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On 2016-05-16 17:59, spike wrote:<br>
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<p class="MsoNormal"><span
style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:windowtext"><o:p> </o:p></span></p>
<span
style="font-size:14.0pt;font-family:"Calibri",sans-serif;color:windowtext">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<o:p></o:p></span>
<pre><span style="font-size:14.0pt;font-family:"Calibri",sans-serif;color:windowtext"><o:p> </o:p></span></pre>
<pre><span style="font-size:14.0pt;font-family:"Calibri",sans-serif;color:windowtext">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.<o:p></o:p></span></pre>
<pre><span style="font-size:14.0pt;font-family:"Calibri",sans-serif;color:windowtext"><o:p> </o:p></span></pre>
<pre><span style="font-size:14.0pt;font-family:"Calibri",sans-serif;color:windowtext">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%.</span></pre>
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Hehe... good story. <br>
<br>
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
<a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/Infinite_product">https://en.wikipedia.org/wiki/Infinite_product</a> 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.<br>
<br>
This is the kind of math Stuart and me used to look at backup copy
immortality:<br>
<a class="moz-txt-link-freetext" href="http://www.fhi.ox.ac.uk/indefinite-survival-backup.pdf">http://www.fhi.ox.ac.uk/indefinite-survival-backup.pdf</a><br>
<br>
<br>
<br>
<pre class="moz-signature" cols="72">--
Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University</pre>
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