Dunbar's equations

Slouch

This is probably laughably simple to people on this forum, but I have my doubts that the anthropology forum would be quite as good as explaining the mathematics to me. I'm trying to get my head around Dunbar's equations for the relationship between the relative size of the neocortex and the size of the cognitive group.

Here's a link to the paper; http://eebweb.arizona.edu/faculty/dornhaus/courses/materials/papers/Aiello%20Dunbar%20humans%20brain%20group%20size.pdf

I don't know how to tyope mathematics on boards.ie, but the equation I'm interested in is the first one, which he refers to as 'the reduced-major-axis equation', where N is mean group size and CR is the neocortex ratio. The r squared is what has me confused in particular, since it does not appear in the equation itself and I don't know its relevance. Is it supposed to be the same as the coefficient of determiniation used in statistics?

I'm coming at Dunbar's equation from an archaeological point of view, so please forgive my painful mathematical ignorance. I would therefore be very greatful if the jargon was kept to a minimum, though I realise some will be necessary.

MathsManiac

One would really want to check the original article to be sure, but at first look at this document, I'd say you are correct: it's the coefficient of determination for the model.

The information in brackets after the equation is telling you about the statistical basis for the model. It's a bit confusing, because the N here is not the same as the N in the equation!. My understanding of what this is saying is that the model (i.e. the equation) is based on a sample of 35 data pairs, that the correlation coefficient for the sample is sqrt(0.764), and that this correlation coefficient is significant at the 0.001 level or better.

Each data pair in the sample consisted of a mean group size N (treated as the dependent variable) and a neo-cortex ratio CR (the independent variable). Dunbar presumably found that the best fitting model is one that fits a linear relationship between the logs of these quantities.

sponsoredwalk

It's a logarithmic equation using the mathematics of logarithms!
Yes his explanation in the paper is very confusing but the article itself is
very interesting. I notice it's from 1993 & I came across this link just now in
which some author is putting forward their own hypothesis on the evolution
of language. Disregarding whether or not it means anything I notice the
author stops at the Upper Paleolithic 40,000 mark for the final stage in
syntax. Since it's from 2010 would I be right in assuming that more evidence
since 1993 has come in to show that the people in your article arguing
language arrived earlier were wrong?

Slouch

Sorry for taking ages to get back to you guys. Thanks very much for your help. All I really needed was to be able to say that those details at the bottom were part of the statistical basis of the equation. They were what had me all confuserplexed. It was for a presentation and I didn't want to be asked about it without being able to explain it reasonably well.

To answer the last question, that depends on who you ask. Dunbar's view on the matter has not really shifted, though he now prefers to present his ideas in the more vague form of the 'social brain hypothesis. He recently published a book on it with Clive Gambell and someone Gowlett (forgotten the first name). There are so many theories on the origins of language and the arguments haven't really changed much. The only significant development I know of is a number of recent publications by Sarah Milliken and Joao Zilhao demonstrating symbolic behaviour in neanderthals. My thesis, incidentally, is an examination of neanderthal group size at two recently discovered sites in Iberia, comparing the findings to Dunbar's view. For the record, that site you linked to is not one I would be inclined to trust.

Since this is a math forum, I will give the most superficial outline of views concerning the origin of language possible:

Noam Chomsky says humans evolved an inherent universal grammar, developed specifically for speech, but doesn't seem to have strong views on when it happened.

David Bickerton says a proto-language with a fully developed syntax and a non-lexical vocabulary must have developed before full language. He believes this existed in early hominids. This leaves the earliest possible date at 1.2MYA. Realistically though, he would probably put it with the appearance of neanderthals 350,000 years ago.

Steven Pinker says there may have been a proto-language consisting of words without grammar, though there may have been some simple rules, such as agent first, i.e. 'bear kill man' meaning a bear killed a man. So, language would probably develop shortly after the capacity for speech; probably as soon as the supralaryngial vocal tract is fully developed and the Fox P2 gene is present.

Alison Wray believes there was a 'holistic proto language' and simple sounds would have been used to convey complex messages, such as a monkey howling to say 'there is a snake approaching; get high in the tree for safety'. This would suggest that pre-language exists in animals as well, and that human communication is just a more developed form of this.

Terrence Deacon says all of the above is oversimplistic nonsense and several faculties of the brain must be preadapted for language, as the belief that something as complex as language just happened to develop because language is useful makes absolutely no sense in an evolutionary context. This places the origins of language after the brain has become fairly well developed.

Steven Pinker believes language is an evolutionary adaptation for an instinctive mode of communication. Other than that, he is largely in line with chomsky.

Dunbar believes language developed as a substitute for social grooming, as homo sapiens could save 30% of their grooming time through the use of language. This places language after humans develop reasonably condensed social groups.

They all vary signigicantly as to when they would place the origin of human language.


There are, of course, more. Here are honourable mentions worth looking into:

Daniel Dennett

David McNeill

Judy Kegl

Ludwig Wittgenstein is also worth reading for an interesting view on the nature of language, though he doesn't talk about its development much.


After all that, I will now acknowledge the forum I am in by mentioning an interesting paper about adopting mathematical approaches to language, which has this to say;

The importance of mathematical formalization is that it
allows us to think about concepts that we don’t understand
well, such as dependency and constituency, in terms
of concepts that are well understood, such as Turing
machines, sets, and functions. Usually, formalization
proceeds by first defining a concept we think is important
in the language of a well-understood branch of mathematics
such as set theory or logic. Once we have this
definition we can use mathematical principles to deduce
exact consequences of our definition, and then assess how
well these capture reality.

Here is the link: http://wjh.harvard.edu/~mnkylab/publications/recent/odonnell.pdf

I recommend a look at box 2 which discusses a set model for the evolution of artificial languages, which is probably the best proxy we have for the natural evolution of language.


Basically, there are A LOT of views on this