I have posted before about the two cultures of pure mathematicians – the theory-builders and the problem-solvers. Thanks to string theorist and SF author Hannu Rajaniemi, I have just seen a fascinating paper by Freeman Dyson, which draws a similar distinction – between the birds (who survey the broad landscape, making links between disparate branches of mathematics) and the frogs (who burrow down in the mud, solving particular problems in specific branches of the discipline). This distinction is analogous to that between a focus on breadth and a focus on depth, respectively, as strategies in search. As Dyson says, pure mathematics as a discipline needs both personality-types if it is to make progress. Yet, a tension often exists between these types: in my experience, frogs are often disdainful of birds for lacking deep technical expertise. I have less often encountered disdain from birds, perhaps because that is where my own sympathies are.
A similar tension exists in computing – a subject which needs both deep technical expertise AND a rich awareness of the breadth of applications to which computing may be put. This need arises because the history of the subject shows an intricate interplay of theory and applications, led almost always by the application. Turing’s abstract cineprojector model of computing arrived a century after Babbage’s calculating machines, for example, and we’ve had programmable devices since at least Jacquard’s loom in 1804, yet only had a mathematical theory of programming since the 1960s. In fact, since computer science is almost entirely a theory of human artefacts (apart from that part – still small – which looks at natural computing), it would be strange indeed were the theory to divorce itself from the artefacts which are its scope of study.
A story which examplifies this division in computing is here.
Reference:
Freeman Dyson [2009]: Birds and frogs. Notices of the American Mathematical Society, 56 (2): 212-223, February 2009. Available here.
Author Archive for peter
Page 53 of 85
The world beyond our five senses
Over at Normblog, Norm has a typically open-minded discussion about religion and its possible attractions for its adherents:
Both Howard [Jakobson] and Tim [Crane], then, neither of them speaking as a believer, sees religion as making the world, so to say, fuller for its adherents – with more of interest, of meaning, of things, even, beyond our grasp. This reminds me of the occasion I asked a religious friend about the basis of his belief and he cut the conversation short by saying simply that his life would be poorer without it.
All I can say is that this account of religion doesn’t work for me – I mean, to shift me – and for two reasons. The first is that the world seems like an intensely interesting place already, without any extra population of meanings and mysteries. Just look, read. There’s no end of it, never mind a fullness. The second is that I don’t feel free to add a further layer of things to those for which some evidence can be supplied, and if I did, I wouldn’t know where to stop. Why just those mysteries?
I think Norm, and the accounts he cites, miss something that is often important both to religious believers and to practitioners of religious activities (two overlapping but not identical groups, as I have explained before). What is missing is that for many people in these two groups, their interest in religious ideas and practices arises from a contact they have had, or which they perceive they have had, with entities from a non-material realm. This contact usually involves none of their so-called five senses, but is experienced deeply nonetheless. One can know something from merely being in the presence of somebody, as may happen, for example, when we experience the strong love of another person.
Of course, it may be that people who have had such spiritual experiences are deluded in thinking they had them, or even, that they delude themselves. Experiments exciting certain parts of the brain with small electric currents can apparently induce very similar perceptions of religious experiences in people. Even so, such experiments do not demonstrate, or even make likely, the absence of non-material entities; in precisely the same way, patients with tinnitus do not demonstrate that all sound is generated inside our own heads and we all live in a silent universe.
So it is perfectly possible that people who perceive they have had direct contact with non-material realms may indeed have had such contact. This possibility exists even though Richard Dawkins and many another famous person seem not to have had such experiences. Moreover, the lack of spiritual experiences for some people also tells us nothing about the existence or non-existence of spiritual realms and beings. Not all of us are born able to hear, for example, but the fact that some people are born deaf is also not usually taken as a sign that the universe itself is silent. It may thus, indeed, be those who believe that they have not had contacts with a non-material realm who are deluded, or who are deluding themselves. In a situation of such widespread ignorance, with neither replicable evidence for the existence of spiritual entities nor any evidence against their existence, it behooves no one to be arrogant about his or her position. (For the record, I do not count Norm in this combined category of arrogant atheists and arrogant religious believers.)
And to Norm’s larger point: If a person has had such an experience, what does she find? First, she finds that the experience is entirely discounted by science, since it cannot be replicated via experiment. This arrogant disdain for phenomena that it cannot yet explain has sadly been a feature of western science since its inception. Second, she finds that she cannot talk openly about this experience, at least not in a modern western office or university. In the supremely rationalist environment of our business and education worlds, talking about spiritual experiences among colleagues is one sure way nowadays to receive laughter, scorn and derision. That is very different from, say, the situation in the West in the middle of the 19th century, or the situation still today in Africa or in Australian Aboriginal society, societies where spiritual experiences are widely respected. Having lived in both the West and in Africa, I know this difference very well. Third, she would find no explanation or meaning for her experience in any academic discipline, apart from theology and poetry, and perhaps the arts and music. She would, however, likely find great sympathy from pure mathematicians, who grapple daily with entities which seem to have existence and properties independent of the material realm, entities which are entirely imaginary, outside the world of our five senses, and yet which seem to exist in some fashion, often sublimely connected with one another. (The square root of minus 1, for example, is entirely imaginary, yet its properties are not random, to be invented as we might wish from whole cloth, but are decidedly what they are.)
For Norm, the material world is rich and interesting enough as it is, and needs no further explanation. If you have ever experienced something beyond the material, then I suggest that finding an explanation or interpretation of that experience which makes some sense of it for you is not nothing, and is a quest not to be ridiculed or derided, however quixotic that quest might prove. Personally, I cannot understand how anyone who has encountered the Euler Equation – which links an imaginary number with two important transcendental numbers, along with the respective identities for addition and multiplication – could possibly believe that the material world is all there is.
In defence of secularism
Edmund Adamus, director of pastoral affairs at the Roman Catholic diocese of Westminster, London, is apparently upset at modern, liberal secular society, claiming (inter alia) that:
Our laws and lawmakers for over 50 years have been the most permissively anti-life and progressively anti-family and marriage, in essence one of the most anti-Catholic landscapes, culturally speaking – more than even those places where Catholics suffer open persecution.”
This is nonsense. It was secularists – atheists, agnostics, non-believers, liberals, and anti-bigots – who led the campaign in Britain for Catholic emancipation, the right to vote, and the right to sit in Parliament, granted in 1829. It was secularists who achieved the right for Jews to sit in Parliament from 1858 and the right to vote in 1867, something that the same political party currently ruling Britain stymied for a quarter century. (The bill emancipating Jews passed the House of Commons in 1833, but was repeatedly blocked in the House of Lords by Conservative peers and bishops. What reasonable person with knowledge of this history could belong to such a party?) It was secularists, not the religious, who led the campaign which ended the deaths of women in illegal back-street abortions and gave equal rights to people regardless of their gender or colour or sexual orientation. It was even secularists who passed a law in 2001 – yes, 2001! – that finally allowed Catholic priests and former priests to sit in the British Parliament. If not for secularism and the progressive extension of political and social rights to all citizens, regardless of their religion or race or gender, Edmund Adamus would not even have the freedom of speech to voice his obnoxious opinions.
Few things make me angry. Religious bigotry and racial prejudice are among them. So too is this stupidity of religious conservatives, unable to see where there own self-interests lie. Their interests are best served by a secular society and state which guarantees equal rights to all, not special rights to some on the basis of their religious beliefs or their gender or any other biological or social construct. Britain is still not entirely there yet, with the fact of unelected, unrepresentative, and unaccountable Church of England Bishops still sitting in the House of Lords (and thus voting on legislation that impacts us all), and the country’s denial of religious freedom for the Head of State and his or her immediate family. But the great progress in extending freedom to all that has been made these last 200 years is due to secularism and secularists, not to religious bigotry or obscurantism.
On growing up Catholic
The Australian Labor Party split in two three times during the 20th century: over military conscription during WW I, over economic policies during the Great Depression, and over entryism by Catholic anti-communists in 1954. A Catholic-dominated splinter party from that last split, the Democratic Labor Party (DLP), now looks likely to be represented in the Australian Federal Parliament again after 36 years absence, by winning the last Senate seat from Victoria in last week’s election. I therefore thought it interesting to collect the views of several lapsed Catholics on their education.
Here is Germaine Greer, educated in Melbourne by Catholic nuns of the Presentation Order, in an essay in the collection, There’s Something About a Convent Girl (Edited by Jackie Bennet & Rosemary Forgan. London, UK; Virago, 1991):
I am still a Catholic, I just don’t believe in God. I am an atheist Catholic – there are a lot of them around. One thing lapsed Catholics do not do is go in for an “inferior” religion with less in the way of tradition and intellectual content.”
And Catholic-raised Terry Eagleton on reason in religious education:
[Richard] Dawkins considers that all faith is blind faith, and that Christian and Muslim children are brought up to believe unquestioningly. Not even the dim-witted clerics who knocked me about at grammar school thought that. For mainstream Christianity, reason, argument and honest doubt have always played an integral role in belief.”
Catalan & American philosopher George Santayana, who ended his life, though a lapsed believer, in a convent in Rome:
Catholicism is the most human of religions, if taken humanly: it is paganism spiritually transformed and made metaphysical. It corresponds most adequately to the various exigencies of moral life, with just the needed dose of wisdom, sublimity, and illusion.” (Persons and Places. London, UK: Constable, 1944, p. 98)
British author David Almond, in an interview with Sarah Crown, quoted on his Catholic upbringing in Newcastle, UK:
Readers and critics have labelled Almond’s novels modern fairytales. But for Almond himself, “the pressing thing is the realism. Skellig had to be in a real garage. Kit sleeps in a real mine. The Fire-Eaters, while it has a miraculous element to it, takes place in a real coastal town, and features a real fire-eater – he was based on this character we used to see on the Quayside in Newcastle when I was a kid. Once you’ve got that solid, touchable world you can do anything. Maybe that’s something else to do with being brought up as a Catholic: you’re taught to think about the other world, but you grow up in this one, and you realise there couldn’t be anything better. So you find the miraculousness in reality.”
Hilary Mantel says something similar:
In the ideal world, all writers would have a Catholic childhood, or belong to some other religion which does the equivalent for you. Because Catholicism tells you at a very early age the world is not what you see; that beyond everything you see, and the appearance – or the accidents as they’re known – there is another reality, and it is a far more important reality. So it’s like running in the imagination. I think that this was the whole point for me – that from my earliest years I believed the world to have an overt face and a hidden face, and behind every cause another cause, and behind every explanation another explanation, which is perhaps of quite a different order.
And if you cease to believe in Catholic doctrine it doesn’t mean that you lose that; you still regard the world as ineffable and mysterious and as something which perhaps in the end can’t quite be added up. It could be summed up as saying “all is not as it seems”, and of course that’s the first thing Catholicism tells you. And then it just runs through everything you write and everything you touch, really. Plus, it’s good to have something to rebel against.”
Irish writer John McGahern, in a 1993 essay, “The Church and its Spire”, on his upbringing in 1950s Eire:
I was born into Catholicism as I might have been born into Buddhism or Protestantism or any of the other isms or sects, and brought up as a Roman Catholic in the infancy of this small state when the Church had almost total power: it was the dominating force in my whole upbringing, education and early working life.
I have nothing but gratitude for the spiritual remnants of that upbringing, the sense of our origins beyond the bounds of sense, an awareness of mystery and wonderment, grace and sacrament, and the absolute equality of all women and men underneath the sun of heaven. That is all that now remains. Belief, as such, has long gone.”
Journalist Antony Funnell in an article about the violence in Australian Catholic education also says:
It was many years before I started to truly appreciate the full effect that the Catholic education system of the 1970s and early 80s had on my psyche. From the [Marist] Brothers I retain, and cherish, a sense of what’s often called “Catholic social justice”: a deeply held belief that what’s important in life is to make some form of difference to society, no matter what you do and no matter how small your contribution; that treating everyone as your equal is important; that your goals in life should rise above the simple pursuit of material wealth.
How odd then that I also learned from them how base and brutal and petty human beings can be.”
I think this sense of the absolute equality of all arises from the universalist ambitions of Catholicism (all people are called to embrace it and be saved), which it shares with Islam. Those forms of Protestantism which focus on an elect, the people whom God has decided will be saved (even, according to believers in predestinationism, so chosen before their birth), do not share this bias for absolute equality. Of course, within the Church itself, with its priesthood currently restricted to men, and then only some men, the tradition of equality is dishonoured more than honoured. And the universalism of Catholicism, coupled with its global presence, mean that a welcoming community and familiar rituals can be found by adherents most anywhere they go (again like Islam). Perhaps only participation in a global martial arts community, such as karate or aikido, offers anything similar.
And since Catholics hold that it is the-people-as-the-Church that receive grace and are saved, not people as individuals, there is a bias toward community and social cohesion that runs counter to the prevailing individualistic ethos of capitalism.
Note: The image that once was on this page was one of the many woodcarvings in the Catholic Church at Serima Mission, near Masvingo, Zimbabwe.
What is music for?
What is music for? What purposes do its performers achieve, or intend to achieve? What purposes do its listeners use it for? Why do composers or song-writers write it?
These seem to me fundamental questions in any discussion about (say) the public funding of music performances and music education, or (say) the apparent lack of knowledge that some people in Britain have about some types of music, or (say) how to increase audiences for particular types of music. But no-one seems to debate these questions, or even to raise them. As a result, there seems to be little awareness that aims and purposes may vary, both across cultures, and over time. (I am reminded of Alfred Gell’s anthropological theory of art which understands art as the creation of objects liable to be perceived by their audience as objects with intentionality, that is, objects carrying some purpose.)
The philosopher John Austin once said that every science begins with a classification. In that spirit, I have tried to list some purposes and functions which I have understood to be intended for music by composers, performers and/or listeners (in no particular order):
- To entertain, to give pleasure. The pleasure may arise from the sounds themselves (eg, elements such as the sound qualities, the melodies, the harmonies, the overtones, the timbres, the beat, the rhythms, the combinations or interplay of the various elements), or the performance of the music (the skills of the performers may provide pleasure), or the construction of the music (eg, repetition or novelty, contrapuntalism or other structural features, the composition or improvisation techniques evident to a listener), or allusions to other sounds and music.
- To express some emotion or mood in the composer/writer, or in the performer. Indeed, music may be a form of encrypted communication, with messages able to be understood by the target audience but not by any others who hear it. According to Larry Todd, Fanny Mendelssohn wrote lieder (art-songs) to communicate to Wilhelm Hensel her feelings about him; he was later to become her husband, but at this time her parents had forbidden them to meet or to write to one another, even on occasion intercepting a letter he had had written against this order.
- To evoke some emotion or mood in the listener. The sturm-und-drang movement in the mid-18th century, for example, led symphony writers to imitate thunderstorms and other effects, often seeking to frighten or surprise listeners. Bach expert, Peter Williams, for example, wrote that Bach’s sacred choral music (his Cantatas, Passions, and Masses)
were conceived to instruct, affect, alert, startle and entrance the listener, originally doing so mostly in church services but today anywhere;” (Williams 2016, page ix).
Or, as Rachmaninov said of his Preludes:
“If we must have the psychology of the Prelude, let it be understood that its function is not to express a mood, but to induce it.”
- For listeners to become aware of their own feelings in reaction to music they hear. The pianist Roberto Prosseda has argued that one function of music is to help listeners to become aware of their own internal emotions that arise in response to the music.
One of the most significant “side-effects” of making music at an in-depth level is surely the fact of becoming aware of one’s interiority, knowing how to listen: this doesn’t just involve a more acute sense of hearing, but above all the capacity to be able to look inside oneself in order to recognize and experience one’s emotions with awareness.”
I have met quite a few otherwise-intelligent people who are, manifestly, not always aware of their own emotional reactions to events taking place outside themselves. For such people, practice in listening may be a very important function of music.
- To express solidarity and communality, whether by performers or by listeners. See, for instance, Mark Evan Bonds’ great book on how Beethoven’s symphonies were perceived by their audience as expressions of and occasions for communality. Singing of national anthems and songs by football crowds is an everyday example of expressions of communality. John Miller Chernoff’s observation that African people express their opinion of a musical performance by joining in (themselves performing, singing, beating time, or dancing) is an example of this particular aesthetic of music. Other examples include the playing of the US national anthem at the Changing of the Guard at Buckingham Palace, London, on 13 September 2001, and the programming of music by American composers for the Last Night of the Proms in London that same week, both acts of solidarity with the USA after the 9/11 attacks. Given the fact that the US had to fight a war against the British crown to achieve Independence, and indeed had fought a subsequent war with Britain, these were very strong statements of solidarity.
- To inspire listeners to action, as, for example, with the music of the 19th century nationalists such as Verdi, Chopin, Dvorak, Smetana, Sibelius, Hill, etc. Such nationalist aesthetics may be very powerful: The white minority regime in South Africa, for example, banned the singing of the hymn, Nkosi Sikelel’ iAfrika (“God Bless Africa”), because of its association with the movement for majority rule. (The hymn is now the national anthem of South Africa.) Similarly, although Japan’s illegal military occupation of Korea ended in 1945 and both countries are now democracies, Japanese pop music was still banned in the ROK (South Korea) as late as 1992.
- To induce altered mental states in performers or listeners, for example, as an aid to entering a trance or to prepare them for some other spiritual experience. In words of Indian musician Gita Sarabhai (1922-2011) that influenced John Cage, for example, music’s function is “to sober and quiet the mind, thus rendering it susceptible to divine influences.”
The Russian-Israeli pianist Boris Giltburg, after performing all five Beethoven Piano Concertos with the Brussels Philharmonic (under Thierry Fischer) across three evenings in February 2020, wrote (on 18 February 2020):
The high point for me was No. 4, during which I experienced something which until now I’ve only felt while playing Russian music: a kind of floating, when your brain disengages or splits in two. One (small) part is alert and following the performance, and perhaps directs the musical flow a little bit, the other (much larger) part is completely sunk into the music, experiencing it in a kind of visceral, instinctive way which precludes logical thinking and seems wired directly to your deepest feelings, without any buffers or defenses. After that concerto I was drained, bewildered, exhilarated – a complete mess. But what an unforgettable night.”
Actors have told me of achieving a similar, but infrequent, transcendence in performance, when they feel the character they are playing is a real person, whose mind they are inside, instead of being in their own body and mind performing the character.
- To facilitate some other activity, such as dancing, singing or the recital of poetry, or the ready memorizing of secret espionage codes.
- To think. Contrapuntal music, in the North German tradition that reached its peak in the middle of the 18th century, used fugal writing as a way of articulating the possible mathematical manipulations (eg, overlay, delay, inversion, reversion) of the theme. These manipulations may be viewed mathematically as group actions on a musical space. Similarly, the tradition of western art music from the mid 18th century through to the present day has focused on the articulation of the musical consequences of a theme or motif. Beethoven, who was never very good at melody-making, was perhaps the best composer ever at development, with Mendelssohn a very close second. Chopin, by contrast, was good with melodies, but not at complex development.
The development of musical material during improvised performances of modern jazz, of Indian ragas, or of Balinese gamelan scales are further examples. See, for instance, Paul Berliner’s account of his learning to improvise in jazz.
Likewise, much minimalist music forces performer and listener to pay careful mental attention to aspects of music, such as rhythm and metre, ignored in the dominant uptown tradition, and how these vary, concatenate and interleave with one another. Similarly, the focus, particularly by composers in the American experimental tradition this last 100 years (eg, Cowell, Varese, Cage), on the materiality of sounds and their making is another form of thinking; it is the intelligent exploration of the features of sounds and sound-generating mechanisms, and of the consequences of these features. - To facilitate thinking. I have a computer scientist friend whose attempts to prove mathematical theorems is greatly enhanced if he listens to Bach fugues while doing so. Likewise, many large corporations transmit low-decibel, high-frequency white noise through their office speaker systems to facilitate work in open-plan offices.
- To effect some change in the listener. Bianca Bosker, writing about visual art in her book Get the Picture, has said (page 273), “Art knocks us off our well-worn pathways. Other things can do that too, but art . . . is arguably designed specifically for that purpose.” This goal of a composer and/or a performer overlaps with others in this list. I think immediately of Pekka Kuusisto’s wonderful recording of Vivaldi’s The Four Seasons, which is decidedly not twee or smug, as performances of this work can be, but deliberately abrasive.
- To come to know oneself. Using music (or any form of human expression) as a form of thinking, one learns about oneself: how one thinks, about what one is thinking or obsessing, and what one perceives. Many visual artists draw or paint to know themselves better, with the resulting drawing or art-work a mere by-product of the process. The same is true of musicians and composers and listeners, and it is why people may be drawn to life as a musician (or artist) despite the many negative consequences. (I am grateful to conversations with Patricia Cain for this insight.)
- To enable one to seek mastery of the skills and arts involved in composing, performing and/or listening, to train oneself in these arts, to undertake a practice (in the Zen sense of that word). The Australian composer, James Penberthy, in his late memoir, spoke of his need to spend several hours each day composing, in order to achieve mental balance, something he only fully realized in his later life.
Over years, with persistence and dedication, the physical skills involved in a daily musical (or other) practice can cease to require the full attention of our conscious minds, and thereby allow the mind to float above the actual musical activity: we may “enter the zone”, a transcendent flow state. After years of playing the piano, I can usually and consistently reach this state on the piano within minutes. After years of playing the violin, I have yet to reach it on the violin even once.
- To pray. Much western religious music is expressed in a form of supplication or worship to a deity. Composing, performing or listening to music may also be understood as acts of piety in themselves, akin to the copying out of sacred texts which some religions, for example, Nichiren Shu Buddhism, consider to be pious actions.
- To channel messages from the spirit world, as Zimbabwean mbira players are aiming to do when playing. Jazz pianist Craig Taborn has said that he believes “creative endeavours are informed by the interaction with metaphysical forces” and that “Music functions as a means to ‘call down’ those spirits [the spirits of the black improvisational music tradition], so in a very real sense I am not doing anything when the music is truly being made. It isn’t really me doing it.”
- To communicate with non-material (ie, spirit) realms. Much prayer, indeed, perhaps the overwhelming majority, is primarily intended neither as entreaty nor worship of a deity, but instead communion with spiritual entities. Music can be a form of such communion.
- To provide soteriological guidance to performers or listeners. Composing, playing, or listening may help one achieve or progress towards salvation. Jazz pianist Craig Taborn again: “All the things people say when they talk about music have to do with entertainment, or some kind of aesthetic advancement. Yet when they talk about how music moves them, they talk about other things: feelings, times of life, etc. So I suppose that for me, music is one of the things we use to get ourselves through life.”
- To provide an unobtrusive background to other events, as Muzak seeks to do, and as much film music appears to be seeking to do.
- To pass the time. It is true that time would have passed anyway, but one’s perception of the duration and speed of its passage may be altered.
These goals may overlap. For instance, music may entertain by providing an opportunity for musical thinking. For musics such as modern jazz improv or classical Indian ragas, the composers, performers or listeners may gain considerable pleasure from the thinking they undertake in order to write, to perform, or to listen to the music. A listener to music may gain intellectual pleasure by discerning and re-creating the thinking that the composer undertook when writing a piece, or that was undertaken by a performer engaged in an improvisation. Such pleasure at thinking, in my experience, is similar to the pleasures which people gain by doing crosswords or doing Sudoku puzzles; it may also be a form of mathmind. This is (writing, performing or hearing) music as thinking, in exactly the same way that drawing is a form of thinking. As with drawing, the cognitive abilities required to think via music, especially on the fly, should not be underestimated.
References:
Paul F. Berliner [1994]: Thinking in Jazz: The Infinite Art of Improvisation. Chicago, IL, USA: Chicago University Press.
Mark Evan Bonds [2006]: Music as Thought: Listening to the Symphony in the Age of Beethoven. Princeton, NJ, USA: Princeton University Press.
John Miller Chernoff [1979]: African Rhythm and African Sensibility: Aesthetics and Social Action in African Musical Idioms. Chicago, IL, USA: University of Chicago Press.
Allen Forte [1977]: The Structure of Atonal Music. New Haven, CT, USA: Yale University Press.
Kyle Gann [2006]: Music Downtown: Writings from the Village Voice. University of California Press.
Alfred Gell [1998]: Art and Agency: An Anthropological Theory. Oxford, UK: Clarendon Press.
Peter Williams [2016]: Bach: A Musical Biography. Cambridge, UK: Cambridge University Press.
A computer pioneer
I have posted before about how the history of commercial computing is intimately linked with the British tea-shop, via LEO, a successful line of commercial computers developed by the Lyons tea-shop chain. The first business application run on a Lyons computer was almost 60 years ago, in 1951. Today’s Grauniad carries an obituary for John Aris (1934-2010), who had worked for LEO on the first stage of an illustrious career in commercial IT. His career included a period as Chief Systems Engineer with British computer firm ICL (later part of Fujitsu). Aris’ university education was in Classics, and he provides another example to show that the matherati represent a cast of mind, and not merely a collection of people educated in mathematics.
John’s career in computing began in 1958 when he was recruited to the Leo (Lyons Electronic Office) computer team by J Lyons, then the major food business in the UK, and initiators of the notion that the future of computers lay in their use as a business tool. At the time, the prevailing view was that work with computers required a trained mathematician. The Leo management thought otherwise and recruited using an aptitude test. John, an Oxford classics graduate, passed with flying colours, noting that “the great advantage of studying classics is that it does not fit you for anything specific”. “
Of course, LEO was not the first time that cafes had led to new information industries, as we noted here in a post about the intellectual and commercial consequences of the rise of coffee houses in Europe from the mid-17th century. The new industries the first time round were newspapers, insurance, and fine art auctions (and through them, painting as a commercial activity aimed at non-aristocrat collectors); the new intellectual discipline was the formal modeling of uncertainty (then aka probability theory).
UPDATE (2012-05-22): The Telegraph of 2011-11-10 ran an article about the Lyons Tea Shop computer business, here, to celebrate the 60th anniversary of the LEO (1951-11-17).
The DDR and the invasion of Czechoslovakia in 1968
In a recent post, I briefly reviewed Hans Kundnani’s fascinating book about the German left, Utopia or Auschwitz: Germany’s 1968 Generation and the Holocaust. I said that he had overlooked that the army of the DDR joined the Warsaw Pact forces which invaded the Czechoslovak Socialist Republic in August 1968. It turns out I was wrong.
My apologies to Mr Kundnani, to whom I also owe the knowledge of this correction. Although forces of the army of the DDR, the National People’s Army (NVA), did assemble near the border ready to invade, at the last moment their action was stayed. The decision to stay them seems to have been made in the Kremlin on the advice of senior Czech communists who were supporting the invasion, a fact only confirmed recently. Interestingly, it seems that during and subsequent to the invasion, the SED Government of the DDR never corrected reports which said that they had participated.
It was not until 2008, at an international joint project on the ‘Prague Spring’, that researchers from the Austrian Ludwig Boltzmann Institute in Graz, from Russian institutes and archives [sic] from other research institutions were able to provide a clear answer. In Moscow they found previously unknown documentary evidence that the decision for the non-participation of the NVA in the invasion was indeed made on short notice by Soviet Party leader Leonid Brezhnev following requests by high-ranking Czechoslovak opponents of Dubcek.” (Wenzke, p. 155)
References:
Rudiger Wenzke [2010]: The role and activities of the SED, the East German State and its military during the “Prague Spring” of 1968. pp. 137-164 in: M. Mark Stolarik (Editor): The Prague Spring and the Warsaw Pact Invasion of Czechoslovakia, 1968: Forty Years Later. Illinois, USA: Mundelein.
Hans Kundnani [2009]: Utopia or Auschwitz: Germany’s 1968 Generation and the Holocaust. London, UK: Hurst and Company.
The Matherati
Howard Gardner’s theory of multiple intelligences includes an intelligence he called Logical-Mathematical Intelligence, the ability to reason about numbers, shapes and structure, to think logically and abstractly. In truth, there are several different capabilities in this broad category of intelligence – being good at pure mathematics does not necessarily make you good at abstraction, and vice versa, and so the set of great mathematicians and the set of great computer programmers, for example, are not identical.
But there is definitely a cast of mind we might call mathmind. As well as the usual suspects, such as Euclid, Newton and Einstein, there are many others with this cast of mind. For example, Thomas Harriott (c. 1560-1621), inventor of the less-than symbol, and the first person to draw the moon with a telescope was one. Newton’s friend, Nicolas Fatio de Duiller (1664-1753), was another. In the talented 18th-century family of Charles Burney, whose relatives and children included musicians, dancers, artists, and writers (and an admiral), Charles’ grandson, Alexander d’Arblay (1794-1837), the son of writer Fanny Burney, was 10th wrangler in the Mathematics Tripos at Cambridge in 1818, and played chess to a high standard. He was friends with Charles Babbage, also a student at Cambridge at the time, and a member of the Analytical Society which Babbage had co-founded; this was an attempt to modernize the teaching of pure mathematics in Britain by importing the rigor and notation of continental analysis, which d’Arblay had already encountered as a school student in France.
And there are people with mathmind right up to the present day. The Guardian a year ago carried an obituary, written by a family member, of Joan Burchardt, who was described as follows:
My aunt, Joan Burchardt, who has died aged 91, had a full and interesting life as an aircraft engineer, a teacher of physics and maths, an amateur astronomer, goat farmer and volunteer for Oxfam. If you had heard her talking over the gate of her smallholding near Sherborne, Dorset, you might have thought she was a figure from the past. In fact, if she represented anything, it was the modern, independent-minded energy and intelligence of England. In her 80s she mastered the latest computer software coding.”
Since language and text have dominated modern Western culture these last few centuries, our culture’s histories are mostly written in words. These histories favor the literate, who naturally tend to write about each other. Clive James’ book of a lifetime’s reading and thinking, Cultural Amnesia (2007), for instance, lists just 1 musician and 1 film-maker in his 126 profiles, and includes not a single mathematician or scientist. It is testimony to text’s continuing dominance in our culture, despite our society’s deep-seated, long-standing reliance on sophisticated technology and engineering, that we do not celebrate more the matherati.
On this page you will find an index to Vukutu posts about the Matherati.
FOOTNOTE: The image above shows the equivalence classes of directed homotopy (or, dihomotopy) paths in 2-dimensional spaces with two holes (shown as the black and white boxes). The two diagrams model situations where there are two alternative courses of action (eg, two possible directions) represented respectively by the horizontal and vertical axes. The paths on each diagram correspond to different choices of interleaving of these two types of actions. The word directed is used because actions happen in sequence, represented by movement from the lower left of each diagram to the upper right. The word homotopy refers to paths which can be smoothly deformed into one another without crossing one of the holes. The upper diagram shows there are just two classes of dihomotopically-equivalent paths from lower-left to upper-right, while the lower diagram (where the holes are positioned differently) has three such dihomotopic equivalence classes. Of course, depending on the precise definitions of action combinations, the upper diagram may in fact reveal four equivalence classes, if paths that first skirt above the black hole and then beneath the white one (or vice versa) are permitted. Applications of these ideas occur in concurrency theory in computer science and in theoretical physics.
AI's first millenium: prepare to celebrate
A search algorithm is a computational procedure (an algorithm) for finding a particular object or objects in a larger collection of objects. Typically, these algorithms search for objects with desired properties whose identities are otherwise not yet known. Search algorithms (and search generally) has been an integral part of artificial intelligence and computer science this last half-century, since the first working AI program, designed to play checkers, was written in 1951-2 by Christopher Strachey. At each round, that program evaluated the alternative board positions that resulted from potential next moves, thereby searching for the “best” next move for that round.
The first search algorithm in modern times apparently dates from 1895: a depth-first search algorithm to solve a maze, due to amateur French mathematician Gaston Tarry (1843-1913). Now, in a recent paper by logician Wilfrid Hodges, the date for the first search algorithm has been pushed back much further: to the third decade of the second millenium, the 1020s, a thousand years ago. Hodges translates and analyzes a logic text of Persian Islamic philosopher and mathematician, Ibn Sina (aka Avicenna, c. 980 – 1037) on methods for finding a proof of a syllogistic claim when some premises of the syllogism are missing.
Representation of domain knowledge using formal logic and automated reasoning over these logical representations (ie, logic programming) has become a key way in which intelligence is inserted into modern machines; searching for proofs of claims (“potential theorems”) is how such intelligent machines determine what they know or can deduce. It is nice to think that automated theorem-proving is almost 990 years old.
References:
B. Jack Copeland [2000]: What is Artificial Intelligence?
Wilfrid Hodges [2010]: Ibn Sina on analysis: 1. Proof search. or: abstract state machines as a tool for history of logic. pp. 354-404, in: A. Blass, N. Dershowitz and W. Reisig (Editors): Fields of Logic and Computation. Lecture Notes in Computer Science, volume 6300. Berlin, Germany: Springer. A version of the paper is available from Hodges’ website, here.
Gaston Tarry [1895]: La problem des labyrinths. Nouvelles Annales de Mathématiques, 14: 187-190.
In defence of futures thinking
Norm at Normblog has a post defending theology as a legitimate area of academic inquiry, after an attack on theology by Oliver Kamm. (Since OK’s post is behind a paywall, I have not read it, so my comments here may be awry with respect to that post.) Norm argues, very correctly, that it is legitimate for theology, considered as a branch of philosophy to, inter alia, reflect on the properties of entities whose existence has not yet been proven. In strong support of Norm, let me add: Not just in philosophy!
In business strategy, good decision-making requires consideration of the consequences of potential actions, which in turn requires the consideration of the potential actions of other actors and stakeholders in response to the first set of actions. These actors may include entities whose existence is not yet known or even suspected, for example, future competitors to a product whose launch creates a new product category. Why, there’s even a whole branch of strategy analysis, devoted to scenario planning, a discipline that began in the military analysis of alternative post-nuclear worlds, and whose very essence involves the creation of imagined futures (for forecasting and prognosis) and/or imagined pasts (for diagnosis and analysis). Every good air-crash investigation, medical diagnosis, and police homicide investigation, for instance, involves the creation of imagined alternative pasts, and often the creation of imaginary entities in those imagined pasts, whose fictional attributes we may explore at length. Arguably, in one widespread view of the philosophy of mathematics, pure mathematicians do nothing but explore the attributes of entities without material existence.
And not just in business, medicine, the military, and the professions. In computer software engineering, no new software system development is complete without due and rigorous consideration of the likely actions of users or other actors with and on the system, for example. Users and actors here include those who are the intended target users of the system, as well as malevolent or whimsical or poorly-behaved or bug-ridden others, both human and virtual, not all of whom may even exist when the system is first developed or put into production. If creative articulation and manipulation of imaginary futures (possible or impossible) is to be outlawed, not only would we have no literary fiction or much poetry, we’d also have few working software systems either.