So, my point regarding the speed.
In the middle of working out a problem, I had to find the limit of
S = 1/e + 2/e^2 + ... + n/e^n + ...
I had never seen this sum before, so now cleverness is required. If I assumed guess C was true, that would imply
e/(e - 1) = (e - 1)S
This claim is much easier to check,
(e - 1)S = 1 + 1/e + 1/e^2 + ... = 1/(1 - 1/e) = e/(e - 1)
We know what S is, and the... (read more)
I'm not sure. I'm trying to work towards a career path which uses as much of my ability as I can. The most important job for a professional programmer, was understanding what your client wanted. This is a fine job, but being good at algorithms isn't necessarily a requirement.
When talking to an engineer at Google, I asked what he thought a good career choice was for working on hard problems. His immediate first thought was graduate school, then he sort of mentioned robotics.
My ideal dream isn't being a professor, it's working on something that needs inference, that uses my mathematical abilities. So I'm leaning towards research, but that's the implication not necessarily... (read more)
I agree, that I have a wealth of information to work with right now. Just trying to honestly balance it (felt like LW fit the theme somewhat).
On the one hand, both of those scores are my first time, and they were taken cold. And, I could argue I thought a lot of homework in school was unimportant and unnecessary (because of a poor philosophical attitude).
But of the 26 questions wrong or incomplete on the practice Math subject test, roughly 16 of them I had sufficient knowledge, but I simply wasn't fast enough. And the Algebra class, was really hard, and I did do homework eventually.
It's not like I haven't been very successful... (read more)
I'm sorry if this is the wrong place for this, but I'm kind of trying to find a turning point in my life.
I've been told repeatedly that I have a talent for math, or science (by qualified people). And I seem to be intelligent enough to understand large parts of math and physics. But I don't know if I'm intelligent enough to make a meaningful contribution to math or physics.
Lately I've been particularly sad, since my score on the quantitative general GRE, and potentially, the Math subject test aren't "outstanding". They are certainly okay (official 78 percentile, unofficial 68 percentile respectively). But that is "barely qualified" for a top 50 math program.
Given that I think... (read 264 more words →)
I'm not quite sure what the following means:
if you add details to a story, it becomes less plausible" is a false statement coming from human interaction.
I don't care whether it's false as a "human interaction". I care whether the idea can be modeled by probabilities.
Is my usage of the word plausible in this way really that confusing? I'd like to know why... Probable, likely, credible, plausible, are all (rough) synonyms to me.
So plausibility isn't the only dimension for assessing how "good" a belief is.
A or not A is a certainty. I'm trying to formally understand why that statement tells me nothing about anything.
The motivating practical problem came from this question,
"guess the rule governing the following sequence" 11, 31, 41, 61, 71, 101, 131, ...
I cried, "Ah the sequence is increasing!" With pride I looked into the back of the book and found the answer "primes ending in 1".
I'm trying to zone in on what I did wrong.
If I had said instead, the sequence is a list of numbers - that would be stupider, but well inline with my previous logic.
My first attempt... (read more)
Can someone link to a discussion, or answer a small misconception for me?
We know P(A & B) < P(A). So if you add details to a story, it becomes less plausible. Even though people are more likely to believe it.
However, If I do an experiment, and measure something which is implied by A&B, then I would think "A&B becomes more plausible then A", Because A is more vague then A&B.
But this seems to be a contradiction.
I suppose, to me, adding more details to a story makes the story more plausible if those details imply the evidence. Sin(x) is an analytic function. If I know a complex differentiable function has roots on... (read more)
I disagree, I read the Feynman lectures in high school and learned a great deal. His presentation taught me more about how to think about these things then Giancoli did.
Giancoli better prepared me for what the standard format was for test questions, but it didn't really articulate how I was supposed to use the ideas to generate new ones. Feynman's style of connecting claims with whatever you happened to know, is extremely important. Giancoli doesn't demonstrate this style quite as well.
Of course it was my first textbook, so I could go on and on about why I like it...
Perhaps I should've said, hard in the wrong ways. The long term goal for a good professional programmer seems to be understanding what the client wants. Some math is needed to understand the tools, so you can give some context for options. But I spend most of my creative energy making sure my programs do what I want them to do, and that is really hard when each language has it's own prejudice motivating its design.
I seriously considered looking into real time high risk software applications. But I just decided that instead of learning new languages until I ran out of youth, it'd be more fun learning general relativity, or even measure theory. The ideas in those subjects will probably hold out a lot longer then python.