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Humans and Estimating Probability

by John G. Cramer

Alternate View Column AV-146
Keywords: human, probability, estimate, odds, winning, streaks
Published in the March-2009 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted
10/07/2008 and is copyrighted ©2009 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


We human beings have evolved with brains that have amazing capabilities for rational thought, pattern recognition, judgment, creativity, and imagination, none of which can be readily duplicated by the best computer simulations.  However, there is one area in which the human brain is sadly lacking:  the ability to accurately assess probabilities and act on these assessments.  The successes of lotteries, Las Vegas, and tribal casinos provide ample evidence that when it comes to estimating the odds and acting accordingly, we humans as a species are really deficient.  We think that "winning streaks" are real, that slot machines are "overdue" for a jackpot, that the past pattern of random events somehow influences the odds for the next event.

One example of this deficiency in probability understanding was provided recently when CERN's Large Hadronic Collider (LHC) began preliminary operation near Geneva, Switzerland.  In the physics literature there had been some rather strained speculations that if certain theories involving extra dimensions were valid, then the proton-proton collisions at the LHC might produce tiny black holes with masses of a few trillion electron volts (TeV).  (See my May-2003 AV column, "The CERN LHC: A Black Hole Factory?".)  The same theories that tentatively predicted such black hole production also predicted that, if created, the tiny black holes would be super-hot objects that would dissipate themselves almost instantaneously into a thermal cloud of lighter particles, primarily electrons, positron, and photons.

Not surprisingly, many individuals seized on the idea that the LHC might produce black holes and imagined a scenario in which the black hole would not instantaneously dissipate, but instead would began to suck in nearby matter, grow larger, and devour the Earth.  Lawsuits were filed to stop the LHC from beginning operation.  A joke web site ( even appeared that purported to show real time web-cam shots of a black hole devouring the CMS experiment at the LHC.

Physicists working with the LHC were asked to estimate the probability that such a disaster might occur, and they responded by saying that the scenario was "extremely improbable".  The problem is that in such situations a scientist can never say "never" because the variety of theories available, some right and some wrong, provide the capability of analyzing an unlikely scenario and producing the probabilities that are absurdly small (but not zero).

For example, can you walk through a brick wall?  Common sense would say no, but in quantum mechanics there is a process called "tunneling" that allows an object to disappear from one side of a barrier like a brick wall and appear on the other side.  This phenomenon literally should allow one to "walk through walls", but with an extremely low probability, say one part in 101000 or less.  So if you ask a physicist whether is possible to walk through walls, he cannot say "no".  He'll have to say "yes, but with an extremely low probability".

It is human nature, via the wiring in our brain, to interpret "very improbable" as meaning that such an event is at least possible and should be worried about.  Therefore, the big story in the media recently was not that the LHC was beginning operation (and promptly blew out a string of superconducting magnets for a multi-month halt) but that it was possible that the Earth was about the be devoured by a black hole.

Another close-to-home example of this phenomenon is the recent collapse of AIG, a company that insured investment "vehicles" associated with packaged home mortgages.  Insurance companies are in the business of estimating the odds accurately and profiting generously from the unwillingness of most of us to accept risks.  In the case of the mortgage-based investments that AIG was insuring, the risk estimates were based on the "independence" assumption, the assumption that the probability P of the default of any given mortgage was unrelated to the default of any other mortgage in the investment package.  Under this assumption, the risk of n mortgages in the investment failing is Pn, which is a very low probability, making the insurance premium cheap.  The fallacy in this calculation was that mortgage failure probabilities are NOT independent when a housing bubble is about to burst, and the insurers grossly underestimated the failure probabilities.  The moral is that even as professionals in the business of estimating probabilities, we humans frequently get it wrong.

Another area where probability estimates are important and sometimes mangled is laboratory safety management.  I am an experimental physicist who has worked at many large accelerator facilities, including those at a number of universities and national facilities at Los Alamos, Livermore, Berkeley, Argonne, and CERN.  The scientific equipment used in experiments in nuclear and high energy physics employ high voltages, ultra-cold gases, potentially explosive gas combinations, and gases at high pressures.  The experiments create nuclear reactions that can produce potentially lethal radiation exposures to gamma rays, neutrons, and charged particles.  Considering all this, there are surprisingly few injuries and accidents among experimentalists.  In part, this is because a few highly trained individuals are charged with the responsibility of identifying potential problems, assessing their probabilities, and instituting safety procedures.  This usually works well, but there are a few exceptions.

I know of a radiation safety officer employed by a large defense contractor who insisted on assessing acceptable radiation exposure based on the "lowest possible exposure" rather than the "lowest reasonable exposure".  That doesn't sound like much of a difference, but it added huge costs to the operation.  The reason is that we do not live in a radiation-free world.  Our annual exposure to cosmic rays from space and to environmental radiation from granite, radon, potassium-40, etc. is fairly large, perhaps 0.25% of a mean lethal dose of radiation.  Is it reasonable to make sure that a radiation worker receives a radiation dose from his work that is less than 1/10 of the radiation dose he receives from the outside world?  Most safety officers would say no, but this particular individual, who seemed to have a particular problem in understanding the estimation and use of probabilities, insisted on very expensive additional shielding in an attempt to reduce the radiation exposure from the facility to zero.  Not long after, the project was cancelled due to cost overruns.

In another case at Brookhaven National Laboratory, one of the safety officers developed the peculiar conviction that helium was a deadly gas, presumably because a person placed in a room filled with helium would die of suffocation.  Brookhaven's  Relativistic Heavy Ion Collider (RHIC) Facility, which was then being designed, would contain lots of liquid helium that would cool the superconducting magnets used for bending and focusing the heavy ion beams to be accelerated.  When such superconducting magnets are in operation, occasionally they "quench", meaning that the superconductivity goes away, the stored magnetic field energy heats the magnet coils, the system temperature rises, the liquid helium boils, and a great deal of helium gas is produced and must be dealt with.  Normally, the magnet system includes a "blow-off stack" to deal with this problem, a long pipe leading up through the ceiling that blows off the excess helium at roof level.

However, the safety official in question decreed that this could not be done, because helium was a deadly gas that might suffocate people in the event of such a magnet quench and blowoff.   Instead, it was required that the RHIC facility must have vacuum vessels designed to completely contain the many atmospheres of pressurized helium that would be produced in a quench event.  The RHIC component magnets were designed in this way, at substantial extra cost.  RHIC was completed and scheduled to go into operation in 1999.  The full RHIC ring of superconducting dipole bending magnets and quadrupole focusing magnets, interspersed with a few lengths of pipe as "placeholders" for possible future expansions, was assembled.

The problem was that, since the RHIC machine was designed to withstand many of atmospheres of helium in its vacuum system, this had to be tested before the initial operation could begin.  The system was sealed and the pressure test was duly done in early 1999, and then the vacuum system was pumped out, the magnets were cooled to liquid helium temperature and tested at high fields, a beam of gold ions was injected into the machine, and initial operational tests began.

Beam transport problems were soon encountered.  The gold beam went through a few magnets, then hit something.  The accelerator physicists did some gymnastics with steering magnets to get past the unexpected obstacle, and the beam was able to go through a few more magnets, but then is was again stopped by another unexpected obstacle.  This pattern of failures was repeated all during the Summer of 1999, while many of us who had come to Brookhaven for the initial RHIC operation waited impatiently for the machine to deliver gold-gold collisions to our detectors, STAR, PHENIX, PHOBOS, and BRAHMS, which we has spent the last decade constructing.  But in 1999, the 50th anniversary of the founding of Brookhaven National Laboratory, those collisions at RHIC never came.

Finally, in September of 1999, the accelerator physicists gave up their attempts to get beam through the machine.  They warmed up the magnets and opened up the vacuum system to see what the beams had been hitting.  There they discovered distorted "bellows" vacuum fitting and "RF fingers" that had been damaged during the high pressure helium tests and were sticking into the beam path.  It was realized that while all of the magnets had been carefully designed to withstand the high pressures, no one had worried about the expansion of the placeholder pipe sections in the ring, and these had expanded during the pressure tests and damaged the vacuum fittings.  It took much effort and cost many millions of dollars to fix this damage, but in 2000 the RHIC facility was able to began what has become a very successful string of operating periods.

Because helium had been declared a deadly gas by the safety officer, a full year of operation of the RHIC facility was lost, millions of dollars in extra costs were incurred, and an army of physicists like me spent frustrating months at Brookhaven waiting for the beams that did not come.  Interestingly, the training that we RHIC experimentalists had to take in 1999, teaching us the actions to take in the event of a magnet quench that filled the accelerator vault with deadly helium, curiously disappeared from the safety training in subsequent years.  I feel that the inability of the human brain to accurately estimate probabilities and act on them played a key role in this fiasco.

Why are we wired this way?  Wouldn't it be a strong evolutionary advantage to be able to "see" probabilities and act accordingly?  I am not sure I know the answer to this puzzle, but let me try to answer with a parable.

Many millennia ago, when we were first emerging from the trees and beginning to function as humans, there was a river separating two hostile tribes that constituted most of humanity.  On the north side of the river lived the Prob Tribe, a group that had the ability to easily see probabilities and act accordingly.  On the other side of the river lived the Numbskull Tribe, a group more like modern humans who believed in luck and winning streaks and other such fantasies.  The vigorous male Probs hated the Numbskulls and wanted to rush across the river and kill them, but their enhanced abilities showed them that it was far safer to stay on their side of the river and not engage in combat.  The Numbskulls felt no such compunctions.  On a night when the moon was dark, they stole across the river and killed all of the Probs, to a man, woman, and child.  Thus, we are all descended from the Numbskulls.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .

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This page was created by John G. Cramer on 06/11/2009.