Why do mathematicians always agree?

Science is a lively social activity, with many claims being lively debated. What about mathematics? The cliché about mathematicians being poor at managing social relations is quite strong and widespread. One of the most famous joke on the topic goes like this:

Question: How can you spot an extrovert mathematician?
Answer: He looks at YOUR shoes when he talks to you.

Is mathematics "less social" than other academic disciplines? Some support for a 'yes' answer can be found in a recent piece of news. A famous mathematician, Nelson, had claimed to give a proof of a rather surprising proposition: “Peano Arithmetic is inconsistent.” Two other famous mathematicians, Tao and Tausk, said the proof included one specific mistake, which they spelled out. Nelson's reaction was: "Ah, you're right. So I have not proven that Peano Arithmetics is inconsistent". End of the story. No fight, no disagreement, no formation of alternative schools of thoughts, no playing with how to interpret this or that claim. Just plain boring consensus.
 
Peano Axioms

(These are the axioms that Nelson claimed were inconsistent. They are supposed to express central propositions true of our system of natural numbers with addition. They are used to prove things about an object that is central in many cultures.)


Mathematics is full of that: easily achieved consensus. Everybody agrees. No debate, and yet, the consensus is not socially induced in any standard way.

In a recent blog post, The (in)consistency of PA and consensus in mathematics, Catarina Novaes takes this as a nice illustration of some points made by philosopher Jody Azzouni, who argues that mathematics is unique as a social practice.

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How cultural is cultural epidemiology? 2- Cultural embedding

This is the second part of Christophe's series of posts on what culture does to culture (the first post is here).

Most cultural phenomena are embedded in other cultural phenomena. For one thing, any cultural phenomenon takes place within a community that already has many traditions, cultural practices, rituals and beliefs of its own. The important point, however, is that the embedding cultural phenomena are likely to have some effects on the embedded cultural phenomenon and to partially determine its evolution and the content of its constitutive representations.  Religious beliefs can have effects on economic practices; economic practices can have effects on kinship relations; etc.

Let us call “cultural embedding” this aspect of cultural evolution.  Cultural embedding is certainly what motivated some cultural anthropologists to have a holistic view of culture: every aspect of one culture will be related, more or less directly, to other aspects of the same culture.

Cultural epidemiology on promiscuous causality

For cultural epidemiology, cultural phenomena result from social cognitive causal chains that go from mental processes to social interactions (e.g. communication, imitation, the production of artefacts) to mental processes again. Some of these chains involve many members of a community, last through time and eventually have the effect of stabilising the distribution of cultural items in that community.

Read more: How cultural is cultural epidemiology? 2- Cultural embedding

How cultural is cultural epidemiology? The case of enculturation

When discussing about cultural epidemiology with informed colleagues, I often come to think that they tend to underplay the extent to which cultural epidemiological accounts can integrate enculturation and other cultural phenomena that are generative of culture.

Here is a key claim of cultural epidemiology: understanding, learning and memorising what others communicate or transmit are micro-cognitive processes at the basis of cultural phenomena, and these cognitive processes are strongly constrained by the properties of the mind. Cultural epidemiologists have especially worked on specifying the consequences of universal properties of the mind for culture: naive theories and the memorisation of religious beliefs for instance; or face recognition and the success of masks as cultural artefacts. However, what is understood, learned and memorised is also dependent on those properties of the mind caused by previous enculturation. This is nearly a truism: one can learn better to read if one already knows the alphabet, one processes differently a sentence in French if one knows the language that if one does not, and, more controversially, and can more easily learn how to build a canoe, if one already knows what each part is made for. True, most of the time these things are learned in concert - but transmitted information is nonetheless processed sequentially, and the order of the elements in the sequence is sure to matter.

This has at least the following consequences:

Read more: How cultural is cultural epidemiology? The case of enculturation

Politics and the psychology of irrational decisions

In my previous post (Cases of institution that make us smart), I have been considering a proposal about increasing taxes on junk food and decreasing taxes on fruits and greens. The proposal differed from campaigns of information (see picture as an example) because it implied direct action on the relative prices of different kinds of foods: changes would have been made on the structure of incentives rather than on people's beliefs. I was considering this proposal as an attempt to frame the environment for fostering beneficial decisions and behaviour.

In Mean Genes, Burnham and Phelan provide a list of tricks that could help people to have a healthy diet. Most of them consist in changing their environment. It is not groundbreaking science (it does not claim to be so) but it points to an important trend: the use of psychological research on behaviour departing from some rational norm for policy making and individual decision making. One important idea is that one can change the environment so that known psychological mechanisms lead to decisions that are advantageous to the individual or to the community.

Picture: "Manger Bouger": the French city of Nîme's advertisement campaign on the benefits of a healthy diet.


Read more: Politics and the psychology of irrational decisions

Cases of institutions that make us smart


Evolutionary psychologists assert that our genetically driven cognitive endowment has evolved during the Pleistocene. As a consequence, our innate cognitive mechanisms are adapted to the environment of that period (the EEA) but not necessarily to our changed modern environment. One instance of mal-adaptedness is the fact that human crave for fat and sweet food. This craving was adapted to the Pleistocene environment where high energetic food was rare, but is not to the modern environment of rich societies. There is a mismatch that causes obesity to spread, thus decreasing fitness.


The adaptedness of cognitive processes is characterised by a fit between the process and the environment. The fit means that the processes reliably lead to positive outcomes or tend to maximise results. The processes, however, do not lead to beneficial results because they perform a comprehensive analysis of the situation and an evaluation of the each possible output. In fact, such processes work, and can be considered rational, only in a specified environment. They make the most of properties (esp. statistical properties) of specific environments. They are, as Simon and Gigerenzer put it, "ecologically rational".

There is a puzzle that comes with the above assertions: if our cognitive apparatus is best adapted to the Pleistocene environment and if our modern environment depart more and more from this original environment of evolutionary adaptedness, then we should be less and less adapted, less and less ecologically rational, ... dumber and dumber. But this does not really seem to be the case.

Read more: Cases of institutions that make us smart

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