The Dirty Bomb Equation; Predicting Radioactive Terror

A  mathematical equation provides useful input to prediction of radiological terror. This is because radioactive decay proceeds as a natural, inexorable process, affecting the ability of terrorists to amass a stockpile.

Markov chains model radioactive decay, providing precise predictions of how long a radioactive substance will remain potent, resulting in the simple equation presented here. Decay proceeds with the precision of an atomic clock, and cannot be slowed by “proper storage” or any other treatment by man. (Markov chains will also be used in a future discussion of power projection.)

Use of dirty bombs has long been anticipated, yet the threat has not so far materialized. To understand why, and to offer an insight as to when it might, we must consider the terrorist problem, which is to accumulate a stockpile prior to use. The more radioactive material can be assembled in one place, the more harmful the effect will be.

A stockpile of a radioactive isotope undergoes exponential decay, decreasing in potency by half every half-life. The half-life of a particular isotope is precisely known and unchangeable. The physical bulk of a source remains, but containing an ever-increasing proportion of inert, stable isotopes. Isotopes used in hospitals have half-lives between days and years.

  • Most radioactive substances  in hospitals are used as tracers. Injected into the body, a tracer concentrates in particular tissue, providing diagnostic information. Tracer isotopes have short half-lives, decaying rapidly, avoiding persistence of radioactivity in the patient. Tracers have little terror potential.
  • In brachytherapy, a tumor is irradiated from a source placed inside the body. These sources are more powerful and longer lasting than tracers. Cesium-137 is  used as an implant to a tumor. With a half life of 30.17 years, it must be removed from the body after treatment. The discarded implants  have terror potential. Amassing a stockpile requires collection of many discarded doses.
  • The most dangerous isotopes used by hospitals are found in external radiation machines, which direct an intense beam of radiation into the body. The standard isotope is cobalt-60,  contained within a thick lead capsule with a bore hole at one end. Cobalt-60 has a half-life of 5.27 years.

Cesium-137 and cobalt-60 do not fit well into  the conventional definitions of low or high level waste. While a single hospital source is far less radioactive than a single spent reactor fuel rod, collected discarded sources over time can accrete to massive levels. But there is a limit, determined by the half life of the isotope.

Suppose some  individuals in Peshawar, perhaps a nuclear medicine technician or physician and an analytical chemist,  put themselves in the illicit business of collecting, assaying, and reselling radioactive sources to terrorists.  Suppose that, on the average, they manage to collect a fixed amount of a particular isotope per year, perhaps a few ounces. Every source in their stockpiles decays relative to when they acquired it. For this example, let’s consider cobalt-60.

After some years of collecting, the total radioactivity in their possession will almost plateau, as an asymptote. They more isotope they have, the more is decaying. At some year relative to start of their enterprise, the amount lost to decay is merely balanced by the amount of their annual collection. The stockpile continues to increase in bulk, becoming ever harder to concentrate for dirty bombs, yet no more radioactive.

This is the cash-out point. Some time relative to it, both the terrorist and the technicians  make a deal. We cannot predict the actual event of use  but we can estimate the cash-out point, when the stockpile reaches a point of diminishing returns. Nothing can be done to change the rate of decay.

Where

h = half life of the isotope

t = the elapsed time from start of collection

R = rate of collecting discarded sources, in whatever unit of radioactivity you prefer

ln is the natural logarithm

Q is the  quantity of isotope in the stockpile

Q_T is the maximum amount of isotope that can be accumulated given the rate of collection R

we have

Q = [h*R/ln(2) ] * [1  – 2  (to the power of (- t/h))]

while the maximum size of the stockpile (the asymptotic value) is

Q_T = h*R/ln(2)

For cobalt-60, the point of futility, the cash-out point, when the amount collected is about 84% of Q_T, with the bulk ever increasing, is about 15.5 years. Cesium-137 can accumulate for a much longer time.

This calculation is independent of how much isotope is collected annually, assuming only the same amount each year. If the collecting started in the early 2000’s,  the time is about now.

 

 

 

Putin and Rap in Russia

(BBC)  Putin wants government to “take charge” of rap music.

We cannot ring out the year without taking up the challenge rap  presents to Russian state power.  Yes, take charge of it.  Sex, Drugs, and Rock & Roll almost sunk the Brits, who survived only by heavy state repression. The pivotal role of MI-5 is yet to be revealed.

Essentially, implement a “loyalty test” to challenge a rapper’s professed loyalty to the Russian state.  The Romans had the same problem in the first century A.D.  They devised extreme methods to vet their centurions. This documentary video re-enacts the Roman test, which I hope will be helpful to Vladimir Putin:

Roman Loyalty Test.

 

Withdrawal from Afghanistan, Part 1

LIndsay Graham, one of my favorite senators, strongly opposes Trump’s decisions to withdraw from Syria and Afghanistan. (Newsweek) Lindsay Graham Calls for Immediate Hearings on Trump’s Syria and Afghanistan Decision, Warns of Second 9/11. This is about Afghanistan, which fails the ROI test that the U.S. presence in Syria currently passes. This is described in U.S. Withdrawal from Syria re Providing for the Common Defense.

A second 9/11 is possible, this time involving dirty bombs. An  end to the U.S. role in Afghanistan adds some incremental risk. But risk abounds elsewhere; Peshawar, in Pakistan, is a market for low-level radioactive waste.  Quoting (Reuters, 5/15/2008) How real is the Pakistan nuclear risk?,

Al Qaeda is known to be actively seeking nuclear material. Pakistan could be the place they finally manage to acquire some.

“It’s not going to be a risk where rogue elements take over Pakistan’s nuclear assets and then launch them at India or launch them at the U.S.,” Kuusisto said. “It will be a radiological bomb exploding somewhere that is traced back to Pakistan.”

The United States has given Pakistan assistance in checking containers leaving from key ports for radioactive material. But Vickers said smuggling radioactive material out of the country would not present a major problem for militants.

What is the incremental risk of Afghanistan? With risk all over the   globe, could a reduction be achieved by reallocation of resources? Terror originating in Afghanistan must transit through a third country, most likely Pakistan.

We fear handing Terror a nation-state, but what degree of accommodation would the Taliban offer to it? In 2001, the Taliban refused to give up Bin Laden, but is this still relevant? (Reuters) ‘Very positive signals’ after U.S., Taliban talks: sources. This is one of the most important pending intelligence estimates.

Part of this blog is about the skill of prediction, which deeply involves recognizing previous situations that analogize with the present. The news sites present snapshots of the present, leaving us vulnerable to all our hopes and fears. Sloppy analogy with past can leave us vulnerable. Carefully drawn analogies,evaluated in number and quality,  bind the future to the past. So what is the quality of historical analogy available for the four top issues?

  • Iran: Current Iran approaches have limited but useful analogies with the neoconservative approach to  Iraq in 2003.
  • Russia: Limited analogy exists to expansionism dating to the 18th century, and to balance-of-power policies.
  • China: There is no precedent for the rises of China.
  • Afghanistan: Numerous, extensive analogies with  Vietnam exist.

With Afghanistan, as with Vietnam, it can be hard for the best minds to differentiate between the desired outcomes, foreign policy goals, and the work of prediction, when we try to exclude confirmation bias. Like most Western readers, I would prefer to imagine the outcome of an Afghanistan with a civil government that has at least limited secular, inclusive aspects. The situation of Pakistan, which is more a failed state than a model, would actually be progress in Afghanistan.

So let’s start with Vietnam. As painful as the experience was,  the lesson lived in memory for little more than a generation. The goals of our fathers for Vietnam were fairly modest. The  corrupt rule of South Vietnam’s elite was supported because, so it was thought,

  • The doctrine of Containment of world communism required it.
  • Absent the lock-down of a rigid ideology, South Vietnam would continue to evolve.
  • The goals were achievable.

A magnificent book recounts  the cautionary tale. The Best and the Brightest, by David Halberstam, documents and dissects. The best thinking of the time, employing the best tools of the time, statistics, estimation theory, game theory, and operations research, could not predict the failure of the massive U.S. military and logistical footprint to defeat a small, economically primitive country with an army of foot soldiers.

The analogy, already obvious, deserves elaboration. To be continued shortly.

 

 

 

 

 

U.S. Withdrawal from Syria re Providing for the Common Defense

In the past few years, U.S. strategics priorities  have evolved, with reduced  importance of the Middle East, while China and Russia are identified as primary strategic competitors and possible adversaries. So  Trump’s personal decision to withdraw of U.S. forces from Syria does not go against the new strategic priorities, but this does not mean it is tactically correct.

No view or doctrine can anticipate the specifics of every place and time. Historically, U.S. foreign policy has oscillated between isolationism, and “the best defense is a good offense.” Neither of these very general, simplistic ideas can replace strategies particularized for time and place.

We could attempt to understand  Trump’s decision as stemming from the colossal failure of “the best defense…”,  in SE Asia and Iraq. It may  fail again on a global scale in the attempt to extend Pax Americana further into the 21st century. But another strategic metric/strategy, virtually  unused in U.S. foreign policy, has to our chagrin been employed by Putin’s Russia, and Xi’s China. Yet it’s essentially capitalist in nature.

This is ROI, return on investment. Compared to interventions of recent history, the U.S. deployment in Syria has provided very  good ROI. The Kurds, who seem to have a natural affinity for the West, are also among the best proxies  we’ve ever had. The ROI metric says, support the Syrian Kurds.

The NSC staff and Secretary Mattis have cogently stated the case for the Kurds as proxies, both to shape the Syrian state, and to impede the extension of Iranian influence to the shores of the Mediterranean. But the Kurds are a stateless people, with tragedy as their companion. Let us suppose that at some point in the future, overarching U.S. objectives require their abandonment. Foreign policy and stateless tragedy are bedfellows.

There is a moral question. It is possible that the moral question and U.S. interest coincide, at this moment of time, and possibly into the distant future. This is left to the reader to decide for himself.

Huawei, Security, and British GCHQ

(Reuters) Britain says Huawei ‘shortcomings’ expose new telecom networks risks and (Financial Times) Huawei caves in to UK security demands.

GCHQ are congratulating themselves on their due diligence. Quoting,

Senior UK security officials have repeatedly stressed that their concerns are related to technical deficiencies and not the company’s Chinese origins or any evidence of espionage or malicious activity.

It surprises that the astute heads at GCHQ would segment the Huawei threat in such an ostrich-like manner — if an ostrich could segment. It reminds me of the tongue-twister, “How much wood would a woodchuck chuck if a woodchuck could chuck wood?”

This kind of segmenting, with burial of one of the segments, is probably due to British exposure to China economic pressure. As I am not a party to the funeral, let’s spell it out. The Huawei threat has two parts, both enabled by the nature of integrated circuit design and testing:

  • Visible at the pins of the chip, as errors of protocol. This includes vulnerabilities in key exchange protocols, and the existence of chip-states that should be disallowed. These fall into the loose category of the 71% of a chip that can be tested through the external terminals. (I think this is due to Karpovsky.)
  • Buried in the chip firmware/gate arrays, invisible at the external pins of the chip. This is feasible when chips are made by a supplier affiliated with the Chinese state, such as Huawei, because the combinatorics makes testing impossible even with a  test duration on the order of the age of the universe.

Both exploits have advantages:

  • With use of the visible exploit, the attacker’s identity can frequently be concealed, or at least reduced in certainty. It’s frequently the case that multiple attack vectors can exploit the same protocol vulnerability.
  • The invisible exploit is activated by codes that are so improbable that, if detected, they point with perfect certainty to the maker of the chip. (Is there a way around this? Read down.)

Can a chip die be scanned, perhaps by a synchrotron light source, to recover the mask and completely analyze the functionality? As Huawei becomes self-sufficient in chips, reference masks will become unavailable. As chip geometries continue to shrink, with the move to 3D, scanning  becomes a very hard problem.

There remains one question. Exploits of the second type, if discovered, seem to inextricably implicate the attacker. With the application of great cleverness, is there a way to disguise this?  I think there is. Think spread-spectrum and slow data rates.

GCHQ, you may think you’ve done due diligence, but this is an error. Think of what we can do, and in your imagination, go one better.

 

 

Speaking Truth to Power

The readership indicators for Providing for the Common Defense; Report of National Defense Strategy Commission, Part 1and  Part 2 suggest that undermining the report is not a pleasant concept.  This is sometimes happens when speaking truth to power. It’s not pleasant to me either.

The U.S. military needs not only the best weapons but also the best circumstances in which to fight. This acquires urgency with the pending fact that in coming years, we may face a potential adversary with greater industrial capacity than our own. This has not occurred since the American Revolutionary War, which was a defense on native soil. It was not the case in World War II, when U.S. industrial capacity alone vastly exceeded that of the entire Axis.

To say that defense of the China seas will become nonviable is not the same as to say we should acknowledge the compromised international status of those seas. It is the consequence of the choice of regional nations to advance economic integration with China in spite of competing territorial claims. It’s something to work around, if not through.

Remarkably, China sliced off a sliver of Philippine territory without deflecting a trajectory away from the U.S. towards China. Empty bellies take precedence, and there are plenty in Asia who want to be part of the China miracle, national sovereignty be damned.

The real battle involves soft power. There seems to be a new awareness that even in SE Asia,  marketing of the U.S. as an alternative involves client economic opportunity first, with client security a distant second. This is precisely the game China has been  playing  for 20 years. Now we’re playing catch up.

We’ll continue with Markov chains and the Kolmogorov equation in a bit.

 

 

 

 

Providing for the Common Defense; Report of National Defense Strategy Commission, Part 2

We continue from  Providing for the Common Defense; Report of National Defense Strategy Commission, Part 1. Our goal is to undermine it.

The report consists of findings, not arguments against a hypothetical assertion that current defense allocations are sufficient. The geopolitical goals are also stated, not argued. These come out of a broad consensus that is wrong in certain areas. Wrong, not because the goals are not worthy, but because no reasonable, sustainable projection of power could achieve them.  One of these goals, maintenance of the international status of the China seas,  forces an exposed flank.

This is not the fault of military science. It is the result of a consensus that compels nonviable commitments. There is an honorable exception in the reluctance to commit U.S. soldiers in land battle. But the game of deterrence can be as deadly with sudden, greater casualties. The  authors of “Providing for…” are committed to a game of chance. Such games can be studied with rigor, with a demonstration later in this series.

Arguments come in different quality grades:

  • In the lowest category reside arguments about religion, politics, and the rights of man. The issues are supremely important, but data is not analyzed by anything resembling science.
  • The social sciences and psychology are in the next  category. These fields make use of data in a scientific way, but produce conclusions that are consistent only in their inconsistency.
  • Medicine is in the middle, a mix of modern miracles and pseudoscience. Application and abuse of the scientific method.
  • The physical sciences are close to the top, with rigorous application of the scientific method. Argument remains an intermediate phase,  reduced by the method to an essential residual of doubt.
  • The pinnacle is occupied by mathematics, which is not a science. It has an advantage over  the others, because it is about itself.  Instead of arguments, we have proofs. Kurt Gödel showed there is a flaw. But it’s the best we can do.

Military science has highs and lows.  The design and simulation of weapon systems is highly scientific. But strategy and command retain highly intuitive inputs. The military have a “can-do” attitude, an essential in the fight. But it provides no brake on the tendency of geopolitical strategists to build risk into policy.

Since “Providing for…” proclaims goals, it can’t be contradicted by antithesis. That results in shouting matches.  But there is an alternative. It’s common experience to choose between two opposing arguments that do not intersect. You choose the one that “sounds better.” If not due to prejudice, you have chosen the argument that appears to be of higher quality.

To argue against “Providing for…”, on the same low level, we would have to issue our own contradicting proclamations.  Instead,  we provide a better argument, meaning, we move up the list. Our argument will take the form of an objection, in the form of a problem that cannot be circumvented. It has roots in a subject that came to prominence in World War II, Operations Research.’

“OR” seems to have gone missing  in current discussions. I find no reference to it in the papers think tanks are currently pushing. Perhaps this is because OR was developed in the UK to solve problems for which there is already operational data, not hypothetical ones that may arise from bad strategy.

If you want to know, statistically,  how many tanks an Apache helicopter will destroy before being destroyed itself, that’s an OR problem. (The answer is about 21.)  Ship convoy strategy, developed during the Battle of the Atlantic, is a classic. The slightest, indirect reference to OR in “Providing for…”  is the note of inadequate inventory of certain precision guided munitions. The stockpile is ludicrously low, perhaps 1/20 of a reasonable number. It is low because unlike dumb bombs, smart weapons have a shelf life and require expensive periodic overhaul.

Although not historically used for the purpose, OR can also be used to identify problems, consequences of strategy, that are not remediable. This we shall shortly do. In the meantime, have a look at Pivot To Asia; Force Projection, Part 3. It’s about power projection. We will elevate the argument above  “Providing for…”  by drawing on OR.

There’s gonna be some math, but it will be accompanied by a wordy, intuitive explanation, so as to make the math somewhat optional. We’re going to use the Kolmogorov equation on Markov chains. It’s going to be highly portable, so you can take it around to your math buddies for 2nd, 3rd, and nth opinions. If you are math inclined, the calc can be done on multiple cocktail napkins.

It will be a little sand in the gears. It might be fun to take your stack of napkins around to policy meetings, wave them and say, “But this calculation shows we can’t do it”, and enjoy the mute stares.

Don’t worry, I got your back.

In Memoriam; George H.W. Bush

Jacob’s Ladder (c;lick to enlarge)

Why do some people try so hard to be good, not just in acts of historical import, but in their manner with every person they meet? In search of the reason, some look upwards. But Jacob’s Ladder is something we see only in our dreams. In our more lucid moments, we see the perfection of the cosmos, but not moral guidance.

My personal observation is that the guide to being an exemplary person is not to be found by looking up.   It comes from within. This connects with modern physics. In space-time,  space of 4 dimensions,  everything that was and will be exists. Our consciousness, which exists only in the instantaneous moment, extends to infinity in both directions.

In 4-space, each of us becomes an author of pages in the 4-dimensional Book-of-the-Universe, which could be viewed in the leisure time of a being who occupies 5 or more dimensions. Some of us want to write the best book we can.

I dedicate Jacob’s Ladder, a simple painting, to George H.W. Bush, who was a very serious author.

 

 

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