[ExI] Nuclear probabilities (Was:] Repudiating the national debt)

Anders Sandberg anders at aleph.se
Mon May 16 21:14:07 UTC 2016

On 2016-05-16 17:59, spike wrote:
> Anders, this is an interesting number because of a popular educational 
> video I saw in the late 1970s.  The fictional US president was being 
> briefed on the work of his military mathematicians who had determined 
> that the probability of a nuclear war that calendar year was about 1%, 
> with the risk of war in each subsequent year declining by a factor of 
> about 0.9
> So in a mere seven years, by the end of that president’s term, the 
> risk of nuclear war would be about half a percent in that year.
> The new president was delighted with that news (this was the 1970s 
> when the cold war was threatening to hot at any time.)  As the 
> mathematicians were packing up to leave, he asked: oh by the way 
> professor, using your model, what are the chances of nuclear war 
> eventually?  Answer:  100%.

Hehe... good story.

Of course, the math is a bit different. The probability of *no* eventual 
nuclear war is P = prod_t=0^\infty (1-0.01*0.9^t), and this infinite 
product converges (see https://en.wikipedia.org/wiki/Infinite_product 
for some ways of showing it). Better, it can converge to something 
larger than 0. Consider the case of 1% risk that halves every year. That 
will eventually sum up to 2% risk.

This is the kind of math Stuart and me used to look at backup copy 

Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University

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