I have noticed that panpsychism, which is the idea that some or all elements of  matter possess some form of consciousness, subjective experience, mental awareness, or whatever you would like to call it, seems to be gaining favour these days. Noted neuroscientist Christoff Koch has recently suggested that consciousness may be a property of matter like mass or charge. I was just listening to a Philosophy Bites podcast where philosopher Galen Strawson (listen here) was forcefully arguing that panpsychism or micropsychism was in fact the most plausible prior if one is a physicalist or monist (i.e. someone who believes that everything is made of the same stuff).  He argued that it was much more plausible for electrons to possess some tiny amount of consciousness then for it to emerge from the interactions of a large number of neurons.

What I want to point out  is that panpsychism is a closeted form of dualism (i.e. mind is different from matter). I believe philosopher David Chalmers, who coined the term “The hard problem of consciousness“, would agree.  Unlike consciousness, mass and charge can be measured and obey well-defined rules. If I were to make a computer simulation of the universe, I could incorporate mass and charge into the physical laws, be they Newton’s Laws and Maxwell’s equations, the Standard Model of particle physics, String theory, or whatever will replace that.  However, I have no idea how to incorporate consciousness into any simulation. Deeming consciousness to be a property of matter is no different from Cartesian dualism.  Both off-load the problem to a separate realm. You can be a monist or a panpsychist but you cannot be both.

Log normal

A comment to my previous post correctly points out that the income distribution is approximately log-normal. What this means is that while income itself is not normally distributed, the logarithm of income is.  The log-normal distribution has a pretty fat tail for high incomes. A variable will be log-normal if it is the product of a lot of random variables, since the log of a product is a sum. It has been argued for many years that achievement should be log-normal because it involves the product of many independent events. This is why a good programmer can be hundreds of times better than a mediocre one.  I even gave a version of this argument here. Hence, small differences in innate ability can lead to potentially large differences in outcome. However, despite the fact that income may deviate from log-normality in some cases and in particular between sectors of the economy (e.g. finance vs. philosophy), there is still a question of whether the compensation scheme needs to follow log-normal even if productivity does. After all, if small differences in innate ability are magnified to such a large extent, one could argue that income should be pegged to the log of productivity.

Nonlinearity in your wallet

Many human traits like height, IQ, and 50 metre dash times are very close to being normally distributed. The normal distribution (more technically the normal probability density function) or Gaussian function

f(x) = \frac{1}{\sqrt{2\pi}\sigma}e^{-(x-\mu)^2/2\sigma^2}

is the famous bell shaped curve that the histogram of class grades fall on. The shape of the Gaussian is specified by two parameters the mean \mu, which coincides with the peak of the bell, and the standard deviation \sigma, which is a measure of how wide the Gaussian is. Let’s take height as an example. There is a 68% chance that any person will be within one standard deviation of the mean and a little more than 95% that you will be within two standard deviations. The tallest one percent are about 2.3 standard deviations from the mean.

The fact that lots of things are normally distributed  is not an accident but a consequence of the central limit theorem (CLT), which may be the most important mathematical law in your life. The theorem says that the probability distribution of a sum of a large number of random things will be normal (i.e. a Gaussian). In the example of height, it suggests that there are perhaps hundreds or thousands of genetic and environmental factors that determine your height, each contributing a little amount. When you add them together you get your height and the distribution is normal.

Now, the one major thing in your life that bucks the normal trend is income and especially wealth distribution. Incomes are extremely non-normal. They have what are called fat tails, meaning that the income of the top earners are much higher than would be expected by a normal distribution. A general rule of thumb called the Pareto Principle is that 20% of the population controls 80% of the wealth. It may even be more skewed these days.

There are many theories as to why income and wealth is distributed the way it is and I won’t go into any of these. What I want to point out is that whatever it is that governs income and wealth, it is definitely nonlinear. The key ingredient in the CLT is that the factors add linearly. If there were some nonlinear combination of the variables then the result need not be normal. It has been argued that some amount of inequality is unavoidable given that we are born with unequal innate traits but the translation of those differences into  income inequality is a social choice to some degree. If we rewarded the contributors to income more linearly, then incomes would be distributed more normally (there would be some inherent skew because incomes must be positive). In some sense, the fact that some sectors of the economy seem to have much higher incomes than other sectors implies a market failure.

Obesity references

I’ve been asked about references to papers on which my New York Times interview is based so I’ve listed them below.  You can find summaries for some of them as well as the slides for my talks and posts related to obesity here.

K.D. Hall, G.Sacks, D. Chandramohan, C.C Chow, C. Wang; S. Gortmaker; B. Swinburn, `Quantifying the effect of energy imbalance on body weight change.’ The Lancet 378:826-37 (2011).

K.D. Hall and C.C. Chow, `Estimating changes of free-living energy intake and its confidence interval,’ Am J Clin Nutr 94:66-74 (2011).

K.D. Hall, M. Dore, J. Guo, and C.C. Chow, ‘The progressive increase of food waste in America’, PLoS ONE 4(11): e7940 (2009).

C.C. Chow and K.D. Hall, `The dynamics of human body weight change’, PLoS Computational Biology , e1000045 (2008).

K.D. Hall, H.L. Bain and C.C. Chow, `How adaptations of substrate utilization regulate body composition’, International Journal of Obesity, 31 , 1378-83 (2007). [PDF]

V. Periwal and C.C. Chow, ‘Patterns in food intake correlate with body mass index’, American Journal of Physiology: Endocrinology and Metabolism, 291 929-936 (2006) [PDF]

Causality and obesity

The standard adage for complex systems as seen in biology and economics is that “correlation does not imply causation.”  The question then is how do you ever prove that something causes something. In the example of obesity, I stated in my New York Times interview that the obesity epidemic was caused by an increase in food availability.  What does that mean? If you strictly follow formal logic then this means that a) an increase in food supply will lead to an increase in obesity (i.e. modus ponens) and b) if there were no obesity epidemic then there would not have been an increase in food availability (i.e. modus tollens). It doesn’t mean that if there were not an increase in food availability then there would be no obesity epidemic.  This is where many people seem to be confused.  The obesity epidemic could have been caused by many things.  Some argue that it was a decline in physical activity. Some say that it is due to some unknown environmental agent. Some believe it is caused by an overconsumption of sugar and high fructose corn syrup. They could all be true and that still doesn’t mean that increased food supply was not a causal factor. Our validated model shows that if you feed the US population the extra food then there will be an  increase in body weight that more than compensates for the observed rise.  We have thus satisfied a) and thus I can claim that the obesity epidemic was caused by an increase in food supply.

Stating that obesity is a complex phenomenon that involves lots of different factors and that there cannot be a simple explanation is not an argument against my assertion. This is what I called hiding behind complexity. Yes, it is true that obesity is complex but that is not an argument for saying that food is not a causal factor. If you want to disprove my assertion then what you need to do is to find a country that does not have an obesity epidemic but did exhibit an increase in food supply that was sufficient to cause it. My plan is to do this by applying our model to other nations as soon as I am able to get ahold of data of body weights over time. This has proved more difficult than I expected. The US should be commended for having good easily accessible data. Another important point to consider is that even if increased food supply caused the obesity epidemic, this does not mean that reducing food supply will reverse it. There could be other effects that maintain it even in the absence of excess food.  As we all know, it’s complicated.

FACM12 talk at NJIT

I’m currently at the New Jersey Institute of Technology for the ninth annual Frontiers in Applied and Computational Mathematics conference.  Here are the slides for my talk.  It’s on computational neuroscience and has nothing to do with obesity.  Also, it only seems like lots of slides because of the animations.