A work in progress.
Topic of Discussion: (As posted by Daedalus on the clan's MotD board.)
The failure of science to win hearts and minds has two causes. The first is that the many forms of mysticism have made better use of marketing and political influence. The second, which the first relies upon, is that the human mind craves certainty, and will purchase it at the cost of the increased likelihood of being in error. Science, and the philosophy behind it, will tolerate 'big picture' uncertainty to achieve a reduction in error. The man on the Clapham omnibus craves day to day certainty, and as science fails to deliver it he clings to superstition, myth and religion.
Alexander Quandle considers Daedalus' thought on science and religion. "Whilst I suspect that you may have a point there, there are other reasons as well. People seem to want to see a greater intelligence at work. Consider the conspiracy theorists, especially the wilder end. Princess Di gets killed in a car crash, and she must have been assassinated by someone. Can't just be contingent chance."
"Like Einstein said 'God does not play dice with the universe.' And that was Einstein; he wasn't superstitious as a rule. A lot of people feel that way. Also, people who try to be honest very often desperately want to believe that 'Cheats never prosper', whereas experience sadly belies this."
"I have found myself almost believing in an afterlife where the 'good' are rewarded and the 'bad' punished, when someone has taken the piss, and I feel that they're laughing at me. Clearly nothing more than wishful thinking, but it can be quite powerful at the time. There's probably lots of other things going on as well."
Alexander Quandle muses further, but has nothing more to add for the moment.
Alexander Quandle pops his head back in the clan halls. "Another point, the difference between the abstract theory of science, and the 'sociology' of science (for want of a better word) can be quite startling. Richard Dawkins, in 'The God Delusion' suddenly knocks all standards of science on the head, and uses the same modes of argument as the most rabid of creationists. With absolute certainty. Yet he would be seen by many to be on the side of science not religion, and not unreasonably so since the whole content of the book purports to be pro-science and anti-religion. The whole spirit of the book is profoundly anti-science however.
Also myth is used in science exposition. I learnt some chemistry at school (way back when I was a nipper). Took it as a subject from the age of fourteen to sixteen, took exams, then went on to take it further from sixteen to eighteen. One of the first things they told us there, was that 95% of what we'd earlier learnt was wrong. Now we'd learn things which were only 90% wrong. Of course if I was following The God Delusion's mode of argument, I'd be forced to conclude that the whole of science is rubbish. I didn't do anything of the sort of course, I just accepted that you need to build up to understanding something, and that the level you're learning is where you need to be at that moment in time. It's only going to be an approximation. All you can hope for is better and better approximations. And that is exactly what myth is.
In the case of religion, some people need to think of one or many gods as independent physical entities much like themselves, when they progress, if they progress, they obtain deeper and deeper insights into what religion is, and what 'God' is. To reject the whole of religion on the basis of understanding God as a physical being is as absurd as rejecting the whole of science because basic mechanics treats billiard balls as hard objects, but quantum mechanics disagrees. So to return to the point, myth is integral to the understanding of science. In the other hand, many deeply religious people are also very rational people as well. Um I seem to have ranted on a bit there, not entirely coherently either.
Alexander Quandle realises that he has got a bit overexcited, and goes to use the Onsen to calm himself down a bit.
LATER IN DAY 2.
Daedalus agrees with most of what Alexander has said, but has some reservations. "Einstein wrote "The old one does not play dice.." While this is usually paraphrased as 'God', it suggests an ironic reference to his dismissal of an anthropic concept of a deity. The (mis)quote is often cited as a trump card by deists, but rests on an assumed reverence of Einstein as the father figure of.."
Alexander Quandle gets out of the Onsen, and sees Daedalus. "Ah hello there old bean. Haven't actually run into anyone here in a while, we all seem to come and go at different times."
Daedalus says, ".. post Newtonian physics, that I'm not sure Einstein would have been comfortable with. Even if Einstein was at heart a deist, what of it? The man was, at the end of the day, just a man."
Daedalus pauses in his ramblings when he sees a freshly 'onsened' (?) Alexander. "Hello Alexander. Good to see you. Yes, time zones are playing havoc with us."
Alexander Quandle replies. "That's very true. And I wasn't trying to imply that Einstein was a deist (although you're right of course, what he actually believed is irrelevant, it's why he believed it that is potentially interesting.) I was trying to use this as an example of someone who felt that things had to happen for a reason, it was almost an article of faith that led him to reject Quantum mechanics. In his case his 'ultimate cause' if you will, was deterministic laws. In many other peoples case they pin this belief that 'everything happens for a reason' on a 'God', and that is one of the foundation stones for religion and superstition, and why it's still so strong in this 'age of science'."
Daedalus says, "Indeed, and (it) is just this seeking a first cause, which Einstein unsuccessfully sought in a 'grand unified theory of everything', that my original message alludes to: "The desire for certainty". Einstein was horrified at Heisenberg's Uncertainty Principle exactly because it undermined Einstein's quest for certainty, the natural response of a mathematician. Likewise, the conspiracy theorists, apart from their love of the dramatic, have a kind of certainty imbedded in the irrefutable nature of their claims. And your comments about Dawkins are an excellent example of how this can lead to confusion. Dawkins, as you point out, is clearly as much a zealot as the Pope is."
Alexander Quandle says "Hmm, I think we're starting to argue the same side now, or else I'm coming round to your way of thinking. It's a sort of certainty in the working of the universe rather than a personal certainty that you know what is going on. Hmm. The conspiracy theorists don't have personal certainty; they grow and expand their theories, (although they're subject to the same confirmational bias that we all are.) rather the conspiracists believe in an overarching conspiracy controlling everything. A certainty in human affairs, as it were. This seems to be quite a fundamental human need then, rather than down to marketing and political influence."
Daedalus says, "I would suggest that conspiracy theorists form a sort of church of 'demonisation', and derive the same sort of comfort as deists do. They both depend on their theories being irrefutable as much as.."
Alexander Quandle: "I also think that superstition, myth, and religion are quite different things (albeit overlapping things). Myth is the telling of explanatory stories, often ones with deeper meanings."
Daedalus says, "..plausible. The political influence I refer to can be seen in the rise and rise of the religious right in the US, and historically in the influence of the church in matters of state in Europe .."
Alexander Quandle "Sorry, I interrupted there."
Daedalus says, ".. prior to the so called 'Enlightenment'. The marketing is exemplified in the old Catholic maxim: "Give us a child until he is 7, and he is ours for life". By exerting influence on education, the bastion of religious thought undermines the attempt to instil rational thought as authoritative. Phew .. sorry .. that was a mouthful."
Daedalus grimaces as his narrator taps impatiently on his watch. "Yes yes, I'm coming.. soon.. ish. Alexander, I'm afraid I'll have to ask for an adjournment. He .." with a nod to the 4th wall, ".. is rabbiting on about some "RL priorities."
Lance Corporal Alexander Quandle smiles. "I've got someone similar looking over my shoulder, saying much the same. Till next time then."
Daedalus says, "Feel free to continue 'musing out loud' here, and I'll pick it up later. Or we could shift it to the Enquirer forum, and start a 'controversial' thread?"
Daedalus says, "Later then. Enjoyed the chat! Byeeee."
Alexander Quandle has been thinking, and goes off on one into a prepared speech:
Myths in Science
Ahem. *clears throat*. You chaps and chapesses may recall that D. and I (that's Alexander Quandle for those who haven't guessed) were debating what could loosely be described as 'Science vs. Religion, Myth and Superstition'. I suggested that science too had it's myths, and I feel it's incumbent on me to give examples. This one first, and then I'll go on to give another.
Humans are descended from apes. Utter balderdash. We and the apes are descended from a common ancestor. Just because that ancestor doesn't look all that human doesn't mean that it must therefore be ape. Present the same picture to apes, and they'd probably conclude that apes descended from humans.
This seems to be wrapped up with humans rather petty ego, which always wants to be 'the best' at everything. (I must stress here that I'm as bad as anyone at this.) In this case we're a 'natural improvement' on apes. To paraphrase Douglas Adams, we're more intelligent than apes because we've got on and invented fire (?) and cities and nuclear weapons. All the apes have ever done is muck about in the woods enjoying themselves.
We've managed to get over the fact that our planet isn't at the centre of the universe. We've managed to move on from believing that our species was created seperately. But ultimately, we still haven't really managed to accept that we're not the crowning glory of creation.
In one sense humans are 'special' to me. I'm one of them, which makes them uniquely fascinating. We're all the centre of our own universe.
So. Myth as comfort to the ego, to save us from having to face reality.
Daedalus is pleased with his efforts. "Ta da .. cold room access from the kitchen!" He makes a coffee and reclines on a couch to contemplate Alexander's discussion on myths. He muses out loud .. "I agree that there are myths in science, but I'm not sure that the claim of superiority of homo sapiens over other species is one of them. I'd argue that it's more of a failure to understand the process of evolution." Resisting the urge to make a joke about it being a 'mythunderstanding', he continues: "The nature and purpose of myths is a rich field in itself."
Daedalus says, "For anthropologists, a myth is a value laden, and driven, narrative intended to explain or justify events or social constructs. I'm referring to the ideas of Malinowski and Levi-Strauss here. So the 'myth' of human primacy is supported by the misconstrued implications of Darwinian evolution. But this is not a myth 'within' science, as I understand it. Rather it's an attempt to incorporate science as an authoritive basis for the myth. What I think is significant about the claim of species superiority is what it suggests about how we deal with those 'not like us'."
Daedalus continues: "This is not limited to species-ism. It extends to sexism, racism, .. any relationship that can be described as 'those people (or things) are not one of us'. "How do we, or perhaps how should we deal with 'the other'? I suspect there is an argument to be made that the human psyche seeks out other-ness as a means of self identification, or adding value to our own membership of a group." He takes a sip from his coffee and adds: "But that's a different topic, perhaps for a later discussion? I can think of two myths within science and both serve to explain events. Namely: 'How did (name) think of that?'
One is that Newton 'discovered' gravity when an apple fell from a tree and hit him on the head. The other is that Archimedes 'discovered' buoyancy when he got into a bath. Both of these have an element of historical truth .. Newton often reposed in a orchard, and Archimedes was interested in displacement but there is no, or at best very little, evidence of the occurrence of the events described in the myths. They persist because they offer an explanation of the 'Eureka' moment."
Daedalus says, "I could go on and on about this." He pauses to chuckle: "In fact I already have .. but my point is that these myths are about science, not scientific in and of themselves. Indeed, I might go so far as to suggest that to speak of a 'scientific myth' is self contradictory. The two concepts reflect essentially different ways of thinking, and reasons for doing so."
Daedalus puts down his now empty coffee mug and sighs. He really must resist the temptation to bang on for ages about this stuff.
Sergeant Alexander Quandle considers D.'s words on myth. "Not quite sure what constitutes 'value laden'; is that moral values? As far as 'narrative intended to explain events' goes, that sounds like exactly science. Aren't those chaps always wanting an explanatory model? General relativity has 'curved spacetime'. Pure myth. In fact G.R. is a whole bunch of whacking great clever looking equations. I saw them once. Fair gave me the collywobbles just looking at them. Had to sit down to get my breath back. All it really says is - if you feed one collection of numbers in at one end, then you get a different collection of numbers out at the other, and these tell you what you're going to see if you look in the right place in the right way. All this 'curved spacetime' is what gives these numbers meaning. Helps those physicist chappies see what they're doing. Very powerful tool too, I'm sure."
Alexander Quandle notes "In modern culture, the word 'myth' has acquired the connotation incorrect (in some sense). Think for example of the term 'modern myth' to mean story purported to be true, but which, in fact, isn't."
Daedalus says: "Hmm, I interpret 'value laden', in the sense used by those anthropology chappies, to refer to community (in whatever scale) values, so perhaps ethical values rather than personal morals. Although that might be splitting hairs between 'morals' and 'ethics'. As for science being a narrative to explain events etc., yes, I'd agree it's quite apt. Does this mean that there is no difference between myth and science? I would disagree. Up to this point we have been using the word 'science' in a vague and widely encompassing way, and I invite someone to narrow it down."
Daedalus says, "In the meantime, I wonder if we're heading towards a distinction in types of 'knowledge'? Does this entail questions about how we value different 'classes' of knowledge? Why yes, I think it does. And I empathise with your comments about pure mathematics and theoretical physics. I have been known to suggest that pure mathematics is a way of forming limited models of what is happening, .."
Alexander Quandle staggers in from a hard days jungle fighting. He is absolutely exhausted and looking forward to a good soak in the onsen. A plan he puts into effect.
Daedalus continues ".. and that those models should not be considered a complete picture of reality. Not a point of view the practitioners were inclined to accept readily, I might say." Daedalus smiles wryly, and concludes: "But then, along with religious practitioners and post-modernists, they are simply sitting ducks for a game of 'Devil's Advocate', if that's your inclination."
Alexander Quandle calls from the onsen. "I would agree that science is different from myth. I was trying to suggest that science has an element of myth in it. I would also suggest that 'primitive' myth is (in part) an attempt to understand the world around them. Thunder and lightening is some hairy chap getting annoyed and so on. Science has added concepts of testability and predictive power. (And jolly good ideas they are too.) It seems to me that maths has become rather more abstract than that. Physics is not a complete description of reality. Maths isn't a description of reality at all. It's an abstract language, which is used by physicists (amongst others.) The divorce between the can be pin pointed to that lecture by Riemann in 1854: "On the Foundations of Geometry". That's when mathematics started looking at alternative, 'Non-Euclidean' geometries, without the constraint of worrying about how real they are. Of course later on, these got used to provide descriptions of the universe at large. But how accurate these descriptions are is of no theoretical interest to mathematicians." (That is, as you might expect, a simplifying myth(!), but not a bad approximation.)
Daedalus smiles as the sound of a rubber duck being squeezed punctuates Alexander's thoughts. He may only be imagining that though. Daedalus headtilts slightly. "Are you quite sure that accuracy is of no interest to mathematicians?"
Alexander Quandle: "Different types of knowledge? Well yes. It's occurred to me that one classification scheme is how 'truth' is measured. Particle physics and chemistry, where you can test things by manipulation. Astronomy and economics where you're far more constrained, and have to wait for evidence to turn up. Courts of law. Personal experience, and so on."
Daedalus says, ".. and perhaps myth and metaphysics. Art? What constitutes 'knowledge'?"
Alexander Quandle is indeed playing with his rubber duck. He finds that it helps him think. "No. Not whilst wearing their mathematician hats at any rate." Alexander is talking figuratively here. Obviously. But accuracy is the wrong word. It's like asking if a grammarian is particularly interested in the accuracy of a description of reality written in a natural language."
Daedalus may have been playing with the notion that 'accuracy' could be argued as being an entirely mathematical concept.
Sergeant Alexander Quandle: "Well our hypothetical grammarian probably is. But not as a grammarian. The technical correctness of the grammar is his domain, not whether a politician is telling the truth or not. A mathematician is just interested in the beautiful logical structure that the physicists have failed to build. Mathematicians routinely think in 3,4,5, or n dimensional space."
Daedalus says, "Doesn't the grammarian, as distinct from the wider discipline of linguistics, measure accuracy against a set of rules?"
Alexander Quandle goes on: "Just because one dimension or another turns out to be a better model for this universe we happen to find ourselves in won't stop them playing with other dimensions. Infinite dimensions often."
Daedalus looks as if distracted from beyond the 4th wall, and may be away for a few minutes.
Alexander Quandle replies: "Well yes, I suppose you could argue that accuracy in maths point if you wanted. Although that's not the word normally used. Logical rigour is a phrase more often bandied about."
Alexander Quandle is playing with his duck, and waffling on as per usual. "I suppose that the mathematicians do so often seem to moan about the physicists using their tools badly. Physicists don't ever do any maths themselves, they just use the tools that mathematicians make. And they usually use them badly, and end up making an appalling mess of the whole thing. Look at calculus. First done by Newton and Liebnitz. Very sloppy 'Hey wow man! This seems to work!' Didn't check to make sure at all. Of course when Newton and Liebnitz and Bernoulli did it, they were sure-footed and knew what they were doing. Other less talented folk tried using it. Terrible time! Mistakes everywhere. Following all of the formal rules they'd been (taught) blindly. As physicists are apt to do. Took till the nineteenth century with Cauchy and Riemann (again) before calculus was put on a proper footing."
Alexander Quandle realises that he has strayed from the subject somewhat, and also wonders where he's got this knowledge of maths history from all of a sudden. He shrugs his shoulders. Daedalus grins silently as the sound of Alexander's rubber duck is joined by the 'clip clop' of a hobby horse. He's quite enjoying Alexander's ruminations though!
Daedalus says, "So, to link back to our previous area, you're saying that mathematics is a specific language, and reflects a particular value of a class of knowledge?"
Alexander Quandle: "As for mathematical models forming a complete description of reality, well, if anyone tells me that what I feel when I see a pretty woman can be modelled mathematically, then I'll laugh at them."
Daedalus is a creature of very little mathematical brainliness.
Alexander Quandle is distracted back from his thoughts of pretty women. "Oh. Yes. A specific language. I wasn't actually thinking about it being a class of knowledge, but I wouldn't disagree with that either."
Alexander Quandle had noticed that D. seemed to know what he was on about when he was talking about lenses. He was using a mathematical language then. A very specific typesetting language from pre-EMP times.
Daedalus says: "So, can we say that,.. and I'm making this up as I go along so I may discard it later, .. a body of knowledge is a set of ideas about which 'we' feel .. confident?"
Alexander Quandle asks "Did you ask for a precise definition of science? Well there are at least two. Do you want the abstract theoretical 'Falsifiable theories and testing' definition.."
Daedalus quite possibly filched the whole of that lens theory from a pre-EMP source, and thought that crediting the source would only be a source of confusion. He did once briefly study photography though.
Alexander Quandle: "A set of ideas about which 'we' feel confident? Yes that seems like a good working definition. Plato or Aristotle or one of those old chappies defined knowledge as 'Justified, true, belief.' Although defining knowledge in terms of 'true', means that you're going to get some very circular thinking when trying to decide if you know something. Biting your own tail straight away."
Daedalus used 'we' as a stand in for 'the adherents or advocates of that set of ideas'. It was easier to type, and fit within the word limit. (Murmers: "Oh dross practicality, that limits our expressions so")
Alexander Quandle: "Or so it seems to me anyway. As you said in a particularly thoughtful message of the day once: 'One must always remember the difference between truth, fact, and reality'."
Alexander Quandle: "Well yes. That is more or less what I took 'we' to mean." He realises that the quote from D., while relevant, was not directly what he was saying.
Daedalus once wrote a paper outlining his thoughts on the distinctions between 'Truth', 'Fact' and 'Reality'. He was quite proud of it at the time. (Daedalus laughs as the synchronicity gremlin intervenes.)
Alexander Quandle also realises that he has been playing with his duck in the onsen for far longer than he intended. He gets out and hunts for a towel, feeling rather prune like.
Daedalus says, "To summarise, I suggested that Truth is what I believe, Fact is what we agree on, and Reality is what is actually going on 'out there'."
Alexander Quandle is falling asleep now. He is going to have to wonder home to bed soon.
Daedalus says, "The summary, as is so often the case, doesn't really do justice to the argument."
Alexander Quandle: "Slightly different idea of truth than normal surely? Are you saying that in the twelfth century it was true that the Earth was flat? But now it's untrue that the Earth was flat then?"
Daedalus also has to be away soon .. RL is getting persistent in its demands for attention.
Daedalus says, "By defining the terms so, yes, that is a logical consequence. Though I might say that it was a Truth then, and isn't, for me at least, now."
Alexander Quandle : "I'd have used the words 'truth' and 'reality' the other way round myself. Fact is socially constructed? I suppose. The etymology of the word agrees with that."
Daedalus says: "Consider that we don't prosecute someone for perjury if what they say under oath is not what is later accepted as 'fact'. They weren't lying; they were relating 'truth' as they knew it .. but neither may reflect what 'really' happened."
Alexander Quandle yawns whilst putting on a fresh pair of trousers. "Well. It's been a fascinating chat, but I really must be going. Till next time then. Bye bye." Daedalus nods in agreement. "'Til later, Alexander."
Alexander Quandle is distracted (again) by the last statement. "That's a fair point. I take back what I said."
Daedalus muses as he wanders out: "That is, we don't prosecute for perjury just because what is said ... is not what is later accepted ..
(From Clan MotD)
Mathematics as perfect truth. Again, utter balderdash. As a mathematician myself let me let you in on a secret. Mathematics is a human activity, done by human beings. Humans aren't perfect, and so maths isn't perfect. Mathematics does not exist in some perfect realm of Platonic Idealism, or if it does, then it's not something that we can ever know anything about. Maths without people knowing it and doing it, is nothing at all.
If anyone wants a concrete example of the imperfection of maths, then one can do no better than the book 'Proofs and Refutations' by Imre Lakatos. In this, Lakatos traces the history of Euler's formula for polyhedrons: (No. of verticies) minus (No. of edges) plus (No. of faces) equals two. (V-E+F = 2). Some people might recognise this from school. It might even be in the maths textbook that one sometimes runs into out in the jungle, I haven't checked. In the Lakatos book, this formula is proved. Then a counterexample is found. So the original statement is refined to 'What we really meant'. Then another counterexample is found. The process repeats several times. If maths is so bally perfect then how can you find a counter example to something that's already been proved?
This is quite a widespread myth, many people I've talked to on this subject are jolly surprised when I point this out to them. Why is it there? It's not just an approximation to reality, I don't know what it is to be quite honest.
Anyway. Time to go and have a nice cuppa and think some more.
Some time later .. in the clan hall garden .. Daedalus plants seedlings, watched by the domesticated Interuptring Cow
Daedalus says: "My mother always said "Plant tomatoes at the full moon". Now, is this a myth, superstition, tradition, or actually a wise homily with some grain of validity? He carefully avoids the adjective 'mere'." Daedalus digs a patch in the fruit area for the tomato seedlings he acquired from (Moo!). "In this case it doesn't really matter which it is, but in other contexts it can be useful to make the distinction."
Daedalus says, "Now, Alexander invites us to evaluate the status of "mathematics as perfect truth" as a myth." Moo? "Yes Cow, you can join in. What terms do we need to agree on? .. Well, I think there are four. These are 'mathematics', 'absolute', 'truth' and 'myth'. If we don't share a common understanding of these terms, then our evaluations are likely to differ, perhaps irreconcilably."
The cow chews it's cud reflectively, emanating bovine wisdom.
Daedalus says, "We have already canvassed different interpretations of these terms, except for 'absolute'. Fortunately it's nuance here is largely, I'd suggest, adjectival, and not crucial to the nature of the main proposition. Although it does .. Moo! .. alright, it might suggest an interesting alternative notion that truth sometimes isn't absolute. But perhaps that's for another time. Daedalus suddenly recalls that Alexander said 'perfect', and not 'absolute'. He sighs. "That's the problem with cogitating when weary. Fortunately, though, what I said about 'absolute' also applies to 'perfect'. So, we have an historical example of a mathematician who has had to repeatedly modify his proposition, as it was shown to be flawed. I concur that this demonstrates that mathematical propositions can and should be questioned. "Moo". "Yes cow, and apparently they are questioned. So, if 'myth' is taken to be the same as 'erroneous', and the example to prove that mathematicians do sometimes make and perpetuate mistakes, does this substantiate the claim that "Mathematics as a perfect truth is a myth"? Well, no. It confuses the practice with the practitioner, at least, and perhaps also confuses practices with principles. But, importantly, this is not to say that 'Mathematics as perfect truth' is a valid proposition. Rather, that the example doesn't refute it."
Daedalus leans on his spade, wearily. "That's more than enough for now." Moo. "Yes, my pleasure, Cow. Thank you too." and he wanders back out.
Alexander Quandle arrives, weary from a hard days monster bashing. He is looking forward to the Onsen. He toys with the idea of wearing his Admiral's hat and playing with his toy boats, but overhears D.'s cogitations. He puts his hat back and takes out the rubber ducks instead. Slipping back into the onsen he enjoys the feel of the warmth seeping into his tired bones. He starts thinking about the echoes and replies.
Alexander Quandle: "Minor detail, Lakatos was actually tracing the history of the proposition over the course of a couple of hundred years or so, rather than modifying his own proposition. More importantly, how can one not confuse the practice with the practitioner? What is maths if it's not 'What mathematicians do'? (Where 'Mathematician' is defined as 'Those people who do mathematics.') I still assert that mathematics without people doing it is nothing at all. As such, mathematics is Not perfect. Now, back to definitions: .."
Alexander Quandle: "Just what do we mean by 'myth'. Even if we use the 'falsehood' definition it needs something else. If I were to claim that I wasn't in the onsen but up in the tower right now then that would be a falsehood, but hardly a myth. Actually I think that the 'falsehood' part should be dropped altogether. What was the definition you came up with before?" Alexander Quandle splashes about with his ducks. "Value laden story' was it? Something like that. Well I would like to take, as an example, the Alamo. Davy Crocket and all that. Actually happened, so I believe. But that's almost irrelevant. It's a powerful story. It's a myth in the sense that it's a powerful story that helps define a people's values, the sort of ideals they aspire to and so on."
Alexander Quandle continues: "On a smaller scale, in England, everyone knows about Captain Oates and Scott of the Antarctic. 'I'm going out now, I may be some while.' and all that, also 'Charge of the Light Brigade'. Going to meet your doom gracefully. Keep on going no matter how ridiculously hopeless you're situation is. I would add the band on the Titanic to that list. I would suggest that this is a more useful concept of myth, and also that it's not at all opposed to science, rather orthogonal to science." The rubber ducks are played with some more.
Alexander Quandle strolls back in, gets a cuppa from Tiff, who had the kettle on as soon as he walked in the door, "Thank you Tiff." "You're welcome sir" and settles down comfortably on a sofa in the living area. I'd like to recast the previous argument if I may. D. talked about confusing the practice with the practitioner. If the practice is indeed separate. Then what is it? To be concrete, what does the statement "2+2=4" mean? Is the number two some sort of object that can be added to itself? Where does it live? In some sort of world of Platonic Ideals? I would suggest that the existence of this world of Platonic Ideals might feel right, but is in fact intellectually rubbish. Some sort of world that we can't interact with in any way, but which guides our perceptions more reliably than vision or hearing? Dubious. Or is '2+2=4' just some string of symbols that you can manipulate according to formal rules? (Formalism) This is intellectually rigorous (or can be made so) but emotionally sterile. 2+2=4 damn well means something! Some sort of system that some (by no means all) entities seem to roughly follow? Um, I've taken up far too much space here. I'll pipe down again. Tattybye one and all." So saying he toddles off.
Daedalus settles into an armchair, and muses out loud, "When I previously referred to confusing a practice with the practitioner, I should have been clearer, I meant 'with a particular practitioner' Thus, encountering a dangerous driver doesn't make driving dangerous, per se. And a swimmer drowning doesn't mean that swimming always entails drowning. So a mathematician making an error tells us little about the nature of mathematics. Could mathematics still be a 'perfect truth' if practitioners make mistakes? I think it could. I don't think it is, but not for that reason."
Daedalus sips his coffee reflectively. "I'd also readily (agree to) dismiss the idea that 'myth' equates to falsehood. It is often used in that way, as a pejorative to diminish what it is attached to, but that's not the sense I use it in. So to perhaps conclude my comments about Alexander's 'Myth 2 - Mathematics as perfect truth - utter balderdash', I agree completely that it's balderdash, but I don't think it's a myth. I'd call it a popular misconception, but that's not myth. To explore why it's popular is to hark back to my first point, about Science vs myth, religion etc, .."
Daedalus puts down his now empty coffee cup, continuing: "but let's stay on the subject of 'myth' for the moment. You're quite right, I earlier defined myth as a value laden narrative, borrowing from major thinkers in anthropology. In that context myth is used to perpetuate a community's values; it has a normative function. Using Alexander's cited examples, imagine I find concrete proof that Crocket soiled his pants and tried to run away from the Alamo, or that Oates was delirious and thought he was going to the corner store for a packet of Rothmans? How would it be received?"
Daedalus says, "Historians might be excited, but I'd expect some resistance from the great unwashed. They are caught up in those stories' myth value .. that 'we should follow the examples of these characters'. This underscores a major difference between myth and science. For myth, historical accuracy or objective 'facts', are of virtually no importance. Why? Because myth isn't used to teach history, but values."
Daedalus says, "So, finally, mathematics versus idealism. Gosh, I don't think I'd be brave enough to categorise Plato (et al)'s dualism as 'intellectually rubbish'. I recognise it has limitations but that's a big call."
Daedalus says, "Doesn't your assertion that mathematics can't exist without mathematicians suggest that mathematics is in fact an idealist exercise? If nobody thinks about it .. the ideation .. it doesn't exist?" Yes, 2 + 2 does mean something, but only within the context of the of the body of knowledge that is mathematics. If you're using 'means something' in an emotional sense, then perhaps we've discovered why you're a mathematician. And why I'm not (a good one, anyway)."
Daedalus yawns expansively. "Something about these chairs makes me go on and on for ages. So .. time to be elsewhere." He deposits his coffee cup in the kitchen and toddles out.
Establishing the kitchen in one of the unused offices was a surprisingly arduous project. When completed it comprised a working small commercial kitchen, with a centre bench topped with granite. The Academy was pleased to recruit Cookie's protege, Tiff, as the clan's resident chef. What follows is the completion of the kitchen, and Tiff's arrival.
Daedalus is heard driving a stake into the ground outside the almost complete kitchen. He tethers a captured Interrupting Cow to the stake with a long lead, allowing it to graze on the nearby grass. Daedalus says, "Right then, that's .. Moo! .. our dairy goods sorted."
Daedalus (now a Joker) re-enters several hours later. He approaches the external wall of the kitchen and takes out an odd looking marker pen. Working quickly he draws a typical kitchen - garden door. The ink glows green. Daedalus steps back from the door outline and taps the drawing 3 times with his cane. There is a bright flash and the drawing is replaced by a door. Daedalus sighs in evident relief. "Phew, it worked. Last time I tried that the wall turned into chocolate mud and collapsed." Daedalus opens the door and enters the kitchen through the door, which, thanks to its improbable origins, will only open to clan members. He steps back to admire his work. The door swings shut gently.
Daedalus glances at the repetition gremlin gremlin. "That's a lot of 'doors'" he chides with a smile. The gremlin giggles and scampers away away. Daedalus says: "Thinking of gremlins, time to see if Cookie has found our chef yet." He wanders off towards the Common Grounds."
Daedalus returns later in the company of a gremlin chef. "So, Tiff, welcome to the Academy. It'll all be a bit strange at first, but take your time to look around." Daedalus smiles as the gremlin explores the hall, with growing confidence. "It's bigger than I thought, but I like it, nice .. old feel. Lot's of nooks and crannies to explore." she finally announces.
Daedalus says, "The kitchen, you will have noticed, is over here. We've only just finished most of the fit out, so everything's new." Tiff enters the kitchen, wide eyed. "It's .. tall!" Daedalus nods. "We learned a solution from Cookie's experience to solve that." He points to the end of the benches, where a series of small notches forms ladders at gremlin scale. "And these .." Daedalus gestures to ledges set into the sides of the benches, ".. are to walk around on, rather than the preparation surfaces. Same set up as the Common Ground". Tiff grins. "Works for me!"
Daedalus says, "Excellent. So .. 'Tiff', .. short for Tiffany?" The gremlin sighs. "Not really. Cookie and I used to have .. heated discussions about food sometimes. The others used to say we were having a 'tiff'." Daedalus has an 'Ah ha' moment as the gremlin concludes: "finally 'Tiff' just sort of .. stuck. I like it though." Daedalus says, "I see. OK, if that's what you prefer. Can I ask what your real name is? Tiff looks reticent. "It's a gremlin word, quite unpronounceable in English."
Daedalus says, "Fine, Tiff is good. Well, we'll get the last of these benches in as soon as we can, though putting that door in might have complicated things. I didn't think of that." Daedalus scratches his head for a moment. Tiff looks around. "If you take out this table, which looks a little like an office desk .. can you put the benches back to back in the middle .. an island bench?" Daedalus looks a little abashed. "Yes .. it is an old office desk. It was all we had. But you're right; an island bench would do nicely." Daedalus wrestles the desk out of the kitchen, leaving it near the bookshelves. He has an even greater struggle getting the two remaining benches into the kitchen, but manages it, eventually. Daedalus pushes the benches back to back in the middle of the kitchen. The granite tops protrude, leaving a gap between the cabinets. "Hmm .. you'll need to keep that clean." Daedalus grins as Tiff walks into the gap, which is wide enough that she can't touch both sides at full stretch. "Easy, plenty of room to get in here". Daedalus thinks for moment. "Just a sec.."
Daedalus sifts through the left over construction materials and finds some boards. Improbable as it seems, they fit exactly from the floor to bottom of the bench tops. He closes the gap at each end. Daedalus takes out the marker he used to create the kitchen door, and draws a gremlin sized door on one of the panels closing the gap. As before, the ink glows, and flashes when tapped with his cane.
Daedalus laughs as Tiff stares wide eyed at the process. "Ahh .. more storage space?" she murmurs. "No, we have plenty of storage space. This is your place. We all need some privacy sometimes". Daedalus draws a line along the edges butted edges of the bench tops. He smudges the ink with his finger and taps it with his cane. There is a flash and the bench tops are fused into one piece.
Daedalus sighs, wearily. This joker stuff is hard work! "Can't have you under a leaky roof. So .. is it big enough?" He gestures to Tiff to enter the space. She looks uncertain. Daedalus arches a brow as the gremlin hesitates. "What's wrong?" "But .. what's it for? What am I to do in there?" she asks. Daedalus is momentarily confused. "Whatever you want".
Daedalus watches as Tiff opens the tiny door and peers inside. "My place? For me? It's huuuge. It's .. I've never had a place .. Oh my." Daedalus senses that this might be one of those privacy times. "Well I have work to do. Settle in .. we'll talk later." Tiff turns and says, simply "Thank you" as he walks away.
Daedalus exits the halls, murmuring "This was a good day".