## Search found 135 matches

Wed Mar 24, 2010 3:51 am UTC
Forum: Mathematics
Topic: Four color theorem
Replies: 82
Views: 21511

### Re: Four color theorem

Yeah, aren't there hundreds (thousands?) of cases that a Pornography Storage Apparatus verified for the proof? It's an accepted proof but isn't it possible that something went wrong that we haven't found yet? Isnt that true of every proof? Not to this degree I don't know about that; what is the lon...
Fri Mar 12, 2010 6:12 am UTC
Forum: Mathematics
Topic: Some statistics questions
Replies: 4
Views: 950

### Re: Some statistics questions

The standard deviation in a binomial distribution of something that has a probability p is sqrt(np(1-p)), so the standard deviation for the proportion should be (sqrt(np(1-p)))/n I think the error is here - the argument that SDBinomial/n = SDProportion. This derivation shows that the standard devia...
Thu Mar 11, 2010 1:25 pm UTC
Forum: Mathematics
Topic: representing domains as sets
Replies: 13
Views: 1094

### Re: representing domains as sets

My understanding of set theory pales in comparison to most folks here, so I apologize if I'm mistaken, but should {R - 0} not instead be R \ {0} or R - {0} ? My rationale being that the difference operator is applied to sets, and removes all elements in the set following it from the set preceding it...
Sun Feb 07, 2010 2:07 am UTC
Forum: Mathematics
Topic: Double Majoring Physics/Math
Replies: 23
Views: 6879

### Re: Double Majoring Physics/Math

My undergraduate university offered (at least some) concentrations (in philosophy, iirc) as elaborations on majors; that is, you could acquire a generic philosophy B.A., or a philosophy B.A. with a concentration in (e.g.) eastern thought. Minors occupied their usual role in our academic structure (a...
Fri Jan 22, 2010 7:43 pm UTC
Forum: Mathematics
Topic: Taking Microeconomics I to fill in time...
Replies: 9
Views: 1852

### Re: Taking Microeconomics I to fill in time...

BlackSails - Agreed, but key distinctions reside in whether: A) framing your model within the paradigm of optimization theory actually improves your understanding of the model, and B) the quantity being maximized is normatively good . Microecon. tends to assume the latter, and essentially all of its...
Thu Jan 21, 2010 4:50 pm UTC
Forum: Mathematics
Topic: Taking Microeconomics I to fill in time...
Replies: 9
Views: 1852

### Re: Taking Microeconomics I to fill in time...

If you'd like to further explore what Vleifer mentioned about the differences between people and the optimizing models of econ., as well as get a bit of extra math in and read a fairly sophisticated economist's work, you could check out Sam Bowles' Microeconomics: Behavior, Institutions, and Evoluti...
Wed Jan 20, 2010 8:25 pm UTC
Forum: Mathematics
Topic: Taking Microeconomics I to fill in time...
Replies: 9
Views: 1852

### Re: Taking Microeconomics I to fill in time...

In my experience, a sufficiently large proportion of economic theory really is math at its heart that pursuing the math in a more rigorous tone could only help him understand what's being said of the various models. It's really just a bag of "assume person/firm X optimizes function Y, then watc...
Wed Jan 20, 2010 6:16 am UTC
Forum: Mathematics
Topic: Some Basic Analysis Questions
Replies: 13
Views: 2604

### Re: Some Basic Analysis Questions

Thanks, Mostly! You've been extremely helpful; I appreciate it. I'll have to drag my probability book with me when I head to classes tomorrow; I didn't attempt the combinatorics question again because I couldn't recall off-hand how to expand the binomial. aka , I didn't try multiplying by that expre...
Wed Jan 20, 2010 5:25 am UTC
Forum: Mathematics
Topic: Taking Microeconomics I to fill in time...
Replies: 9
Views: 1852

### Re: Taking Microeconomics I to fill in time...

Pick up Varian's Microeconomics text, or a random mathematical microeconomics text, and work problems from either of those which parallel the developments in your class. You might also check the appendices in your text; authors of undergrad econ texts seem to stuff the math into appendices. (our int...
Wed Jan 20, 2010 4:59 am UTC
Forum: Mathematics
Topic: Some Basic Analysis Questions
Replies: 13
Views: 2604

### Re: Some Basic Analysis Questions

Ah! In case anyone's still paying attention to this thread, I thought I'd run an answer I produced for another question by you all. I believe it's correct, but the abstractions are sufficiently unfamiliar for me that I'm... not sure. In any event (I include only superscripts - infinity - and not sub...
Wed Jan 20, 2010 2:10 am UTC
Forum: Mathematics
Topic: Some Basic Analysis Questions
Replies: 13
Views: 2604

### Re: Some Basic Analysis Questions

jesting , That does sound like a good habit to cultivate, and I've been trying to apply the theorems/lemmas previously employed in the book as often as possible, seeing how clunky and aggravating applying the definitions directly can be. I think the result you're talking about will probably come in...
Tue Jan 19, 2010 5:07 pm UTC
Forum: Mathematics
Topic: Some Basic Analysis Questions
Replies: 13
Views: 2604

### Re: Some Basic Analysis Questions

Alrighty -- it's before class this morning, and I've given another whirl at 30, part e , following some of the advice above: a_n = (\sqrt{4 - 1/n} - 2) n = \frac{-1}{\sqrt{4 - \frac{1}{n}} + 2} Hence, if a_n converges to -1/4, then \sqrt{4 - \frac{1}{n}} + 2 must converge to 4, so: |\sqrt{4 ...
Tue Jan 19, 2010 2:38 pm UTC
Forum: Mathematics
Topic: Some Basic Analysis Questions
Replies: 13
Views: 2604

### Re: Some Basic Analysis Questions

Thank you for the help, all! I haven't had much spare time to sit down and play with the problems again since making this post, but I will soon. Skeptical / MostlyHarmless - The author does define a sequence's limit in this chapter, on p. 37, as the unique real number to which a sequence of numbers ...
Mon Jan 18, 2010 3:50 pm UTC
Forum: Mathematics
Topic: Some Basic Analysis Questions
Replies: 13
Views: 2604

### Some Basic Analysis Questions

Hey all! So, I've been working through Edward Gaughan's Introduction to Analysis ; I've read up through about half of chapter 5, but only recently started working through the problem sets. I'm happy to say I finished the Chapter 0 problem set (concerned with preliminaries -- definition of a set, uni...
Wed Jan 13, 2010 1:11 am UTC
Forum: Science
Topic: Brain= ???? Bytes
Replies: 74
Views: 8224

### Re: Brain= ???? Bytes

Probably a more intuitive measure of information in the brain is: what's the length of the shortest possible program that can simulate you (to the required level of accuracy)? But this is just another way of asking the same question. The length of the program depends on what programming language yo...
Tue Jan 12, 2010 4:26 pm UTC
Forum: Science
Topic: Brain= ???? Bytes
Replies: 74
Views: 8224

### Re: Brain= ???? Bytes

Yes, absolutely - when I say the heuristic, statistical approach is unlike much of today's software, I have in mind a very brittle abstraction as my exemplar of "today's software." I think that's probably decreasingly accurate as time marches forward, with software that relies heavily on a...
Tue Jan 12, 2010 3:56 pm UTC
Forum: Science
Topic: Brain= ???? Bytes
Replies: 74
Views: 8224

### Re: Brain= ???? Bytes

Nath's post corresponds well to how I understand ANN data processing, and may be the most appropriate way to address the OP's question. That being said, someone mentioned (I think gmailvuk) that human information processing proceeds very differently from the way typical software handles problems - t...
Thu Dec 17, 2009 6:56 pm UTC
Forum: Science
Topic: Quantum Conciousness
Replies: 18
Views: 2452

### Re: Quantum Conciousness

Hey Mike! Phil here. I'm glad doogly brought up Penrose; his name was on the tip of my tongue when you asked earlier. Not that I know terribly much about them, but the main Penrose references here seem to be his books The Emperor's New Mind and Shadows of the Mind . There's also a longer quantum min...
Tue Dec 01, 2009 8:01 am UTC
Forum: Science
Topic: Laughlin and the emergence
Replies: 26
Views: 2065

### Re: Laughlin and the emergence

In the Wiki entry, it´s called weak and strong emergence, it seems ( http://en.wikipedia.org/wiki/Emergence ) Those seem convenient enough. I'm really just not fond of anything to do with ontology, but maybe that's the epistophile in me. In a Sci-fi mindset, those two are the same, but anyways I fi...
Sun Nov 29, 2009 2:16 am UTC
Forum: Science
Topic: Laughlin and the emergence
Replies: 26
Views: 2065

### Re: Laughlin and the emergence

They are connected I think, yes. There's a point on which they differ as well, though: the role of approximation. I don't think predicting anything with complete precision is really all that important; I think we need to incorporate some sophisticated notion of a "reasonable approximation"...
Sat Nov 28, 2009 11:05 pm UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 66822

### Re: Internet Crazy Person: John Gabriel

skeptical scientist wrote:
Yakk wrote:XKCD has ridiculous pagerank.
It is a one-to-one correspondence with N; they're just calling it Z+ instead. Although I see I had a typo.

Z+ just means "all integers which are positive" -- i.e., the natural numbers, or N, right? I thought that was pretty broadly accepted notation.
Sat Nov 28, 2009 11:01 pm UTC
Forum: Science
Topic: Human evolution (why are we so smart?)
Replies: 46
Views: 4283

### Re: Human evolution (why are we so smart?)

If anyone's interested, here's a terse, clear description of the Baldwin Effect: The Baldwin eff ect can be conceptualized in two distinct phases: (i) initially, the ability to learn a task gives some subset of the population a selective advantage, resulting in subsequent generations becoming increa...
Sat Nov 28, 2009 10:21 pm UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 66822

### Re: Internet Crazy Person: John Gabriel

Ah, but there's no mutual exclusivity! He could very well be a p-zombie driven by a neural net.
Sat Nov 28, 2009 10:10 pm UTC
Forum: Science
Topic: Laughlin and the emergence
Replies: 26
Views: 2065

### Re: Laughlin and the emergence

And thing is every level so far has NOT had emergent behaviours. You CAN derive chemistry from nuclear physics, it's just not a good way of doing chemistry. You CAN derive classical mechanics from quantum mechanics (given a few assumptions) it's just a really bad way of doing it. You CAN derive opt...
Sat Nov 28, 2009 9:52 pm UTC
Forum: Science
Topic: Human evolution (why are we so smart?)
Replies: 46
Views: 4283

### Re: Human evolution (why are we so smart?)

I tend to think of intelligence as something akin to the capacity to identify patterns, abstract them from their surroundings/particular media of implementation, and manipulate them to solve problems; this definition is similar to that originally provided by Charles Spearman, iirc and Arthur Jensen'...
Sat Nov 28, 2009 9:30 pm UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 66822

### Re: Internet Crazy Person: John Gabriel

Wow, you really called that J. Gabriel would find this XKCD thread, Yakk.

Further proof that neural nets can predict human behavior!
Tue Nov 17, 2009 5:12 pm UTC
Forum: Mathematics
Topic: Quick Probability Question
Replies: 5
Views: 930

### Re: Quick Probability Question

Incidentally, that mistake has a name: probability matching (not to be confused with the Matching Law, for those few psych folks who check the math board). Concerning the OP: I think Lopsidation's reply is accurate. Also, the binomial probability distribution with p = q = 0.5 should let you figure o...
Mon Nov 09, 2009 12:02 am UTC
Forum: Mathematics
Topic: Math Books
Replies: 379
Views: 282742

### Re: Math Books

I'm looking for a good book on the general linear model at work in multivariate statistics. I'm not looking for a multivariate statistics book with a chapter or a few special sections devoted to the general linear model; I already own a few multivariate stat's books, and am looking to improve my kno...
Wed Sep 23, 2009 4:12 am UTC
Forum: Science
Topic: Biology Books - Suggestions?
Replies: 17
Views: 2104

### Re: Biology Books - Suggestions?

Good stuff! Keep it coming, all .
Sun Sep 20, 2009 12:21 am UTC
Forum: Science
Topic: What does "net gain of energy" mean?
Replies: 4
Views: 871

### What does "net gain of energy" mean?

Fri Sep 18, 2009 1:06 am UTC
Forum: Science
Topic: Biology Books - Suggestions?
Replies: 17
Views: 2104

### Re: Biology Books - Suggestions?

Fantastic, guys! Those responses are exactly what I was looking for - much appreciated.

I think I have enough to chew on for a while.
Thu Sep 17, 2009 4:29 am UTC
Forum: Science
Topic: Biology Books - Suggestions?
Replies: 17
Views: 2104

### Re: Biology Books - Suggestions?

Good idea, Biggles; I'll try there, too. XKCD is actually the second forum I posted this request in, so I'm getting used to it emigrating.
Wed Sep 16, 2009 1:00 am UTC
Forum: Science
Topic: Biology Books - Suggestions?
Replies: 17
Views: 2104

### Re: Biology Books - Suggestions?

Thanks, biggles! The Double Helix was actually one of the books in a Stuart Kauffman bibliography, I think, that I'd decided I wanted to read. I appreciate the reminder.

Any other takes? I know XKCD's science forum is pretty physics-heavy, but I'd be interested in physics-biology overlaps, too.
Tue Sep 15, 2009 1:22 am UTC
Forum: Science
Topic: Biology Books - Suggestions?
Replies: 17
Views: 2104

### Re: Biology Books - Suggestions?

DNA , Thanks for the reminder! I actually own a copy of The Third Chimpanzee; I got about a hundred pages into it a while back, but got distracted - I will have to jump back into finishing it. Regarding the books I listed: I hope you enjoy them! Just be aware, as I said in the OP, that they're not ...
Tue Sep 15, 2009 12:35 am UTC
Forum: Science
Topic: Biology Books - Suggestions?
Replies: 17
Views: 2104

### Biology Books - Suggestions?

This is going to sound rather broad, but I'm interested in reading more about biology; anything pertaining to the history of biological thought, molecular biology, evolutionary biology, population genetics, genetics more generally, or mathematical/computational biology (esp. mathematical biochemistr...
Fri Aug 28, 2009 4:48 am UTC
Forum: News & Articles
Topic: Quantum Mechanics gets a bit stranger.
Replies: 34
Views: 4801

### Re: Quantum Mechanics gets a bit stranger.

I am, as others, a bit suspicious of the jump from entropy-increasing quantum events necessarily leaving no information trail to "memories form and are erased," but, regarding those who point out it's not a verifiable/scientific theory - his abstract argues exactly that, by dubbing the se...
Fri Aug 28, 2009 4:20 am UTC
Forum: News & Articles
Topic: Quantum Mechanics gets a bit stranger.
Replies: 34
Views: 4801

### Re: Quantum Mechanics gets a bit stranger.

Where are you guys getting that his theory "contradicts" established science? My admittedly lay understanding of the Second Law of Thermodynamics is that it holds statistically, not absolutely, and the article's description of the 'theory' acknowledges that. I am, as others, a bit suspicio...
Wed Aug 26, 2009 3:59 am UTC
Forum: Mathematics
Topic: Optimization Tools
Replies: 3
Views: 732

### Re: Optimization Tools

There are free, limited versions of LINDO/LINGO available from their producers. I'm not familiar with full access, optimization freeware (though I imagine it must exist), but if your problem doesn't involve too many variables or constraints, the LINDO/LINGO sample packs might do the trick.
Mon Aug 17, 2009 3:40 am UTC
Forum: Mathematics
Topic: How many digits of Pi do you know?
Replies: 445
Views: 108530

### Re: How many digits of Pi do you know?

3.14159265 .. and then I can never remember whether a 3 or a 4 follows next.

I thought I was doing pretty well at that length! Seems I've got a long way to go on my pi mnemonics is I want to be competitive 'round here.
Sun Aug 09, 2009 7:40 am UTC
Forum: News & Articles
Topic: Artifical Brain in 10 years?
Replies: 117
Views: 10978

### Re: Artifical Brain in 10 years?

The problem with your second definition of reinforcement is that firstly you have to assume that something is desirable or undesirable to an organism (which is not a huge problem, but slightly mentalistic) but the second, and bigger problem, is that undesirable things can increase the probability o...