How not to destroy the world

Does anyone else remember someone in the 90s saying something about the superpowers having enough nuclear arms to destroy the world "10 times over". Have you ever wondered if it's true.

So what does it mean to destroy the world really? Fortunately if you mean all of humanity that means we've got a lot of land to cover, all the oceans and all the land just to be sure. That's a whopping 510,072,000 square kilometers. That's a lot, trust me. So let's assume that if you're out at ocean during the apocalypse, it's too late for you, and if you're on an ice cap you've removed yourself from the gene pool anyway, crazy researchers :) Then there is only 148,940,000 square kilometers of land left, according to Wikipedia.

Ok, now onto the destruction. Although we all know the awesome power of the atomic bomb, they don't actually do all that much destruction in comparison to the world. Yeah, there's a radioactive dust cloud etc, but let's ignore that since it is really survivable. The largest ever exploded nuclear weapon was the Soviet Union's Tsar Bomb at 50 Megatons. At this size it is powerful enough to cause third degree burns at 100km, and light damage at 700km from the epicentre. Now not every bomb is a Tsar bomb, and actually most have significantly less yield. A number of sources including Encarta and wikipedia state a typical nuclear weapon causes moderate damage up to 24kms away.

Quantity has definitely decreased in recent years. Today there are less than 5,000 active warheads. If we expand it to the available inactive warheads as well there are a total of 20,000. So now we've got our quantity and maximum yield. 

 SO if we take the 148,940,000 square kilometers of land area divided by 20,000 bombs with a coverage of 24kms we get about 50% coverage. So it's not 10 times over, but it's not too shabby either, but that's only the land area. If we go to the full earth it's only 15%. Now of course we could target cities and so forth, but it's nice know that it's a pretty safe bet some people would survive in the nuclear apocalypse.

Why do I always loose?

The good news is, you don't. Statistically everyone should win the same proportion of times.

A lot of it comes down to conformational bias. When a piece of toast is dropped it lands on the group butter side down 50% of the time, it's basically a coin (arguably it could be higher, but the difference is negligible).  What happens though is that for many of the times that the bread lands buttered side down you pick it up and continue on your way without really noticing. On the other hand when it lands buttered side down it sucks. You make a big deal, quote the line, and have to clean it up.

I believe it anything is over 60% people notice it as an unfair coin. So when a few of the buttered side up are ignored it seems that the bread is favouring the buttered side more.

Now that doesn't mean you can't have a streak, even a really long one. Loosing or winning. Probabilistically it could happen for someone's entire life, although the it would be extremely rare, like one person ever, it's not you, don't worry. Even if you flip a coin 100 times you'd expect to see a string of head (or tails) at least 7 long.

When these streaks happen people often think they are lucky or cursed, but their luck will eventually turn, it's all in the numbers. The thing to remember is that the probability of each instance is fixed, it has nothing to do with anything before. Even though you got a string of 15 heads in a row, the probability on the next one is still 50%.

How the universe is "normally" distributed

On the average day, nothing is absolute. It's not exactly minus 5 degrees, the air isn't exactly one atmosphere, and gravity isn't even 1g. At any given time there's a random fluctionation around some central point. A distribution around a mean.

The easiest way to see it is when you're making a cake, or whipping cream. A single band forms around the middle of the bowl, with fewer and fewer specs out from the middle. If you were to plot the distribution of these points you would get something like this

This is called the Normal Distribution. This is what "normally" happens. Most things are around some central value, but everything is possible, it's just less and less likely the further you get from the middle. That's why there's whipped cream on your fridge. If you run the beeters for long enough, the one in a million chance can happen, and that rare value way off on the curve is far enough out to leave the bowl and go wizzing across the room to hit your fridge.This is the basis of a large part of statistics. As you can see the probability drops of very quickly. Something called the Empirical rule tells us that we should expect almost 70% of the values within one standard deviation, and a whopping 95% within 2 standard deviations. By the time we get 3 standard deviations out we covered 99.6% of all possible outcomes from the population.

This is how so called anomalies occur. The bulk of observations are pretty close to the middle, occasionally there are some that are slightly off the mean, but once in a blue moon (That's two moons in one month btw) truly crazy stuff happens. We call those outliers.

And although the formula for it is rather unpleasant you'll notice that both pi and e (a number like pi) and the square root of two are all part of it. For math types, this is deep. Potentially the three most impotant numbers in science all part of a formula that came out of everyday experience. Pretty awesome. So the next time something truly incredible and strange happens, just remember it's "normal".