Yeah, my first test question for W|A was "population of Brooklyn" and it didn't offer us as an option. You have to ask about Kings County, NY to get Brookyn-related info.
Who is the cat who won't cop out when there is danger all about?
It even corrected your prissy contractionless input.
They seem to have put a fair amount of effort in on the song lyrics front.
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No more masturbating to Karl Malden (or his nose).
And holy crap, he was 97?
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Unfortunately it can't tell me if it was the movie or the making of Fitzcarraldo where someone learned to love again.
At this point they're just fucking with you.
I figured the primary engine at the core of the system is Wolfram himself. From his point of view, it's sorta like a 24-7 trivia game.
max
['You already ASKED that! Ask something else! Christ! I work my fingers to the bone typing these answers over and over again and all you people do is complain and not give me money! The internet sucks!']
14: Apparently not. (Actually, a rather uninteresting fail other than the suggested "countries" to try. But which did lead me to try this one, on which it did pretty well.)
Here's the clear proof Wolfram isn't writing the answers.
Here's the clear proof Wolfram isn't writing the answers.
I'm sure after a week or so, he did some outsourcing.
max
['These people ask stupid questions! I am thinking deeply!']
Hrmm. I like 'articulated lorry'. It makes no sense.
max
['My search engine is not as good as Google. BUT! I can give people the wrong answers and the geeks will keep generating page views looking for stupid responses, and I will use those numbers to make an initial public offering!']
And if you click "More", the synonyms switch to "afoul" and "abduct".
The other day I stumbled upon this 1987 book about the IAS (mostly physics and astrophysics) at a used bookstore for $2, so I picked it up. Skimming it, it mostly seems pretty boring (I was hoping for gossip or funny anecdotes, but there's little of that). Anyway:
Stephen Wolfram's principal activity is abstract scientific research. "If I wanted to go out and make a bunch of money," he says in his Institute office, "I wouldn't be here doing research. I'm more interested in research than in making money."
Making money, though, is Wolfram's hobby. "Some people make furniture and sell it as their hobby," he says. "I develop practical applications of computer science and sell that."
This just before he left for UIUC, where Mathematica was developed. I guess the hobby took over.
There's nothing very revealing or surprising about him, but it sort of reads as if his ego was a little more to scale at the time (though still quite healthy).
Possibly because I misspelled "hoard".
OT, but the country is going to come to a halt on July 30th.
If there's one thing this country can't handle it's an infense protest.
Examiner.com is a fun organization to write for.
30: Oh no! I want to read "Tag! You're Dead!" but it's not even cached anymore.
28: That's just going to look like a bunch of people taking vacation, which is already happening tons of places throughout July and August. Timing, people! Timing!
28: In France everyone gets a minimum of five weeks of going Galt per year, whereas here in the home of Ayn Rand we only get two weeks. I blame the left.
34: FOX News Alert: Thousands of people apparently going Galt jammed LA area freeways Wednesday night between the hours of 5 and 7 PM. "I'm through, I'm going home", said one exasperated man from his car. "Why would I stay a minute longer?", asked another as he hurried away from his office. Traffic helicopters reported jam-ups that reached for miles on all major freeways in the Greater LA area, but the pattern was highly asymmetric with the worst congestion found in the lanes leading away from major centers of employment. Some observers noted that the mass exodus occurred during the administration of while Barack Hussein Obama.
I just learned about Alpha today while looking for something online that would graph a complex function. I think it's cool. I also think e^ix is amazingly cool. How is it that they don't teach you in trigonometry class the actual definition of sin in terms of the exponential function? I always wondered a lot about that. I guess because they generally haven't covered complex numbers yet.
Are sine and cosine defined in terms of Euler's formula, or is that just a super-cool identity?
I mean, "actual definition" is kind of weird there, since trigonometry was studied before e was studied, no?
Maybe "actual definition" isn't the right phrase except in a Metamath context, which I've been immersed in lately.
But the only "concrete" definition you get in trig is an informal one in terms of a circle, not any equations.
39. They're generally defined using their Taylor series (or using exponentials, for example sin z = (exp(iz)-exp(-iz))/(2i)). This way you can apply them to complex numbers.
But the only "concrete" definition you get in trig is an informal one in terms of a circle, not any equations.
The one in terms of a circle is a perfectly good definition that's easy to understand and reason about. Defining it as an infinite series, on the other hand, is utterly unenlightening. (Unless you understand the complex plane and the geometric picture of complex multiplication well enough, in which case you can see it agrees with the definition in terms of a circle.)
But I'm not talking about the series definition.
I was assuming exp(x) was defined as a series....
Here's another way to put it: if someone can't explain to me what the sine and cosine functions have to do with a circle, then I would conclude they don't understand what sine and cosine are. I wouldn't say the same for understanding how they relate to exp(ix).
The definition in terms of a circle may not be very good for putting into a formal system, but what's wrong with it?
Nothing's wrong with it. I can agree with 47 and still feel educationally cheated.
Essear's got his head screwed on right.
exp(x) is just e^x.
... which is defined as a series. Or maybe as a limit of (1+x/n)^n or something. In any case, which has a formal definition that is not very enlightening.
50: You can certainly feel educationally cheated. This stuff was in the standard curriculum at my high school, although my high school was nonstandard.
52: I wouldn't say e^x is defined as a series, though it can be. But then perhaps I'm not one to talk about definitions.
I remember in HS Calculus solving a problem from the book in some unexpected way that made it super easy, exploiting that r cis θ jazz, so I guess I learned it, but I doubt I understood anything about it aside from that one time.
52: I wouldn't say e^x is defined as a series, though it can be. But then perhaps I'm not one to talk about definitions.
You can try to come up with a better definition, but it isn't easy. (Do you have one in mind? If you haven't thought it through, defining a^b in a rigorous way is probably harder than you expect, even for real a and b, much less complex a and b.)
Anyway, yes, complex numbers are sometimes magical, so sorry for being so critical of your enthusiasm; occasionally, randomly studying how some function behaves when you plug in a complex number instead of a real one gives you a dramatically new way of looking at things, and turns a difficult problem into a trivial one.
One slick approach for real numbers is to prove that there is a unique increasing function with f(x y) = f(x)+f(y) and f(a)=1, call this the log base a, and define a^x as the inverse. But for complex numbers this doesn't seem to extend in a nice way.