The death of the pianist and musicologist Charles Rosen (1927-2012) last month led to many tributes. While I have read and admired much of Rosen’s writing, he had a strange and unreasonable dislike of Mendelssohn’s musicwhich led his thinking astray.
Continue reading ‘Against anti-Mendelssohnism’
Author Archive for peter
Page 31 of 83
Mathematical hands
With MOOCs fast becoming teaching trend-du-jour in western universities, it is easy to imagine that all disciplines and all ways of thinking are equally amenable to information technology. This is simply not true, and mathematical thinking in particular requires hand-written drawing and symbolic manipulation. Nobody ever acquired skill in a mathematical discipline without doing exercises and problems him or herself, writing on paper or a board with his or her own hands. The physical manipulation by the hand holding the pen or pencil is necessary to gain facility in the mental manipulation of the mathematical concepts and their relationships.
Keith Devlin recounts his recent experience teaching a MOOC course on mathematics, and the deleterious use by students of the word-processing package latex for doing assignments:
We have, it seems, become so accustomed to working on a keyboard, and generating nicely laid out pages, we are rapidly losing, if indeed we have not already lost, the habit—and love—of scribbling with paper and pencil. Our presentation technologies encourage form over substance. But if (free-form) scribbling goes away, then I think mathematics goes with it. You simply cannot do original mathematics at a keyboard. The cognitive load is too great.
Why is this? A key reason is that current mathematics-producing software is clunky, cumbersome, finicky, and not WYSIWYG (What You See Is What You Get). The most widely used such software is Latex (and its relatives), which is a mark-up and command language; when compiled, these commands generate mathematical symbols. Using Latex does not involve direct manipulation of the symbols, but only their indirect manipulation. One has first to imagine (or indeed, draw by hand!) the desired symbols or mathematical notation for which one then creates using the appropriate generative Latex commands. Only when these commands are compiled can the user see the effects they intended to produce. Facility with pen-and-paper, by contrast, enables direct manipulation of symbols, with (eventually), the pen-in-hand being experienced as an extension of the user’s physical body and mind, and not as something other. Expert musicians, archers, surgeons, jewellers, and craftsmen often have the same experience with their particular instruments, feeling them to be extensions of their own body and not external tools.
Experienced writers too can feel this way about their use of a keyboard, but language processing software is generally WYSIWYG (or close enough not to matter). Mathematics-making software is a long way from allowing the user to feel that they are directly manipulating the symbols in their head, as a pen-in-hand mathematician feels. Without direct manipulation, hand and mind are not doing the same thing at the same time, and thus – a fortiori – keyboard-in-hand is certainly not simultaneously manipulating concept-in-mind, and nor is keyboard-in-hand simultaneously expressing or evoking concept-in-mind.
I am sure that a major source of the problem here is that too many people – and especially most of the chattering classes – mistakenly believe the only form of thinking is verbal manipulation. Even worse, some philosophers believe that one can only think by means of words. Related posts on drawing-as-a-form-of-thinking here, and on music-as-a-form-of-thinking here.
[HT: Normblog]
Time, gentlemen, please
Much discussion again over at Language Log over a claim of the form “Language L has no word for concept C”. This time, it was the claim by Wade Davis (whose strange use of past tense indicates he has forgotten or is unaware that many Australian Aboriginal languages are still in use) that:
In not one of the hundreds of Aboriginal dialects and languages was there a word for time.”
The rebuttal of this claim by Mark Liberman was incisive and decisive. Davis was using this claim to support a more general argument: that traditional Australian Aboriginal cultures had different notions of and metaphors for time to those we mostly have in the modern Western world.
We in the contemporary educated West typically use a spatial metaphor for time, where the past is in one abstract place, the present in another non-overlapping abstract place, and the future in yet a third non-overlapping abstract place. In this construal of time, causal influence travels in one direction only: from the past to the present, and from the present to the future. Nothing in either the present or the future may influence the past, which is fixed and unchangeable. Events in the future may perhaps be considered to influence the present, depending on how much fluidity we allow the present to have. However, most of us would argue that it is not events in the future that influence events in the present, but our present perceptions of possible future events that influence events and actions in the present.
Modern Western Europeans typically think of the place that represents the past as being behind them, and the future ahead. People raised in Asian cultures often think of the abstract place that is the past as being below them (or above them), and the future above (or below). But all consider these abstract places to be non-overlapping, and even non-contiguous.
Traditional Australian Aboriginal cultures, as Davis argues, construe time very differently, and influences may flow in all directions. A better spatial metaphor for Aboriginal notions of time would be to consider a modern city, where there are many different types of transport and communications, each viewable as a network: rivers, canals, roads, bus-only road corridors, railways, underground rail tunnels, underground sewage or water drains, cycleways, footpaths, air-transport corridors, electricity networks, fixed-link telecommunications networks, wireless telecommunications networks, etc. A map of each of these networks could be created (and usually are) for specific audiences. A map of the city itself could then be formed from combining these separate maps, overlaid upon one another as layers in a stack. Each layer describes a separate aspect of reality, but the reality of the actual entire city is complex and more than merely the sum of these parts. Events or perceptions in one layer may influence events or perceptions in other layers, without any limitations on the directions of causality between layers.
Traditional Aboriginal notions of time are similar, with pasts, the present and futures all being construed as separate layers stacked over the same geographic space – in this case actual geographic country, not an abstract spatial representation of time. Each generation of people who have lived, or who will live, in the specific region (“country” in modern Aboriginal English) will have created a layer in the stack. Influence travels between the different layers in any and all directions, so events in the distant past or the distant future may influence events in the present, and events in the present may influence events in the past and the future.
Many religions – for example, Roman Catholicism, Hinduism, and African cosmologies – allow for such multi-directional causal influences via a non-material realm of saints or spirits, usually the souls of the dead, who may have power to guide the actions of the living in the light of the spirits’ better knowledge of the future. Causal influence can thus travel, via such spirit influences, from future to present. Similarly, the view of Quantum Mechanics of space-time as a single 4-dimensional manifold allows for influences across the dimension of time as well as those of space.
I am reminded of an experience I once witnessed where the only sensible explanation of a colleague’s passionate enthusiasm for a particular future course of action was his foreknowledge of the specific details of the outcome of that course of action. But these details he did not know and could not have known at the time of his enthusiasm, prior to the course of action being executed. In other words, only a causal influence from future to present provided a sensible explanation for this enthusiasm, and this explanation only became evident as the future turned into the present, and the details of the outcome emerged. Until that point, he could not justify or explain his passionate enthusiasm, which seemed to be a form of madness, even to him. Contemporary Western cosmology does not provide such time-reversing explanations, but many other cultures do; and current theories of quantum entanglement also seem to.
Contemporary westerners, particularly those trained in western science, have a hard time understanding such alternative cosmologies, in my experience. I have posted before about the difficulties most westerners have, for instance, in understanding Taoist/Zen notions of synchronicity of events, which westerners typically mis-construe as random chance.
Snow jobs
Advice from Geoffrey Pullum, when faced with people who tell you that Eskimos have multiple words for “snow”:
Stand up and tell the speaker this: C.W. Schultz-Lorentzen’s Dictionary of the West Greenlandic Eskimo Language (1927) gives just two possibly relevant roots: qanik, meaning ‘snow in the air’ or ‘snowflake’, and aput, meaning ‘snow on the ground’. Then add that you would be interested to know if the speaker can cite any more.
References:
G. K. Pullum [1989]: The great Eskimo vocabulary hoax. Natural Language and Linguistic Theory, 7: 275-281. Available from here.
C. W. Schultz-Lorentzen [1927]: Dictionary of the West Greenlandic Eskimo Language. Meddelelser om Grønland, 69, Reitzels, Copenhagen, Denmark.
Public appearances
I have argued before that it is an abuse of power for major newspapers to run obituaries of obscure back-office staff, simply because they can. This is an abuse since a newspaper is a public organization, playing a very public role in public life, not some private family newsletter shared, like samizdat, between close relatives over kitchen coffee.
The Guardian now runs, as the cover story in its Saturday Review section, extracts from the piano-learning diary of its Editor, Alan Rusbridger. Perhaps there is nothing actually unethical about a major newspaper running long cover stories about its Editor’s private hobbies, and promoting his new book. But one has to ask: Is The Guardian now the private family newsletter of its Editor?
PhD Vivas
Awhile back, I posted some advice from my own experiences on doing a PhD. Since then, several people have asked me for advice about the viva voce (or oral) examination, which most PhD programs require at the end of the degree. Here are some notes I wrote for a candidate recently.
It is helpful to think about the goals of the examiners. In my opinion, they are trying to achieve the following goals:
1. First, they simply want to understand what your dissertation says. This means they will usually ask you to clarify or explain things which are not clear to them.
2. Then, they want to understand the context of the work. This refers to the previous academic literature on the subject or on related subjects, so they will generally ask about that literature. They may consider some topic to be related to your work which you did not cover; in that case, you would normally be asked to add some text on that topic.
3. They want to assess if the work makes a contribution to the related literature. So they will ask what is new or original in your dissertation, and why it is different from the past work of others. They will also want to be able to separate what is original from what came before (which is sometimes hard to do in some dissertations, due to the writing style of the candidate or the structure of the document). To the extent that Computer Science is an engineering discipline, and thus involves design, originality is usually not a problem: few other people will be working in the same area as you, and none of them would have made precisely the same sequences of design choices in the same order for the same reasons as you did.
4. They will usually want to assess if the new parts in the dissertation are significant or important. They will ask you about the strengths and weaknesses of your research, relative to the past work of others. They will usually ask about potential future work, the new questions that arise from your work, or the research that your work or your techniques make possible. Research or research techniques which open up new research vistas or new application domains are usually looked upon favourably.
5. Goals #3 and #4 will help the examiners decide if the written dissertation is worth receiving a PhD award, since most university regulations require PhD dissertations to present an original and significant contribution to knowledge.
6. The examiners will also want to assess if YOU yourself wrote the document. They will therefore ask you about the document, what your definitions are, where things are, why you have done certain things and not others, why you have made certain design choices and not others, etc. Some examiners will even give the impression that they have not read your dissertation, precisely to find out if you have!
7. Every dissertation makes some claims (your “theses”). The examiners will generally approach these claims with great scepticism, questioning and challenging you, contesting your responses and arguments, and generally trying to argue you down. They want to see if you can argue in favour of your claims, to see if you are able to justify and support your claims, and how you handle criticism. After all, if you can’t support your claims, no one else will, since you are the one proposing them.
The viva is not a test of memory, so you can take a copy of your thesis with you and refer to it as you wish. Likewise, you can take any notes you want. The viva is also not a test of speed-thinking, so you can take your time to answer questions or to respond to comments. You can ask the examiners to explain any question or any comment which you don’t understand. It is OK to argue with the examiners (in some sense, it is expected), but not to get personal in argument or to lose your temper.
The viva is one of the few occasions in a research career when you can have an extended discussion about your research with people interested in the topic who have actually read your work. Look forward to it, and enjoy it!
Your local neighbourhood top-secret Global Military Command Centre
In WW II, the British military paid friendly nationals in neutral Sweden, Switzerland, and elsewhere to subscribe to provincial German newspapers in order to garner intelligence about life in Germany. Among other things, printed death notices were used to estimate casualty numbers in German military units, since particular units tended to recruit from particular regions; casualty rates were a means to assess the degree of success of Nazi military campaigns those units were involved in.
Let us hope now that Britain’s enemies are not reading provincial newspapers such as The Wiltshire Times (14 June 2011):
It is hard to believe that the central communications hub for the entire British Army sits unassumingly on the outskirts of the quiet Wiltshire market town of Corsham.
. . .
The centre, at Westwells Road, in Neston, is home to GOSCC – the Global Operations Security Control Centre – a top secret centre which houses up to 600 specialists working behind the scenes to make huge military operations such as those in Libya, Afghanistan and Iraq a reality.”
I guess not revealing the street number keeps the location of the top-secret centre safe.
Feats of memorization
Anthony Tommasini writes in the IHT on the trend to allow concert pianists to play from music, instead of playing recital solos and concertos from memory. A good thing too! While playing from memory is an impressive feat to watch, it certainly takes additional practice effort to achieve: I would rather good performers played more different music than that they played a smaller collection from memory.
I saw Angela Hewitt play the Bach 48 from memory in Cottonopolis a few years ago. At the first concert, a woman in the front row was reading from a miniature score. After the first few preludes and fugues, Ms Hewitt quietly asked the woman to put her score away, as the page turning was distracting. My guess is that the page-breaks were happening at places other than where Ms Hewitt had memorized. (As an aside, her performance was very good but her interpretations undermined by rubato. I prefer my Bach straight, not with flavoured mixers.)
Note: The hands shown are those of Szabo Daniel.
Glasperlenspielen
Lars Pålsson Syll on “orthodox, mainstream, neoclassical economics”:
Economic theory today consists mainly in investigating economic models.
Neoclassical economics has since long given up on the real world and contents itself with proving things about thought up worlds. Empirical evidence only plays a minor role in economic theory (cf. Hausman [1997]), where models largely functions as a substitute for empirical evidence. But “facts kick”, as Gunnar Myrdal used to say. Hopefully humbled by the manifest failure of its theoretical pretences, the one-sided, almost religious, insistence on mathematical deductivist modeling as the only scientific activity worthy of pursuing in economics will give way to methodological pluralism based on ontological considerations rather than formalistic tractability.
If not, we will have to keep on wondering – with Robert Solow and other thoughtful persons – what planet the economic theoretician is on.” [page 54]
I agree with the general thrust of this essay, which resonates with some of my own thoughts on the Glass Bead Game of Economics, for example, here and here.
Mind you, I don’t agree with everything that Syll says in this essay. For example, he argues that good predictive capabilities require models to bear resemblance to their target domains. But we know many counter-examples to this claim, from Newton’s model of planetary motion to Friedman’s billiard players. Prediction and explanation are two orthogonal dimensions of a model, which may or may not be related in any particular case.
His essay also overlooks the fact that the so-called “real world” which is the target domain of economic models contains, at least in the case of macro-economics, mostly humanly-constructed artefacts, such as the “variables” known as inflation and unemployment rates. Having sat in working parties defining and redefining such artefacts, I am always surprised that any economist could possibly imagine they are modeling an independent reality.
Reference:
Lars Pålsson Syll [2010]: What is (wrong with) economic theory? Real-world Economics Review, 55: 23-57.
Shackle on Rational Expectations
The Rational Expectations model in economics assumes that each economic agent (whether an individual or a company) can predict the future as perfectly as the modelers themselves. To anyone living outside the rarified bubble of mathematical economics, this is simply ridiculous. It is clear that no one associated with that theory has ever made any real business decisions, or suffered their consequences.
Here is non-mainstream economist George Shackle, writing to Bryan Hopkins on 1980-08-20:
‘Rational expectations’ remains for me a sort of monster living in a cave. I have never ventured into the cave to see what he is like, but I am always uneasily aware that he may come out and eat me. If you will allow me to stir the cauldron of mixed metaphors with a real flourish, I shall suggest that ‘rational expectations’ is neo-classical theory clutching at the last straw.
Observable circumstances offer us suggestions as to what may be the sequel of this act or that one. How can we know what invisible circumstances may take effect in time-to come, of which no hint can now be gained? I take it that ‘rational expectations’ assumes that we can work out what will happen as a consequence of this or that course of action. I should rather say that at most we can hope to set bounds to what can happen, at best and at worst, within a stated length of time from ‘the present’, and can invent an endless diversity of possibilities lying between them. [Italics in original]
Of course, unlike John Muth or Robert Lucas, Shackle had actual real-world experience of investment decision-making from his experience during WW II on national infrastructure planning.
Reference:
George L. S. Shackle [1980]: Letter to Bryan Hopkins. Quoted in: Stephen L. Littlechild [2003]: Reflections on George Shackle: Three Excerpts from the Shackle Collection. The Review of Austrian Economics, 16 (1): 113-117.