This video is interesting but is misleading.

It reports that the average estimate of one hundred and sixty people asked to guess the number of jelly beans in a jar was just 0.1% higher than the actual number of 4510.

But one person estimated the number at 50,000, ten times the actual number. So if that person had not been included in the survey, the average estimate would have been 312 beans lower than the actual number, a 6.9% underestimate.

So an important question not addressed in the video is how representative was the result obtained in the particular sampling of 160 guesses?

To answer that question, it would be necessary to repeat the experiment many times. We would then have an idea of the variability in, or reliability of, the “wisdom of the crowd.”

But even without such an estimate, we can be pretty sure that the error is usually larger than that reported in the BBC’s single trial, given the dependence of the “accuracy” of that result on just one extremely wild guess.

A further question is how consistent is the “wisdom of the crowd” on a variety of tasks. Guessing the number of jelly beans in a jar is not that difficult. The jar is a cylinder with dimensions that can be fairly accurately estimated by eye. The volume can therefore be calculated and one then need only estimate the number of jelly beans per cubic inch or centimeter and multiply that number by the volume in the same units to get a total for the jar.

But what if the container were an irregular shape: a jar in the shape of a kangeroo, for example? Would the estimate of the crowd be as good? What if the container were very much larger or the contents very much smaller? For example, how good would the crowd be in estimating the number of grains of sand in a life-size sand sculpture of a blue whale or an elephant?

And what of the technical expertise of the crowd? Would a crowd of engineers make a better estimate than a crowd of music teachers?

Typically, the BBC fails to ask these and many other interesting and important questions. Instead, it presents one with a little nugget of information of dubious validity to squirrel away without further reflection.

But perhaps a reader can help out. How, for example, does this kind of experiment tie in with Bayes theorem and the value of guesswork in drawing inferences from limited data? Comment from all Bayesians wecome!


From time to time someone provokes outrage by suggesting that lithium be added to public water supplies (and here).

The rational for this proposal is that lithium in very small amounts appears to have many public health and social benefits including better mental health and less crime.

Studies in Texas, central Japan and throughout Austria have shown a negative relationship between suicide rate and the amount of lithium naturally present in public water supplies.

In Texas, an inverse relationship was observed between lithium in drinking water and crime, particularly violent crime.

A study conducted in North Carolina suggested a negative  relationship between community drinking water lithium content and mental hospital admission rates.

Double-blind clinical studies have shown trace lithium to be mildly effective in improving the mood of drug users undergoing withdrawal.

Research has shown that lithium reduces violence of incarcerated criminals, retards the development of senile dementia, increases brain mass, and enhances longevity in man and other animals.

If all these benefits were attributable to an element such as calcium, which as a carbonate mainly accounts for the hardness of water, most people would likely support its addition to public water supplies.

However, lithium is widely known as an anti-mania drug, capable of reducing the demented to a condition of docility. Naturally, therefore, calls for lithium supplementation of drinking water are interpreted by many as evidence of a plot to enslave the population.

What is not generally recognized is that the potential benefits of lithium to the population at large are attributed to amounts of the element in the range of 50 to 100 millionths of a gram per day, whereas a therapeutic dose of lithium for the treatment of mania is several thousand times as much, and close to the threshold for toxicity.

But if trace amounts of lithium represent no hazard to the public, their addition to the water supply is nevertheless questionable in the present state of knowledge, despite the potential benefits.

Research in this field will not be undertaken by the pharmaceutical industry because lithium cannot be patented. What is needed, therefore, is a broad-ranging program of publicly funded research to evaluate claims that have been made concerning the role of lithium in human nutrition and health.

In the meantime, those interested in experimenting with lithium as a nutritional supplement can drink lithium-rich mineral waters such as Catalan Vichy (1.3 mg of lithium per liter), enjoyed by the Romans more than two thousand years ago, EDT Rocky Mountain Lithia Water (0.66 mg of lithium per liter) or San Pellegrino water (0.2 mg of lithium per liter).

See also:
Medically Induced Mental Illness

The close DNA sequence similarity between men and apes has led some to suppose that a man is no more than a wimpy chimp with a slightly swollen head. Further, it has been suggested, since the genetic difference between men and apes is so trivial, there must be creatures somewhere in the limitless expanse of the universe at least as superior in intellect to us as were are to chimps. So, according to this line of thinking, despite the modest enlargement of the human fore-brain, we have little to be swelled-headed about.

But this view reflects a misunderstanding of the difference between men and apes and the significance of that difference.

Both men and apes are mammals, which means that they are built to the same plan. They have liver and lights, stomach and spleen, four limbs, a head and a tail. At the cellular level the similarity of design is even closer: the same membranes, organelles, nucleic acids and enzymes. So inevitably men and apes share much the same DNA sequence, as they do with horses and hamsters, and even with reptiles and fishes, fungi and forest trees.

There is a underlying biochemical unity to the life of this Earth. But that does not make the fangs of a tiger and the molars of a camel functionally equivalent. Small changes in the proportions and slight differences in the elaboration of a basic design can result in fundamental differences in function.

Thus with the brains of man and chimp. In the lobes and their connections the two are largely similar. But the human brain has approximately twice the mass of the brain of a chimp, and there is a many-fold difference between the two in the size of particular features. The human brain is thus adapted to functions unknown to the mind of a chimp.

And it is possible for very slight genetic changes to result in such qualitatively transformational changes in function. For example, a single-gene mutation that results in one additional rounds of cell division in a portion of the embryonic brain would double the final volume of this or that portion of the brain.

Why, then, it might be said, if the only thing distinguishing a man from an ape is a small collection of single gene mutations, the difference between us is trivial indeed. But that is to misunderstand the evolutionary step that man has made and which no other ape can ever make.

To evolve a larger brain, an organism must have a use for a larger brain. The brain is an energy intensive organ, requiring a continuous infusion of glucose and oxygen. A chimp with a brain like that of a human would be at a severe disadvantage. It would want to sit around and think but it would need to work harder than every other chimp to obtain the food necessary to keep its costly brain alive.

The only way such a chimp could survive would be to invent language, create a civilization and its associated technologies thereby raising the chimp living standard while lowering the hours of work.

That is what mankind achieved. And that is what no other species on Earth can achieve while mankind exists because mankind has preempted the resources of the entire planet.

As to the claim that an extraterrestrial intelligence would likely consider the mind of man as feeble a thing as we humans are inclined to consider the mind of a chimp, the answer should be, “give us time.”

It took humans about one hundred thousand years to exchange the lifestyle of an ape for that of a yuppie. But most of that transformation occurred, with exponential acceleration, in the last ten thousand years.

Humanity is now at a critical point in its existence. We have technology that puts the entire accumulated knowledge of the species at the fingertips of every one of seven billion humans at practically zero cost. The result is an explosion in technological innovation that will likely either destroy us within a matter of decades or grant us the power of gods.

Not only do we have the ability to educate every receptive mind to a point far beyond the reach of Aristotle or Newton, but to build intelligent machines that can outperform the human intellect by orders of magnitude.

This is precisely the transformation that any intelligent civilization created by organically evolved creatures anywhere in the universe must have undergone. It is the transformation from advancement through haphazard accumulation of mutations and genetic rearrangements that yield short-term survival advantage, to the engineered improvement of the human organism and its enveloping civilization.

And once evolution is intelligently planned, it likely follows the same course anywhere in the universe. We are about to become a species of the gods, provided we avoid destroying ourselves before we figure out how to manage technology for our own good.