Your computational aboriginal art is really quite amazing! I think you can give AARON a run for its money. In your post previous to your artistic one, you brought up the notion of lateral thinking. I think part of why it is difficult is because we draw heavily on memory as part of perception. This is well-captured in Leslie Valiant’s Probably Approximately Correct book [p. 142]:
In different parts of the world the same word may have different meanings, or the distribution of examples may be different. In these cases the Invariance Assumption would be violated, and shared meaning would not be achieved. Misunderstandings would result. There are pernicious obstacles to shared meaning even beyond those inherent in differences in meaning and distributions. These further impediments are imposed by the constraint of a limited mind’s eye interacting with an internal memory full of beliefs. We may all be looking at the same world through our mind’s eyes, but since we have much control of what information to allow in, dependent on our beliefs, we may not see the same world. In the mind’s eye we process not only the information coming from outside, but also information internally retrieved from our long-term memory.
As you know, I was in Quebec City last week for the workshops following the Computational Neuroscience Meeting. I spoke about associative memories and how a little bit of circuit noise can improve recall, but also heard an interesting talk by Byron Yu on how it may be difficult to learn things you are not used to. Details on learning things off-subspace will soon be published in an experimental neuroscience Nature paper.
All of this talk about informational inputs, outputs, and internals has gotten me thinking about whether one can define a useful notion of information metabolism, in analogy to metabolism, which (as per Wikipedia) is the set of life-sustaining chemical transformations within the cells of living organisms. These enzyme-catalyzed reactions allow organisms to grow and reproduce, maintain their structures, and respond to their environments. [There is apparently already Kepinski’s notion of information metabolism, but I believe I want something different.]
In an earlier post, I suppose I did discuss metabolic processes of waste, primarily allometric scaling laws for waste production by mammals. Though as I mentioned, some of renewed interest in scaling laws comes from the science of cities. One might wonder, then about scaling laws for waste as functions of city population rather than animal mass. Luis Bettencourt has called cities a sort of social reactor that is part star and part network, and so understanding physical flows might be inspirational for understanding informational flows. Of course sanitation is super essential to public health and welfare in its own right.
As it turns out, there are quite a few people interested in scaling laws for waste in cities, and there seems to be a growing debate in the scientific literature. Let me summarize discussions on air pollution.
- Using data from the Emissions Database for Global Atmospheric Research (EDGAR), Marcotullio et al. find that larger cities have more greenhouse gas emissions (CO2, N2O, CH4, and SF6), in that a small increase in population size in any particular area is associated with a disproportionately larger increase in emissions, on average.
- Curating a variety of data sources on CO2 emissions, Rybski et al. argue that cities in developing countries are different from cities in developed countries. In particular, in developing countries, large cities emit more CO2 per capita than small cities with power-law exponent 1.15, where in developed countries large cities are more efficient with power-law exponent 0.80. (These exponent numbers seem to have numerical significance, as per Bettencourt)
- Fragkias et al. also look at CO2 emissions, focusing on cities (metropolitan statistical areas) in the United States, but do not find too much increase in efficiency, but find a near-proportional increase.
- Oliveira et al. also consider CO2 emissions in American cities (more concentrated than MSAs), but find a strongly superlinear increase, with a power-law exponent of 1.46.
So there seems to be a great deal of uncertainty on what is happening empirically. Notwithstanding, theories that link together emissions with traffic congestion have also been proposed.
To add some more fuel to the fire, I thought I might plot out some data too. Rather than emissions, I looked at air quality measures. As an example, I took population data and air quality data for some cities in India, and joined them, ignoring data where either was missing. Note there are often multiple measuring stations within a given city, and I treat them as having their own air quality value, but the same population value. Here are the results for sulfur dioxide.
So maybe nothing too conclusive there. I wonder if there are other air quality indicators that have some connection to city population.
Sorry for this information snack full of empty calories.