Since I perhaps shall not have the opportunity again to correct Nick on a point of language (unfortunately its most trivial aspect but that is to be expected as I am a near illiterate in comparison), his pronunciation of Euler is incorrect it is not “ule-er” but “oil-er” (I see Joe has already said the same thing)

Nick also reads out the wrong thing for Euler’s constant. He says it is:

1+1/2+1/3+1/4+…

which is the Harmonic series. In fact this series goes off to infinity i.e. gets as big as you want if you go along far enough (this is not meant to be an obvious fact). In general if I have some expression f(n) then I can consider the series f(1)+f(2)+f(3)+…

examples:

f(n)=1/2^n so the series is 1/2+1/4+1/8+… = 1

f(n)=1/n^2 so the series is 1/1+1/4+1/9+1/16+… which Euler showed equals pi^2/6 (even less obvious).

Given such a series one can compare it with an integral (i.e. the purple area here: https://upload.wikimedia.org/wikipedia/commons/0/04/Gamma-area.svg ) in order to show the series has a finite value or an infinite value. In the case of the harmonic series one compares it with an integral which ends up giving the function log(x) (i.e. the natural logarithm). The fact that log(x) goes to infinity as x gets large shows that the harmonic series also goes to infinity. Euler’s constant enters the picture when you ask how good an estimate log(n) is to 1+1/2+1/3+…+1/n. You define a new series by:

f(n)=(1+1/2+1/3+…+1/n)-log(n)

Euler’s constant is then the value of this series as n goes to infinity (i.e. it tells you overall how good an approximation log(n) is). As Nick says the number starts off with 0.5772156… and the goes on with seemingly no pattern (interestingly it is not known whether the number is rational i.e. whether the string of digits eventually repeats itself).

]]>From my (very amateur) understanding it would be much easier to sneak the required materials across a border for a start. I also recall seeing reports that ISIS has re-established one of Saddam’s old factories for this purpose (might search later, when not at work).

—

On South Park: I only recently started watching it again after a number of years (it seemed to be treading water and becoming quite predictable). This season especially, but the previous one to a lesser extent, has been nothing short of amazing. I think the most recent episode (with the school newspaper) might be the best so far: we are now starting to see the threads all start coming together, but it has introduced an interesting swerve which means we cannot be sure where the stable ground is.

*apologies for any weird phrasing here. I’m not the most elegant writer at the best of times, but I also have a stinking headache to contend with too!

]]>And besides if Nick so truly believes this is a likelihood, he should be seriously considering moving a long way from London.

]]>But the very fact that in several decades now of international terrorism no cell has managed to procure a device would seem to imply that it is rather more difficult to acquire a device than you seem to believe.

I think my worry with intervention over ISIS is that without a plan as to what exactly would happen afterwards we are just going to cause more pain misery and suffering to save ourselves from direct attacks. (Note, this was pretty much precisely my worry over Iraq). I am fairly comfortable with the idea of that organisation no longer existing, but not if it’s just going to be replaced by a worse one. I am also highly suspicious of the idea that in of itself UK intervention in the form of a few extra bombs will have a significant effect.

]]>