Open letter to Lakoff about his book on math

Dear Prof. Lakoff

A short note to say how much I am enjoying "Where Mathematics Comes From". It is providing closure for me.

In the 1980's, I fell in love with math during a college course based on the very foundations-conscious Calculus text by Spivak and although I enjoyed the rigor and beauty, I could not help but feel a bit uneasy at the hoops one had to jump through for the proofs to work, all this in the name of eliminating intuition.

I eventually ended up on the "applied" side, to the regret of my wonderful teachers, because I felt much more at ease with the way things seemed to work out intuitively. Successive approximations to non-linear functions using the university mainframe seem to do the trick of finding solutions to things I was curious about. Infinitesimal approaches, simplex algorithms and Fourier series implemented in WATFOR to solve hard differential equations numerically were simple but magical approaches to understanding. I was gratefully standing on Turing and Church's shoulders.

Anyhow, over the years I kept looking for insights as to why the pure math left me a bit uneasy since I still admired the beauty of it, (like pining for a high-school sweetheart) in all kinds of places including David Foster Wallace's overly baroque book on the math of infinities (yikes).

Your book reconciled the comfort of the applied and the beauty of the formal for me. There is a cognitive continuum after all, between the purists and us engineering/computing folk.

It connected the dots, clarifying the things that seemed like bridges by grounding them. By focusing on the metaphors for infinity it helped in categorizing things that were both computing and theory, but that could only exist because of computing: compiler theory, the Aho-Ullman stuff derived from Chomsky. I can now see why there was all this cognitive dissonance when I was learning Analysis.

For example, the space-as-points versus space-containing-points argument you and Nunez make is beautiful and could be applied to the philosophy of physics as well. The notion of particle comes to mind. I think Feynman the intuitionist in physics is a counterpart to Poincare in the world of math. His explanations of energy quanta and fields address the analogous notions of space and points in the world of physics, where it seems some still cling to the Platonic reality of math. The intuitionists, like Poincare, were very courageous and insightful as well as demonstrably able to make new discoveries as they sidestepped the Gottingen school's rejection of intuitive geometry and Cantor's objectification of infinities. Set theory is nice but infinity is just NaN.

I had read Kline's history of math some years ago and although I agreed with his view that a rift in math was created at the time when intuition was relegated to a sideline, there seemed to be something missing, much more to say. Your work with Nunez closed that loop for me.

I am now curious and encouraged to find out more about any research to make rationals (the real Reals :-)) the basis for discretization, as well as links between foundations work and Chomsky's formal grammars. I agree as the book infers that terminology in math is key to disambiguation - but technical terms like Real and continuous are too deeply entrenched of course. Maybe intro calculus courses should begin with a review of those specialized semantics. Like lawyers learning contract terms...

I am also curious about reactions to your work from the math community (rather than by the pedagogical folks) since I think the arguments are revolutionary and deeply original. I looked cursorily on the Web but found little of substance in reaction or support of the ideas in the book. Are mathematicians looking into closing the gaps you identify? Did you get much substantive opposition to your views? Finally, kudos for the other wonderful work on political discourse. Sorely needed. I wish I could be young enough again to enroll as a student of your faculty, but I will continue to follow your research with great interest nonetheless.

Last Year at Marienbad and Kubrick lovers

Resnais/Robbe-Grillet's movie could have never been made by Kubrick, by any American. It is a gulf that cannot be bridged. It is a great film that defines the distance between two cultures. A defining artefact.

But let's look at the commonalities first. Formalism, cinematography, music, all these are components of the medium, mastered by both sides. Influences are acknowledged, Marienbad left its mark that way.

The difference is in the extreme surrealism, if that is at all a possible term. Resnais does not hesitate to go all the way, and manages to get it made as a mainstream film. Cultural considerations could never trump commercial ones that way in Hollywood. Never.

It was panned by American critics. It was a challenge to their perceived cultural hegemony. I am not sure what the current critical status is, other than it being something which has taken place, that exists and that cannot be taken back. This is the advantage of reproducible media over museum pieces, stone temples, things that can be annihilated in war. It is also the curse of the commercial interests who want to charge toll, but who at the the same time want mass consumption.

There are others like it, Tarkovsky's Nostalghia comes to mind, but very few that speak universals without compromise or banality.

Marienbad tiptoes and steps on formalism, uniqueness, understanding, ambiguity, misunderstanding, romance, and pretentiousness, and succeeds in being unique, beautiful, and influential.

Commoditization of Relationships

All rights reserved A. Barake 2013

Finding a partner for love, for life is part of the journey for most, and it is a bit of a paradox that we need to think of that person as special for it to gel. The search for the click of compatibility is at odds with what biology has evolved for us. Put random male and female animals together and they will usually mate. Of course there are exceptions, and it may well be that we as a species are evolving away from this facility so as to ensure our survival in this increasingly competitive environment.

What made me think of this topic, the selection of mates, is the age-old cultural stigma around pornography, around commoditization of desire. I think that one reason this feeling exists is that it tends to devalue the specialness felt around love, around desire. It compartmentalizes it and ultimately makes it a consumable. Nothing new here. Prostitution, pornography and sexual entertainment, to coin a phrase, have always been part of commerce. I think it is useful to think of them clearly, as subsidiaries of humanism, as ways to make us conform, to be farm animals in the corporate culture. The test is that someone profits from them. They also represent an area of potential emotional confusion, because they link very strong feelings and instincts with something that is too tightly framed and packaged as a consumer item. It is not a good idea to become attached to consumables, and it is not a good idea to separate your emotions in such a way as to be able to cater to those needs in exchange for currency. The malaise I feel is akin to the distinction made between a soldier and a murderer. The cultural definition is clear, but not completely rational, it is based on emotional separation. (An aside: the current CBC attention to post-traumatic stress disorder is the tip of a very big iceberg, one that they will never acknowledge, since they are an instrument of the state, a placebo for culture, a fucking depressing lie, but all we have left in the mainstream.)

Marcuse, in An Essay on Liberation makes a case for the way we internalize comfort and consumerism, becoming willing corporate subjects. Subjects are manipulated, held. Reading between the lines, one can see that conformity is part of the enabling mechanism, and commoditization of our humanity is the precipice to stay away from. Individual feeling, specialness, and its protection from influence, including advertising are survival mechanisms too. The difference between a surviving consumer culture and one that thrives on equality is sustainability. At some point, if we follow the former to its logical conclusion, we will have to eat dollars and copulate with machines.

The Continuity of Consciousness

http://en.wikipedia.org/wiki/William_Pereira

Were the Greeks onto something when they coined the roots of the word "consciousness" and "continuity"? To be conscious is to remember the last moment of perception and to link it to the next, to have your brain relate perceptions into some coherent short term stream, so that you can feel and act on it.

Consciousness is continuity of perception. As you fall asleep, that continuity gets fragmented and you tend to forget the next moment, you lose consciousness and continuity.

Consciousness depends on the existence of the short-term cache used to process incoming data from the senses. It has to be fast, and it has to integrate the information for the deeper layers, the one that drive action and long term memory. It has to draw upon memory as well. Short term memory is limited in size because it is big on processing power. Lots of neurons required.

Current research on cognition suggests that we have a bunch of neural bundles in the brain that do this work all in parallel, that these compete for bandwidth, and the resultant dynamic network signals are what we can call consciousness. The signals that have control of the bus at the time, and that pulse it to make us act and remember are the Self.

This model does not address the big question of the Me. What makes a writer want to take this flow of perceptions, call them ideas, record them on secondary external memory and publish them so as to possibly communicate and affect the behaviour of others. The Will to Power?

What links us to the world as Beings. This is what the better religions are struggling with, and Zen Buddhism comes close to understanding it when it concludes that the universe is Me, and that the relationships between beings is the Universe. Still, a loop. Maybe language is the issue. We have an object-oriented language, and that is a flawed model, as many programmers and programs are discovering. The world cannot be entirely described as a hierarchy of "objects" What is an object anyhow, except an integration by the senses, a model. Another loop.

Some drugs like alcohol, anaesthetics, and sleep hormones allow these neural bundles to slow down, to rest and possibly to re-organize, do to maintenance. Caffeine and other stimulants speed up the bus somehow.

We feel and act differently under these influences because our front end processing changes, the continuity of short term memory and of sensual processing changes, thus affecting our sense of self and our relation to our longer term memory and patterns of integrated behaviour.

Musicians and visual artists discover new patterns under the influence. Whether they create "better" work or play better is difficult to say, but I think that the intent is to explore different avenues, which can lead to better work when edited. Write drunk and edit sober said the late Kingsley Amis.

Two Movies about Sex and Love

From my flickr

Both are Canadian made, both are based on autobiographical novels, both are small, relatively unknown, and both treat sex and obsession realistically, without the usual prudish conventions. The theme of lost childhood also runs through both, with scenes in playgrounds and scenes from childhood. The differ in the the gender perspective, which makes the  juxtaposition interesting to me.

The more recent is Lie with Me (2005), and the other is The Favorite Game (2003).

Lie with Me, based on the novel by Tamara Berger, deals with the obsession of a young woman with a stranger, and his reciprocation, and it follows their affair as it evolves. It explores sexual obsession and love, love as questioned and ultimately defined by words and acts, love as visceral need. The point of view is subjective but switches between the lovers. The inevitable weakness is that the viewer cannot understand why their mutual attraction is stronger than attraction to the other players, say the other girlfriend, or the other men she meets. One must accept the coup-de-foudre as it is presented, in documentary fashion. There are few words, the movie is all subtext, and the subtext can be interpreted broadly. It is about the space between lovers, and succeeds in reflecting the mystery of falling in love, the insecurity and excitement, and the release.

The Favorite Game, based on Leonard Cohen's first novel deals with Leo's (as he is called in the movie but not in the book) search for love, and tries to explore the basis for his behaviour through flashbacks. Leo is afraid of commitment but is obsessed with beauty and with sex. The movie follows his affairs from his point of view, making the viewer identify with him maybe too strongly, and the weakness here is that despite his callow and selfish behaviour, he remains a sympathetic and charming fellow. It is a male perspective. The women are well cast, developed as characters, as much as the novel allows, but the movement of the movie leads to an implicit acceptance of Leo's inability to give enough of himself. It is a sort of visual justification of his remoteness and egotism.

Juxtaposing the two points of views above is interesting, in that in Lie with Me, there is a search for more, for extreme attachment, for physical and emotional welding, whereas in the The Favorite Game, there is is search for detachment despite the need for physical intimacy. It is not about sexual possession, only about sexual conquest.

As movies, they suffer from the fact that the viewer is necessarily outside, a manipulated, carried-about observer, and cannot be made to feel what the characters feel. We must watch what goes on in documentary fashion and try to catch a reflection of the subtle emotions at play. The acting, writing and direction are good, but the medium and form are restrictive. Love and sex in movies are extremely difficult to convey accurately. The most sucessful and best example I can think of is Paris Texas, by Wim Wenders. There are no sex scenes, there is only talk and glances, and the point of view is omniscient. Wenders succeeds through word images, landscape, haunting guitar, and almost cliche settings. Strange and beautiful. Eric Rohmer's movies succeed in the same way.

Oh, one last thing, Lie with Me is set in Toronto, in the Annex, and The Favorite Game mostly in Montreal. No significance.

Fake Control Through Cheap Realities

Just reread Susan Sontag's famous book on photography. One of the later essays starts with what could be a comment on the Internet: images are necessary to alleviate the anxieties of modern culture, things like class and money stress, consumerism, emptiness and lack of privacy. Images provide a surrogate sense of power, of ownership and control over reality as well as enough variety to keep desire down, or at least to channel it.

Hey, this is why the Internet is not censored in our culture. It is a pacifier.

We have more than just the photos Sontag was writing about, more of the pseudo-real to keep us occupied and calm. Hell, interactive stuff too, live feeds, tweets that are like ESP antennae hums, and eyes everywhere taking and framing pictures that are pasted to a map. It reduces the biological need for face to face, for real politics, for making art and for ultimately making trouble...except when it is used an means of communications and of organizing. So we need to watch out for that, to suck it up and store it so that we can incriminate those who use it that way.

Keep on doing selfies.