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cosmology on a human scale
I came across an amusing observation today. The age of the universe is about 1018 seconds. That's about 30 billion years. The lifespan of a human on Earth is on average 67 years, and there are about 6.5 billion people now alive. The combined lifespan of everybody now alive well exceeds the current age of the universe. You could line people up, side by side in time, and reach back to the beginning of time. On the other hand (no pun intended), if all of these people held hands, they could form a chain about 12 billion kilometers long. Sure, this could wrap around the earth thousands of times, but it wouldn't even make it one-millionth of the way to Alpha Centauri.
It's often said that there are now more people alive than have ever lived. Or sometimes there's a restriction on this statement, like that there are now more physicists around than the total of all physicists before this generation. But this fact is true for any population which at least doubles from one generation to the next, because of the curious fact that if you add up the first N powers of two, you get one less than the next power of two, a fact known and loved particularly by computer engineers, as it becomes obvious when expressed in binary, eg: 10000 - 1 = 01111, e.g. 2^4 - 1 = 2^3 + 2^2 + 2^1 + 2^0.
It's often said that there are now more people alive than have ever lived. Or sometimes there's a restriction on this statement, like that there are now more physicists around than the total of all physicists before this generation. But this fact is true for any population which at least doubles from one generation to the next, because of the curious fact that if you add up the first N powers of two, you get one less than the next power of two, a fact known and loved particularly by computer engineers, as it becomes obvious when expressed in binary, eg: 10000 - 1 = 01111, e.g. 2^4 - 1 = 2^3 + 2^2 + 2^1 + 2^0.
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coherence
Re: coherence
nukes
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never mind... I don't think the non geniuses in your readership were supposed to get that :)
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The last comment though of course depends on there being some sort of exponential growth with base at least 2 in recent history, which is I suppose the surprising fact. I would be surprised if that were true for human population as a whole, but not at all surprised with regards to academics of any particular type. (Though in a couple decades I'll be surprised if those still hold, because the fast exponential growth will have been in a previous generation, and not the recent past any more.)
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You know, I was trying to figure out, for a piece of writing I did a few years back, the following:
If, starting today, everyone who died got their minds downloaded into a network, how long would it take for the number of living virtual humans to exceed the number of living physical humans? And how long to exceed the number of physical humans who had EVER lived?
I ended up punting and saying "a few decades." Can anybody come up with anything more precise than that?
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