115
Views: 13637

Re: God is... or ____ is

God is unfalsifiable. God as an explanation for phenomena does not actually explain anything, nor can be disproved. (Self-proclaimed) theist: God makes the rain. (Self-proclaimed) atheist: No, the water cycle makes the rain. Theist: That's how God makes the rain. God is intuitive. Intuition leads u...
by afarnen
Wed Jun 17, 2009 1:06 am UTC
Forum: Logic Puzzles
Topic: The Absent-Minded Miner
Replies: 38
Views: 4817

Re: The Absent-Minded Miner

I'm assuming that by orientation you mean his upside-down-ness, and not his compass direction in addition to this (his full 3D direction)? If the latter, then I don't think it should be assumed that he can either stay in the same direction all the time or that he always knows what direction he's in....
by afarnen
Tue Jun 16, 2009 9:36 pm UTC
Forum: Logic Puzzles
Topic: The Absent-Minded Miner
Replies: 38
Views: 4817

Re: The Absent-Minded Miner

Suppose each chamber is a circle, with its shaft entrances on its circumference. When a miner walks into a chamber, he has to know which exit to take. In this example, he uses rotation about his own up-to-down axis. Now suppose the shafts are reminiscent of the twisting hallways from the Ocarina of...
by afarnen
Wed Jun 10, 2009 7:42 pm UTC
Forum: Logic Puzzles
Topic: The Chicken or the Egg?
Replies: 41
Views: 5150

Re: The Chicken or the Egg?

I heard a joke on this subject: A chicken and an egg are lying in bed together. They've just finished the most mind-blowingly-awesome sex they've ever had. The chicken, with a cigarette in its beak, turns to the egg, smiles, and says "well, I guess we answered THAT question!" And so [/thr...
by afarnen
Tue Jun 09, 2009 8:34 pm UTC
Forum: Logic Puzzles
Topic: The Sierpinski walk
Replies: 53
Views: 11052

Re: The Sierpinski walk

There is no iteration where (1/3,1/3) is removed, therefore the carpet (the limit of those iterations, or really the intersection of all those iterations) will still contain that point. So that mean only points which are on the edges of square holes are actually on the carpet? Otherwise it can be r...
by afarnen
Tue Jun 09, 2009 7:32 am UTC
Forum: Logic Puzzles
Topic: The Sierpinski walk
Replies: 53
Views: 11052

Re: The Sierpinski walk

I'm confused as to how you can define a point on the Sierpinski carpet, when there are actually no points on it. What I mean is with enough iterations of the fractal, any chosen point can be proven to be not on the Sierpinski carpet, so if you're considering the fractal iterated ad infinitum, there ...
by afarnen
Sat Jun 06, 2009 4:42 pm UTC
Forum: Science
Topic: Miscellaneous Science Questions
Replies: 2958
Views: 723004

Re: RELATIVITY QUESTIONS! (and other common queries)

This is not exactly a question, but more like a confirmation of an understanding of mine about general relativity. It's a bit more mathematical than scientific. The surface of a sphere is in a two-dimensional curved space (if you live on a sphere, you can move north, south, east, and west). However,...
by afarnen
Thu May 28, 2009 3:30 pm UTC
Forum: Computer Science
Topic: Thoughts on P = NP
Replies: 32
Views: 8008

Re: Thoughts on P = NP

Honestly, this is why we should never have named it NP in the first place. Between the general public thinking it means Not Polynomial (for a restricted definition of general public), and then all this business about nondeterminism. Bah! Henceforth, NP is the class of problems which have an efficie...

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