Great project! What will the copyright be? I’m interested in putting a few essays into a course reader.
Mark_Eichenlaub
Karma: 638
A decent approximation to exponential population growth is to simply use the average of 700m and 50m
That approximation looks like this
It’ll overestimate by a lot if you do it over longer time periods. e.g. it overestimates this average by about 50% (your estimate actually gives 375, not 325), but if you went from 1m to 700m it would overestimate by a factor of about 3.
A pretty-easy way to estimate total population under exponential growth is just current population 1/e lifetime. From your numbers, the population multiplies by e^2.5 in 300 years, so 120 years to multiply by e. That’s two lifetimes, so the total number of lives is 700m2. For a smidgen more work you can get the “real” answer by doing 700m 2 − 50m 2.
Is there an automatic Chrome-to-Anki-2 extension or solution?
Cartman: I can try to catch it, but I’m going to need all the resources you’ve got. If this thing isn’t contained, your Easter Egg hunt is going to be a bloodbath.
Mr. Billings: What do you think, Peters? What are the chances that this ‘Jewpacabra’ is real?
Peters: I’m estimating somewhere around .000000001%.
Mr. Billings: We can’t afford to take that chance. Get this kid whatever he needs.
South Park, Se 16 ep 4, “Jewpacabra”
note: edited for concision. script
A bit of an aside, but for me the reference to “If” is a turn off. I read it as promoting a fairly-arbitrary code of stoicism rather than effectiveness. The main message I get is keep cool, don’t complain, don’t show that you’re affected by the world, and now you’ve achieved your goal, which is apparently was to live up to Imperial Britain’s ideal of masculinity.
I also see it as a recipe for disaster—don’t learn how to guide and train your elephant; just push it around through brute force and your indefatigable will to hold on. It does have a message of continuing to work effectively even in bad circumstances, but for me that feels incidental to the poem’s emotional content. I.E. Kipling probably thought that suffering are failure are innately good things. Someone who takes suffering and failure well but never meets their goals is more of a man than someone who consistently meets goals without tragic hardship, or meets them despite expressing their despair during setbacks.
Note: I heard the poem first a long time ago, but I didn’t originally read it this way. I saw it differently after reading this: http://www.quora.com/Poems/What-is-your-view-on-the-Poem-IF-by-Rudyard-Kipling/answer/Marcus-Geduld
I’m the author—thanks for the feedback. I think you’re right that a more-topical title could help. Edit: done.
I see, thanks.
I just looked this up. It seems the text has been altered, and in the original, Linus said “Are there any openings in the Lunatic Fringe?” http://www.gocomics.com/peanuts/1961/04/26
All of them are obviously still chances. I never said that a very small probability wasn’t a chance. I said that it might rationally be treated in a different manner than larger chances due to risk-aversion.
Re: other stuff on ballot. Yes, that’s right. I was just replying to the content of the post.
Sorry, I don’t understand what was meant by your first sentence.
I rarely make decisions involving such low probabilities, so I don’t really know how to handle risk-aversion in these cases. If I’m making a choice based on a one-in-ten-million chance, I expect that even if I make many such choices in my life, I’ll never get the payoff. This is quite different than handling one-in-a-hundred chances, which are small but large enough that I can expect the law of large numbers to average things out in the long term. So even if I usually subscribe to a policy of maximizing expected utility, it could still make sense to depart from that policy on issues like voting.
BTW, in my state, Maryland, Obama has a 18-point margin in the polls. That could easily be six standard deviations away from the realm where I even have a chance of making a difference.
You’re right. That would be true if we did n independent tests, not one test with n-times the subjects.
e.g. probability of 60 or more heads in 100 tosses = .028
probability of 120 or more heads in 200 tosses = .0028
but .028^2 = .00081
Thanks. Sometimes I learn a lot from people saying fairly-obvious (in retrospect) things.
In case anyone is curious about this, I guess that Eliezer knew it instantly because each additional data point brings with it a constant amount of information. The log of a probability is the information it contains, so an event with probability .001 has 2.3 times the information of an event of probability .05.
If that’s not intuitive, consider that p=.05 means that you have a .05 chance of seeing the effect by statistical fluke (assuming there’s no real effect present). If your sample size is n times as large, the probability becomes (.05)^n. (Edit: see comments below) To solve
(.05)^n = .001
take logs of both sides and divide to get
n = log(.001)/log(.05)
I think I see what you mean. To clarify, though, tension doesn’t have a direction. In a rope, you can assign a value to the tension at each point. This means that if you cut the rope at that point, you’d have to apply that much force to both ends of the cut to hold the rope together. It’s not upward or downward, though. Instead, the net force on a section of rope depends on the change in the tension from the bottom of that piece to the top. The derivative of the tension is what tells you if the net force is upward or downward. This derivative is a force per unit length.
In general, tension is a rank-two tensor, and is just a name for when the pressure is negative.
I’m not really sure what you mean by “upward tension”, sorry. Tension in one dimension is just a scalar. The very bottom of the spring is under no tension at all, and the tension increases as the square root of the height for a stationary hanging slinky.
Thanks for the tip.
The center of mass of the slinky accelerates at normal gravitational acceleration. The bottom of the slinky is stationary, so to compensate the top part goes extra-fast. I did a short calculation on the time for the slinky to collapse here http://arcsecond.wordpress.com/2012/07/30/dropping-a-slinky-calculation-12/
What is the Mantra of Polya?
And clearly my children will never get any taller, because there is no statistically-significant difference in their height from one day to the next.
Andrew Vickers, What Is A P-Value, Anyway?
WolframAlpha is pretty good for calculating all this automatically—probably much faster than the spreadsheet. For example:
Thanks!