I was reading a biography of Richard Feynman, and when his sister was around 13 - 16 (I think) he gave her an upper level textbook on physics to read. She told him, I don't understand any of this. And what he told her to do was read until you stop understanding and then start again, this way...
This interesting thought experiment was brought up by my philosophy TA last week and I thought I'd pass it along in hopes for a lively discussion.
The game is as follows. You flip a coin.
H TH TTH TTTH ...
$2 $4 $8 $16
If you flip heads, the game is over and you...
One interesting development is called "Doubly Special Relativity", (the only person I recognize who was a part of it is Lee Smolin). Where they expand on Einstein's Second Postulate about the absolute nature of the speed of light, and replace it with an upper energy bound. This doesn't really...
Yes, I would agree with you there. Furthering technology does not require emotion or conciousness. I don't think anyone would disagree with that. What I'm arguing is that its possible that future generations of AI could develop these features independent of what we require from it. Perhaps I'm...
But the thing about the eye is that its flawed. We design the camera to be better. The human body is not by any stretch of the imagination a perfectly functioning system. So I don't see your argument... The argument here is whether AI systems CAN develop emotions and conciousness, NOT whether...
Just looking at the evolution of humans and the brain, we already have a billion year head start. So to think that we could compress that process into a matter of decades might be unrealistic. But, I think if clever enough software and powerful enough software were set up so that a computer...
For the pendulum, think in terms of trigonometric functions. If you set the rest position to (0, 0) and you know the radius is 0.5 m, for what values of \theta will the height be 1 cm? Once you figure that out, you can find the times fairly easily.
Ok so:
m = \frac{5 \sin{120\pi 1.001} - 5...
sorry, just to clarify.. r = \frac{1}{9 \cos{t}} for -\pi \le t \le \frac{\pi}{2} and r = 1 right?
For the lower bound on r, I believe it is \frac{-1}{9} , but I'm not entirely sure about that, maybe someone else can look at this.
In terms of the iterated integral here's a few tips:
x = r...
Yes, that's a pretty close approximation and will give you an answer within 2.35 % of the exact answer. Question, have you ever done any calculus before? (and yes, I do realize this is the precalculus section)
Maybe if you gave the equation you'd get something more definite. But for polar coordinates what i'd do personally is convert it to a set of parametric equations and integrate those separately with respect to the parameter.
R is usually given by a polar equation, I'm not quite sure what you're...