Odd Socks And The Dangers Of Nuclear Proliferation

Before talking about nuclear proliferation I am going to explain a concept which people may have covered at school – odd socks in a drawer.

For some reason all of my socks are odd. How many different combinations I have depends on the number of socks in my drawer. If I have two socks I obviously only have one combinations or two if I differentiate between different socks on different feet. If I have three socks then:


I have three different combinations. If I have five socks I have


ten different combinations.

Let us say I have n socks. Then it can be paired with (n-1) other socks since it cannot be paired with itself. Therefore the total number of combinations is n(n-1) or n(n-1)/2 if I do not care about which sock goes on which foot.

Hopefully you should be able to see where I am going with this. If instead of socks we talked about conflict between nuclear armed states then we can apply a similar analysis. With the current number of nuclear states – 9 – then there are 36 possible possible conflicts between nuclear states. If the number of nuclear armed states increased to twenty then there would be 190 combinations and with fifty then 1225 different combinations.

I know that this analysis is much too simple however it does show how the possibility of nuclear war does increase non-linearly with the number of states with nuclear weapons.

It is unlikely that the UK will go to war with France – after all they are both in NATO. An even more important point is that all 28 members of NATO are under NATO’s ‘nuclear umbrella’. So perhaps a more accurate diagram might look like this:


Any war between a nuclear armed state and a non nuclear state might result in a conflict between nuclear armed states due to various treaty obligations. One treaty obligation is that covering North Atlantic Treaty Organisation (NATO) countries which covers 28 countries.

In 2008 there was a limited war between Russia and Georgia1. If Georgia was part of NATO (which it looks likely they will be in the future) then it may have resulted in a NATO – Russia conflict. However, a similar situation could possible arise with current NATO countries such as Estonia where there has been a lot of tension with Russia2 including an attack on the Estonian internet3. It also raises the interesting question of whether a cyber attack could invoke article 5 of the NATO agreement4 which basically states that an attack against one is an attack against all.

Accidental Nuclear War

A nuclear war does not necessarily arise from intentional confrontation between two nuclear weapon states. It can happen by accident particularly during times of heightened tensions. For example during the Cuban Missile Crisis in 1962 there were at least nine false alarms5. There were also several miscalculations and misunderstandings that could have resulted in nuclear war. For example the US was not aware that there were tactical nuclear weapons already in Cuba which may have been used if the US invaded as many people were advocating6.

The US also tried to use signalling depth charges to bring a Russian submarine to the surface. However, the submarine crew mistook it for an attack and thought that war had broken out. They prepared to launch a nuclear torpedo and agreed to launch if three of the senior officers agreed. Only one person disagreed and saved the world from nuclear holocaust7.

Incidents such as the Cuban Missile Crisis is not just something from the bad old days of the Cold War. Russia is not pleased about anti-ballistic missile systems being placed close to its boarders by NATO and in 2008 threatened to move strategic bombers to Cuba8.  If another period of high tension occurs between NATO and Russia we might not be so lucky.

Back To Non-Proliferation

I digressed slightly to show the dangers of accidental nuclear accidents. That was between two nuclear powers. As I have shown above if there are 50 nuclear states there are 1225 different possible conflicts – so we have to be over 1000 times more lucky.

If you think that a nuclear war between India and Pakistan would not significantly affect us then it is time to think again. Studies have shown that even a small scale conflict could result in 2 billion deaths9.

1 Russia–Georgia war, Wikipedia (http://en.wikipedia.org/wiki/Russia%E2%80%93Georgia_war)

2 Tensions worsen between Russia and Estonia, The New York Times, 2 May 2007 (http://www.nytimes.com/2007/05/02/world/europe/02iht-estonia.4.5537016.html?_r=1&)

3 Hackers Take Down the Most Wired Country in Europe, Wired Magazine 15.09, 21 August 2007 (http://www.wired.com/politics/security/magazine/15-09/ff_estonia?currentPage=all)

4 “The Parties agree that an armed attack against one or more of them in Europe or North America shall be considered an attack against them all…”, What is Article 5, NATO (http://www.nato.int/terrorism/five.htm)

5 20 Mishaps That Might Have Started Accidental Nuclear War, Alan F. Philips, M.D, nuclearfiles.org (http://nuclearfiles.org/menu/key-issues/nuclear-weapons/issues/accidents/20-mishaps-maybe-caused-nuclear-war.htm)

6 Apocalypse Soon, Robert MacNamara Foreign Policy, May 5, 2005 (http://www.foreignpolicy.com/articles/2005/05/05/apocalypse_soon)

7 Vasili Arkhipov, Wikipedia (http://en.wikipedia.org/wiki/Vasili_Arkhipov)

8 Russian Bombers Could Be Deployed to Cuba, Washington Post Foreign Service, Tuesday, July 22, 2008 (http://www.washingtonpost.com/wp-dyn/content/article/2008/07/21/AR2008072102478.html)

9 Nuclear Famine: Two Billion People At Risk?, International Physicians for the Prevention of Nuclear War and Physicians for Social Responsibility, 2013 (http://www.ippnw.org/pdf/nuclear-famine-two-billion-at-risk-2013.pdf)


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