An Evil Guest science errors

Gwern Branwen · 04 Jan 2010, 16:07 · from 2010-January.txt.gz

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From: gwern0 at gmail.com (Gwern Branwen)
Date: Mon, 4 Jan 2010 11:07:18 -0500
Subject: (urth) An Evil Guest science errors
Message-ID: <cbf55b101001040807k746b10c5r263738f07e799eee at mail.gmail.com>

I forgot to include this in my tone email, but another thing that
bothered me coming from an engineer is the apparent sloppiness with
his scientific assertions.

Reis claims that even if humans didn't age, we'd still only get 2 or
300 years because of accidents and murders and self-slaughter. This is
a classically conservative argument against being interested in curing
aging - you're going to die anyway, and soon - but as far as I can
tell, his numbers are just wrong.

I have seen statistics to the effect that a 12 year old who stopped
aging could expect a median lifespan of >1000 years before disease or
something else finally got her. But the mortality rates for young
people in general are low enough that 2 or 300 years is ridiculously
too little, and we can see this very easily,

http://gravityandlevity.wordpress.com/2009/07/08/your-body-wasnt-built-to-last-a-lesson-from-human-mortality-rates/
mentions that 1/3000 or 0.03% of 25 year-olds will die age 25. (Seems
reasonable to me.)

If we assume a cohort of 10x people, and each year 0.03% of them die,
then 1000 years from now, 7.4x will still be alive. 300 years from
now, 9.15x will still be alive, and 200 years will see 9.42x. It's a
low death rate!

Even a little basic figuring would have show 2-300 years to be absurd.
And we can't make the excuse that Wolfe was estimating from the
mid-40s ages of the protagonists, since the mortality rate cited for
42 year-olds is 1/750 or 0.13%. Plug in the 1/750 to the formula and
ask for 300 years from now, and 6.7x are still alive. Heck, 2.6x are
still alive 1000 years from now. 7/10ths or 3/10ths odds are not
grounds for despair and dismissal.

I'm calculating this in a Haskell REPL, GHCi, using this expression
for 100 years: 'take 100 $ iterate (\x -> x - (x * 0.0003)) 10'

You can see that each step is a year, and each step subtracts 0.03% of
the previous year's population-total:
[10.0,9.997,9.9940009,9.99100269973,9.98800539892008,9.985008997300405,9.982013494601215,9.979018890552835,9.97602518488567,9.973032377330204,9.970040467617006,9.96704945547672,9.964059340640077,9.961070122837885,9.958081801801034,9.955094377260494,9.952107848947316,9.949122216592631,9.946137479927653,9.943153638683675,9.940170692592071,9.937188641384294,9.934207484791878,9.931227222546442,9.928247854379677,9.925269380023364,9.922291799209358,9.919315111669595,9.916339317136094,9.913364415340952,9.91039040601635,9.907417288894546,9.904445063707877,9.901473730188766,9.898503288069708,9.895533737083287,9.892565076962162,9.889597307439074,9.886630428246841,9.883664439118366,9.88069933978663,9.877735129984694,9.874771809445699,9.871809377902865,9.868847835089495,9.865887180738968,9.862927414584746,9.859968536360372,9.857010545799463,9.854053442635724,9.851097226602933,9.848141897434953,9.845187454865723,9.842233898629264,9.839281228459674,9.836329444091136,9.83337854525791,9.830428531694333,9.827479403134824,9.824531159313883,9.821583799966088,9.8186373248261,9.815691733628652,9.812747026108564,9.809803202000731,9.80686026104013,9.803918202961817,9.80097702750093,9.79803673439268,9.795097323372362,9.79215879417535,9.789221146537097,9.786284380193136,9.783348494879078,9.780413490330615,9.777479366283515,9.77454612247363,9.771613758636889,9.768682274509297,9.765751669826944,9.762821944325996,9.759893097742697,9.756965129813375,9.75403804027443,9.751111828862348,9.74818649531369,9.745262039365095,9.742338460753285,9.739415759215058,9.736493934487294,9.733572986306948,9.730652914411056,9.727733718536733,9.724815398421171,9.721897953801644,9.718981384415503,9.716065690000178,9.713150870293179,9.71023692503209,9.70732385395458]

-- 
gwern

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