Measuring Risk - Pakistani Nukes Escaping to "Funny Fellows"

UPDATE : Now the Indian Defence Review has published a version of this post as well. You can read it HERE

Measuring Risk - Pakistani Nukes Escaping to “Funny Fellows”

Late Dr. APJ Abdul Kalam, India’s ex-President had a mild phrase for the illogical, fanatic, fringe groups including terrorists. He would address them the “funny fellows” – a term that was the most intense rebuke one of our greatest scientists could draft in his soft spoken manner – but it was always an intense rebuke. I am reminded of the phrase “Funny Fellow” as I sift through the details of disgusting Orlando killing in USA.

The horrific Orlando killing has brought the need for tighter gun control law in USA to the fore. The easy availability of assault rifles and automatic weapons definitely increases the probability of random, indiscriminate and unprovoked shootings and the impact of such shootings on the families of unfortunates who lost their lives or were injured is extreme to put it mildly. The measure of Risk is typically defined in terms of probability of an event occurring and the impact/consequences of the occurrence of the event. It is usually a multiplication of these two quantities, hence, Probability x Impact is the basic measure of Risk. To understand the Risks, let us say if Omar Mateen, the Orlando killer, had access to a nuclear weapon, would he have unleashed it on the gay club members, in the hatred of rage that he was feeling or was indoctrinated with? Of course, this is an implausible thought. But let us replace Omar Mateen by ISIS, or any of half-dozen or so terrorist organizations actively propagating heinous acts of senseless killing of innocent people. What is the risk? A terrorist organization having access to nuclear weapons is the type of horrible dreams that may keep security agencies of the world awake all night. One can argue from where these groups will get the technology and the functioning weapon for a nuclear explosion. North Korea can sell for money. However, the obvious source of such a weapon in the hands of terrorists – specifically Islamic terrorists – will indeed be Pakistan.

Pakistani Nukes – A potential source for Islamic terrorists

SIPRI in its latest report on worldwide nuclear weapons estimates Pakistani nuclear weapons to be in the range of 110-130. In 1998 after the Pakistani nuclear tests in response to Indian tests the estimates were that Pakistan may possess and have the fissile material for about 20 Nuclear warheads with a potential yield of 20-30 Kilo Tons of TNT equivalent (usually called 20KT-30KT).  It was assumed that 20-30 nuclear weapons will be sufficient for Pakistan. However, the numbers have gone up 4 times and there is no indication of stopping the maddening spiral of this race. The relentless illogical increase in number of nuclear bombs with Pakistan is becoming riskier with each new nuclear weapon.

A nation state (the Government and the people of the state) has all the right to possess nuclear weapons till the world is not freed of the nuclear weapons - is the key logic that most countries propagated - who were striving to have the ultimate weapon of deterrence. Even today many countries may like to possess nuclear weapons based on the same logic. The non-proliferation logic of Nuclear weapons being horrible in being a danger to humanity as a whole, hence must not be available to every nation state, especially the irresponsible and rouge states, also is valid as it increases the risk of a nuclear incidence. 

The debate of nuclear proliferation in the world continues – however one danger and the risk of nuclear weapons falling in the hands of terrorists, non-state actors and fringe groups – the “funny fellows”, is not only real it is increasing with every new nuclear weapon being developed.  The probability of a nuclear weapon falling in the hands of terrorists – the “funny fellows” is real. However, what is this probability and how one can estimate it, is not very clear.    

Probability of Nukes in Terrorists hands – A Simple Model

Let us assume that the probability (it is always a number between 0 and 1) of each nuke independently escaping to the "funny fellows" is 0.01% and is a constant; let us call it “p”. If Pakistan has 2 nukes the probability that “at least” one of the 2 nukes escape or fall in the hands of “funny fellows” is computed using the following simple calculation. The probability that first nuke does not escape is 1-p, i.e., 99.99%. The probability that second nuke does not escape is also 1-p.  The probability - that neither the first nuke nor the second nuke escapes to the funny fellows - is just the product of two probabilities i.e., (1-p) x (1-p). This comes out to be 99.98%.We are however interested in the probability the at least one nuke escapes to funny fellows. That probability (let us call it E) is E = 1 – (1-p) (1-p). This number for 2 nukes each with p = 0.01% comes out to be (1-99.98%) = 0.02%. 

For 20 Nukes (the year 1998 estimate of potential numbers with Pakistan) the Probability that "at least" one nuke escapes (let us call it E) to the “funny fellows” is simply E= 1- (1-p)^20 is 0.2%. For 110 Nukes this probability jumps to 1.094% and for 130 Nukes it is 1.292 %.  For 150 nukes with Pakistan this probability is 1.489%. Is it fairly acceptable? Can the world live with this probability of at least one nuke escaping to the “funny fellows”.

However, if we double p from 0.01% to 0.02% the value of E changes for 20 Nukes to 0.399%, for 110 Nukes E comes out to be 2.176% and for 130 Nukes it is 2.567%. For 150 Nukes it is 2.956%. We are still less than 5% probability. May be the world can live with that danger. 

If we increase the value of the constant p from 0.01% to say 0.1%, the value of E for 20 Nukes, 110 Nukes, 130 Nukes and 150 Nukes are 1.981%, 10.442%, 12.196%, and 13.936% respectively.  Suddenly it looks more and more risky. In fact, the grave danger is visible in these simple calculations. 

The chart below provides the variation in these probabilities for Nukes 20 to 150 for probability p ranging from 0.01% to 0.1%. The Y axis plots the value of E, i.e., the probability that at least one nuke will escape or reach the terrorists versus the X-axis with the number of nuclear weapons with Pakistan. Different curves are for various values of p, the probability of a nuclear weapon escaping to the hands of terrorists.

If we increase p to 0.2% then we get for 20, 110,130 and 150 number of nukes with Pakistan, the E (i.e., the probability that at least one nuke escaping to Funny fellows) to be 2.925%, 19.766%, 22.915% and 25.946% respectively. 

The numbers for increasing p to 1% becomes extremely difficult to digest the value of E becomes 18.209% for 20 nukes, 66.897% for 110 nukes (lower estimate by SIPRI), 72.925% for 130 nukes (higher estimate by SIPRI) and 77.855% for 150 Nukes with Pakistan. The graph below shows the shift for increasing the value of p to 0.2% and 1%.

 

Increasing Risk

With the probabilities computed above one can see how much has RISK increased from 20 Nukes estimate in 1998 to 130 Nukes in 2016. RISK has a measure typically defined as R = Probability x Impact. If one keeps the impact of a nuclear weapon getting into the hands of terrorist groups as constant, the risk since 1998 (when the estimate of Pakistani nukes was about 20) has increased by 3.5 times in 2016 when Pakistan has about 110-130 Nukes as the probability of at least 1 nuclear bomb reaching the terrorists has increased from around 18% to about 70%. 

Conclusions and Future

One main lesson, if it has to be reiterated again and again, of Orlando killings is that the terrorists indoctrinated to the core by religious fundamentalism and fanaticism, if have easy access to the gravest weapons and means of destruction that mankind has invented, will not be averse to using them against all those deemed enemies or perceived not from faith. Kalam’s “Funny fellows” indeed are becoming not so funny now. With the easy availability of nuclear weapons, just like the easy availability of automatic weapons, these terrorist groups may not be averse to using them anywhere in the world. Since a nuclear weapon has long term impact and a “big” impact, it will be used in a spectacular way. 

The number of nuclear weapons increasing in the vicinity and with the religious supporters of these groups – on both counts Pakistan qualifies - is a sure indication of increasing Risk of a nuclear incidence. Pakistan’s relentless pursuit of increasing the number of nuclear weapons from 20 to 110 has already increased the probability of at least one nuclear bomb escaping to terrorists beyond acceptable limits. The world needs to pressurize Pakistan to not only increase the security of its nuclear weapons but also to cut-back on the numbers which have gone way beyond any reasonable assessment of deterrence logic. In the tunnel vision of this relentless maddening increase of its nukes in perhaps one of the most terrorist infested region of the world, not only Pakistan, but the world is itself calling for its demise. And the cost of an Omar Mateer with a Pakistani nuke will be much more than a debate about gun-control laws.