There is a nice profile of mathematician Terence Tao in the New York Times magazine this week. Tao is astonishing in his breadth and depth. He could probably master any subject in any field if he just put his mind to it. The article plays up his “normality” in contrast to the stereotype of the eccentric asocial mathematician like Gauss, John Nash or Grigory Perelman, who proved the Poincare Conjecture. However, in my experience, most mathematicians, even the very best, are reasonably normal and sociable. My guess is that the rate of personality disorder among mathematicians is no higher than the general populace. It is perhaps true that mathematicians are more introverted and absent minded than average but rarely to a pathological degree. I think the myth persists because of a few very prominent examples but also that mathematics is a pursuit where having a personality disorder is not a major handicap. One could probably not be a great lawyer, physician or statesman if they were socially abnormal. Thus, if the rate of historically great eccentric mathematicians is high compared to other fields, it is because the sample is biased.
The most dangerous form of bias is when you are unaware of it. Most people are not overtly racist but many have implicit biases that can affect their decisions. In this week’s New York Times, Claudia Dreifus has a conversation with Stanford psychologist Jennifer Eberhardt, who has been studying implicit biases in people experimentally. Among her many eye opening studies, she has found that convicted criminals whose faces people deem more “black” are more likely to be executed than those that are not. Chris Mooney has a longer article on the same topic in Mother Jones. I highly recommend reading both articles.
One of my favourite museums is the National Palace Museum (Gu Gong) in Taipei, Taiwan. It houses part of the Chinese imperial collection, which was taken to Taiwan in 1948 during the Chinese civil war by Chiang Kai-shek. Beijing has its own version but Chiang took the good stuff. He wasn’t much of a leader or military mind but he did know good art. When I view the incredible objects in that museum and others, I am somewhat saddened that the skill and know-how required to make such beautiful things either no longer exists or is rapidly vanishing. This loss of skill is apparent just walking around American cities much less those of Europe and Asia. The stone masons that carved the wonderful details on the Wrigley Building in Chicago are all gone, which brings me to this moving story about passing the exceedingly stringent test to be a London cabbie (story here).
In order to be an official London black cab driver, you must know how to get between any two points in London in as efficient a manner as possible. Aspiring cabbies often take years to attain the mastery required to pass their test. Neural imaging has found that their hippocampus, where memories are thought to be formed, is larger than normal and it even gets larger as they study. The man profiled in the story quit his job and studied full-time for three years to pass! They’ll ride around London on a scooter memorizing every possible landmark that a person may ask to be dropped off at. Currently, cabbies can outperform GPS and Google Maps (I’ve been led astray many a time by Google Maps) but it’s only a matter of time. I hope that the cabbie tradition lives on after that day just as I hope that stone masons make a comeback.
People have been justly anguished by the recent gross mishandling of the Ebola patients in Texas and Spain and the risible lapse in security at the White House. The conventional wisdom is that these demonstrations of incompetence are a recent phenomenon signifying a breakdown in governmental competence. However, I think that incompetence has always been the norm; any semblance of competence in the past is due mostly to luck and the fact that people do not exploit incompetent governance because of a general tendency towards docile cooperativity (as well as incompetence of bad actors). In many ways, it is quite amazing at how reliably citizens of the US and other OECD members respect traffic laws, pay their bills and service their debts on time. This is a huge boon to an economy since excessive resources do not need to be spent on enforcing rules. This does not hold in some if not many developing nations where corruption is a major problem (c.f. this op-ed in the Times today). In fact, it is still an evolutionary puzzle as to why agents cooperate for the benefit of the group even though it is an advantage for an individual to defect. Cooperativity is also not likely to be all genetic since immigrants tend to follow the social norm of their adopted country, although there could be a self-selection effect here. However, the social pressure to cooperate could evaporate quickly if there is the perception of the lack of enforcement as evidenced by looting following natural disasters or the abundance of insider trading in the finance industry. Perhaps, as suggested by the work of Karl Sigmund and other evolutionary theorists, cooperativity is a transient phenomenon and will eventually be replaced by the evolutionarily more stable state of noncooperativity. In that sense, perceived incompetence could be rising but not because we are less able but because we are less cooperative.
If civilization succumbs to a deadly pandemic, we will all know what the vector was. Every physician, nurse, dentist, hygienist, and health care worker is bound to check their smartphone sometime during the day before, during, or after seeing a patient and they are not sterilizing it afterwards. The fully hands free smartphone could be the most important invention of the 21st century.
The Wait But Why blog has an amusing post on why Generation Y yuppies (GYPSYS) are unhappy, which I found through the blog of Michigan economist Miles Kimball. In short, it is because their expectations exceed reality and they are entitled. What caught my eye was that they defined happiness as “Reality-Expectations”. The key point being that this is a subtractive expression. My college friend Peter Lee, now Professor and Director of the University Manchester X-Ray imaging facility, used to define happiness as “desires fulfilled beyond expectations”. I always interpreted this as a divisive quantity, meaning “Reality/Expectations”.
Now, the definition does have implications if we actually try to use it as a model for how happiness would change with some quantity like money. For example, consider the model where reality and expectations are both proportional to money. Then happiness = a*money – b*money. As long as b is less than a, then money always buys happiness, but if a is less than b then more money brings more unhappiness. However, if we consider the divisive model of happiness then happiness = a*money/ b*money = a/b and happiness doesn’t depend on money at all.
However, the main reason I bring this up is because it is analogous to the two possible ways to model inhibition (or adaptation) in neuroscience. The neurons in the brain generally interact with each other through two types of synapses – excitatory and inhibitory. Excitatory synapses generally depolarize a neuron and make its potential get closer to threshold whereas inhibitory neurons hyperpolarize the neuron and make it farther from threshold (although there are ways this can be violated). For neurons receiving stationary asynchronous inputs, we can consider the firing rate to be some function of the excitatory E and inhibitory I inputs. In subtractive inhibition, the firing rate would have the abstract form f(E-I) whereas for divisive inhibition it would have the form f(E)/(I+C), where f is some thresholded gain function (i.e. zero below threshold, positive above threshold) and C is a constant to prevent the firing rate from reaching infinity. There are some critical differences between subtractive and divisive inhibition. Divisive inhibition works by reducing the gain of the neuron, i.e. it makes the slope of the gain function shallower while subtractive inhibition makes the threshold effectively higher. These properties have great computational significance, which I will get into in a future post.
The Science Show did a feature story recently about the discovery of streptomycin, the first antibiotic to treat tuberculosis, which had killed 2 billion people in the 18th and 19th centuries. Streptomycin was discovered by graduate student Albert Schatz in 1943, who worked in the lab of Professor Selman Waksman at Rutgers. Waksman was the sole winner of the 1952 Nobel Prize for this work. The story is narrated by the author of the book Experiment Eleven, who paints Waksman as the villain and Schatz as the victim. Evidently, Waksman convinced Schatz to sign away his patent rights to Rutgers but secretly negotiated a deal to obtain 20% of the royalties. When Schatz discovered this, he sued Waksman and obtained a settlement. However, this turned the scientific community against him and he forced him out of microbiology into science education. To me, this is just more evidence that prizes and patents are incentives for malfeasance.