Showing posts with label Enquiries. Show all posts
Showing posts with label Enquiries. Show all posts

Wednesday, December 30, 2015

Steinbeck on Teaching



"On Teachingby John Steinbeck

      It is customary for adults to forget how hard and dull school is. The learning by memory all the basic things one must know is the most incredible and unending effort. Learning to read is probably the most difficult and revolutionary thing that happens to the human brain and if you don't believe that watch an illiterate adult try to do it. School is not so easy and it is not for the most part very fun, but then, if you are very lucky, you may find a teacher. Three real teachers in a lifetime is the very best of luck. I have come to believe that a great teacher is a great artist and that there are as few as there are any other great artists. Teaching might even be the greatest of the arts since the medium is the human mind and spirit.
      My three had these things in common. They all loved what they were doing. They did not tell - the catalyzed a burning desire to know. Under their influence, the horizons sprung wide and fear went away and the unknown became knowable. But most important of all, the truth, that dangerous stuff, became beautiful and precious.

Teaching, good teaching that is, is indeed an art, both a creative art and a performing art. It is one of the situations in life which turns human interaction into an art form. The teacher needs to attract and hold the attention of the student, provide, at all times, an answer to the question, 'Why am I sitting here listening to this bloke?' You have to be worth listening to. And you have to find ways to communicate something difficult to understand to someone who has no particular reason to want to understand it. If you can't do that you shouldn't be teaching.

The reality of good teaching that Steinbeck remembers is a long way from 'sit down, shut up, study chapter 5, the exam's on Friday, don't look at me, teach yourself or there'll be trouble' which is the idea a lot of teachers have, and a lot of children, as they've never known anything else.

If the teacher doesn't know why the children should learn what he's teaching them, they won't learn it. Learning should be cooperation, not attrition, not conflict, not the ticking of boxes, not getting through the day. Give me children who want to learn, who are keen and sharp and have enthusiasm for life, the present and the future, who understand the importance of learning not in a dry, theoretical sense, nor a profound, mature, analytic way, but in an immediate, unreflecting, this-clearly-matters-now kind of way. Where to find such children? Give me good teachers, and I'll make them for you.


Friday, April 26, 2013

On Nudity

Update: In the comments, Vincent points out that this post is badly in nearly of illustration. Although I am told that it is possible to find pictures of naked women on the Internet, I have added some here to give artistic coherence to the post (Never Knowingly Artistically Incoherent, me).

A Quick Sketch

I have spent a couple of afternoons trying to find a nude to draw. I first looked at Greek statues and eventually decided that there was no actual nude that was what I was looking for. Then today I tried modern photos in diffetent styles. Again I found nothing that wanted me to draw it, but I was struck by the variety of results of applying imagination to the representation of the human form. Not for the first time, I fell to thinking about it all.

The Original
Flesh in Stone, by the Genius of Bernini
There is great beauty in the human body. And great possibility. Despite the great beauty and plasticity of many animals, there is much in the human body that is, or can be, superior to them. One reason is simply the lack of hair, which allows the details of flesh texture and muscle tone and form to be clearly seen even at rest. The ability to be conscious of one's own body, to control its movements in detail, to conceive them with knowledge of how observers will react to them and to present them in a specific context independent of the movements themselves. There is also the important point that the lack of hair allows the play of light and shadow to exist, to be refined and exploited. The animality of the human body is more clearly visible than in other animals.

Naked Flamenco
Then there is the fact that we know and understand the human body, its functions, sensations and responses, far better than those of other animals. And then there is sex. We don't think of want cheetahs sexually.

But sex is not necessarily an important part of this perceived beauty, or even any part of it. I can see beauty in the male as well as the female form. On the other hand, it does appear that the female form is intrinsically more beautiful than the male. Women who appreciate beauty seem to agree with men on this. A beautiful woman is a beautiful thing. A man's beauty cannot so easily be appreciated by other men. Nevertheless, the beauty of the human body is not limited to the female.

Roman, not Greek, but one of the best
Nor is it limited to the young and well-formed. In many kinds of dance the performers tend to be youngish and slimmish, but then many forms of dance are too demanding for the old and fat. Some forms do allow for this. Flamenco rhythms are often danced to by old women. When it is well done, with skill and duende, not only the dancing but the women themselves become beautiful.

I remember a story I once heard about Josemaría Escrivá de Balaguer, in which he cried because he had seen an artist capable of making a chaste Venus. The story was probably apocryphal, carefully crafted to illustrate a point, as so many of the stories he told were, but it means, at the very least, that he thought it could be done, and that it was important.

Looking at pictures of attractive naked women purely- as it were- as beautiful objects, or the subjects of beautiful images, rather than as objects of male enquiry, is very interesting and instructive. The curiosities of anatomy, the signs of life lived and suffered, the differences that exist between what you may think of, at first glance, as similar examples of the Standard Pretty Girl, the ways in which the human body can be twisted, distorted, lit up, perceived, conceived, expressed and impressed. Their is apparently unlimited potential for teh creative mind to find new and beautiful ways to show it to us. I like this fact.

It is possible that that drawing will never be made. These reflections will have to stand in its place.

Wednesday, December 12, 2012

What is an Intellectual?


A word that is thrown around freely by anyone who thinks, suspects or wishes that someone else should be taken seriously. Most people seem to use it of those who appear on TV and give their opinions without swearing or stabbing their finger in anyone’s eye. A more robust characteristic is that they are people who can introduce into debate ideas that have not been prominent in the popular press in the previous 48 hours. When used carefully, the term is applied to people employed in non-technical areas of academia, and to those who work in the arts in almost any capacity.

Those who analyse these things more closely tend to describe an intellectual as someone who deals with ideas as such, rather than with the practical consequences of ideas. Mathematicians, engineers and so on, whose intellectual formation and the concepts they use in their work involve a higher level of understanding and rigour than most TV pundits have, are not generally considered intellectuals. Philosophers (itself a very broad concept), high-brow critics, and the more analytic members of the arts fraternity, on the other hand, do not get their hands dirty, are not concerned with the reality derived from the ideas whose existence they affirm, turning them over in their fingers and pronouncing authoritatively, dogmatically even, on what they should mean.

Fair enough, I’m not going to claim that the word must only be used to mean what I think it should mean. The problem comes from the fact that the greatest intellects in the world today, those whose enquiries, in many different fields, have made, or could make, the greatest difference to human understanding, including of itself and its society, are unknown to the general public (in which I include the popular press) and their contributions to thought and knowledge are neither known nor understood.

It may be said, quite fairly, that it requires no explanation to understand that an engine works or a bridge stays up, while to appreciate the purpose of an abstract idea requires more than observation. On the other hand, mathematicians don’t seem to count as intellectuals, although there are few disciplines more abstract than mathematics. (In the interests of full disclosure, I used to be a mathematician).

At the most basic level of selling advertising, the press requires ‘intellectuals’ to give some impression of seriousness to their own opinions, but they need something that is easy to understand and that will resonate with the readership, or they will lose them. Thus, real intellectuals are not a lot of use. Or rather, those who are not able to speak so that normal people can understand and be interested by them are not a lot of use.

Why then do we expect the kind of people who are thought of as intellectuals to explain practical things about politics? Or do we want them only to tell us how to feel good about ourselves because we believe the right things and others don’t, and then everything will come right by magic?

Of course, what I’m looking for is a definition of intellectual which will clearly include me, but, even when I make the rules, I’m having trouble doing it.

Tuesday, December 4, 2012

On World Peace


How would you work for world peace?

I shall fight the urge to comment on the award of the Nobel Peace Prize to the EU. I doubt there is much I can add that hasn’t been said (not that that usually stops me, but I shall resist the urge*). But I will ask, and completely fail to answer, a question ignored by the process, though not perhaps by Nobel himself, who essayed a form of answer: how do you contribute to world peace in any way that could mark you out for recognition or awards?

“…one part to the person who shall have done the most or the best work for fraternity between nations, the abolition or reduction of standing armies and for the holding and promotion of peace congresses.”

I have long wondered what Nobel meant by ‘peace conferences’. It is probable that he lived in a world very different from our own, and it was possible to imagine that if leaders of nations, or their favoured officials, could be persuaded to sit down together, peace would result from it. Despite the incompetence and corruption of that perpetual peace congress that is the UN, despite the failure of NATO, the EU and similar organizations to keep absolute peace in the areas they try to control, despite the abject failure of many meetings convened for the specific purpose of ending or averting conflict, the fact is that at least they exist, to an extent perhaps unimaginable a century ago, and that a significant number of people cannot conceive of a war breaking out in the country they live in, suggests that things have improved in the presence of such congresses.

Economic growth and the material comfort it brings are undoubtedly important as well, as is a fair bit of luck, but I think our Alfred, casting an eye about him today, would be fairly happy that he had identified a way of bringing some improvement to the world in general.

The abolition of reduction of standing armies is a trickier matter. The negotiated death of the arms race, and the subsequent ending of the Cold War, certainly made the world in general a much more peaceful place, and I think Nobel would consider this within the scope of ‘reducing standing armies (not that those responsible for it were ever recognised by the Nobel Committee). So one up to Sir Alfred.

The dissolution of the Japanese and German armies after WWII led to unprecedented peace in Western Europe and the Far East, but it was an expression of the desire of those countries and their peoples (in the case of Germany at least) not to start further conflict on the scale they had previously been responsible for. The reduction in the standing army was a consequence of the fervent desire for peace, not the direct cause of peace. A scoreless draw there, I think.

And then there is the contribution of armies to peace, something which Nobel could probably not imagine. The idea that armies could prevent conflict rather than be the cause of it by their very existence is unlikely to have entered his head, as it was obviously indisputable at the time that war was caused by armies. I might be misjudging the times, not being remotely expert, but I assume the thought process was something like that. Now an Army, in the sense of a body of men trained and disciplined for certain rôles requiring controlled authority, can contribute to the peace of their own or more frequently other nations.

And then there is the Fraternity between Nations. Hard to define, harder to quantify, but how would you work to achieve fraternity among nations? Much as I hate to admit it, we have to let the governments help us out on this one, not because they are likely to be any good at it, but because they can very easily stop it happening. The global trade, comfortable lives (in some countries at least) and cheap travel that freedom and stability have brought about lead to an increase in understanding and knowledge about people who are not quite like us, and a (slightly) reduced desire to kill each other unthinkingly.

Governments, the press, others with a voice and some kind of control can very easily persuade us (for some value of us) to hate some given ‘them’, and frequently find it useful to do so. They have a harder time persuading us to like ‘them’, usually having to resort to abuse and the law. In fact, you would think from reading the papers that no one would like anyone at all if we weren’t forced by law to pretend that we do.

But the fact is the more we travel, the more we surf the internet, the more we expose ourselves to news, entertainment, food and other artefacts of culture from around the world, the fewer the obstacles to that fraternity which Nobel wanted. There is surely a case for awarding the prize to Bill Gates, Tim Berners-Lee, Freddy Laker, Michael Ryan, or some combination of little-known people who have made communication around the world so much easier. Or from a slightly broader perspective, to the world’s major banks, which have, over the last century, made investment easy, with the result that we have the prosperity that has allowed bars to fraternity to be broken down. A serious suggestion, though perhaps not a popular one.

It has often been observed that free, wealthy countries don’t go to war with each other. To bring about peace and fraternity we should try to bring about freedom and prosperity. We know now how to do that, although there are many who don’t want it to happen.

*In consequence of which the whole of paragraphs 2 and 3, much of paragraphs 4 and 6, and quite a lot of the introduction, have been struck out.

Saturday, December 1, 2012

Press Freedom and all that


The press like to think they are special, that they safeguard democracy, that they have specific rights and freedoms that set them apart from ‘ordinary people.’ The government is looking for ways to control the press, and ‘abuse’ is a good excuse to do it. They could just the laws they’ve already made, but apparently that isn’t enough.

That they are so looking is clear, I think. The Internet frightens them because it gives enormous power to people who are not themselves.

The freedom of the press is the freedom of all of us. Not because they use it well, in the interests of public freedom. They do nothing of the kind. Newspapers and broadcasters are large, often international corporations who want to make money, like anyone else. Journalists have a living to earn and frequently an ego to stoke. The way to make money from journalism is, as with any other business, to find a market and give it what it wants. This may mean sex and celebrities, turgid book reviews, fluffy tales of the columnists daily life pretending to be news, ill-informed ranting disguised as background or comment, support for one or other powerful interest, pictures of the footy, or even intelligent, well-researched stuff about things that actually matter. The point is that the customer does not demand truth, and so the seller has no interest in providing it.

There is a myth that the practice of journalism in the US is protected by the First Amendment. This is a myth that Hollywood is quite happy to perpetuate. (In Hollywood land journalists are always good and brave, while pharmaceutical companies are always evil. I wonder why this might be.) At the time that Amendment was passed the press as we know it did not exist. The text was intended to specifically extend the protection of speech to the printed word. It does not make journalists special.

It’s important to the rest of us that journalists, the press in general, have no more nor  less freedom than the rest of us, because they are the rest of us. We are all free to write about the world and the people around us, or anything else we choose. In Britain and other civilized countries we still are free to do it. A journalist is surely nothing more than someone who thinks of himself as one. There are plenty of people who call themselves journalists but only ever give their own opinions, or restrict their output to material that is not, by any definition, news. Likewise, many people who provide genuine, researched news stories, many bloggers, for example, do not think of themselves as journalists, and are not recognised as such by others.

A journalist, I suspect, is someone who is paid by a (large) media company to produce content for it. This has nothing to do with the public interest, freedom or anything else. The fact that the government would rather like to control them (and Cameron’s spokesmen are denying it, which tells you all you need to know), combined with the fact that they themselves would like to control those who are not them, suggests that this is just more power games, politicians and big business arm wrestling over who gets what part of our money.

The danger is not from a mild regulation of the press, but from the inevitable trade-off, the distinction between what ‘licensed’ journalists are allowed to do, and what the plebs are permitted.* The freedom of the press is our freedom, not because they defend us, but because it allows us to defend ourselves.

*There seems to be some semi-legal protection for ‘official’ journalists who refuse to disclose the sources of their information. The rest of us do not have that privilege. We don’t want the gulf to widen.

Saturday, November 17, 2012

Some Curious Facts about the Origin of the Lakes



I have written again and again about the lakes, and I return to them because I keep discovering new things to enjoy and to learn about them. Every summer I find new paths, new hills, new places to enjoy, even new villages which I bring within my range by starting earlier and riding harder.

And then there are the eternal spots on the banks, where the water is at its best, high points on the hills, from which the views are at their most spectacular, the people-less woods filled with croaking frogs, or squirrels jumping from tree to tree, the quiet places that seem to breathe slowly and calmly as though the world did yoga there.




There is always more to discover, and more to learn. And recently I’ve been trying to find out a little more about the geology of the area, because people ask, and I like to have answers.

The whole region is formed from limestone rocks. An awful lot of geology seems to be about calcium, water and carbon dioxide*, in fact:

The geological formations of Ruidera are, chemically speaking, based on the process of precipitation and dissolving of the carbonates (essentialloy calcite). The conditions for precipitating and dissolving of CaCO3 depend on the relatively high level of Calcium Ca2+ and (H2CO3) ions, or of the carbonate (HCO3-) respectively in the water. The dissolution of a calcareous sediment or of limestone in water with a given level of CO2 can be described by the following reactions:
 
·        Ca2+ + HCO3-  --> CaCO3 + H+.                
·        H2O + CO2 --> H2CO3  y CaCO3 + H2CO3 --> Ca2+ + 2HCO3- 
The chemical process of dissolution or precipitation of CaCO3 depends, among other things, on the following factors:    
·       The carbon dioxide (CO2) content. 
·       The pH of the water: A low pH value favours the dissolving of  CaCO3, and vice versa.  
·       Temperature: The dissolution of  CaCO3 in pure water decreases with an increase of temperature. 

It turns out- I finally got round to looking up the history of the area- that the current lakes are only about 10,000 years old. Our ancestors knew only the river, and earlier there were similar formations at higher levels, the remains of which can still be seen rising above the banks in some places. The Cave of Montesinos, which Cervantes riffed on brilliantly in the Quijote, and the Grieta del Toro, were once part of that system, but are now 100m above it.

The most curious thing, it seems to me, is that, while the banks of the lakes are being eroded away by the water**, they are also being created by it. The karstic formations which form the banks and the divisions between the lakes in much of the system are deposited directly by precipitation of the calcium compounds from the water, which is very rich in them, presumably from having come down from the mountains to the east which are made of them. So while the gentle flow is widening and deepening its own channels and basins, it is also building them up around it. Which will win, over time, will, I imagine, depend on the rate of flow and the exact concentrations of minerals and carbonates in the water. History suggests erosion will win.

*My previous experience of geology, derived from walking in the hills with a friend at University who was studying the subject, suggested it was mostly about drinking beer and whacking things with a hammer before laughing maniacally and jotting strange figures on maps. I now realize there is more to it than that.

**Although they are described as lakes, they are part of the river system, and there is a continuous, though usually very gentle, flow throughout the system, enough to coause erosion over time. And karstic rocks are very soft.

Saturday, September 1, 2012

To What extent are we Responsiblr for Others?


Another justification for restricting the freedom of others is that we are responsible for them, and therefore have a duty to protect them from themselves. I think we can take as read that this true in certain cases, and to differing degrees. The question then becomes one of where, in any given case, the boundary lies, and who decides whether it’s been crossed.

I have no children of my own, but in my professional life I am regularly responsible for the children of others. I restrict their freedom by requiring them to follow certain guidelines, sometimes made up on the spot in reaction to some particular circumstance. I do this partly for their own safety, partly because a certain kind of order is necessary for them to learn well which is what they’re there for, and partly, to be honest, for my own convenience. They are used to being told what to do and so, broadly speaking, they accept it.

If I came across a man in the street, on a cold night, insensible with drink or drugs, I would think it my responsibility to look after him until he could take care of himself, get himself home, or someone else could take charge of him. This, despite the fact that he has freely got into that state, knowing the consequences. If a friend, neighbour, relative were damaging his health and affecting his life through drink, drugs, gambling or any other behaviour, I would consider it my responsibility to be regularly told to bugger off and mind my own business.

I have done all of these things, most of us have, I imagine, not because I am an interfering busybody but because I recognise that there are times when we are responsible for others. We are, I repeat once more, social animals. It is in our instinct to help those around of us who are need of help. As moralistic beings, we translate it into the language of morality, but it comes to the same thing. I should feel that responsibility because in general we do feel that responsibility.

But we are speaking of personal responsibility. Why is it the task of government to take over this responsibility in so heavy-handed a way? There is nothing personal about government, everything is done by force, from behind a barricade. This is as far from the human instinct of looking after your fellow man as it is possible to get.

Thursday, August 16, 2012

On Questions Stupid and Un-Stupid


A stupid question, a really stupid question, is one you don't want to know the answer to. To ask about something because you don't know, or don't understand, shows ignorance, not stupidity. To ask about something when the answer is before you and you would be expected to have seen it, shows distraction, and possibly lack of intelligence, but usually it isn’t the result of genuine stupidity. To ask about something you would be expected to know or understand as a part of your basic education or attention to life may attract comment, but if you are trying to correct that deficiency it is not stupid to ask.

No, the really stupid question is the one that thinks it is a triumphant critique, which expects no answer and believes none to exist, but is based on an ignorance and lack of understanding which it explicitly refuses to recognize or correct.

The canonical example, or at least a good example, is 'If we're descended from apes, how come there are still apes?' This is not a stupid question if you are confused by the apparent ambiguity of the terminology and are looking for an explanation. It is a stupid question if you imagine it will overturn, of itself, nearly 200 years of work on evolution.

Talking of which, I’m reading Darwin’s ‘Voyage of the Beagle’. It is absolutely fascinating, an adventure story full of cowboys, Indians, wild animals, sea monsters, bloodthirsty rebel leaders, lands that can kill you without warning with water, drought, mud, rocks, fire or ice, and all of it accompanied by an indefatigable thirst for biological, geological and sociological observation and experiment. He asks questions about everything, and he finds the answers. He never stops. I imagine there must have been a few conversations along the lines of: CD, 'What's that curious creature with a red crest, webed feet and the essential morphology of the Passerine order?' Passing Gaucho, 'It's a... "biiird".'

Every insect, every bird, every reptile and mammal, every river, every aspect of the geology of the area he sees is identified, described, its habits and type noted in detail, every curious or unknown aspect of its behaviour is the subject of experiments, local people are consulted on it for any further information they might have, samples are sent to experts in England for their comments. It is an amazing story of a small part of an amazing life.

Monday, August 13, 2012

On Guilt


Guilt is an artefact of the human psyche. This seems fairly clear. It is not in itself an external construct, but something that comes from within us. We are social animals, it is in our DNA as it were. What we call guilt is doubtless a mechanism by which our mind recognises when we have acted against the interests of the group.
The thing is, the acts and circumstances which guilt reacts to and attaches to do not seem to be, in general, specific, that is, they are not naturally within us, in our DNA. Most of them are created socially, consciously even, and may often be individual, and unconscious, arbitrary.
This has serious consequences for those, probably a large minority, if not a majority, who are not in full control of their minds.

The existence of guilt causes complications when it is possible to recognise and analyse it with the conscious intellect. Because it is in our mind we treat it differently from the body parts, and we want it to be important.

We analyse it, we use it, we abuse it, we fear it and suffer from it, we invent

Feeling guilty about something gives information about who we were brought up with. It tells us nothing about the intrinsic rightness or wrongness of the act we feel guilty about. This is clearly true because guilt may be felt by one person for doing someth ingwhich another one would feel guilty about not doing. The same person can feel guilt for doing at one time in their life something which they would feel guilty about not doing at another time and in the same situation. Guilt is something we all feel but it attaches to things not for fundamental reasons but because it is told to. It can be anything.

What we feel is a cultural or social invention. Because guilt itself is a part of our nature we need to find something to attach it to, and the environment we are brought up in provides this, in the same way that it provides a broader set of norms with which we determine what we hold to be moral or immoral, right or wrong. We may be happy to accept those norms, some people are comfortable enough to live their whole lives with the morals they learnt as children. Others learn new ideas about right and wrong, or they fashion their own from what they can take from around them.

Guilt, however, can be felt when going against an idea of right or wrong that you once held, or that was once held by those around you, but that you no longer hold. You may do something you believe to be right (or not wrong), but feel guilt because you would once have thought it wrong.

In other worlds, a sense of guilt tells us nothing useful, not even whether we ourselves believe we are doing wrong. We need to think more deeply to determine where an act within a situation lies in the framework of our own moral understanding. If we have one, that is, which can stand up to the pressure of detailed scrutiny without collapsing into incoherence or self-justification.

Monday, August 6, 2012

We are Extraordinary


We are extraordinary creatures. Formed from chemicals that can only be created by the unimaginable pressures and temperatures at the heart of dying stars, endowed with the power to detect our world in various ways that have been developing for hundreds of millions of years. The perceptive powers of our senses are limited compared with large numbers of animals, and we do not have at all some senses that other animals have, and yet these powers, though not the greatest among life forms, are extraordinary enough. That a bunch of chemicals can combine, reproduce, be aware of themselves and process information about the world around them is in fact so remarkable that we cannot even begin to understand it. Science accepts that some things just are.

Yet we can describe how the world works from what we can perceive. We can conceive means to make things easier to understand, we can imagine models that allows us to perceive things with the mind that are beyond the perception of our bodily senses, we can probe the invisibly small and interpret the unimaginably distant, and we can grasp how this affects us, and our place within it.

When I say we, I mean a small number in the most extreme cases, and a larger number who have a more general understanding. I once clung by my fingertips to the coattails of this last group, but it doesn't matter one way or the other. The fact that I share a species with such people is quite something.

We are extraordinary. Why do so many of us choose to be not even ordinary?

Friday, May 11, 2012

A Question on Superstrings


I have been reading Brian Greene’s book ‘The Elegant Universe’, on the theory of superstrings. If nothing else, he has a remarkable gift for getting complex scientific ideas across without simplifying them into uselessness or distorting them into falsehood.* He also know a lot about theoretical physics, having been involved in doing a lot of it for the last 30-odd years. The book leaves out the mathematics, of course, the point of it is to be useful to people who don’t have a background in maths, but its explanation of the concepts is clear and fascinating.

I have a couple of simple and possibly stupid questions about the superstring theory:

Is the theory- the physical ideas and the mathematical physics of it- a description of something real, or just a way of making it possible to talk about it and manipulate it mathematically?

Is it, in fact, possible to tell the difference?


It’s strange to think that, when I was studying Mathematics and Astrophysics at UCL back in the mid-80’s, these ideas were actually being developed in the very building I was drinking learning in. We undergrads didn’t get to much about hear about it, though. We learnt some of the mathematical tools to handle it (I recognised much later) and we learnt from people directly involved in the latest research in other fields, but we were resolutely taught quantum mechanics on the one hand, and general relativity on the other. There was no suggestion that far below, creatures with white skin, thick glasses and an inability to talk to women without giggling were trying to fix the rather serious problem that, as we learnt, and indeed discovered for ourselves, they can’t both be true. I don’t believe I had about superstrings until much later, when I was no longer involved in mathematics.

*Many people seem to think that if they can find an analogy or argument that appears to be coherent, it must automatically be a) true and b) what they were trying so express.