Science and Consciousness

Dialogue Between Two Cultures
Date: November 25, 2002

Topic: Transcription of “Science and Consciousness”

Present:
Erik Fisher (Engineering Management Program)

Arthur Zajonc (Dept. of Physics, University of Amherst)

John Hopkins (Dept. of Fine Arts)

Claudia Van Gervan (Honors Program)

Rolf Norgaard (Program for Writing and Rhetoric)

Gary Bardsley (Interdisciplinary Telecommunications Program)

William West (Dept. of English)

Allan Franklin (Dept. of Physics)

Brian van Way (Herbst Humanities Program)

David Beltran-del-Rio (Dept. of Applied Math)

Mark Benassi (Dept. of Comparative Literature)

Erik Observe that this is our biggest crowd yet for the lecture and one of the smallest yet for our faculty discussion and I think a few people in the faculty group showed up, looked through the windows, gave up and left, not realizing that the seminar was taking place here. So, I don’t know if we’ll have a few people coming in late or not, I know a couple of the members of this group were eagerly passing on some of their observations, that were firing off as a result of reading on e of the three readings so there is certainly a lot of thought going on but I think this will probably be our group. We’re joined by, or will be joined by Brian –

John Maybe we should shift down a little bit so were not so skewed -
Gary I think we ought to upset the natural balance
Rolf Is there water in here by chance?
Erik There’s a fella that is getting a couple glasses of water and that’s the guy I was going to introduce, Brian Van Weigh, I can slip out and get some water. Show of hands, who wants water?
Erik Why don’t we just have a few introductions, Allen would you kick us off?
Allan I’m Allan Franklin, department of physics
Erik Erik Fisher, humanities advisor for the college of engineering
Rolf Rolf Norgaard. I’m with a program for writing and rhetoric and I have a background in comparative literature and rhetorical studies.
Claudia I’m Claudia Van Gervan. I’m rostered with the honors program. I teach writing women’s literature.
Mark I’m Mark Benassi. I’m teaching humanities, still working on my dissertation in translation theory and comparative literature.
Arthur Teach humanities in the engineering school?
Mark Arts and Sciences
Erik But he does have a professional engineering designation
Mark Yeah I used to be an engineer
John My name is John Hopkins, I’m just a visiting professor for the year. I’m teaching in fine arts but I come from geo-physics.
Will I’m Will West I’m in the English department
Gary I’m Gary Bardsley. I’m the interdisciplinary between the telecommunications department and engineering.
Arthur Explain that just a little bit. Interdisciplinary means between what disciplines?
Gary Well we try to incorporate the social sciences, being business, communications theory and integrate that in with the technical theories: signal processing, switching, computers, and information technologies such as these. I’m an engineer by trade, in my mind set at least. But I do try and keep an open mind, and it hurts sometimes.
Arthur Hey I have an undergraduate degree in engineering. University of Michigan, before I switched to physics. So, thank you all for coming how do we proceed?
Erik Well, I’ll just start us off maybe with a question and we’ll se how that goes…
-door opens-
This is Sue, our camera woman. This is Brian Van Way who’s teaching history of technology class four our humanities for engineering program.
Brian And delivering coffee
Erik I guess I’m curious as to what the group made of what two - how do you pronounce his last name, Wemming Tu – was suggesting something, the theme that you picked up on in your talk in separate ways about a sort of yet, as undiscovered yet, as of yet inexperienced way of knowing. Particularly being occasioned by the challenges of understanding quantum physics. But, there’s some suggestion that this may already be in the cards since it seems to be a human capacity or sense of rhetoric or paradigm shift, which oddly the Dali Llama of all people suggested in terms of saying ‘I think there’s something you missed in the experiments.’ Is that something that makes since to people and is that something that you relate to, I guess I want to ask, if in your academic or your personnel work. Does it even enter into where we’ve been talking from in our last few meetings or is it entirely out of left field something that you’re skeptical towards, you’ve rejected, it doesn’t make since to you. Take a temperature reading of where we are at with that idea. We need a locus –
Allan Well I’m skeptical of people who’ve been worrying about quantum mechanics for more than 75 years now and I don’t think we’re any closer to having a coherent interpretation of standard non-relativistic quantum mechanics than we were in the late 1920’s. And so, a lot of smart people, much smarter than I, have thought about it and made very little progress with it. And, I think the experiments have only complicated the thing - The experiments on Bells and Qually, which tell us there can be no local hidden variable theory - just that’s what the experiments say.
Arthur Could you give a 25-word explanation of why it’s so terrible to have a local non-variable.
Allen The thing, as was stated in the readings, the author said, ‘quantum mechanics is a deterministic theory unfortunately it is also a causal.’ What I mean by that, what everybody means, is that you can calculate things precisely. Unfortunately, the only things you can calculate precisely are probability distributions. So the probability is determined but it is only a probability so there is no causal connection that you can say.
Arthur From one microbe into the next microbe into the next –
Allen Yeah. You put a beam of very weak light where you can say its one photon a second through two slits. And, you can then count and detect each photon as it arrives. And only after a large number – where each one arrives, you don’t know, you cannot predict in advance. But what you can predict is that after you have millions of them there will be an interference pattern which is exactly predictable. So that’s what I mean by deterministic and a causal. Now there are certain experiments, and I don’t understand all the mathematics in great detail but, non locality means that you have things that are not linked by a light signal and yet seems to affect one another which goes against at least everything we know about relativity theory. And so the experiments – and other possibilities for the probability is that maybe there are some variables that we don’t see. That something else – there’s another structure underlying it, that we don’t understand, that tells you exactly where each photon is going. And, so what these experiments, in their very complicated and beautifully done, seem to show us is that you cannot construct a theory which involves both hidden variables and events linked by a light signal that is consistent with the outcome of those experiments.
Arthur Einstein really wanted – I mean he was Steve Rosin p.r. experiments – he wanted a world which was more or less like world as we have it, which was ‘I touch this and it moves.’ That’s a local interaction. If I have a magnet and another magnet over here, and I approach it, I may not touch it physically but I imagine then that there is a magnetic field which acts locally on the pole and therefore, causes a force. So, that’s still a local interaction. The field is local to the pole face. And now you have a class of experiments which turn out to be ubiquitous with one mechanics. I mean any time two particles interact; it sets up this paradox, this kind of confusion. Quantum Mechanics is perfectly straight forward how the wave function gets developed and how it propagates and so on. But how to think about it is very elusive -
Allen You can set up two particles together, and they separate, and you decided to measure the z-component of the spin, and you measure it. And, that tells you exactly what the z-component of the other one will be even though they are separated and could not be linked by a light signal. But suppose you decide not to measure the z-component, and you measure the x-component and it determines the x, but you cannot measure the x and z simultaneously. So, what you have over here, seems to have an effect over there.
Arthur - At an arbitrary distance.
? So that’s considered non-local?
Allen Yes
Arthur That’s non-local. The only way you can explain that kind of thing is – if I put a nickel in one hand and a penny in the other, and I shake them up, and I say, ‘You open your hand, and you don’t look and I put one in one hand and the other in the other hand.’ One of you looks and sees the nickel. You know the person’s going to peek immediately. But that was a set up, It was always the nickel and the penny, alright. So, what the experiments have demonstrated is that any account like that, which is local, any such account is – doesn’t work, its impossible. This is Bell’s Theory, which basically says ‘The whole class of theories, which are both local and realistic, and there’s a certain technical meaning to the word realistic, which Einstein wrote, and if you take those two, you basically generate them into a class of such theories.’ That class of theories is eliminated by experiments that have subsequently been done by Aspay and now by many many people. And what that means is that you have correlations of a sort, which - to me it’s like this: There are six cents. I have a nickel and a penny – its six cents. There are two ways the six cents can show up. It can show up this way or it can show up this way. And the only thing that is the same, is the fact that its six cents. And what you were just describing is a similar thing. You know we have an angular momentum state. It’s like six cents. I can decompose that angular momentum state such that I get total angular momentum, say zero, in a couple – lot of different ways. I can measure it this way, in which case in order for it to be zero, it has to show up this way. Or I can measure this way in which case it has to show up this way. Or I can measure there and it has to show up there. So, you pick over here and the other one will comply. Wow, how does it know how to comply? Why doesn’t it just act independently? And you can show if it were acting independently, you wouldn’t get it either? You’d get the wrong correlation structure. So the correlations are perfect in a sense, and for all arbitrary angles they come out with a certain set of definite predictions. So, you can’t compose to yourself a classical object which works this way. This is the problem that then you can say ‘well smart people have thought about this for a long time they haven’t been able to think about it to work that way.’ Now we have quantum computation, which means we have machines that rely on this for their operation, which is a really weird situation because we’ve always been able to look inside a machine like a clock – take it apart – ‘oh so that’s how this works, this gear goes with that gear and so on. Now, first of all, you can’t – you’re not allowed to look inside. Because if you look inside, it collapses to be like a clockwork, it won’t run. So you can’t look. But if you don’t look and you allow this coherent structure of quantum mechanics to propagate thru a set of unitary transformations or basically the program that operates. Then with a certain probabilistic outcome, you don’t get a definitive result the way you do a normal computer, you get a probabilistic result – which can be made highly probable that you’ll get the right solutions. You can check the solutions quickly so you can see when you get the wrong solution. So you develop this structure of a kind of device which cannot be classically thought through, and yet it runs. That’s a very interesting piece, because now you’ve got a man made device, which in some ways formulate – you understand, because you have a full theory of quantum computation, quantum error correction, quantum information theory now. So you can construct instruments that do this work for you. But actually, you still don’t have the kind of understanding that Feynman was talking about, when he said ‘I don’t understand it.’ So, to me, it’s a little bit like this direct perception kind of understanding where you don’t have a direct kind of a per sue like the Galileo experiment, we haven’t gone ‘Oh, I see.’ Then you can say, ‘Why not,’ is there anything in our experience, this would be something from literature, this is actually a place where I would be interested to hear. So here’s the conundrum in science. But, aren’t there things when your working with poetry or literature where there are human experiences, which in a certain sense, we all have intimations of that you can’t define, you can’t codify in a single, well defined manner. So you circle it, you – I don’t know – you know they’re there. Is there anything like that that shows up in your – in your thinking, in your language of understanding and description. Where you basically know its there, you can even work with it, you can have some kind of workman like arrangement with it. But, when you ask what it is, it eludes you?
?’’ In a way in reminds you of in your talk, after thinking about Fish in Livenchops letter and the idea that, hopefully I can remember of it now to make since. But it’s the idea of the creation of the ‘I’. The ‘I’ creates the ‘I’, but in order for it to be the ‘I’ it has to forget that it’s what’s creating the ‘I’. ‘I’ is Identity.
Arthur It’s a little bit – This comes to the Manyanica this other paper which speaks of Buddhist manyatica philosophy where you again have a relational factor, which normally gets left out of the count. But the ‘I’ creates the ‘I’. In other words you have something which is an activity which creates a product. But then, in order for that product to be – if I understood what you’re saying – to be evident, in some ways the activity – your saying – basically gets forgotten. And then you instantiate the ‘I,’ in some ways you reify that, it becomes part of who you are, your persona or something.
?’’ Right. But it’s like you sort of have to forget that that’s what’s happening in order for it to happen. I’d like to -
Arthur Something that’s always hidden in a similar way is continuity of presence or how can we remain sane how can we remain thinking if it involves interactions of neurons in the brain, and do that without a continuous memory but have a continuous memory. How do you explain that? This is where I come out to. And yet I look upon them, because we are starting to look at the experiments that you talked about – a couple photons and photon pairs, we’re finding if you separate them ten miles and change one and the other changes actually. It seems to me that that’s a parallel like with Einstein predicting the contraction of the length and the dilation of time and affects that you have out there. You have those which were later able to be experimentally demonstrated and explained through theories. But, to imagine them before he really had such evidence is just amazing to me. I just can’t imagine how that came about.
?’’’ There’s one other, which I think has some similarities in literary theoretical work: The connection between aesthetics and morality, which on the surface it would seem as though ‘how can it be that aesthetics and morality are connected?’ They are too essentially different but yet they’re intimately connected with each other. And a person’s sense of morality can be changed through a change in their aesthetic sense. Like as a change in a sense of morality can change in our sense of aesthetics. But how is that happening? How can it be that a change in aesthetics changes a moral sense?
Allen Could you give me an example?
?’’’ Uh – in political propaganda, for example, if you want to demonize a certain minority group you present them as being ugly. And so, somehow we want to associate the ugly with the bad.
Allen That I understand. What’s Frankenstein’s monster’s crime? It’s that he’s ugly. The whole thing - he’s the nicest, most admirable character in the whole book, yet he gets treated badly – why? Because he is indeed ugly.
Arthur(?) But you could do the same thing to say that if he was a Jew. I mean they’re not on the surface ugly so you situate them in a context where the reading, even if it’s the normal Jewish face, is red so ugly. So the identity is transferred, the Frankensteinian kind of fate, gets transferred even when it’s just a normal face of the black or the Jew or whatever minority it is that’s being oppressed. So the aesthetic is one where even when they see a normal person, they read that face - that normal face - as being, quote, ugly, and therefore morally reprehensible and so forth. That would take some work that would be the propaganda where you would set out to shift people’s aesthetic regarding the black, or the Jew, or the white or whatever it may be. You could see that that’s an interesting thing – In fact it could work the other way. Let’s imagine that you’re an artist and you discovered through your practice of – sort of sazon type practice, you developed an ability to see connections that most people do not see. The way in which a certain set of colors or a certain set of relationships exist in the world and so thru that capacity, which is an aesthetic capacity, you do a transference and I could imagine that there are moral judgments which may require a similar kind of capacity. If there is this sort of translation towards the other way, it could also be that it relates to expanded moral sensibility. This goes to a biased -
? Is it essential that when you run into a problem like that, where you have a conditional change at distance, isn’t that maybe just an expression of the problem or the limit of the representation, the model of ‘something’ and ‘it’ itself.
Arthur I actually think that’s what it is. One way I think about it is – What it presumes is that you can build up with what spin zero means, or angular momentum zero means, is that there are a set of parts, pre-existing parts each one of which has a pre-existing attribute called angular momentum, such that when you add them up they add to zero. So you start with the concept of parts, and from that you construct a global property, called the ‘total angular momentum state.’ The problem is in quantum mechanics if there are say two ways of doing that you take the first way of doing it and add it up with the second way of doing it. And that’s the entity you have the superposition of now a two particle wave function. Ok so what you’ve done is that you’re still in the language of mathematics, you still working with parts, but now you’ve done it in a way which conflates the two options, sort of binds them together into what is called an entangled state. And then that’s the entity that propagates, and of course you get to pick the basis on which you do the decomposition. So, it’s this kind of holistic entity that propagating. But you’re mentally composing it from underneath, from parts. Now if you take the quantum computer, the reason it gets its exponential speed up – one of a number of things that happen- but one of the reasons is because it doesn’t work that way. It doesn’t ask questions it doesn’t need answers to. It doesn’t presuppose that the world is made of parts. So, rather than having to do all the calculations for all the parts it just grocks the global attribute. You can compose any way you want. In fact, if you insist on knowing how it’s composed, the computer crashes and you won’t get the speed up. So its got to be ambiguous how its composed. The classic example of this is the Deutch and Joseph problem it’s sort of called the fair and unfair coin problem. You take a coin, you don’t know if it’s a fair coin or an unfair coin – it could be heads-heads, tails-tails, heads-tails, or tails-heads – there are four options. I hold up the coin, you see one coin – you still don’t know if it’s a fair or unfair coin – all you see is heads. You’re going to have to flip it around and see the other side and you know. And so the fairness of the coin is determined by the two sides that you see. You have to see both sides to see it. That’s actually two bits of information, and we originally only asked for one bit, namely ‘is it fair or unfair.’ I don’t care about whether its heads-heads or tails-tails, I just want to know it’s unfair? You had to compose it by being heads-heads/tails-tails. So then you have to devise a machine which doesn’t care whether its heads-heads/tails-tails only cares whether its fair or unfair. Take the double slit experiment. If you change phase the same in both you get no change in the interference pattern. So if its heads-heads or tails-tails you’ll get the same interference pattern. If it’s opposite – if its heads-tails or tails-heads - you’ll get a shift. Now, if you say ‘well which one it is, is it really heads-heads/tails-tails,’ you’ll disturb the measurement and it won’t work, the experiment won’t run. So you need the ambiguity. And then, in a single experiment, you just run your experiment once thru, and you get the interference pattern, and you see immediately without having to do anything else. So you get this ‘speed-up’, and what that – to me, going back to what you’re saying – is the model that we’re using have a set of assumptions. Basically it’s the assumption that the world is built up from parts, and if you were to give standing to the wholes, and say listen it’s not about the particle locally having these attributes, it’s the system globally having this attribute. The way it shows up is entirely dependent on the kind of question you ask. Namely ‘ok I’m going to put the measuring apparatus this way, or I’m going put it this way.’ Well that’s your choice, that’s the decomposition you chose, well then, I’ll show up that way. You project back from that measurement to the pre-existing entity, it’s again like that prison, its produced in a prison I would say. So, there’s an interaction which takes place, and it falls out in a particular way. So, but then you push the parts back to the origins of the things, we say it all started out as parts. So, in the case -
Allen We can do the experiment with a spin zero nucleus, and have it emit two photons, and still end up spin zero. You can start with a single entity, and then have here - so I don’t know, it’s knot just putting two particles together with spin-zero state. You have the original entity in a spin-zero state. There’s a small technical detail.
Arthur We can talk about it later. I tend to think, if you look at the way in which the EPR experiments – You do have what you might consider the sixth sense. There are certain things which are drilled at. There are two particles, so it’s a two particle state, and it has, mobile property of a particular side, a particular type. To presume that it’s made of parts, which have individual attributes, by in large most of the people I know in the field - not everybody but I know some people in the field who are prominent - don’t talk that way any more. It’s a global attribute, you don’t think about it in terms of the pre-existing particulars. This connects also to the question that has been issued here about Einstein’s condelation wave contractions, ‘so what is the length of the object?’ If all frames of reference are in the same weight, and you don’t privilege one over the other, what is its length? Is it the proper length becomes a length? Or could you say well the observer has to be in that frame. Well its just one observer, he doesn’t know of any particular privilege. So every observer has a length which they will measure according to perfectly well defined set of rules, which they all use, everybody uses. So the idea of reifying a length as being ‘the length,’ well it’s again a presumption. Or time intervals, or notions of instant simultaneity. There are a whole set of perfectly pragmatic ways of speaking but when you work at those extremes they simply become provably, demonstratively, erroneous. What are the take-home points from that – what do you make out of that? I think it all points to this paper – the reason I like this paper, “Careful Metaphysical Illusions”, is more towards the end where he is talking about relations – the relational nature of biophysics and the relational nature of mayamical philosophy, which he knows as much as you could know about Kant. But Erik asked for a hard paper. So this is one I liked even if I can’t reproduce its argument. Michelle was with us at Darms Eye. He’s brilliant, he’s got a PHD in physics, he’s got an MD degree and a PHD in philosophy.
Erik This might be a trite literary example, but I’ve just been looking for things, and I hit upon something from Shakespeare’s “Antony and Cleopatra,” maybe we’ll get a better quote. Something to the effect of Cleopatra says to her attendant ‘If Antony comes and he’s happy, tell him I’m sick. If he’s glum, tell him I’m dancing.’ This necessary non-quarieness you might call complimentary and another setting is necessary for the whole of this – however one characterizes the romantic, or lustful, relationship to exist.
Allen It doesn’t change her state. That’s the difference. It’s only changing the report of the state.
? But, it changes his state in relationship to her, substantially.
? And it changes the outcome.
? Pursuing the literary analog, I think narrative structures had a lot to do in terms of how you would have multiple frames of reference competing with each other, and also the role of irony in general romanticism has an unsettling function.
? It also dawned on me – I didn’t realize it in reading this article that it was talking about this aesthetic – morality connection is that is one of the issues Kant discusses a little bit in the critique of pure reason in section – I think I need to go back and read this.
Arthur Coming back to this, your example of Antony and Cleopatra, I’m interested in what’s the role of relationship? The relationship in the case of these two entangled particles. They have kind of identity which is, by virtue of the fact of their interaction, or their common production source, whatever it might be. But there’s a kind of state which is produced which is not simply reducible to a sum of the parts, but which has its own character, it has a structure. So the identity is not just a simple sum of the parts but it has integrity. The same kind of thing, you might say, there’s a relational structure in relativity, which is really essential. It’s not incidental. The way things are, is really a reflection of states of motion, relative motion.
Allen Except for the speed of light.
Arthur Except for the speed of light. There are certain variances in special relativity. Those in variance also get more complicated when you get to general relativity. Then you can ask what’s the role of the invariance structure in a particular theory or something like that. But, nonetheless this principle of relational identity as opposed to the notion of objects, which are free of relationships, that are just out there autonomous. They have their own identity structure, inherit of themselves, as opposed to arising from some kind of relational structure. This must be – You think ‘Ok in human affairs, as reflected in each of your disciplines, is it always possible to decompose the world into this person plays in a kind of cardboard cutout kind of way, this role, this one is this character and that’s this character. And they’re kind of one-dimensional, or are they complicated, and is the kind of character they are, what you were describing, depending on their context? So that’s it’s a very mobile and sort of organic set of connections as opposed to a rather inert and mechanical set of point-wise relationships- here’s the role that I play when I come in. There’s the role you play when you come in. I would think a good author will work with that in real ways. So it’s not capricious completely. But the paradox and irony –
? It’s important what your saying, because our own minds are limited in terms of over cook it. So, we have to form a series of approximations, and the approximation that your putting into might be because of lack of knowledge of physical laws – the speed of light, which isn’t a constant, it depends on the medium that your in, there isn’t an absolute maximum, but most of the things that we’re dealing with maybe that we don’t have the mathematics of the conceptual relationships to be able to handle what’s in there. I think about - we deal with the economists and physicist and everything else. If you ask an economist what’s the value of trying to quash two particles together, there is no value to an economist and yet physicists says well what value is there to try to imagine a perfect state of competitions, which doesn’t exist either, and so it seems like as if we have to swing our mind process into one extreme or another or try and find a happy medium, we’re still limited as to the number of dimensions or variables or factors we take into account.
? I was thinking, when you said that the constitution of the ‘I,’ the ego, I mean to some extent it’s an issue of scale, and we keep choosing what we are going to look at. So if I’m a sociologist I would look at this village or if I’m an anthropologist maybe I’ll look at this culture or maybe I’ll look at this individual. Also, the other thing it makes me think of is that book that the two guys from Davis talked about, “Conscilience,” by Wilson. And one of the things that I thought was fabulous there was in sort of 20 pages he sort of figured out how literature worked. It’s Darwinian. It wasn’t exactly that he missed the point except that sort of told you what all literature as a sort of global body, all artistic production is good for, but it doesn’t say anything about this poem, this statue. But it is sort of like we make these intentional or unintentional – we sort of slice things up differently, and then, within that small field we attribute parts. We say, ‘Oh Antony and Cleopatra, that’s such a great whole of Shakespeare or Elizabethan Drama or the latent plays of Shakespeare or Western Theatre.
Erik And that’s a valid observation on one level, and yet there’s another level too. The same way you take a good poem and a bad poem or a good piece of music and a bad piece of music. You analyze them both to understand how one works and then it’s no longer beautiful.
Allen I want to know if in these post modern times whether you’re allowed to say what a good poem really is.
Erik No I’m really not. But there is a phenomenon - Sometimes those observations actually overwhelm the text that you’re looking at and reduce it. Simple. So that’s all you see. Sometimes all they do is enhance it.
? I think where one is using a model that has been imposed on by, for example, like collective – some social process that imposes the parameters of the model on your root, raw, central absorbing of the energy of the universe in hand. So you’re allowing that to kind of impress itself on your own feelings, your self-cognizance. And I think that one certain aspect push-it, push away on socializing models and then sort of apprehend this thing from its root somehow. I’m not very clear on that.
Allen I had to question that author, the thing about perceiving. Does that pursue that Galileo perceives the parabola? I disagree strongly. Galileo only perceives the parabola after he’s done the calculations. You don’t see a parabola. Kepler did no see the ellipse. He saw the ellipse after 71 different calculations of Mars’ orbit when he realized that the ellipse wasn’t an approximations of the oval but that it was the ellipse itself and so you see a curve, you don’t see a parabola.
Arthur When Newton says, I saw the moon passing overhead, and the apple falling as the same thing he really wasn’t seeing it. It’s not to say that he didn’t have to do a whole hell of a lot of calculations to prove it to himself.
Allen No. My guess is that he does make a leap but he doesn’t see it. He sees it in here.
? He sees it through mathematics.
Allen My guess is that Newton hadn’t calculated it yet. He doesn’t find the acceleration of the moon until later. He says that the apple and the moon are the same and then he calculates it later. But, Galileo doesn’t see a parabola. He sees a curve. I never see a parabola. I know it’s a parabola maybe to a certain good approximation, that it’s a parabola. But if you said what the curve is, I couldn’t tell you.
? It’s an expression of the archetypical knowing
?’ How is it you teach it?
Allen I teach it because I show –
Arthur How do you teach it though? What’s the technique?
Allen I do the calculation. I show that if –
Arthur You do the calculation in a way that they will see that it’s a parabola?
Allen I do start with ‘x is equal to v-zero, x-t, and y is equal to v-zero, y-t plus ½ a-t-squared and then I plug in – I start with that as the assumption that it’s a combination of those two and then show if that’s the case then it is a parabola.
Arthur But in some ways that’s what I would mean by ‘seeing’. You can see it in a variety of different ways but the point is your hand calculator would do that work for you. You can just push the solve button. It’s not seeing anything. I would say the student, in order for them to move from doing the hand calculation, to the point where they say, ok now the composition of this plus that has a certain form which is a general structure.
Allen Ah, so seeing then becomes understanding. I’ll agree on that but -
Arthur It may happen that in one case its Newton saying ‘I saw it’ or Galileo. And again you don’t know when they report it in some of these stories are hypocritical and made up after the fact. But the synchronous motion of a pendulum and paduar.
Allen: Todd Whiteside said that he could identify the tree. There are rumors that he said that, that he knew where the tree was, where the apple fell.
Arthur I think that the goal in these cases is – I do think obviously that there is a place for the computation, and sometimes very often especially in the case of the parabola or geometrical forms. You’ve got to say it not only looks this way but it actually is a parabola. We mean something very special by ‘parabola.’ Was it your book where when you’re describing inertia you talk about the history of this problem and the way people who draw these wonderful curves when they draw they go up and the inertia stops and they run out of impetus and then it drops and that’s the way they saw it.
Allen It’s the Woody Wood Pecker concept. Not the Woody but Road Runner, where Wile E. Coyote runs straight out, suddenly realizes he is subject to gravity and falls straight down. Yeah I get that. I don’t think I showed these pictures. Earlier work that nobody remembers.
? I’d like to come back to the pedagogical question which I think is really central because a lot of times understanding happens as a sort of holistic moment. And the calculation that be behind that and there are difference discrete parts, elements of worrying of some sort of experience there. But the insight occurs often in mysterious ways in which students sort of put things together. The trick of course is that no one student will put it together the same way and get the same sort of insight. But the insight does occur at that kind of global holistic moment
? That seems to happen over and over again for one the same student. You see it again differently; it seems like every time you look at the problem.
Allen Well you do get the flat head every so often, ‘Oh my God, I understand’
?’ And you missed it for so long. Once you talked it through with your colleagues, everybody’s doing this
Allen If you ever look there is a very interesting book which nobody reads anymore in philosophy of science, Russel Hansen’s ‘Patterns of Discovery.’ Nobody reads Russ Hansen anymore. But he has all these optical illusions. It’s the old woman and the young woman. The rabbit and the bird. Then there’s one which is up until a certain point looked to be just ink blots, and its supposed to be the face of Christ, and I was explaining once to a student that I can’t see and in the middle of that explanation I saw it. And he explains, he says – he goes through this long explanation where you know ‘this is the beard and this – and still couldn’t see it until. In the old exploratorium, Frank Oppenheimer’s great museum of perception in San Francisco there are things you can look at through the old 3D glasses the two polarizers, and you don’t see the pattern for a while you can reduce it by doing it over and over again but you can’t get the time to see it at zero.
Arthur I use often these random stereo waves, ‘Magic Eye’, and I don’t know if you’re familiar with these magic eyes. It’s a popular think…and you look at it – its just random dots and if you train yourself to basically focus and look at infinity or hold it up to your nose so that you’re forced to look past it, and then gradually pull it out, all of a sudden this magnificent 3D picture comes out, always there. And it’s a wonderful metaphor for this moment where something comes into view which you just didn’t know how to see it, how to move your eyes. And I do think when you read the biographies and their autobiographies of certain scientists…the depths of struggle they have with -