Here are the notes for my 2005 Inaugural Lecture given at the University of Southampton on May 18th 2005:
Inaugural Lecture:
Greg Parker – May 18th 2005:
“Indistinguishable from Magic”
1) <Before starting, run the second track from the Matrix CD to test the sound levels>
2) <Introductory Title Slide>
Good afternoon ladies and gentlemen! This seems to be a little better attended than my average 9 o’clock on a Monday morning lecture, thank you all very much for coming along today. Please forgive me for resorting to notes, this is not my normal style, but there is so much I want to get through in the next hour that there’s absolutely no chance I can rely on my memory alone.
3) <I want to take you on a rollercoaster>
O.K. here we go!
4) <Aim of the lecture>
If I am to live up to my totally undeserved reputation, I will have to say a few things that my Academic colleagues will find outrageous – I hope not to disappoint you in this respect! This lecture will be contentious, provocative, and generally politically incorrect, so those of you with a gentle disposition please plug in your I-pods now.
The purpose of this lecture, if there is one at all, is to leave you wondering at the end whether you, or I, have completely lost the plot.
What is more boring than some grey-haired old Academic talking for an hour about his research? Answer – nothing, nothing is more boring than that. So I will not be spending an hour talking about my research. Instead I will be talking for an hour on some of the events that have made a big impact on my life that led me to eventually undertake the research I do here at the University of Southampton. You will see the path I followed was not planned, in fact we have a scientific term for the course of my career; it is called a random walk.
As we progress you will find there are several common themes that run through this lecture. The main theme is light – and anything to do with, or associated with light. Many processes and applications of light will be covered – even if at a very shallow level, including photography, lasers, image processing and one of my research areas – Photonic Crystals. Another recurring theme is mathematics, including experimental mathematics, symmetry, chaos, fractals, and complexity, and how this part of my recreational research led to a couple of papers in the Mathematical Gazette, and how it got me thinking about new types of Photonic Crystal. Yet another underlying theme will be Mysticism and Magic. The fact that we take extreme technological achievements very much for granted that some other residents of this very same planet would consider magical, I find very interesting indeed. But by Magic I also want to touch on the real stuff, and take us to the limits of the Natural Sciences bordering on what some would call the Supernatural – spooky Mulder stuff!
So where did the title of this lecture come from? Many of you will know the originator was that genius, and one of my few surviving heroes – and with the end of 2004 that came to be a pretty close run thing – Sir Arthur C Clarke.
5) <Two Clarke quotations>
The first well-known quotation was taken from Clarke’s “Profiles of the Future”. It tells us that if anyone came along with a highly advanced technology, it would look just like magic to us. I will try to convince you that we are already at that point in time, right now. The second less well-known quotation was that Information is not Knowledge and Knowledge not Wisdom. I had always felt that this needed a first line, that Data was not Information, and had the cheek to tell Sir Arthur this a couple of years ago – we have been in e-mail contact ever since.
6) <87th Birthday picture>
This is Sir Arthur enjoying his 87th Birthday party on the 16th December 2004 in Sri Lanka where he is resident. As you will know, just 10 days later the tsunami struck Sri Lanka. Although he lost some beachfront property, and all of his diving equipment, he was not injured himself, and lost none of his staff. Natural planetary disasters can be just as devastating as the extraterrestrial things some of us worry about.
I now want to kick off with my timeline that leads us up to the present day. Throughout the course of this lecture I will dip back into this timeline to fill in some of the gaps.
7) <GJP timeline. >
As you can see it all began on the 20th April 1954. The date, not the year has some significance that either you know, or you don’t. Let’s just say that when I visited Berlin with my wife Helga and I stood on the steps of the Reichstag I felt very much at home – and we’ll leave it at that.
My earliest memory age 3 was walking in Hainault Forest with my brother Tony; he fell into a river and blamed me when we got home – I was 3 remember. Nearby was a school that would take children at age 4 rather than 5. Mum wanting me out of the house as early as possible sent me off to this one. It lasted just a couple of weeks; I won’t go into the details here today, but as you can imagine they were extraordinary. My first real school was based in Newbury Park, that’s on the Central Line in Essex. In 1963 the first scientific things that became deeply ingrained in me first came to my attention. Although the laser had been invented a few years earlier, it only made its first appearance on the cover of the Daily Express, my parents’ daily paper, in 1963. For some reason this hit a resonance with me and triggered a fascination with lasers that lasts to this day.
8) <Flashtube picture, Maiman, and laser schematic>
Here are pictures of the Xenon flashtube that powered the laser, a photo of Ted Maiman the laser inventor, and a schematic of the first laser made to operate, the ruby laser. I only realised a few strange connections when putting this lecture together, and that flashtube is one of them, it will make an appearance again a little later. But the thing that really got to a 9 year old’s mind was this amazingly intense red light that could be made from firing a flashtube at a single crystal of ruby. This was the early 60s; this was a time when you could find lots of old non-functioning wristwatches in the house, and what did old wrist watches contain? Rubies, and the number of rubies were often written on the watch as some sort of class of distinction. No matter, I wanted the rubies out to make a laser. So I became expert at digging out the ruby bearings from old wristwatches, and I got a magnifying glass and focused the Summer Sun’s rays onto the crystal. You cannot imagine the disappointment that despite trying for over a year I never did made a laser, but that experience has clearly stayed with me ever since.
9) <Put the timeline up again>
Dr. Who is once again a topical subject. Dr. Who appeared in November 1963; William Hartnell came to the screen in black & white not long before Christmas 1963. In fact the first episode was shown, and because a lot of people missed it and heard it was so good, the BBC took the unusual step of repeating the first episode the following week, some of you may remember that.
Somehow I passed the 11+ and we moved to Clacton on Sea where I attended an excellent school, Clacton County High, but for only a year. The following year 1966 we left by boat for New Zealand. In those days it was more usual to do a long trip like that by boat rather than plane, unless you were extremely rich. Today of course it’s precisely the other way round, things sure change a lot in 40 years. So we went by boat from here at Southampton to New Zealand via the Suez Canal (we came back via the Panama canal). Now 1966 to you will probably mean the World Cup, the last time we won anything serious, but it was also the time of Harold Wilson and that was the last straw as far as my parents were concerned (Daily Express readers remember) which is why we were pushing off (last one out turn off the light syndrome). But 1966 was also noted for something else, for those of you who can remember that far back, it was the year of the 6-day war, and where were we when all hell broke loose? Yep we were in the Suez Canal. We were the last passenger boat to get through; the one behind us spent 10 years there, with the passengers ducking as the missiles flew over the week after we got through. A parting gift as we left Aden was a grenade thrown at the dock – I was still getting quite an education even though I was nowhere near a school.
10) <Takapuna beach>
The two-year period spent in New Zealand was one of the many watersheds in my life. For a city kid who yearned for the outdoor life the place was a paradise. I lived on the beach for two years. I fished, spearfished or surfed just about every day, and once again the formal education suffered a little – especially as there was a fantastic fishing spot just behind the school!
You can see in the photo the volcano Rangitoto out in the bay, and the black volcanic rock thrown up by the volcano (which is 3 miles away) in the foreground. Just off the end of those black rocks was my favourite fishing ground.
After two life-changing years we returned to the U.K. I still remain very unhappy about that!!!
11) <Timeline back up again>
Some more moves and some more schools, while I went to Westminster City School we actually lived at the top of the Sir John Soanes Museum in Lincolns Inn Fields, Holborn, which was excellent for me. Somehow we ended up in Devon, and somehow I got 3 “A” levels which was sufficient to get my first job at U.K.A.E.A. Harwell, the atomic energy place. The first 3 months at Harwell was training, I then moved onto another site, the Culham Laboratory for Fusion Research where I got to play with high-power carbon dioxide lasers and that was great. However, my initial time at Harwell gave me the first indication of the problems you can have with what might be called the “scientific method”. After a few weeks on the Harwell site it had come to my attention that there were a lot of guys walking around with gammy legs, or gammy feet. Well, I was no idiot I’d just left school with 3 science “A” levels, I knew what was going on here, this was radiation poisoning and I was right in the middle of it. Already beginning to feel queasy from the effects of all that radiation that was around me I staggered to the training officer in a pretty scared state. “What’s the problem?” he said. I said, “Look, there’s all these people walking around with duff legs and such. What’s going on here? Has there been a radiation leak that we haven’t been told about.” This was the first, but not the last time I’ve driven someone into fits of laughter. “No Greg, not quite.” He said. “We are the Scientific Civil Service. We are a Government body. What we are doing as a large organisation is what other large organisations are meant to do and don’t. We take on the correct percentage of disabled people for an organisation of our size”. Things are very often not what they seem!
Moving rapidly forward now. I did day release at Culham and for the first time in my life worked very hard at things academic. I got a good H.N.C. in Applied Physics, and a taste for learning that saw me entering the University of Sussex in 1975 to take a B.Sc. in Physics with Mathematics and Astronomy. I was there for one reason only, to get the best degree I could. To this end for the first year I did 100-hour weeks, for the second year I dropped down to 80-hour weeks, and in the third year I cut right down to just 60-hour weeks. The result, fortunately, was a First Class Honours Degree, but when I tell my tutees about that work schedule they look at me as if I’m from another planet – and maybe they’re right.
I left University to work at the Philips Research Labs in Redhill, Surrey, and at the same time enrolled for a Ph.D. at Surrey University. This was a great way to get a Ph.D. as I was in paid full-time work and did the Ph.D. based on my Philips research.
Leaving Philips I had a couple more jobs, set up my first company Parker Technology Ltd. In Oxford, got married, and had a son in 1986. Now needing to create some stability for the first time in my life we all moved to Hampshire and I started at this University one week after my 33rd Birthday in April 1987.
12) <New timeline slide>
Very slowly I climbed the ranks becoming a Professor in December 2000. Note I’m now sticking my age in brackets after the event; age is now becoming very important, as is the passage of time, which appears to be accelerating – Dr. Who again maybe! I span out the company Mesophotonics from my Photonic Crystal research in July 2001, and returned full-time to the University just a few months ago in September 2004. A month later I was made Head of the Group I had left 3 years earlier, well 3 years earlier it was called the Microelectronics Group, but the work within the Group had diversified so much I felt a name change was required and we are now the Nanoscale Systems Integration Group. Fast-forward 7 months and here I am.
O.K. that’s the timeline, so what now?
Before putting this Inaugural lecture together I had not realised the significance that one light capturing process – namely photography – had played in my family’s life. The photography gene had clearly been passed down from my Father, who in order to escape the squalor of the East End in the early 1900s (he was actually born in 1900) joined the army – clearly well-underage – to serve in World War 1. This saw him sent to the North-West Frontier, or Afghanistan as we now refer to it, and also saw him in Egypt down in the Valley of the Kings at the same time that Carter found Tutankhamen’s Tomb. In fact my Dad tagged along with Carter’s wealthy visitors as he showed them around, much to Carter’s disgust. So where does the photography come in? Well for some unknown reason my Dad decided he would put together a photographic setup out there in the middle of absolutely nowhere. Let’s get this into perspective. We’re talking large format glass plates here, not film, we’re also talking about a dark-room that is a black cloth, like a mini-tent, that goes over the upper half of your body, and an East End kid (in fact a real Cockney born within the sound of Bow bells) with a highly limited technical background playing around with all sorts of new chemicals in a War Zone, and he’s carrying the whole lot around with him on horseback together with the rest of his survival kit.
I’d like to show you a handful of photographs that survived my parents being bombed out twice (Second World War this time) first time it was a V1, second time it was a V2. Apparently there used to be trunks full of these photos, but these were hard times and I am reliably informed that the photos had little value in our home then, and were even used on some occasions to light the fire!
This first photo is very interesting.
13) <Massoud and soldiers doing a deal>
I was watching Russian gun ships in Afghanistan on the television as a teenager, so this would have been when we were down in Devon, and I remember saying to my Dad that the Afghanis didn’t stand a chance. He replied much to my surprise, and this was right at the beginning of the war, that far from having no chance, it was the Russians that wouldn’t win. Dad was pretty old and I didn’t tell him what I thought of his comment – but he carried on. “When we were out there, better armed and better trained, we didn’t win either, we didn’t even come close. The only way we managed to get safe passage up the Khyber Pass was to pay one tribe to keep it clear of all the other tribes for us, otherwise we couldn’t have operated there at all”. So this first photo actually shows one of the many deals being done to pay the locals not to shoot at them!
14) <Pontoon bridge -people>
The British Army had excellent engineers of course that could quickly put up these enormous pontoon bridges to carry people,
15) <Pontoon bridge – camels>
And camels.
16) <Camel train – Himalayan foothills>
Camels were clearly a popular mode of transport through the Himalayan foothills.
17) <Fakirs>
Dad took a series of amazing character shots. Look at these Fakirs. Or is it the Student’s Union Bar – no, no that’s the Fakirs, and they’re obviously into the Atkins’ diet big-time.
18) <Johnny Massoud>
Then we have this imposing Massoud chief. Today it is the Taliban and the Muja Haddin – in those days it was the Massoud.
19) <Men in chains>
In this next shot I was wondering why Dad was getting the evil eye from these locals at the market – and then I noticed that these two guys on the right were chained up – I have no idea what the story was behind that one.
20) <Massoud and small family>
We then have a friendly Massoud and his small family,
21) <Wood gatherer>
Here’s a man who knows how hard it is to earn a quid,
22) <Wood gatherer and wife>
And here’s a man and his wife who both know how hard it is to earn a quid,
23) <Boy in basket>
And finally a bit more Political Incorrectness, he doesn’t look too happy does he? Well by that I mean the one carrying the load, the one in the basket seems pretty much used to this mode of transport!
I thought there might be some train enthusiasts in the audience, so here’s an unbelievable piece of hardware that clearly carried people and goods around the place.
24) <Steam train>
Everyone you have seen in those images is of course long dead. Very old photons (light particles) have been locked into a piece of paper as an image that we can look at today. Photography as we shall see in this lecture, is very many things, including a time machine to the past – it is a magical process.
25) <Photography – As a Time-Machine!>
Let’s take a quick break from things photographic and have a very quick look at some of this current day technology that I think falls under Clarke’s heading of magic. For starters, I am presenting this lecture from a small notebook computer as you can see. A tiny machine that today can carry a 120Gigabyte memory around with it, and process data at very high speed.
26) <Interlude – Matrix cut>
That video performance, that we take very much for granted nowadays, wasn’t even on the horizon when I took charge of my first 286 personal computer, which ran at just few Megahertz, and had a hard disk drive of just a few Megabytes, when I joined this University Department in 1987! Our ape descendant brain has a remarkable capacity for forgetting earlier primitive technology and eagerly accepting and utilising the most up to date gadgets. There must be some useful survival mechanism involved here. That hard disk memory of 120 Gbyte capacity allows this tiny machine to carry around something like 120,000 paperback books, more than your average library! Even Star Trek wasn’t that bold in its stories! Let’s have a closer look at the magnetic disk memory of today’s computers.
27) <Hard disk drive pictures>
Many of you will be familiar with these things, hard disk drives, the non-volatile high-density memory in today’s computers. The one on the left is the sort you get in a standard desktop machine, the little 2.5” drive on the right is the sort you get in laptops and notebooks like this little VAIO machine. Now these hard disk drives have a spinning disk inside which can be magnetised, very much like the old magnetic tape recorders, by a read-write head that floats on a cushion of air a very small distance above the disk.
There is a popular analogy for the interaction of the read-write heads and the rotating magnetic disks (which are called the platters) that goes something like this: The interaction of the read/write heads and the magnetic disks in a typical HDD is similar in scale to a 747 flying a few feet off the ground at its cruising speed of just over 500 m.p.h. This already sounds fairly extreme, but it also sounds quite reasonable, we should check out whether it is reasonable. I have chosen the HDD technology as an example for several reasons, one it is familiar to anyone who uses a computer, two it is an excellent example of a mass-produced item that has seen a price drop from $150 per megabyte in 1982 to less than half a cent per megabyte today, and three it is a very good example of extreme engineering.
28) <Hard drive numbers>
The read/write heads of course do not fly as such over the disks, they ride on a very thin cushion of air that is being dragged around by the platters themselves.
The head sliders (also called pico sliders) are about 1.25mm (long) x 1mm (wide) x 0.3mm (high). They float on a cushion of air that is just 15 nm thick (15 x 10-9 m). If we take an average track diameter on the disk as 63.5mm and the disk rotational speed as 7,200 R.P.M. (note, there are faster disks), then the average speed we need to calculate is given by using v = r x w.
Now 7,200 R.P.M. is 120 R.P.S. or 120 Hz, and w = 2 x p x f where f=120Hz, so w = 754 radians per second. Hence v = 31.75 x 754 x 3,600 = 8.62 x 107 mm per hour, or 86.2 km per hour, or roughly 53.4 m.p.h.
Now we need to scale everything up from that 15nm floating head height to bring the dimensions into the macroworld that we are more used to. This all becomes a bit arbitrary, but let’s have the heads at a height of 3cm above the platters (rather than the Jumbo a few feet off the ground) and see how the numbers scale. Well 3cm is a factor of 2 million (2 x 106) greater than 15nm, so we can see that some of these numbers are going to get a little large.
29) <Now scale everything up>
The read/write heads become 2,500m long by 2,000m wide by 600m thick, that is 1.5 miles long by 1.24 miles wide by 0.37 miles thick, which is just a little bit bigger than a 747 I think.
The speed of the heads above the platter becomes 1.72 x 109 km per hour, or 106 million miles an hour. At this speed of roughly 29,000 miles per second you would reach the Moon in 8.62 seconds.
Don’t forget these mile long heads are travelling at 29,000 miles per second at just over an inch above the magnetic disk.
I think all this goes to show just how tame the popular analogy really is!
Read-write heads are an example of nanotechnology engineering that’s been around for quite a number of years now, and is an excellent example of extreme engineering.
Having introduced the dreaded grey-goo terminology, it’s worth pursuing this line of thought for a moment longer and seeing where this all came from.
30) <Richard Feynman>
It was in fact another one of my heroes, unfortunately not still alive, Richard Feynman who first seems to have suggested that we were missing a trick by not trying to work with matter at very small length scales. He discussed his ideas in a very famous talk called “There’s plenty of room at the bottom”. This in turn made me think about whether there was “Plenty of room at the top” as well, in other words, engineering-wise, what is the range of the length and size scales that man has manipulated so far? The results may surprise you.
Here is an example of the biggest engineering feat I could think of, I believe it will be familiar to most of you.
31) <The great wall of China>
That’s pretty big engineering. Now what about manipulating matter at the very small scale?
32) <Quantum corral>
This is bordering on the totally unbelievable in terms of what has been achieved, and certainly comes pretty close to what I would define as Magic. What we see in this image are individual atoms of cobalt that have been arranged into an ellipse using an instrument called a scanning tunnelling microscope (STM). Within this ellipse of cobalt atoms has been placed a single cobalt atom at one of the foci of the ellipse. Now a theory called quantum mechanics tells us that particles can exhibit wavelike behaviour, and we see a manifestation of this wavelike behaviour by the appearance of a “phantom” cobalt atom at the other focus of the ellipse as it is here that the “real” cobalt particle waves are focused. This may look a little far-fetched even for Science Fiction – it is hard science fact! The STM image on the right shows that if you make the “quantum corral” circular, you don’t get the focusing of the cobalt matter waves.
33) <Clarke’s second Law> Read the slide.
Back to photography again. In 1986 I set up Parker Technology Ltd. to design and manufacture portable high-power, high-speed Xenon flashguns (there’s that flashtube again!). The reason I got into portable high-power flashgun design and construction – a number of years earlier – was due to my eldest brother who was to end up spending 33 years at Scotland Yard as a Forensic photographer. His hobby however was bird watching, and bird photography, and at the time, a portable, battery driven, high-power Xenon flashgun system wasn’t commercially available.
At first I didn’t think the required flashgun specification was possible with the technology at the time, and it did turn out to be quite a challenge. The outcome after quite a bit of research and development was these beasts:
34) <Your flash units>
With over 3,000 volts and 250 Joules stored on the capacitor inside these things, you can see you don’t want to go touching the charged capacitor in one of these units, and quite clearly you don’t play with these units in the bath.
35) <Balloon>
By using a sound-operated trigger you can fire the flash from a pre-determined noise level, in this case I used the popping of a balloon to fire the flash. By moving the microphone further away from the sound source you catch the action a little later in time, so in the second picture you see the balloon has collapsed a bit further.
36) <Light bulbs>
One forty-thousandth of a second is a pretty short time interval and lots of everyday things will be frozen in time with a light pulse of this duration. These light bulbs were shot with an air pistol and again the flash was triggered by the noise of the imploding bulb.
However, the main application of these units was for nature photography, and the next few images show how my brother put these units to work in the field – literally!
37) <Barn owl>
Here is a Barn Owl returning with dinner having built a nest in an old church.
38) <Kingfisher/Archer fish>
Here we have a Kingfisher returning to the nest with dinner, and an Archer Fish shooting a grasshopper from a leaf with a well-aimed jet of water. The Archer Fish shot is clearly a set up using an aquarium, but all the bird shots are taken in the wild.
39) <Swallow>
A Swallow is seen entering a barn at full lick – again the action is stopped dead and every feather can be seen in fine detail with no motion blur at all.
40) <Bee Eater>
My brother is now living in Surfers Paradise on the Gold Coast, Australia (bastard), and took this picture of a Bee-Eater returning to its underground nest with a nice blue butterfly that will make an appearance again a little later.
The bird pictures are all triggered by an invisible infrared beam unit I built for the purpose. A pulsed infrared beam is bounced off a reflector crossing the path the bird will take in flight. When the bird breaks the beam it takes its own picture. After a few shots the bird gets used to where the beam has been placed and will work its way around it if it can. This means re-positioning the beam every so often to keep the bird guessing!
41) <Woodpecker>
As the slide says – sometimes 1/40,000 of a second is just too quick to give a natural looking picture. This woodpecker looks decidedly deceased.
42) <Photography as a time machine, and a means for freezing short instants in time>
So we have seen photography as a time machine, and for freezing instants in time. It can also be used as a political weapon and a means to save lives – even if unwittingly.
Did you know that in the Iranian Embassy siege in London, one of the terrorists survived and is in jail today? What’s this got to do with the price of fish you say? Well, the reason this guy is alive today is due to my brother, the one that took those bird pictures, and more specifically due to photography. Now the Prime Minister of the day was known to be a bit of a hard case and I don’t think its breaking any official secret to say that as far as the Iranian Embassy siege goes the word from the top was that none of the perpetrators should leave the place in one piece. So my brother goes in with the SAS taking pictures for Scotland Yard as he goes, he always manages to get really riled that the BBC guy got an award for the siege footage when he had much better pictures that were never seen publicly. Anyway, he was standing at the foot of a staircase as all the hostages were being thrown from one SAS man to the next down the stairs to be lined up on the ground outside, and my brother was taking photos of this. Come to count up time and there’s one hostage too many on the grass, yep one of them was a terrorist. He was soon identified and was about to be led around the corner for a chat with Mr. Browning (or it could have been Mr. Smith and Mr. Wesson) when one of the hooded SAS men pointed to my brother and the camera – and that terrorist is that only one that got out alive.
43) <Power of photography! >
Such is the power of photography!
It’s all been a bit too easy for you so far – rather like a First Year lecture. Now we’ll crank the handle up a bit. This is where the Maths theme will come in.
Now a famous author was told that for every mathematical equation he gave in his book, his book sales would be halved. This is the guy:
44) <Hawking book>
He didn’t do too badly despite the warning, but then again he did only give one equation. I will try not to give even one equation.
It might be hard to believe that something like Mysticism might be associated with that most hard core of the Sciences, Pure Mathematics, but history shows us otherwise.
Every “A”-level student of Pure Mathematics has to battle with Leibniz’s legacy of the calculus. You’ll be glad to know I’m not going to write down any calculus, but what I do want to tell you is what Leibniz was actually trying to do when he came up with the calculus, and once again this is that kind of brilliant uncluttered thinking that these people with no technological props seemed so good at. The following can be found in Frances A Yates’ excellent book “The Art of Memory”.
45) <Art of Memory book cover>
Leibniz was working on a project known as the characteristica. Lists were to be drawn up of all the essential notions of thought, and to these notions were to be assigned symbols or characters. The idea then was to invent an arithmetic that manipulated these characters so that they could be used in logical combinations to form a universal art or calculus for the solution of all known problems! What a brilliant idea! Allied to the characteristica or calculus in Leibniz’s mind was a project for an encyclopaedia, which was to bring together all the arts and sciences, known to man. When all knowledge was systematised in the encyclopaedia then the “characters” (his characteristica) could be assigned to all the notions and the universal calculus would be applied to give the solution to all known problems. So the phrase “Let us calculate” attributed to Leibniz did not mean let us sit down and work out this hard sum, it meant let us take this passage from the Bible, and by applying the universal calculus let us see what it is really telling us! Pretty amazing stuff for someone who has never heard of the semantic web! Although Leibniz’s dream didn’t materialise in the form that he was working on, the fall out was a very powerful mathematical technique now used by every scientist on a regular basis.
Where is all this taking us? It is meant to show you that mathematics, if not mathematicians, is a little strange. Some aspects border on the Mystical, and yet it has always been out there, all we do is occasionally turn over a new rock and find some new piece of mathematics that has always existed. We’ll come back to this one towards the end of the lecture.
The pure aspects of mathematics have always fascinated me and soon after getting my first computer I purchased different mathematical packages to undertake another hobby – experimental mathematics. This is a polite term which describes an almost complete mathematical illiterate playing with things he doesn’t understand – but it can be enormous fun all the same. Like most people, I really like the complex patterns from those mathematical entities known as fractals, such as those shown in this slide.
46) <Show some nice fractals>
There’s something about the colours and patterns of these things that seem to have deep hidden meaning. However, what is very interesting about fractals is that very short and very simple programs can often generate this highly complex behaviour. We call these routines algorithms, and it really is very surprising how very complex behaviour can result from very short, very simple algorithms. Very complex behaviour can also result from very simple physical systems as well. Who would have thought that bashing two bits of metal together could level a city? Well it can of course if the metal happens to be Uranium. Returning to mathematical complexity we can create the following chaotic behaviour:
47) <Bifurcation diagram>
For example, this complex chaotic bifurcation was generated from 3 very short lines of code. Chaos, fractals and symmetry are all quite closely interrelated and will make further appearances as we progress.
It was while playing with what are called “Towers of Power” that I discovered the following strange result.
48) <I to the power I>
By taking the square root of minus 1 to the power of the square root of minus 1 again and again, and plotting the real and imaginary parts of the resulting complex number you get this three-barred spiral. This had been known from earlier work but the reasoning behind the three-barred pattern and the final iteration point in the centre had not been discussed before. Never knowing when to stop, this piece of work led me to take each of the points shown in the diagram themselves to higher and higher powers.
49) <Cluster of galaxies>
This is the result of this exercise which looks like the local cluster of galaxies except for the odd horizontal line at y=0, and it was that odd horizontal line that started me on this piece of work in the first place. It shows that the square root of minus one raised to the power of the square root of minus one, that is a pure imaginary number raised to the power of a pure imaginary number, gives rise to a real number, very strange.
I couldn’t leave it there as this behaviour had all the hall markings of a hidden fractal. To cut a long story short, I managed to extricate the fractal (with the help of Steve Roberts who was one of my PhD students at the time) and the result is shown in the next slide.
50) <Playground>
It was not only published in the Mathematical Gazette, but also made the front cover as well, a very pleasing result.
51) <Sunflower>
I played around with these complex numbers and other geometric patterns for quite a while, including this sunflower type geometry, and then left them for other things. The sunflower however will make an appearance again later on.
52) <I have seen things soundtrack>
53) <Well not attack ships>
Well I’ve not exactly seen attack ships off the shoulder of Orion, or C-beams near the Tannhauser gate, but I’ve certainly seen Orion.
54) <Observatory>
This is what we have at the bottom of our garden. If you are married to someone who is into everything to do with light including instruments and instrumentation, you can expect things like this to pop up in your garden. This is not, as my wife likes to call it a portaloo, it is my observatory.
55) <Two views of telescope>
Inside the observatory is a Schmidt-Cassegrain reflecting telescope that has its own built-in GPS and computer positioning system.
You can of course look through the telescope (I even have a binocular attachment so you can use both eyes to observe) and see some pretty amazing deep-sky objects, but the eye only works in black and white when incoming light levels are very low and you’re working in the dark. Also you’re quite limited in the dimmest stars you can visually observe through the scope.
56) <Hyperstar and CCD>
All this of course changes when you bolt a sensitive CCD camera onto the scope, and things really change if you bolt the CCD camera onto a lens assembly called a Hyperstar shown in this photograph, that allows you to undertake imaging at an f number of 1.85. If you’re a photographer you’ll know what that means, if you’re not a photographer it means the system is incredibly fast allowing very faint deep-sky objects to be recorded in just seconds.
I will now quickly shoot through some deep-sky images taken with this telescope from the back garden of a house in the New Forest.
57) <Markarian’s Chain>
If you’re just imaging stars, it’s good to work not only in black and white, but also with the negative, this really brings out the fainter stars. The dimmest stars in this image are around magnitude 19 or 20. This is the tail end of a chain of galaxies in the constellation Virgo, it’s called Markarian’s chain.
58) <Stephan’s Quintet>
A nice galaxy is in the top left hand corner of this photo, but what I was after was the five small galaxies within the red circle, which are called Stephan’s Quintet.
59) <The Coma cluster of galaxies>
In this image, just about everything with the exception of the 3 bright stars near the centre, is a galaxy. This is the famous Coma cluster in the constellation Coma Berenices that lies below the handle of the plough (Ursa Major). There are over 100 galaxies in this image!
60) <M81 in Ursa Major>
Here we see a rather nice large spiral galaxy in Ursa Major – the Plough.
61) <Machholz>
We’ve had a comet visitor recently and I got this shot of it when it was near another deep sky object NGC1333 which is a reflection nebula.
That’s all very well and good, but the whole point of a colour CCD camera is to take colour pictures of pretty objects.
62) <M45>
This is a shot of M45 also known as the Pleiades, or the seven sisters, or Subaru. This is the constellation that looks like a question mark in the sky near Orion, but what the eye doesn’t see is the blue reflection nebulosity that surrounds these stars. You need the CCD camera, or sensitive film, in order to record this nebulosity.
63) <M31>
This is a mosaic of 9 frames showing most of the Andromeda Galaxy M31. This galaxy is simply huge and I haven’t managed to capture all of it yet as you can see. The last bits will need to be filled in later this year.
64) <My God, it’s full of stars, sound bite>.
65) <The Flaming Star nebula in Auriga>
This is a nebula in the constellation Auriga called the Flaming Star nebula. This is a very deep shot, meaning a very long exposure totalling around an hour was made which results in stars going down to around 20th magnitude. It is also in a rich star field region as you can see, so the image really is full of stars.
66) <Rosette>
A winter constellation, just to the left of Orion is Monoceros. It contains this gem called the Rosette nebula, which is huge. The field of view of my setup is one degree by three quarters of a degree. A full Moon is only half a degree across, so a full Moon would sit comfortably in a quarter of this frame. I will need to return to this object next winter to get the whole thing in by making a mosaic.
67) <M42, M43 and the Running Man nebula>
Moving to the right from Monoceros we come to the astrophotographer’s happy hunting ground – Orion. In Orion there are dozens of amazing objects to capture on CCD. This is the famous great nebula in Orion – no attack ships – but there is a Running Man. Here you can see his head, his outstretched forward arm, his leading leg and his trailing leg.
As I said, Orion is a great hunting ground for astrophotos. If you go up from the great nebula and turn left a bit towards the leftmost star in Orion’s belt, named Alnitak, you come to the most photographed region of the night sky.
68) <Horse and flame>
This is the famous Horsehead nebula, the brilliant overpowering star is Alnitak, and the orange mess that looks like some poor paint shop pro add-on below Alnitak is in fact the flame nebula, it’s for real! Just below, and to the left of the horse is another reflection nebula. This is an extremely rich and well-photographed region of space.
69) <Horse alone>
If we zoom in and take a very long exposure shot of the horse head region alone, this is what we get. If you do not feel both insignificant and awestruck at the same time when seeing this image – then you have no soul!
70) <Photography as Zen>
We have seen photography as a time machine, as a stopper of fast action, as a lifesaver, and now as a Zen sect!
I now want to return to symmetry, complex systems, light, and the only practical demonstration you will see in this lecture.
71) <Overload>
72) <Dummy slide – the mirror>
Here we have a mirror, perhaps the oldest and simplest optical device known to man, or perhaps it is even the most complex? Remember, simple systems can sometimes show very complex behaviour. It is apt to have a mirror involved in a lecture with Magic in the title, mirrors have long been associated with Magic and Magic tricks.
So, what I want to look at with this mirror is something that everyone is familiar with, that is lateral inversion, or mirror writing. When I hold this writing up to the mirror and show you the reflection, you get what you expect, laterally inverted writing, nothing new in that. But how does the mirror do this? And if it inverts left-right then why not top-bottom as well?
73) <Mirror papers>
For those of you that think maybe this is a stupid question, and why should a mirror invert top-bottom as well as left-right, here are three papers on this very subject taken from reviewed Philosophical Journals. Now Richard Feynman wouldn’t have said anything good about anything coming from Philosophy, but we do need to remember that this has been considered to be an important question to discuss, important enough to appear in peer-reviewed journals, and we should try to answer it. I should mention in passing that the second two papers really show that the authors have very little understanding about symmetry and how a mirror works.
I sat down for a morning to use the scientific method to try and sort this problem – remember I’ve run into trouble using this before. By the way, have you heard of the alcoholic Physicist who decided to use the scientific method to get over his drink problem? On Monday he drank Rum & Coke until he passed out. On Tuesday he got paralytic on Bacardi and Coke. On Wednesday he thought he’d try Vodka and Coke and made himself thoroughly ill. Satisfied with his accumulated results he threw away all the Coke in the house. Anyway, coming back to the mirror, if you look at this thing with a critical and unbiased eye it is absolutely clear what a mirror does, it simply reflects straight back whatever is in front of it. There is no left-right reversal, or up-down reversal; it is a purely passive optical device. But we see the writing is laterally inverted. But the mirror isn’t doing anything, so the mirror isn’t laterally inverting the writing – so who is? This is where the symmetry argument comes in. Somehow there is a 180-degree symmetry rotation being brought in here, but from where?
Now as I bring this writing up to the mirror so you can see the reflection of the writing from the mirror, you can see where this 180-degree rotation comes in. There, did you catch it? I’ll do it again. YOU rotated the writing yourself when you brought it up to the mirror to see what it looked like in reflection.
I can tell you are neither convinced nor impressed, that’s o.k. If what I’m saying is true, then if you rotated the writing 180 degrees before bringing it up to the mirror, then when you looked at it in the mirror it should be the right way round – shouldn’t it. So that’s why I have put this writing on a piece of transparency. I can rotate the transparency by 180 degrees and then bring it up to the mirror again. Hey presto, the reflected writing is the right way round – and the scientific method seems to have worked for once with me. Why doesn’t the mirror invert top-bottom as well? Because I only rotated the paper in one plane, if I had turned it upside down as well then there would have been a top-bottom inversion too. But people don’t usually do handstands when they want to look in a mirror. And that is how a mirror laterally inverts an image – it doesn’t!
74) <Ambidextrous Universe>
After having satisfied myself that this was the correct explanation I was pleased to find that Martin Gardner who used to write the mathematical column in Scientific American had come to exactly the same conclusion in his book “The Ambidextrous Universe”. So there are a few people it seems who seem to know how the simplest optical device, known from antiquity, actually works.
As we’re getting near the end of this lecture I had better say a few words about my research, it is after all what got me the Professorship in the end. I look at tiny optical devices called photonic crystals, which have almost absolutely nothing to do with what most people understand by the word crystals.
75) <The Icon>
These devices are waveguides for light, that is a structure that will confine light to move within it, and this waveguide has a pattern of tiny holes drilled through it which can greatly modify how light will move through the waveguide. This region of holes is called a crystal as sometimes the pattern of holes can follow a crystal structure. The key thing that governs the functionality of the photonic crystal is the size and placing of these holes, so now you can see why patterns and symmetry might be important in photonic crystal design.
76) <Waffle>
We actually made our first photonic crystal by accident; we were making something completely different. This waffle structure was the starting point for making very tiny single crystal pillars of Silicon , these are what we were trying to make.
77) <Deep etched holes>
There’s a 20um bar marker at the top of this scanning electron microscope photograph. To give you an idea of scale, the diameter of a human hair is roughly 80um, so these things are pretty small; in fact their linear dimensions are of the same order as the wavelength of light itself.
The waffle was the starting point to use a special etching technique that allowed these very deep etched holes to form at the point of the inverted pyramid. If you oxidise, and then remove the oxide from the Silicon a number of times, you will be left with the thick piece of Silicon that links the deep etched holes together.
78) <Rods of Silicon>
In other words you are left with this array of Silicon rods, which is what we were trying to make in the first place. However, these rods didn’t do what we were hoping they would do and the project came to an end.
Something like 6 months later I was reading an article on these things called photonic crystals, something I’d never heard of before, and realised that the precursor structure to the Silicon rods:
79) <Deep etched holes again>
Was actually one of these photonic crystals. So we took this sample off the shelf and measured it optically and this ended up as a paper describing the first near infrared photonic crystal ever to be made. My research into photonic crystal circuits and devices took off from this point on.
Photonic crystals can be used to manipulate light in the same way that semiconductors like Silicon can be used to manipulate the flow of electric current. This means we can do things like bend light around tight corners, slow light down, and make things called superprisms that can spread light out much more efficiently than a conventional prism.
However, with a conventional pattern of holes, like a triangular or rectangular pattern, you can only get these effects by picking certain particular directions through the crystal. What I wanted was a pattern of holes that allowed you to pick any direction through the crystal for the effect you wanted, and this is where the earlier recreational mathematics work comes in. It turns out that what you want to make is a highly symmetric photonic crystal structure, and a high symmetry means you need to get away from the regular patterns you typically see in conventional crystals, and use patterns that you see in other areas of nature, and these patterns are called quasicrystals.
80) <SEM of 12 fold>
Here is a scanning electron microscope picture of a 12-fold symmetric photonic crystal pattern that has been etched into a waveguide. At first sight it looks like a random array of holes, but if you diffract a laser beam off this structure you get a diffraction pattern that shows 12-fold symmetry:
81) <12 fold diffraction>
This was the first practical demonstration of a photonic quasicrystal structure and led to a Nature publication, which in our business is a big deal. My PhD students during this period were Martin Charlton and Majd Zoorob. On the right hand side you see the 6 back-reflected beams being bounced back from the photonic crystal, which runs horizontally across the middle. There would also be 6 forward diffracted beams if the photonic crystal did not block the particular wavelength light we used in this case.
However, interesting as 12-fold diffraction was, it wasn’t enough for me, I wanted infinite symmetry. It turns out that there are patterns that show very high orders of symmetry. One is this pinwheel pattern that was discovered accidentally by the mathematician John Conway:
82) <Pinwheel structure>
And the second structure that shows extremely high symmetry is this one, which you may recall from earlier on:
83) <Sunflower>
Yes it’s that sunflower pattern again. These two high symmetry photonic quasicrystal structures are currently under investigation by my PhD student Tom Lee. And as these are scanning electron microscope images, you can see he has already made them and he’s now optically characterising them.
As Nature seems to be providing us with some interesting solutions to these geometrical problems, it is probably worth looking further afield to see if she will provide any more evolutionary solutions to our problems. It turns out that she does:
84) <Morpho butterfly>
The colour of this butterfly wing is due to its microscopic structure, it is not due to pigment. This is a natural photonic crystal, and was the inspiration for one of our Patents on an entirely new class of photonic crystal device.
85) <Beetle>
The blue colouration of this fossilised beetle is also due to structure and not pigment. It is a fossil, and if you’re a fossil hunter you will know that you don’t usually get colouration in fossils! Nature seems to resort to this micro structuring solution for producing blue rather than using pigments. I shall be researching why this should be with a zoologist from the Natural History Museum.
So we’re now practically at the end of this lecture, so how can I conclude in a suitably politically incorrect fashion?
(Put on sunglasses??)
It’s with the mathematics again.
86) <Wigner paper front page>
It really is very strange that mathematics should describe our physical world so well. There is after all no good reason why certain mathematical functions should so precisely describe what goes on in our physical world, unless there is of course some hidden link between these two sciences. In fact some people find this so peculiar they have written papers on the subject, as Eugene Wigner first did with “The unreasonable effectiveness of mathematics in the physical sciences”.
87) <Einstein and Wigner quotation>
Einstein is said to have remarked, “The most incomprehensible thing about the universe is that it is comprehensible.” And I think this guy knew what he was talking about.
To quote Wigner:
“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”
Is this one of those cases where you introduce complexity when it isn’t really there, or is there something deep and meaningful here? Why should mathematics be able to describe physical events so well? As any Mathematician will tell you, the maths is already “out there” it has an existence of its own independent of us, all we do is occasionally turn over a new stone and find a new piece of maths that had always “been in existence” independent of us. Likewise with our physical measurements and experiments, the results of these experiments has always “been there” we just came along at this particular point in time to uncover some of them.
If you were to apply Occam’s Razor to this problem, where Occam’s Razor states that the simplest most logical answer is usually the right one – you might be led to conclude – as some people firmly believe, that the reason mathematics so “unreasonably” describes the “real” world we live in is because we really are “living” inside a computer simulation – the Matrix had it right all along!
Thank you for listening, have a good evening, and let’s hope the program doesn’t decide to crash tonight!
88) THE END and the <Matrix end theme. >
