"It's My Own Invention" Eric Laithwaite 1974 RI Christmas Lectures, Lecture 6

[Music] foreign [Applause] [Music] there are all kinds of people thinking about all kinds of things all of the time that sentence sums up what i would describe as the ultimate deterrent to oppose the urge to invent it is the feeling that it's all been done someone must have done this i was born too late all the good pickings were in the last century another such rubbish isaac newton was right when he declared if i can see further than others it is because i stand on the shoulders of giants and you start counting up newton's giants you say right leonardo da vinci galileo archimedes you soon run out of ideas but newton knew nothing of father dave maxwell rutherford max blank niels bohr geiger einstein our list of giants runs into hundreds so the opportunities for new inventions and discoveries are never greater than they are today and of one thing we can be sure they will be equal they will be even greater next year now last time i left a bit of unfinished business about the magnetic river which we didn't squeeze in so i propose to do that now uh it will illustrate for you how inventions take place it is often the pressure of something else like transpose 72 or a chance remark and i make most of my inventions when i'm talking to other people they've come to see me about something or other we get to talking about something else i drag them from their interest into mine and then they thank me when they leave and i feel as if i should pay them a fee because i feel that i've used their brain to sort of reflect from now when you discover something or observe something the first time you think what about that i know that works you know then you make one and you look at it and you decide you better find out how it works and so you said about a detailed series of experiments and eventually of course you have to do the sums it wouldn't be respectable without doing the sums and so you do the sums and then you publish it as a paper in a learned society journal and when you do this you write it as if it were done from the front as if on morning one you said i will now invent a magnetic river you see where you go and you do the sums and this very unfortunate phrase keeps coming in now it is clear that and clearly obviously sort of none of it's obvious it wasn't not the day before you started no you do it from the back first we made a magnetic river for transport 72 and then i asked one of my postgraduate students helen edward if he'd make me a machine that would sort of simplify it down so that we might understand what we were doing and he came up with this machine with just three of the long row of cores that you saw last time and there was some question about how the width of the aluminium sheet would affect the stability so you begin with a very small voltage until you can just just lift it off and it's stable then you try a wider plate at the same voltage that's all right it's a little bit skewed but that may be a defect in the apparatus now you must remember that at this time a commercial company was making the transpose 72 model and they realized it it was much more difficult than flying an airplane in addition to pitch and roll and you're you've got lateral disturbance vertical bounce and propulsion to look after as well you want stability in five axes and propulsion in the sixth and you'd like to get critical damping now the first vehicle they made went along the track all right but once it was disturbed in roll it rolled all the way it was hardly damped at all and they discovered that if they made the plate wider then it dumped out the roll and i said to them but i bet it makes it less stable and they said oh yes it's not not as good in lateral shift i mean this one's quite good you can move it quite a long way so you try a bigger one that's higher still that's gone really skewed and it's a little bit more shaky on its legs in that direction and you put a very big one on and it falls off either side so i went armed with this information to see the firm and said look you're losing stability by doing that and you've got to go higher yet and a thing which is stable just that sort of thing when you try and raise it to two inches of course it'll go totally unstable i said look i'll show you we start with the one which is unstable that is not going to stay there it falls off would you just like to hang on to it bill what i hadn't realized was you should take your courage in both hands never mind winding the current down you should wind it up is one of many reversals i've had to make in my inventing you think you're going along the right path and all of a sudden it gets darker ahead and all the time you should have been going the other way who would have known that you had to raise the plate increase the current to make it more stable well now we then saw the magnetic springs and i thought i'd like to show you the forerunner of the magnetic spring experiment because um it does display something new this is a pendulum in which the sheet of aluminium has been replaced by a piece of steel with some copper wire wrapped around it and joined now i can switch this on and start i pulled away i thought i felt something good yeah thank you they i can think of a good three reasons why that pendulum should not begin absolutely from rest but i'm going to switch it on and then hold it in the most steady position i can find and you'll see if you have the patience start from absolute rest that doesn't look as if it's going to oscillate does it and even if it begins a little oscillation you suspect that's only some defect in the structure you can't see how that could go on building up higher and higher and higher you've got your two linear motors that we're on an arc back to back when it reaches the end of the travel it hits some real springs not magnetic ones and then it runs rather smoother so there's a magnetic spring plus mechanical spring [Applause] now this is an old chestnut with modern modifications i didn't show these in 1966 first of all it is the ordinary jumping ring experiment that began in 1880 it still fascinates people you put the ring back it appears to float you can go on arguing about where this should float which is only half as thick and you might come to the conclusion it should float in the same place and you try it and it does and so it isn't very interesting and this is where the invention part comes in if you're not an inventor you say yes it should float in the same place and you try it and it does and so you put the apparatus away and you go home but if you're an engineer and you are a curious engineer you say i may finish still it's down a little all right make it finish still oops down a lot now why is that and you start to work out reasons why this is until you're convinced that you know why this is too thin if i put a thinner one on still of course it'll not have any lifting force at all or will it what do you think you think it will well you're wrong it doesn't this is a bit of household kitchen foil just shows the beginnings of lift and i was satisfied that i then understood this until one night i've been showing someone and left this thing switched on as i usually i collected the rings together and sort of put them over the top as i was doing it i noticed something happened um [Applause] [Music] and immediately you've got a new world you've got a new white rabbit to follow you've got a new curiosity look at that now you can't tell me that the current in this poultry ring is attracting the current in that poultry ring because it isn't it's this one that's shoving this up so why didn't a niche of it before i've not really been able to exploit this yet all i know is it's got possibilities because our normal idea of loading something is to put more weight on it like loading a camel and so the last straw breaks it's back but in this case the more straws you put on and the higher it lifts this thing gets better as it gets more weight on it look you can go unloading it and loading it until you use up all your small ones and you start on the thicker ones it comes up a bit more and you're starting your thicker one again comes up some more the bigger the better now um can we lose this one now ready other side sorry it's not that's nice thank you the liquid ah some cooking perhaps no something more earthy than cooking writing with printers ink that's not printers ink it's too thin for printers ink it's got the viscosity of water it is in fact kerosene with certain additives but as you see it behaves in everywhere like a normal liquid there's a rather curious smell but it's um adjust the liquid for the moment this by the way is made of porcelain this is an aluminium sheet nor is there an aluminium sheet embedded in it hmm what's he gonna do with that he's gonna get himself a great big magnet and he's going to hold a plate the liquid over the magnet a heap of liquid no less and a large attractive force holding it down take away the big magnet and we'll do it with some alternating current magnets we'll try it on as well and alan's levitating you're gonna watch it doesn't crawl over the side because it crawls over the side it makes a dreadful mess of everything all right it should be on having a try out that other side now those are virtually only single phase fields now we're going to try putting a three-phase putting at least a moving field on by using our ball floating coil and shading it as we call it with a piece of aluminium to produce a traveling field you now carefully place the plate on there we'll switch on again where are we here whoa it's like a cauldron boiling it's what's more it's dividing up into walls we've seen that before with iron filings this is really only an extension of the iron filings game it shows you the the best natural position for traveling magnetic fields as far as the magnetic circuit is concerned this is magnetic liquid what shall we be doing in a year's time well one of the things i hope is that we shall be able to make particulate smokes of this material and then have not a magnetic gas but at least a magnetic smoke and then we can really see fields in three dimensions this is a tremendous tool in the hands of the research worker thank you now even though no two people are exactly alike there are ways of classifying you not only by whether you're left or right-handed or by race or religion or age but by your outlook and just as every man and i hate to add as opposed to every woman is a better driver in his own opinion than all the other idiots they allow on the road so every man and every woman is a potential thomas edison or marie curie never noticed a second einstein always the discoverer the inventor now it is said of people in the army that every private soldier carries a field marshal's battle in his knapsack so i can tell you with every confidence that each of you at one time or another has had a quite original thought and this is the result of your unique combination of inheritance from your parents and subsequent experience which is what we call you now mostly these new thoughts have passed unheeded because inwardly you felt that um your thoughts couldn't really be of all that much importance not earth shattering it is as you grow older that you begin to take yourself more seriously and taking yourself seriously is very bad it means that you spend the autumn of your life when you retire in writing to professors like myself who have more than plenty to do telling them about those unfortunate professors that is telling them about the the world beaters that you've invented and a very common species of world beta that i have literally hundreds of letters about is an electric motor that drives a generator and you use some of the output from the generator to drive the motor and then you've got all the rest spare for solving the world energy crisis now i don't want any more of those please but although that seems ridiculous it is surprisingly easy to pull the wool over your eyes especially in some of these mathematical proofs that naught is equal to one where we gonna do this next well i think yes we were i'm very fond of this geometrical proof because you can do it without actually ever saying anything which is wrong you take a square you draw a square and then imagine you've got compasses and you place compass point on this corner and you make the compasses the length of the side and you strike an arc down there like that i'll draw this next line in a different color to make the diagram clear that is an arc now since that point is now lower than the top of the square i can join it by a line which must obviously slope downwards and the middle point of that line will be to the right of the middle point of the top side of the square so if i bisect that longer line at right angles it comes down there and if i then bisect the sides of the square the vertical line that vertical line will cut the horizontal the other line it must do because that was no longer bisecting a horizontal line and the rest is just drawing lines you join from this corner to the point of intersection you join from this corner to the point of intersection and you join from this corner of the point of intersection and from there and we're going to consider i'll draw that line in red we're going to consider those two triangles they don't look much the same but that's just my rotten drawing now let us consider what is equal to what well that's the side of a square that side of the triangle it's equal to that side of the square which is of course equal to that side because there's a two radii of a circle and then this line is the same length as that because they are a pair of triangles resulted perpendicular bisection so that equals that and similarly these two longer lines are result of bisecting at right angles that base and so you've got that line equal to that line so you now have two triangles which are three sides equal so a congruent even though they don't look it and among other things this angle is equal to this angle now this angle is made up of 90 degrees plus shall we say angle a which is that well since that angle a is the same as this angle a because there were congruent triangles at the bottom then this other angle is 90 degrees plus a plus this angle b and subtracting naught equals b well if you haven't seen it before it might worry you for a little while uh the fact is remember i said i didn't say anything that was wrong i did something that was wrong i didn't say anything wrong now it would be equally disquieting however if having sort of put off the would-be inventors of perpetual motion if as a result of what i'm now saying none of our elder citizens with a mountain of experience of life behind them were to dissent from writing to me about an idea that they've been tossing around for years and never had opportunity to get a second opinion take a case in point it is now nearly two years ago that i was telephoned by a man called alexander charles jones who asked me if he might bring me a box of apparatus which he said when put on frictionless casters and set in motion inside would displace itself outside its own dimension immediately i knew this man was different any ordinary crank would have said alex not a crank it's only others who say he is uh no i mean i should have said any ordinary crank would have said um how would you like to see newton's laws disobeyed see but alex said outside its own dimension so he knew already the old chestnut if you put a ball of lead in a box and a spring behind it and you compress it against this side of the box and then when you release it the more or less the the lead stays where it is in the box does that and you say oh look action without reaction but of course the center of mass has stayed the same but he said it will displace itself outside its own dimensions so i said um does your box contain anything that might loosely be described as a gyroscope and he said in the box there is a gyroscope i said i think you'd better come and show it to me why did you say why why the question i said well because i know enough about gyros to know that they're like electromagnetism and i've studied electromagnetism for 30 years and i know darn well i don't understand it and i don't understand gyros either but i can invent new things in electromagnetism once a year and if you've got something new about gyroscopes i wouldn't see it and he brought it and it did and that was the start of a new line of research for me and then about a year later i met a second enthusiast called edwin rickman who added his own brand of instinct that impressed the id that to improve the ideas we'd already got let me say of alex jones that since i first met him i've been convinced of the both of the validity of his argument and been impressed with his feel for what i call the elements of nature a thing that the more learned acknowledged men of science and mathematics have seldom had a natural feel for what goes on and combined with the rickman id i may say that neither these gentlemen can be described as elder citizens unless you describe me as one because they're the same age as i am so there is the first message for all of you as potential inventors take your own ideas a little further before giving them up keep your experience like a sort of treasure house that you can draw on whenever you like but never never let it be your master be on the lookout for impossible things the sort the red queen dreamed up before breakfast for example in three dimensions you know we're not very good at thinking three dimensions we've said that before but i've cut a hole in a piece of paper the size of a five penny piece and i am now going to try and pass through that hole a temporary piece which is obviously bigger than the hole and i must not tear the paper in the process how difficult is this really it's not difficult at all is it can you imagine what is the smallest diameter of hole in relation to the diameter of a temporary piece that i can pass through without tearing there is a problem for you to worry about on the way home and i think a profitable problem from the point of view of stretching your brains a little so now let's go to three dimensions and see if we can repeat the trick there are two cubes of the same size i am going to pass one cube completely through the other that ought to be good in it but i first of all have to show you how much of this cube i have to cut away in order to do it and what's more in what direction i have to cut it in order to do it take out the wrapper and see the skeleton of the cube that's left inside is like that it came out of there you know it did don't you so you'll have no objection if now i push the white cube completely through the black one [Applause] [Music] that takes that takes more making than you'd think now jacob's ladders fascinating things a standard sort of christmas party trick all the faces of that are red except the top one we're going to send the top one on a journey down the back come on let's come at the bottom now is that what really went on did that really let's just see if we can send it back again then take it down and turn it forwards this time see it makes any difference come on is that really what's going on is the green one going from top to bottom no what is happening is that that one is turning over that is kicking the next one back that's kicking that one over that's kicking the next one back and that's kicking the bottom one over you see they all turn over this is a game of odds and evens and this one was just a trick thank you now i used to think that rudyard kipling's poem if made too many demands on a man these four lines i think are directed aimed straight at the would-be inventor if you can dream and not make dreams your master if you can think and not make thought your aim if you can meet with triumph and disaster and treat those two imposters just the same you have to be that rugged to do inventing you have to see your problem like the north face of the iger today and when you solved it it crumbles into a little heap of dust so small you wonder how you caught your toe in it rudyard kipling went on if you can trust yourself when all men doubt you but make allowance for their doubting too i'm not sure i'm not good training people for invention is another game games games are very good training for invention chess of course is very mind stretching domino's is said to be for um old gentleman in public houses your sets of things like this and you have to put the two facing the two and a four at this end facing a four you can go at different angles if you wish and they find that a sufficiently brain taxing now if you play on a draft board so that the dominoes just fill the squares you can ask yourself this interesting question i've cut out the two corners as you see before i did that there was eight by eight pattern of squares the 64 squares now they're only 62. suppose i gave you 31 dominoes each of which will cover two squares could you cover those squares with 31 dominoes you don't know well you might have a try and you might waste a lot of time the question i'm asking is can you prove that it can't be done this is the sort of thinking that leads to an inventive mind you say well look the two i've cut out were both pink squares so of the 62 that are left 32 are white and only 30 are pink one of these dominoes can only cover one pink and one white so you can never do it you'll always have two white squares left over these are proof now extending the idea of dominoes first of all going backwards that's a monomino that's not very interesting is it well it can be made interesting it can be made into two-dimensional dominoes if you put spots on because you can have to mate up a one with a one and then a two with a two and then a blank with a one that won't go you can stick a three on the outside there and you're playing two-dimensional dominoes which is more fascinating than ordinary straight line dominoes and those were played with monomi nose that's a domino we've seen a domino what about trommy nose well trommy knows they're three on that's and that's not one they're only two trominos but you can have a variety of combinations of spot can't you my goodness this is really two-dimensional playing and if you try and think work out the number of possibilities of just putting the spots what blank one two three or four on two pieces one of two pieces that size and shape you'll be amazed you'll have a much bigger set of trommy nose than you did of dominoes and the brain stretching will have gone a little further if you go on to tetrominos you find there are more of them there's one two three and four tetrominos now we don't put spots on these but it gets too complicated the game gets you know not worthwhile and yet it's too simple with just the four shapes that there are even though that as a left and right handedness and so is that these two are symmetrical in one sense let's just jump past those and go on to the pentominos which are far more interesting pentominos are made up from five squares and there are 12 of them 12 different shapes all made out of five squares those are all the possible shapes now i'd like a member of my audience to come and i'll teach you to play trominos someone who's not been before yeah can you climb over can you come to this side and then we can all see what you're doing now all you have to do is to place a pen tommy now anywhere on the board the object is to try to stop me from placing one on and i shall try and stop you so you can start where you like any peace any position he might think that this is a random position that he makes but it isn't it's like chess it has almost the complexity of chess now your turn the idea is not so much to make patterns as to prevent them that's rather clever not sure i'm going to win this one you know very carefully yes yes that's nice and clever what have i got left no not so the problem's all yours isn't it you give it you will well you shouldn't give anyone there look thank you very much now [Applause] [Music] if you tired of that game then all you've got to do is to separate these pieces into symmetrical and asymmetrical pieces that looks asymmetric but it isn't just the same upside downs there as far as this game is concerned so is that this one's asymmetric turn them upside down in fact i've colored the asymmetric ones a different color on the back the symmetric ones have left white because there's no point in turning them over now we've got symmetrical ones and asymmetric ones and now you can play these either way up and that gives you yet another dimension and now you can go on of course and do hexominos that's when you get bored with this and hexamine those really get rather numerous these are all the shapes you can make with six squares they don't fit that board anymore you see how any of that are why are they divided into piles like that the answer is it's like cutting out the corner problem every hex amino in this set covers three pink squares and three yellow ones three blacks and three whites these cover four of one and two of the other so these are the odd ones and these are the even ones and rather than playing games people have spent lots of time trying to put those together into interesting shapes of which i got an example here showing clearly where the odd ones lie and that is a difficult thing to do that is simply an exercise in two-dimensional topology but a man who made it three-dimensional produced this fantastic thing he said look there are twelve pentominos each matter five squares twelve fives are sixty there are six sides on a cube if you could put ten squares on each side of a cube you want to be able to make all the twelve pentominos fit exactly around the cube if you make the side of the cube equal to root ten so we stick them together like that if you examine that at the moment you'll see that it contains all the shapes i've got here if i pick any shape at random i can find it on this either one way up or the other i'm having a job with this one i know it works because i can you see it somebody come and point it out to me on the side on can you come sure i can't see it from you i'm standing too close to it where does that fit that fits there i think we've got a mistake on here somewhere anyway the one thing that's not wrong is the outline i think the two of these are like and um there's a left and a right-handed one of those and there shouldn't be a thing anyway what he did was to turn it over and put the folds in at an angle to the lines of the pentominos an angle 10-1-3 and then when he folded up the cube the bits that were hanging over were filled in exactly by the holes in the other bits so that by the time you'd folded it all around you had in fact completely filled the cube now imagine imagine starting off to try to solve that without knowing whether or not it could be done this is what amazes me about people who can do problems in topology like that let's go uh three-dimensional let's talk about uh monocubes and bicubes and tri-cubes and straightaway there are two kinds of tri-cube that's one and that's the other i mean that's the same turned over but when you go to tetracubes there are all sorts of them there's that one and of course that one and that one and that one left and right handed ones uh what else have we got you mustn't put them skewed like that doesn't count that's the same as a square oh let's have a look at the whole set bill there's a left and a right-handed one of those there's one of those one of those one of those and one of those what's this that's a that's not one of them is it you need this one to make again this also is sold commercially the uh thing is that with four cubes in each six fours at 24 to make a three by three by three cube you need 27 so you put a tri-cube in and then you try to put them together to make a cube and we're so novice at this that we don't try and do it in public like this because we never get it right uh you think you're doing all right until you get the last one i'm in a mess now so we got one made up beforehand so you should see that it was possible and i can take it apart and show you that there are the necessary pieces and there is more than one way of putting the cube together i don't know how exactly how many but it runs into teens i think in a lot of ways not including mirror reflections but cubes are not the only thing you can make you can make all these pretty things there's an armchair as a tea and a easy chair a monolith or monument [Applause] gravestone and and mr coats here says that's a grave but i think if it is a roman swimming bat and we've spotted them up to coincide with these so you can see exactly where each piece has got to fit that one's going in there because it's got the same colored spots and then the question comes can you really make all those and if not which one can't you make it's like looking for the absence of pins isn't it it's a very difficult thing this is actually the one you can't make because you look at the spots on the back you finally left some off because you couldn't do it even though it has 27 cubes in its makeup so this is a great game this also has been commercialized well now i got my ladies to produce me a very beautiful set uh before those the uh the transparent cube i've gotten to build me a beautiful set of transparent cubes all these spots on and this is for three-dimensional dominoes you'll need one spot on each of these because the spots on the different faces are all different and when you were starting a game you'd start by putting one down then you'd say well i want a red on that side have i got a red yes i got a red there put that there two yellows on the top gold no what's on the front green all right and straight away you see you'll be in a three-dimensional game and now they all have to fit on all sides and that can while away many an hour and when you're tired of that you can play three-dimensional knots and crosses by dropping little colored balls into some of the blocks and building those up so you can see where your moves were but of course the would be rather expensive commercially and the commercial version of these is shown here where you have four decks and you have colored counters that when you put them in the reds and blues and you make a move and your opponent makes a move and so on and now there are a lot more ways of getting a row a winning row can be four along there which on our blackboard we show you how many possibilities there are of producing a row like that horizontal parallel to the edges i've got it there 32 possibilities uh diagonal in the horizontal plane that's the usual knots and crosses one across the top and there are eight of those vertical parallel to an edge there are 16 of those that's a winning line too and then diagonal in a vertical plane of course across there that's a winning row and finally the most complex of all right across the diagonal one in and one across in each case then two in and two across and three and three across like that makes the most complex one now did you notice you don't have a three by three matrix like you do for knots and crosses why is that well if you try it you'll find that the one who starts can always win so you have to make it more complicated so you have to have a four by four by four matrix now we think that we get confused with the third dimension the one that einstein the fourth dimension or the one that einstein meant but really a mathematician knows no boundaries as far as how many dimensions are concerned which is i can play four dimensional knots and crosses very easily if you want four of these and now you've got some new kinds of rows you never even thought of because now this is to be regarded as a row one in the first two in the second three in the third four in the fourth that constitutes a row so does this there are all manner of rows you can have now the most complex of which is one in there one in there one in there and one in there that's the ultimate diagonal but again you'd find it too easy to win so now you have to have a five by five thing and five decks and five of them and that's playing in four dimensions well one i'm playing five dimensions another six by six six decks of them six rows and six rows this way and then you can play in six dimensions and extend them down to sevens and so you can keep building cubes on and now you see how the mathematician knows no limit in his concept of n dimensions we tend to think of dimensions somewhat differently i know as engineers but the games are certainly very uh brain stretching and thought provoking now let's go back and think a bit more fundamentally about ordinary things how many spheres can you place in contact so that each one touches each other the answer is only four you can't put a fifth one underneath because it wouldn't touch the top one and yet we think of spheres it's perfect let's try another shape i think we'd better get out the board this time thank you let's try uh coins or big discs i can actually put these five so they're all in contact with each other you start off with two on top of the third one like that and then you can just put the other two so that they touch the red one at the bottom touch the sides of the others and touch each other at the top and there are five five discs or five coins all in contact with each other well is there another shape it's dry cylinders rods how many of these do you think we could put in contact six says somebody all right well to do six you stick them together like that and you make another set with the opposite handedness that's like that and you managed to put one lot on top of the other if they're long enough compared with the diameter you can make them up to look like this and if you then arrange those in exactly the right way you can just get each one to touch each other by the time you get to the tip to make six rods all in contact with each other and you walk away and say clever boy am i five four spheres five discs six rods seven rods you can put another in the middle all those are in contact with each other and the question i leave with you is is there a better shape can you do eight if so what was the shape you began with these are exercises for stretching the brain puzzles conjuring tricks this is a spring very ordinary thing we've joined up the end so you can't cheat we're going to drop a ring onto it so that we can just lift it off again would someone like to come and lift it off yeah come on out of the front they're north sea come and lift the ring off the spring how you doing i said oh you're done you got it over two now yeah yeah you see the mistake you know is bringing over the end i know it looks ridiculous to bring it over there but look all you've got to do is lift it off okay are you lifted off you all want to make one of these never mind i'll show you look [Music] [Applause] a spring is after all only a straight piece of wire you must be able to push it on and lift it off wasn't you now a little story about a mathematical postgraduate student called arthur stone who was at manchester university in 1939 and he got a fellowship to go to princeton and there he met up with some fellow mathematicians notably a man named tukey a man named feynman and bryant tuckerman and arthur stone found that his english binders for his notes were smaller than the american standard piece of paper and so very laboriously cut off all the strips about an inch wide from all his american paper and he thought what a waste of paper so he started folding them and he came up with such interesting things he showed them to tuckerman and feynman and dukie and they formed a flexigation committee they were the world's first flexigators and here is a very simple flex again what you do with the flexagon is to open it out it's like a book there's page one page two three and four would someone like to come and pound me page five hmm come on by flexing find me page five stand this side and turn around that way and you show me where page five um is got it straight away you see pull it open not miss right you've got to flex it pull the spline of the book apart now fold it up and then pull that's it five and six thank you very much the only thing was he forgot to look for seven and eight every piece of baby got two sides and that's a simple flex again but what about this this is a hexaflexagon that's orange colored and there are three patterns there are diamonds triangles and circles they make a hexagon or a star or a circle what you do is to flex it about one corner and open it out like a flower and you get another color another pattern and then you do it again and you get uh third color green now when you've got one color oh look on the back you've got another you've got diamonds in yellow now green you've got circles when you flex green you've got hexagonal green there and you've got orange on the front and you can go on around doing this almost as long as you like and it's a fascinating thing to do oh look we've got another color we got a red what are we going to get now orange it's a different one in the center but it's not very interesting no try again we've had yellow that green hey what's this purple that's five colors good grief yellow burn again actually i don't seem to be playing with this at random i do actually know what i'm doing because there's a sixth one now what i was doing then was going through the motions in such a ways to bring up all the six colors and all the six patterns in the smallest number of moves and that was invented by tuckerman and he named it tuckerman travis you now see there are six colors and three patterns that is 18 possible combinations but you can only get 15 of them there are three combinations you can never get into the middle they always stay as fragments on the outside now these are very bright fellas and the this was long before the permissive society they made one with pictures on so that when you got into the mill you've got the satisfaction of seeing the picture that you've made up and when you flex it you get a different picture don't flex about that corner what about that sorry there's one nice picture of flowers and when you get one of the rarer ones they get to be more interesting because on some of the that one open one two here comes an interesting one three why is it interesting because it's got what the originator called pictures of commonly undraped young ladies in the corners whoo i'd like to get that in the middle come and let it go of course those are the three you can never get in the middle and he therefore named it a hexa-sexafrostagen analogs again analogs think analogs all the time it's all there is it's your only sheet anger anchor for both research and invention an ordinary child's pipe as you might use for blowing bubbles drilled right through to the bottom and an endless belt of wool that's been joined to make an endless loop now why does that interest me well just because of the shape of the wool when i blow the pipe the shape look at the top see that little kink it's always there it seems impossible that the air from here could get up there there's some very strange dynamics going on up there and it's to do with gyroscopes and it must have its counterpart in electromagnetism and so it might just be fruitful to go looking for that kink in an equivalent electromagnetic system little king always there now the search for a tidiness in pure science has probably been as hindering to progress as it was in the old alchemist days of everything made of earth fire air and water that's all neat and tidy we go home happy nothing is perfect said the philosopher in james stevens the croc of gold there are lumps in it what a lovely description of the whole of science when you think you've sewn it all up there are lumps in it when we dabble with left and right with duals and parity and with mirrors we become more conscious of human limitations than perhaps with any subject outside biology we find a true humility that can be nothing but good mostly i think we delude ourselves and create bigger problems than whatever arranged for us by nature let me quote you from a man who estimated the number of particles in the universe and found it to be less than a google a what a google when i say a things i don't deduct it means exactly what i mean to say and the man who invented the google apparently asked his small son he said i've got a new new number here what what's a good name for it and his son said to google he said ah that's it now google is 10 to the power 100 did the chalk and eddington estimated that there were only 10 to the 80 something particles in the universe so 10 to the power 100 is one with a hundred naughts written on it now the mathematicians wanted a bigger number still a whole order of magnitude bigger so they went to 10 to the power of google i'm not sure i spelled that right but uh maybe al i'm not sure but 10 to the power of google they call the googleplex and if you notice you can never write that down in decimal digits because you need more pieces of paper than there are particles in the universe said eddington however successful the theory of a four dimensional world may be it is difficult to ignore a voice insiders which whispers at the back of your mind you know that a fourth dimension is all nonsense i fancy that voice most often had a busy time in the past history of physics what nonsense is that this solid table here on which faraday as well as myself was leaning at one time that this is a collection said eddington of electrons moving with prodigious speed in empty spaces which relatively to electronic dimensions are as wide as the empty spaces between the planets of the solar system looks solid to us what nonsense to say that the thin air is trying to scrush my body with a load of 14 pounds every square inch what nonsense that that star cluster i can see in the sky now is a glimpse into the past age millions of years ago let us not be beguiled by this voice it is discredited says eddington we have found a strange footprint on the shores of the unknown we have devised profound theories one after another to account for its origin at last we have succeeded in reconstructing the creature that made the footprint and lo it is our own we are the only monster king carnos in the play laughter of the gods says a man is a small thing and the night is very large and full of wonders at the time we were doing our first experiments on the offset gyro i was in the basement workshop below this theater beside it on a wall is a huge portrait of michael faraday used to work here and a copy of his own handwriting here's the picture that you see downstairs there is a copy of the handwriting below it as i'm doing this bill running shorter time only you'd like to set up start setting up the gyro and i'll read you what it says of this note here it says this note was made by faraday on the 19th of march 1849 when he set out in search of a connection between gravity and electricity and magnetism we've been getting fairly near to that this week haven't we the final link of material forces in which he at his faraday so firmly believed he did not succeed in this quest but the note expressed clearly the prime tenet of his scientific philosophy which he followed with such outstanding success this note reads all this is a dream alice through the looking glass was a dream still examine it by a few experiments nothing is too wonderful to be true if it be consistent with the laws of nature and in such things as these experiment is the best test of such consistency we're going to do one more big experiment with the big gyro because we haven't done it before i want you all to know how very very much i am indebted to many people for the assistance i had this week from the bbc without whose cameras we couldn't have shown you half the things and all their stuff but especially to bill coates barry owen cliff johnson and some of my boys who are doing research would you like to thank them in your own [Applause] [Music] way [Music] [Applause] [Music] have we not had to with alice to the looking glass a sort of dream in which at the same time we followed faraday and tested it experiment by experiment did his quest really fail i wonder let me send you away with this experiment and faraday's words all this is a dream nothing is too wonderful to be true there are no words that i can add to better those [Music] [Music] so [Music] you

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Length: 59min 32sec (3572 seconds)

Published: Thu Apr 30 2020