p vii b

Two Comments on `Two Cultures’ (I)

 Perhaps there is a difference in the use of our brains between the so-called two cultures. This does not assert that the difference is due to genetics (but it is not easy to deny the contribution of the genetic components just as almost all human nature and potentials). Later in this book, the author suggests that those who cannot manipulate mathematical concepts without relying on natural language cannot do mathematics in the true sense of math capability. There are supporting facts. See the next item.

Math is nonverbal in its core! ( unfinished )

Halberda et al., Individual differences in non-verbal number acuity correlate with maths achievement 

Nature  455, 665 (2008)

There are large individual differences in the non-verbal approximation abilities of 14-year-old children, and these individual differences in the present correlate with children's past scores on standardized maths achievement tests, extending all the way back to kindergarten. 

 This correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. 

The following review article is also of help; Numerical skills are rooted in nonlinguistic biological primitives:

A Nieder and S Dehaene, Representation of Number in the Brain

Ann Rev Neurosci.,  32 185 (2009)

*Numerical skills are rooted in nonlinguistic biological primitives. 

*Numerical information is represented and processed by regions of the prefrontal and posterior parietal lobes, with the intraparietal sulcus as a key node for the representation of the semantic aspect of numerical quantity.

Two Comments on `Two Cultures’ (II) (more serious comment)

 This is a much more serious comment on Snow’s `Two Cultures’ than `I’ above. It is about the question whether it was appropriate to quote C. P. Snow’s discussion on `Two Cultures’ in the context of Preface. Since the reason to quote Snow is simply to mention and to respect the source of the clause `The Two Cultures,’ this is not an important question in the context, but a serious problem whether C P Snow is qualified to speak about such an important issue. As you can see below the author feels his qualification is rather questionable.

 Before any criticism let us quote the relevant original sentences:

A good many times I have been present at gathering of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: {¥em Have you read a work of Shakespeare's}?'' (C. P. Snow,  The Two Cultures and the Scientific Revolution, The Rede Lecture 1959 (Cambridge UP, 1961) p15-6)

Some problems will be pointed out later, but this statement itself is respectable.

 May, 2009 was the 50th anniversary of this lecture, Nature  459 published a commemorating article (p32-)

Dissecting The Two Cultures

Fifty years ago today, Charles Percy Snow argued in an influential lecture that the failure of science and the humanities to converse, and the lack of scientists in positions of power, was disastrous for society. In the first of three essays marking this anniversary,  Martin Kemp [ emeritus professor in history of art at the University of Oxford] contends that the real enemy of understanding is not these ‘Two Cultures’ but specialization in all disciplines.

 This article describes Snow as a person who cannot understand literature at all (this may well be true):

In 1962 Leavis (English literature critic) subjected Snow and ‘The Two Cultures’ to a stinging assault. ....

Leavis despised Snow’s literary works: “as a novelist he doesn’t exist; he doesn’t begin to exist. He can’t be said to know what a novel is.” Leavis also dismissed Snow’s authority as a cultural guru. … It is ridiculous to credit him with any capacity for serious thinking about the problems on which he offers to advise the world.”

Leavis acclaimed great literature as the true guardian of human values. ... For Leavis, science ― and the technological society it was spawning ― was devoid of humane values. 

 Does Mr Kemp understand the nature of thermodynamics? He seems to understand it as a topic as special as Derrida’s deconstruction:

Viewed historically, Snow’s way of setting up the debate about the two cultures was founded on a false comparison between knowledge of Shakespeare and thermodynamics. The roots of this mistaken comparison were laid when knowledge in all forms of learning started to become specialized and professionalized, reaching an apogee when disciplines were institutionalized in the nineteenth century. ... Snow’s poser about the second law of thermodynamics would be better matched against a narrower question in literary studies, such as asking what is meant by deconstruction as practised by the philosopher Jacques Derrida.

That is, the discourse of the Two Culture has two aspects: one is the distinction between humanities and natural science, and the other is the contrast between the general culture and narrow specialization. As to the latter aspect, Ortega’s criticisms quoted in the next footnote 3 is far superior than Snow’s, so the author (YO) believes it is not appropriate to discuss the question in conjunction to the Two Cultures [needless to say it is an important problem, but Snow is irrelevant]. However, Mr Kemp does not agree. He thinks now the latter is the central issue raised by Snow:

The issue does not involve two monolithic ‘cultures’ of science and humanities. It is about the narrow specialization of all disciplines and wider understanding.

 This must be grossly off the mark. The cause is very likely that Mr Kemp does not understand thermodynamics. Here, understanding thermodynamics means understanding of its position in the culture and science. This is supported by the following passage:

I wonder how many biologists could answer Snow’s test question, especially in the light of modern physics. I suspect that most scholars in the humanities would fare little better with the Derrida test. The problem is educational. 

Modern physics has nothing to do with the question. If a biologist does not know the second law of thermodynamics, we may question his credential as a natural scientist. However, a specialist of Classic Greek without any knowledge of Derrida can be quite respectable (perhaps more respectable if he does not know deconstruction). 

 In summary, we must conclude that the distinction between the two cultures is not only robust, but also the meaning of the distinction may become incomprehensible.

 However,  did Snow really understand thermodynamics?  The author is bothered by his comparison between the cosmologically universal `knowledge’ called the second law and a not so old local literature. Of course, Shakespeare successfully captured human universality, and as Leavis admires, great literature is the true guardian of human values. However, it is possible to assert that the universality of Shakespeare’s is less than that of Sophocres’ tragedies (Leopold von Ranke seems to agree with this opinion, cf. Uber die Epochen der neueren Geschichite ). Perhaps, Snow’s audience were Britons who were not so well-versed in non-English literature, so Snow’s rhetoric may be forgivable, but still it is fair to say that his comparison lacks suitable balance.