Wednesday, January 16, 2013

Clock: doom arrives in five minutes

...but the sky has already been falling too many times for any credibility to have survived...

You may hear from Fox News and other journalists that the doomsday clock will show 23:55, five minutes before the midnight, as the time indicating the "imminent destruction of humans" for the whole year of 2013 (unless an urgent modification is needed).

We are told that the timing – one that has been said many times before – was calculated and announced by "scientists". When you read a few more paragraphs, you will realize that it's some article written in the Bulletin of Atomic Scientists which is, despite the name, no longer controlled by atomic scientists. For example, the boss named Kennette Benedict is a socialite-type activist who's been working (?) on peace with the former Soviet Union (when it no longer existed) and on education in Nigeria.

We're told that the doom is imminent because of a combination of the large nuclear arsenal of several countries, global warming, and a slow recovery from the Fukushima meltdown.

Holy cow. There hasn't been any global warming for 16 years and even the global warming – by which I mean the increase of the global mean temperature over the timescale of several decades – which was observed earlier is completely unspectacular and probably mundane in the history of the Earth. It is not hard to figure out that the global warming hype has been added to the mix by the climate doom crackpot (not really "atomic scientist"!) Richard Somerville (and perhaps some of his soulmates).

The nuclear arsenal of the superpowers hasn't been used for more than half a century and even when it was used, it killed a few parts per million of the mankind. However tragic these events have been, they were hugely and immensely far from the destruction of the mankind. These weapons are arguably insured against accidental launching more safely than they have ever been and the countries with the "globally dangerous" arsenals are still rational and afraid of self-destruction.

And the most obvious preposterous claim is one about the Fukushima meltdown which was a complete non-event which has killed no one at all (if we talk about the leaked radiation only) and whose extra expenses in the future are unlikely to exceed a few billion dollars, a negligible amount relatively to Japan's GDP (not to speak about the world's GDP). Needless to say, anti-atomic activists are abusing the remaining credibility of the "doomsday clock" to promote their irrational anti-nuclear-energy fears.

The doomsday clock is the "most famous product" of the Bulletin of Atomic Scientists. Maybe it's the only one that matters. Because the clock is showing something very specific, some of the listeners may get the totally wrong idea that the clock is showing something quantitative. It is showing that we are five "minutes" from the doom. But what does it mean? What are those "minutes"? Intelligent people have to ask.

Needless to say, they're not the real minutes. The world won't end at 9:32 am Central European Time today (Wednesday). Most likely, you are reading this text after 9:32 am today so you are a witness of my claim. But if they're not real minutes, these "minutes" don't have too many options what they could possibly mean. They mean nothing. It could be 23:59:59 but the remaining second could still stretch to billions of years much like some "interpreters of the Bible" stretch the Cosmos' First Seven Days to billions of years. The conversion factor may be – and probably must be – dependent on the time that the clock is showing and this warp factor may become singular near 24:00:00 so that an arbitrary (or infinite) amount of time is left regardless of what the clock is showing.

From a rational viewpoint, the clock reading can't mean anything. It's just a tool to spread fear.

Now, let us ask: How would you seriously quantify the risks of the human destruction? Let's imagine that we mean something specific. For example, the human population has to drop below 6 million people. Or whatever number you invent – it may be much higher or much lower. If something truly "existentially catastrophic" happens to the mankind, the population has to drop below such a threshold in a short time, anyway, so the population is arguably a good proxy for any existential catastrophe. The risk of the doom exists at each moment of time. What is the most natural way to define a "single average figure" that summarizes these risks?

Because the natural probability of the events that may occur anytime is "probability per unit time", we're no longer dealing with dimensionless probabilities. We're dealing with probabilities per unit time – or with their inverses that have the units of time. To estimate the risks, you could think that it's natural to consider "the average time that is still left for the mankind",\[

\bar t = \int_{2013}^\infty \dd t\, p(t)\, (t-2013)

\] where \(p(t)\) is the probability that the world ends (i.e. the population drops below the previously declared threshold) in the year \(t\) (or density per unit time, which we take to be one year, that it occurs at \(t\) that is continuous: the results won't change much unless you think that the doom is a matter of months or shorter units). The probability distribution is normalized so that\[

\int_{2013}^\infty \dd t\, p(t)=1.

\] Perhaps, an extra dimensionless term \(p(\infty)\) indicating the possibility that the mankind will be around forever should be added to the left hand side, too.

However, this \(\bar t\) is a bad measure of the imminent risks. Despite the risks, there is surely a substantial probability – arguably greater than 50 percent – that the mankind will be around in thousands or millions of years. So \(\bar t\) is inevitably calculated to be at least of order thousands or millions of years if not more (billions of years and the integral may even diverge; in fact, we may need to add the contribution from \(p(\infty)\) as well, yielding an infinite result), regardless of the risks that the world will end in a few years.

So we have to define a different kind of average that is "shielded" against the contribution of the scenarios with a long-lived mankind. We need to give these scenarios a smaller weight. A natural way to do so is to define the harmonic average:\[

\bar t_{\rm harmonic} = \frac{1}{ \int_{2013}^\infty \dd t\,p(t)\,\frac{1}{t-2012} }.

\] Here, we're averaging not \(t-2013\) but its inverse (I changed the shift to 2012 to avoid singularities). The result must be inverted once again to get a quantity with the units of time. This harmonic average is insensitive to the long-lived mankind scenarios because these scenarios' contributions are suppressed due to the factor \(1/(t-2012)\to 0\) with the nearly divergent value of \(t\to\infty\). On the contrary, this harmonic average is highly sensitive to probabilities of doom \(p(t)\) where the time \(t\) appears in the near future.

Incidentally, you may use the harmonic average to calculate the average speed while you're riding your bike. If you're going uphill and downhill, the same distance, and the two speeds are \(v_1\) and \(v_2\), the average speed on your trip is the harmonic average\[

\bar v_{\rm average} = \frac{1}{ \frac 12\zav{ \frac{1}{v_1}+\frac{1}{v_2} } } = \frac{2v_1v_2}{v_1+v_2}

\] This right answer differs from the arithmetic average of the two speeds because the latter would only be relevant if you spent the same time with both parts of the trip. But because you spend much more time on the slower half of the distance (probably when you're going uphill), this slower half of the distance has a much greater impact on the average speed. If your speed while going up is nearly zero, the average speed \(s/t\) will be nearly zero because \(t\to\infty\) regardless of the huge speed by which you're able to ride down.

If the bulletin were composed of scientists, they would probably try to quantify the harmonically averaged "remaining time of the mankind" above instead of childish doomsday clock whose only role is to spread irrational fear. Fine. What do I think about the value of this harmonic average?

I am confident that even this harmonic average (which is, pretty much by definition, shorter than the arithmetic average) is longer than a few centuries. Even with this counting, the mankind will have more than a few centuries left. A necessary condition for this claim is that the probability of a doom in the next 10 years is (much) smaller than 10%, the probability of the doom in the next 20 years is (much) smaller than 20%, and so on. Similar inequalities imply that the integral in the denominator remains small (the large values of \(1/(t-2012)\) for an imminent \(t\) are multiplied by small values of \(p(t)\) and vice versa) and its inverse is therefore large.

Of course, when I say that there are at least many, many centuries ahead of the mankind, I am not saying that everything about the future mankind will be great according to my tastes. Unfortunately, it almost certainly won't be great and this proposition isn't a sign of pessimism; it's just realism. And incidentally, medieval methods to spread fear such as the "doomsday clock" are significant contributors to the fact that many things about the future mankind will suck.

What do you think about the mankind's remaining time?


  1. The doomsday clock sometimes goes backwards so that disqualifies it from reality.

  2. Another doomsday announcement by some dimwits ... yaaaaawn!

    But the calculations with the harmonic mean are nice

  3. > What do you think about the mankind's remaining time?
    Time for total extinction I have no idea. But for a catastrophic population reduction I think that the next glaciation will do it. By the time the glaciers cover more than 30% of the Northern Hemisphere there could have been mass mortality of more than a billion people.

  4. I think that by that time, people will be living in "artificial atmosphere" almost 24 hours a day.

  5. The mankind's remaining time will be a long bloody fight against the forces of evil. As always. Doomsday announcements are just another diversion for the idiots. Advantage: it gives you a quick info on who you're dealing with. You can either use them or dismiss them.

  6. I do agree that mankind is likely to be around for a very long time although I have no idea what life will be like in a thousand years. Hell, I have been a rotten prognosticator over periods of time shorter by several orders of magnitude.

    By any measure, life is less dangerous than it has ever been. The prophets of doom have always been wrong and they will always be wrong. Catastrophes are still occurring but less often. Things will get better and better albeit slowly.

    I believe, without scientific justification, that people are good at heart. Ann Frank was right and good will triumph over evil in the long run.