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Great project! What will the copyright be? I'm interested in putting a few essays into a course reader.

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.

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:

I'm the author - thanks for the feedback. I think you're right that a more-topical title could help. Edit: done.

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?"

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.

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