The Speed of Jean Sibelius

At The Castle Gate

If you've watched The Sky At Night religiously since the mid 1960s, then you've seen all but a few dozen of Sir Patrick's 700+ episodes. Alas, the ones you missed will probably have to stay missing, their tapes having been wiped or thrown out, if indeed they ever existed (many episodes were simply broadcast live).

You've also heard the opening strains of Sibelius's Pelléas et Mélisande a corresponding number of times, in this recording of the Royal Philharmonic Orchestra conducted by Sir Thomas Beecham. Such long term exposure to that introduction has, you've almost certainly found, two noticeable side effects. One is perfect pitch: at the close of a hi-hat you can sing its opening chord, bell clear and literally pitch perfect, at any time of any day or night. Man, that's got to be the world's most unbelievably annoying earworm. The second effect, and the one exercising me here today, is a very strong and ingrained opinion concerning exactly what tempo the piece should be played at.

Sir Patrick's death last Sunday occurs as I'm completing the central corpus of a symphony collection, and turning to concentrate on other, equally non-vocal, classical musical forms. So naturally, I was prompted to add to the old Micro-SDXC card, this suite of incidental music written for Maurice Maeterlinck's 1892 drama of doomed infatuation. Turning to Amazon, I thought I'd spin the old amateur astronomer, virtuoso musician, composer and Krautbasher in his grave, by downloading this Deutsche Grammophon Masters recording of Berliner Philharmoniker, under the onetime Nazi maestro himself, the Austrian Herbert von Karajan.

Now, I've had plenty of speed issues with certain grand maestro composers before, most notably Herr Herbert here, but also Sir Georg Solti, Leonard Bernstein, and a few others (by contrast, I always find Daniel Barenboim perfectly to taste). But sweet mother of Adolf, nothing in the history of music could ever have prepared me ever for the glacial interminability of this treatment, ever. Whatever the merits of the rest of the suite, that first geologically grinding movement is bloody unlistenable.

What's the Frequency?

Clearly at this point I had to know which was "right", in the sense of being closer to the composer's original intention. Because, you know, that can change everything. If this impossibly, inhumanly lento melodrama corresponded more faithfully to the thoughts of Jean Sibelius, then I'd just have to learn to live without Beecham's much more familiar dancefloor aerobic workout. Luckily we can decide these things independently. On Sibelius's original score, there's a tempo command specifying

which is to say: serious and ... widely? ... expansively I guess, with 48 minims (half-notes) per minute. The time signature is 2:2, so there are two minims in a bar, and the piece comprises 60 bars in total, with no repeats. Oh wait, two of those bars are in 3:2 time - Jean, you crafty devil! - so we'll call it 61 equivalent bars of 2:2 to compensate. That's a grand total of 122 minims, which at a mean frequency of 48 per minute, should take just 2 minutes and 32½ seconds to play.

Run time of the Karajan recording: six minutes dead.

Conclusion

So that settles it then. Just as I'd suspected, Herbert von Karajan was a grandstanding, temporising, scene-stealing, attention-seeking hack of a drama queen. Yes, I have indeed wasted my money with this purchase. And yet...

The funny thing is, once I found the score and followed it along with the music, this interpretation really started to grow on me. And you know, even the canonical Beecham stretched it out to 3½ minutes.

Quantum Computing for the Determined

Moving Pictures

Nobody seems willing to predict when quantum computing will take off. Some are even beginning to question whether it will ever do so. Meanwhile, optimists patiently await that crucial breakthrough, the discovery of the perfect physical realisation of the qubit. There's no shortage of candidates. The Nitrogen Vacancy (NV) centre in diamond is one. NVs are the crystal lattice imperfections in pink diamonds that give them their hue. Then again, a lot of progress has recently been made involving trapped ion systems.

The optimists wait - impatiently, on second thoughts! - for one of these, or for some other exotic virtual particle inhabiting some material (or as yet unknown metamaterial), that will finally and abruptly realise the qubit as coherent, entangled and scalable.

As they wait, they polish their grasp of linear algebra, matrices, the various fundamental and second-order quantum "gates" that have been conceived, and the circuits made possible by these. Rehearse the limitations imposed by their fragility and inscrutability. Marvel at the astonishing algorithms that have been developed in qubit theory, while worrying about their scant number and opaque discoverability.

Almost to a man or woman, they have found and honed their new algebraic skills using The Book: Quantum Computation and Quantum Information, by Michael A. Nielsen (University of Queensland) and Isaac L. Chuang (IBM / Stanford University). Or Mike and Ike, as this revered tome is universally known. A literally pioneering work, it was the first of its kind, and is still today the standard to which all else is inevitably compared (my earlier review is here). In fact it's the most highly quoted physics publication of the last 25 years, and one of the ten most highly quoted physics books of all time (source: Google Scholar, December 2007).

In support of its tenth anniversary edition, Professor Nielsen has released a set of 22 short video lectures on his blog. They're a great introduction to the subject. However, he has stopped just short of completing the course, due to intervening work commitments. He has promised to complete it if there's enough interest in the videos produced so far. Here's the first one:

You know what you must do!

Next time: Single Qubit Gates.

Risk Shift

The Trouble With Politics?

In the LA Times just over a week ago, there was an interesting report about a recent study of teenage drivers:

http://www.latimes.com/health/la-he-teen-driver-laws-20110914,0,7056006.story

Basically, the situation in all the states (California being no more than a particular case in point) has been, for over a decade, that the newest drivers, which is to say 16-17 year olds, have been subjected to various restrictions on their ability to (a) carry passengers, and (b) drive at all during certain times of day. There have also been other restrictions adopted by certain states, such as driving without supervision, or the ability to use mobile phones while driving, but these two have been the main and most popular ones in every state since the first of these so-called "graduated driver licensing programs" was originally introduced in Florida in 1996.

What the study has revealed is that the anticipated - and indeed observed - reduction in fatal accidents involving 16-17 year old drivers, has been "almost exactly matched" by a corresponding increase in fatalities involving 18-19 year olds. In other words, the carnage has merely been pushed two years into the future.

(According to my reading of the evidence, the increase is actually closer to half the earlier reduction, but we'll let that go for now.)

Hot Potato

It's obvious with hindsight, that what these programs have done is to mask the immaturity and inexperience of new drivers for a year or two. By preventing them from being exposed to certain driving situations and environments, the restrictions have of course done nothing to prepare them for such eventual exposure.

Politically, this has become a very awkward truth. During the first couple of years of every such program, public officials have been able to point to a real reduction in young driver related fatalities, and boast with confidence that their policies have been saving lives. Now that it turns out in general not to have been the case, what are the chances that these programs will be cancelled overnight?

Absolute zero, obviously. But for more than just the usual reasons, i.e. short elected terms, and blissful ignorance of the actual evidence. This will not become just another case of badly thought out laws surviving through inertia. For if these programs were discontinued, there would be a bow wave of doubled fatalities lasting for as long as the initial reduction, namely two years, as today's pre-existing 18-19 year olds meet the newly liberated 16-17 year old wave of fresh idiots.

Obviously there's a lot that can be done, in terms of education and training, to defuse these unintended consequences and arrive at a program that does make sense. Still, it's an interesting study, and a good reminder of how shortsighted, wilfully or otherwise, we and our politicians can be.

Logicly

The Digital Division

Little Nephew has a physics exam today, so we've been busy revising the curriculum over the weekend. Near as I can tell he's hitting full marks in the first five out of the six component units: Movement, Radiation, Telecommunications, Electricity, Sound and Music. Not that the sample questions are a great indicator of a candidate's proficiency. I'm certain you could replace your grasp of physics by the algorithm, "Divide the first number by the second", and score about 65% using that stratagem alone. He does seem already to have grasped this fact.

The sixth and final unit covers the basics of Digital Electronics. Whether because it's the most recently introduced (we have previously had multiple sessions on the other areas), or because there are no number pairs to divide into each other, this does appear to be his one comparatively weak spot.

I've written previously about the efficacy of bringing practical demonstrations and aides-mémoires into our lessons, and for several months had been toying with the idea of writing a simulator for the basic digital electronic components - gates, flip-flops, registers, switches, LEDs and so on. Even made a few aborted attempts, in C#, Logo, and Scratch. But these kept getting bogged down by one particular detail: propagation delay. If a given circuit would in reality oscillate, then I felt that the model should do likewise. Unfortunately, this single choice opens the floodgates to a torrent of design decisions, turning the unwary engineer into a startled frozen rabbit...

K.I.S.S.

Eventually yesterday, while he took his well-earned break and game of L.A. Noire between units 5 and 6, I decided I'd reinvented enough wheels for this month; performed a quick web search; and downloaded a 30 day demo of the first digital electronics simulator found. This was Logic.ly, and I could never have wished for a more perfectly dovetailed fit to match our educational requirements. Had it up and running in three seconds. Had example circuits from his textbook entered and working ten seconds after that. Okay I might be exaggerating a little; it's actually a cross-platform web based app, requiring installation of Adobe AIR to provide the offline standalone version. But that's just how it felt. Everything dragged and clicked exactly as expected, working instantly, with not a single word of prompting. Surely the only possible definition of the perfect UI.

Designer Josh Tynjala has Kept It Simple, Stupid. There's no fatally misguided attempt to model propagation delay accurately, which I see now is technology dependent anyway. After all, some ways of constructing real, physical logic gates, instead of allowing runaway oscillating designs, might go into a thermally destructive linear mode. Rather than second-guess your technology tradeoffs, Josh's gates simply tolerate forced inconsistencies, and leave aberrant behaviours to be discovered in later, practical lashups with real components. Bravo.

What's In The Box

The supplied component set was also more than ideal for our needs (hyperbole intended). Gates include inverters, and n-input gates (2 ≤ n ≤ 8) in all flavours (AND, OR, NAND, NOR, XOR, XNOR). A nice touch is the configurability of these last two for either odd/even parity or "=1" behaviour. At the next level of integration, there are flip-flops of the SR, D, JK and T kinds. Input controls include fixed logic levels, toggle and pushbutton switches, and a square wave generator. Outputs can go to either single lamps or 4-input hex digit displays.

Despite my earlier remarks on propagation time, the available components do include a buffer. According to the documentation, this "simply propagates the signal it receives. In the real world, a buffer will boost the electrical signal, if it has lost strength. In Logicly's simulation, one may use the buffer to affect propagation time." Hmm, I read that as: "future expansion".

Three demo circuits are provided to help get you started on more advanced projects: a D Latch memory cell, 1-bit Full Adder, and a Ripple Counter. Best of all, you can try the free demo online (no download required, but does need Flash 10).


Customisation

The circuit editor has configurable grid size and snap. Logic gate symbols are switchable between the distinctive shapes of the ANSI/IEEE standard, and the rectangles used by the IEC. Wire colours are used to indicate logic levels 0, 1 or indeterminate; these colours can be disabled or customised. Finally, unconnected inputs can be assigned a default logic level. When I started playing with chips in the 1970s, everything was TTL, and floating inputs went to logic "1". Some cretins even used this fact in their designs. The same idiots who bequeathed us the millennium bug, no doubt.

My Wish List

A killer feature would be the ability to package your own debugged circuit into its own little chip, a bit like the supplied flip-flop components, making it available for reuse in further designs. That's a lot of work, but I'm sure Josh has already thought of it plenty of times. Just the same, think I'll email him with the suggestion. Alternatively, or additionally, some more components from the MSI range would be good. Shift registers, multi-bit adders, that sort of thing. Lastly, a native Print option in the standalone version might not hurt a lot.

So... Did It Work?

Little Nephew is sitting his exam as I write this. I know he'll do extremely well.

Heroes

When It Happened

Sitting alone in my little office with the door to the adjacent factory area open, as the people there worked cheerfully building their circuit boards, wiring harnesses and custom housings, I was preoccupied with the authoring of some graphics software. Subconsciously listening to the joking going on next door, and to the music of BBC Radio One coming from their tiny communal FM radio. The door to the reception area opened, and my boss appeared there. Glancing at my face, he told me to cheer up. Then he disappeared again, having assured me that "It might never happen."

But then it had just happened. Why did nobody seem aware of it yet? Everything appeared to be continuing as normal. Yet only a moment earlier, loud and clear the radio announcer's voice had punched through the humdrum chatter and pop, telling me that Space Shuttle Challenger had just exploded on launch. That was exactly twenty five years ago today, at this hour, as I'm sitting and writing these words now. My brain took a snapshot of that moment, one that I can still examine today, as if it were a physical photograph.

Looking Back

Like many people at the time, I'd lost much of my initial interest in the American space program. It had seemed routine for a while. As if they had it down to a fine art, a daily set of procedures that always resulted in exactly what it should: yet another successful mission, with no big discoveries or artifacts to share with the world's mass media. Then, the newspapers got wind of NASA's latest publicity scheme: the first civilian in space. Christa McAuliffe, a teacher from Concord High School, New Hampshire, was to fly in the next shuttle and present lessons to her class from space.

Clearly the idea was a successful one, as every news network carried images and interviews with the first space teacher. The concept captured the public imagination. Without the big dramatic climax of say, the moon landings I'd watched since age 10, or the unwelcome suspense of Apollo 13, NASA seemed to have found a cost effective, everyman route, to promote simultaneously itself, and space travel, and science. When I heard the terse announcement that day, all I could think of was that teacher, racing skywards and full of hope, optimism, and the educational purpose that was her life's work.

Thank You

My real life heroes are those champions of the promotion of the public understanding of science: Carl Sagan, Charles Simonyi, Richard Dawkins, and so on. But real life space heroes, pioneers like Christa McAuliffe and her crew mates, combine that dedication with a commitment to exploration. True leaders of mankind, always risking and sometimes losing their lives, they follow remorselessly their vision of a larger and more enlightened universe, and in so doing they create it, for us all to inhabit one day.

Photo: NASA. Christa McAuliffe is in the back row, second from the left. Each January, NASA's Day of Remembrance honours the fallen crews of Apollo 1, Challenger and Columbia, and all of those who have given their lives in the cause of exploration.

Strangely Reassuring

Update (Dec 13): Bonus Material - On Ledes

When Warren Ellis saw the New Scientist article Mystery 'dark flow' extends towards edge of universe, he reacted to its opening sentence, "Something big is out there beyond the visible edge of our universe", with the immortal and appreciative "Now that’s how to write a fucking lede."

Now in his Lede Of The Day, he makes his own contribution to the Plain English Lede society, in his reaction to the somewhat conservatively stated arXiv article, First Observational Tests of Eternal Inflation:

Let me translate this lede from arXiv for you.
Evidence that our universe has been struck by four other universes.

I hear the faint rustlings of a new meme... following the Chuck Norris template. Compare:

• When Chuck Norris crosses the road, the traffic looks both ways.
• Superfluous adjectives, particularly colours, avoid Warren Ellis.

Phys. Ed.

Keeping It Current

Li'l Neph was over last weekend, looking for some more physics tutoring. He's moved on to the "Movement" module, which is some fairly basic stuff about speeds and accelerations, forces, masses, weights, friction, and a lotta balls (golf, tennis, football and cricket feature prominently). It's the third time I've been over this module with him, and he seems to have quite a good grip on the material. [Update, Sep 13: pass!]

So far I've resisted the urge to demonstrate principles of statics by pushing him around, or hanging heavy weights off of him. On the other hand, during a previous "Electronics" module, I did indulge in a little bit of practical demonstration fun. In the middle of our treatment of Ohm's Law, I was suddenly grasped by some phantom teacher's inspiration, ran upstairs, and grabbed my multimeter and a spare, tungsten filament light bulb. We used our knowledge of the mains voltage and the bulb's power rating, to make a prediction of the filament's resistance:

R = V²/P = (240V)²/60W = 960Ω.

Of course, when we then measured the bulb's resistance using my (t)rusty multimeter, it turned out instead to be closer to 100Ω, some order of magnitude too low, and I gave my student a puzzled look. In response, a peculiar expression, a surprising combination of embarrassment and sympathy, flashed across his face, as he began searching for some excuse to exonerate his doddery old uncle...

The ensuing conversation was certainly a rewarding enough outcome from our little empirical investigation. We spoke about the variability of resistance with temperature in a hot filament, and the related issue of catastrophic bulb failure due to asynchronously switched cold surge currents. Also about technological obsolescence: how lucky I'd been to even find an incandescent bulb in the house! That led to a useful diversion, concerning how much of his textbook was, for an educational resource, irredeemably out of date. I mean, fax machines? CRT televisions? FM radio? Telephone dials?

But his look of sympathetic embarrassment, that's the one part of the lesson that I won't be forgetting about in a hurry!

O God, O New Scientist!

Schrödinger's Cat Observed

New Scientist magazine, in the printed, dead-tree edition, has a regular snarky page which lovingly details the copious nonsense and hilarious mistakes often reported in the press under the guise of some or other scientific principle or theory.

Sometimes though, I have to despair for the journalistic and editorial standards of New Scientist itself. As for instance in the current issue, where a moderately interesting article on foundational research in quantum physics offers examples of "physical predictions that are confirmed time and time again by experiment".

The third of these examples: "cats that remain suspended between life and death as long as we don't look at them".

LOL... I had no idea that one had been directly verified, in experiments using actual cats!

Photo credit: Creative Commons Attribution-Share Alike 3.0 Unported.
Title credit: Psalm of Montreal, Samuel Butler, 1878.

Naked Physics

Update: I just checked Google Analytics, and this here entry had 38 (discrete!) hits yesterday. It also happens to be linked from my comment to Raymond's article, which is, you guessed it, comment number 39. I've always said: blogs are the world's first write-only medium.

The Old New Thing's Raymond Chen threw down the gauntlet this week, challenging any and all comers to come up with a real-world, actually-happened, physics-related pun, even more lame than his own prize sample. To give you an idea of the level of competition involved, his example involved meeting two colleagues named "Paul" in the works kitchen, allowing him to quip "Oh no, is this legal? I think it's a violation of the Paul Exclusion Principle."

Beat that for lame, eh? Easy.

I attended the Summer School for an Open University physics - sorry, natural philosophy - course some years (ok, decades) ago. It was held at the University of Sussex, near beautiful Brighton, sunny Sussex by the sea. At that time, the area was famous for hosting the one and only nudist beach in Britain. So on the evening of the first day, a group of us decided to grab our Kodak Instamatic 126es, and go for an off-campus drive (I was easily led). Just to see what we could see...

Never mind what we saw, that's completely irrelevant! We saw the sea. The point is that we made good our "escape", without getting arrested (nor forced to strip).

When we arrived back at the halls of residence, we encountered one of the physics - sorry, natural philosophy - tutors, whom we recognised from earlier in the day. At that time, he'd been telling us about energy levels in the atom, which can either be spaced a quantum apart (discrete), or else overlap (degenerate). We now offered to buy him a drink at the students' bar, and in the course of subsequent conversation, he happened to ask where we'd been earlier in the evening.

We told him we'd gone looking for the nudist beach, but we reckoned we'd managed to get away again without anyone spotting us.

"I see," he said thoughtfully, "you guys are quite degenerate. And yet quite discrete."

Disclaimer: parts of this story are true.
Bonus material: We also have two Pauls in our office. Fortunately they have opposing values of spin.

More Big Numbers

Millions and !!Billion!!s

There's been a bit of comment in recent months about the use of million and billion in the media, particularly with all the bank and big business bailouts that have occurred, and the apparently insatiable appetites of their fat cat executives for telephone number bonuses. And yet, just as truth is the first casualty in any conflict, so perspective is rarely allowed to stand in the way of popular journalism.

As is often the case, Randall Munroe's XKCD nailed it best (click through for the full strip and punchline):

But I'm particularly fond of the way newsreaders and politicians, in mitigation of the above, invariably explode the word "billion" at us, almost as if it begins and ends with double exclamation marks. There seems always to be a multiply exaggerated pause in the middle of the discourse, while they build up the head of steam they judge necessary to shock us out of our reverie, wherein we would otherwise have been certain to have misheard them say merely "million". Then all of a sudden, there's that precisely timed unleashing of - what can only be described as - a bomb of high pressure air, spit, and thunder: !!Billion!!

4,294,967,296

Speaking of billions, I was shocked - shocked I tell you! - on attending my first local [programming language name redacted] users' group those years ago. For some well forgotten reason, the question arose of assigning a unique IP address to each and every one of the "four point something billion" people who happened to be on the planet that day. Did anyone have any idea if IPv4 would suffice? Rhubarb ran around the room.

What's shocking about that? Well, trouble is, the industry was just then at the midpoint of its 32-bit processor "plateau", which had been heralded by the Intel 80386 processor, and so everything was encoded into 32 bits. Now if there's one arithmetical thing more important than multiplication tables to a software engineer, it's her powers of two. Each of the first sixteen is an old friend, the next sixteen are at least familiars, and the last and most important of these, two to the power of thirty-two, is famously around four billion and something. I think it may be a wisdom that's passed on through mother's milk. Remember that old lullaby?

♫ Forty-two, ninety-four, ninety-six; ♫
♫ Seventy-two, ninety-six. ♫

Anyway, I sat there in complete and utter disbelief, chin on floor. In a room full of the very people - software developers of the 32-bit era - most likely to know the answer to this one very specific question, "Can a 32-bit number represent four billion?" To be fair, I don't know how many others were similarly appalled, but I'd certainly like to think it was most of us.

Update, related: Five billionth device about to plug into Internet.

Miles And Miles From Watford

Back again to editorial perspective, and a Telegraph article on the latest Hubble eye candy, NASA's "stunning" new image of a spiral galaxy, places it "trillions of miles from earth". This attempt at an indication fails abysmally, by some nine orders of magnitude, or in other words, by a factor of a billion. The object in question is in fact almost two sextillion miles afar.

It's a significant and most unfortunate failure, in the entire history of the concise and accurate conveyancing of scientific facts. And yet all of the information that would have been needed to improve upon it, why that's already present in the body of the article.

One light year is about 6 trillion miles, and our sun's nearest stellar neighbour, Proxima Centauri, is more than 4 light years distant. So anything at all outside of the solar system is quite literally "trillions of miles from earth". Including, of course, every other single, double and multiple star in our Milky Way galaxy.

But most objects are not in our galaxy, nor anywhere near it. The island universe in question is the very beautiful (and incorrectly reported as "edge-on") spiral NGC-4911 in the Coma cluster. Its distance from ""earth", and indeed from everything else that's in our galaxy and visible in the night sky, is about 320 million light years. That's what I call almost two sextillion miles.

Perhaps the Telegraph article could have read "billions of trillions"? As it stands, it might almost as accurately and meaningfully have said "hundreds of miles from Britain." Either way, it looks like the writer knew what he was talking about, and his editor made him look foolish. Oh well, never mind, thanks for the NASA picture anyway.

Yes, it is a beautiful galaxy. I wonder what its inhabitants think of ours?

Update: here is a pretty good picture (actually more of a photo essay) of a quadrillion.

The Last Find

The Science Blog, as we know that format today, was invented by John Carlos Baez on January 19th 1993, with the first edition of This Week's Finds in Mathematical Physics. And just this very today, an era was brought to an end with the 300th and final edition of that resolutely Web 1.0 bulletin.

Having so recently celebrated the first birthday of this little blog, it's quite sad to have to turn now to an obituary for the demise of a personal favourite. Issue #300 ended quite happily on a high, illustrating for us how to categorify the Riemann zeta function, whilst visiting "lots of our old friends one last time: the number 24, string theory, zeta functions, torsors, Joyal's theory of species, groupoidification, and more."

More indeed. John will continue to contribute at the math, physics and philosophy group research blog The n-Category Café, and the collaborative category theory rich Wiki-lab nLab. His new blog Azimuth will cover diverse subjects: "from math to physics to earth science, biology, computer science, economics, and the technologies of today and tomorrow – but in general, centered around the theme of what scientists can do to help save the planet."

Go, John! But whatever else you may do in the future, to me you will always be the best guy to explain the relationship between the hypercomplex numbers of the four normed division algebras (real, complex, quaternion and octonion); Bott periodicity; and the exceptional Lie groups. The guy who came to my home town, two Septembers ago, to present the Rankin Lectures at Glasgow University, and to talk about his favourite numbers - which happened to be 5, 8, and 24. Obviously.

And as much as I know that I'll thoroughly enjoy following the upcoming Azimuth content, I also know that I will forever miss the crusty old serifs of This Week's Finds. Au revoir, mon vieil ami!

Photograph of John Baez by Lee Smolin.

Public Service Announcement

What’s taking so long, Mr. Babbage?

If you, or someone you know, may have been affected by any of the issues raised in my recent Book Review: Quantum Computation and Quantum Information, you might find it helpful to consult an article published exactly one hour earlier, by the one person who perhaps gets asked more than anyone else (he estimates at least 300 times per day), When can we expect to see the scalable quantum computer?

That person is Scott Aaronson, and this is his answer:

http://scottaaronson.com/blog/?p=446

Notice that Mr Babbage has already replied in the comments section, in of course his typically detached and dispassionate, but clear and concise fashion.

Book Review: Quantum Computation and Quantum Information

The Enigmatic Qubit

The first thing an engineer wants to do, having learned about quantum computational "qubits", is to simulate them. After all, digital simulations of arbitrary analog computers (of which the Gristleizer musical effects pedal is an example) can be realised in any modern synthesizer. The state of an analog machine is nothing more than the list of instantaneous voltages at the outputs of its various amplifiers, integrators, differentiators. Isn't the quantum computer just like such an analog machine, in every essential way?

Further investigation into the mathematical nature of the qubit initially appears to yield more encouragement of this kind. There's a model known as the Bloch Sphere which describes the qubit's state 'ψ' as a tethered vector of standard length, pointing out in some random spatial direction. The surface of the generated sphere is obviously two dimensional. So, just as we would treat each node voltage in a given analog setup as a single floating point number in our digital simulation, doesn't this mean we can model a qubit by an ordered pair of such floating point numbers (such as φ and θ in the diagram below)?

The Bloch Sphere (Wikipedia)

Reading the qubit causes it to "collapse" to an arrow pointing (say) vertically either straight up or straight down. Can't we just simulate this operation statistically, in well-known, classical ways?

Realistically, the answer to all of this is "No." Such simulations involve unbelievably unrealistic magnitudes of repetition, sampling, and hardware scaling. Often the end result is still a hopelessly crude approximation. And as soon as we make the first obvious upgrades, from a single qubit to a pair, admitting as this does the possibility of entanglement, then even this model vapourises; while ascending to larger numbers of qubits, classical approximations rapidly become impossible in principle, even as research simulations - see e.g. the Quantiki List of QC Simulators for coverage, or alternatively Steven Peil's Imitating quantum mechanics: Qubit-based model for simulation (Phys. Rev. A 79, 042320, 2009) for one thoroughly detailed treatment.

Fortunately, it doesn't take a lot of expertise in quantum fundamentals to prove this. And once accepted, you will find yourself already at such a level, and with sufficient theoretical tools of quantum modelling and investigation at your disposal, that you will no longer have any interest in following such a dead end path anyway!

A Comprehensive Introduction

Michael A. Nielsen (University of Queensland) and Isaac L. Chuang (IBM / Stanford University) first published their masterwork in 2000. Since then it has been reprinted better than annually. It is a considerable testament to their foresight, and to their thoroughness, that ten years later, and in the present environment of almost daily revelations and astounding leaps of progress in the field, their work has remained so current, relevant, authoritative, and easy to recommend as either comprehensive primer or full-year course.

The book is unapologetically mathematical in its hardcore technical approach, after all this is a serious course textbook, not a "popular science" title! There are several tables and figures of nomenclature and convention, distributed throughout the early sections of each main book part, to be encountered as and when these are required. The generous use of diagrams is particularly helpful, given the sheer density of topics likely to be completely new to the reader.

As the title implies, this book seeks to furnish a sound working fundamental basis in the theory and practice of both quantum computation, and quantum information systems. Each of these fields has spawned an expository industry of its own, and more modern publications tend to specialise in one field or the other (the cover blurbs include one from a certain Peter Shor of AT&T Research, saying The field is already too big to cover in one book...). It is therefore quite natural and unsurprising to discover that this venerable tome comprises three main parts, once the common fundamental concepts, necessary to make a start in either of these main areas, are factored out into their own introductory section.

Part I: Fundamental Concepts

This is further subdivided into three parts.

Chapter 1, a general Introduction and Overview, provides both basic historical context and remarks about future directions, followed by more in-depth introductions to quantum bits, isolated and multiple; qubit states, gates, circuits and measurements; quantum teleportation, parallelism and algorithms; practical information processing considerations, and information theory in a wider context.

Chapter 2 is a serviceable introduction to prerequisite mathematical subjects, including aspects of linear algebra; the postulates of quantum mechanics; and the nature and evolution of, and measurements within, quantum state space. The chapter ends with an assortment of more specialised discussions on density operators and the Bell Inequality.

Chapter 3 rounds off the introductory material from the perspective of computer science, with Turing Machines, logic circuits, resources and complexity. Here we are introduced to reversible computation, as a means of bringing some important, universal computation gates (Fredkin and Toffoli) into the discourse.

Part II: Quantum Computation

This section of the book deals mostly with the dynamics of closed quantum systems, i.e., those without any unwanted interactions with the outside world.

Chapter 4: Quantum Circuits kicks off the detailed exploration of quantum computation with a survey of the few essentially quantum algorithms known at the time of writing (January 2000, although there has by no means been an interim explosion in these). Next, single qubit operations are explored, and modelled using 2x2 matrices of complex coefficients. This allows the countenancing of compositions, and the introduction of quantum circuit components such as the common single qubit "gates": the Hadamard, H; the Pauli rotations, X, Y and Z; the Phase, S; and the π/8, T.

The general notion of a controlled operation, and particularly the controlled-NOT or CNOT (previously mentioned in the introductory material), then serves as our first example of a multi-qubit gate. The ensuing section, on the analysis and synthesis of higher-order operations such as the Toffoli and Fredkin gates, is particularly rigorous and lucid.

This chapter concludes with useful treatments of topics like quantum measurement, gate universality, computational complexity, the quantum circuit model of computation, and finally some illustrative examples of quantum simulation (an advanced topic).

Chapter 5: The Quantum Fourier Transform and its Applications, after a brace of introductory limericks, focuses down on one of the most spectacular successes (to date) in the search for uniquely quantum algorithms: the Quantum Fourier Transform, an efficient quantum algorithm for performing a Fourier transform of quantum mechanical amplitudes. Here the authors begin to disabuse us of faulty preconceptions engendered by the popular science press, as this is not a faster version of the classical Fourier transform; rather, certain problems thought to be quite intractable on classical systems can be attacked through it. Various applications such as phase estimation, order-finding, the hidden subgroup problem, and of course good old fashioned factoring, are demonstrated.

Chapter 6: Quantum Search Algorithms reintroduces the notion of the oracle, a black box previously alluded to in the introductory sections, showing how its application can be used to speed up a process (such as factoring, although this example has expository rather than practical advantages) in probabilistic ways, effectively by allowing an already "known" answer to become "recognised". Illustrations of Grover Iteration are derived, rigorously presented, and analysed; while one particular full-page diagram, illustrating the quantum addressing of a classical strip of memory, takes the biscuit for effective communication of principles.

Chapter 7: Quantum Computers: Physical Realization is inevitably the least current of all the subject subdivisions on show here. Not a week goes by without one or several new and revolutionary potential mechanisms or improvements being heralded as the vanguard of the ultimate scalable quantum computer. As important and significant as these advances certainly are, they are nevertheless matters of degree, while for theoretical purposes you'd be just as well using any of the implementations detailed here.

Comparisons are made among the various qubit design types - spin, charge, and photon - on the basis of decoherence, and the maximum expected number of operations. Hamiltonian analysis of simplified quantum harmonic oscillators will surely remain extremely important and useful for the foreseeable future (even today, any engineer should know how to solve the Schrodinger wave equation for various sample potential profiles). Then too are considered optical photons and cavities, ion traps, NMR, and some other types that once, a decade ago, must have appeared a lot more speculative than now.

Part III: Quantum Information

The last and largest section of the book covers various aspects of noise, i.e., unwanted interactions between real quantum systems and the world external to these.

Chapter 8: Quantum Noise and Quantum Operations breaks the ice with a brief description of stochastic changes to classical states, traditionally modelled by cascaded independent Markov processes under the assumption that is termed Markovicity, before going on to introduce a powerful tool for describing the evolution of quantum states: the quantum operations formalism. The particularly elegant operator-sum representation (using operators only on the Hilbert space of the main system) is developed and applied to several example cases.

Chapter 9: Distance Measures for Quantum Information gets a bit esoteric, tackling questions like: How close are two quantum states? How well does a quantum channel preserve information? Trace distance and fidelity are discussed (the former being found to have a particularly simple geometric interpretation in the case of a single qubit, namely half the Euclidean distance between the corresponding points on the Bloch Sphere illustrated above). One significant takeaway is a satisfyingly short proof of Uhlmann's Theorem.

Chapter 10: Quantum Error-Correction covers three broad topics relating to the reliable processing of quantum information in the presence of noise; to wit (the basic theory of) quantum error-correcting codes, fault-tolerant quantum computation, and the threshold theorem. Starting with classical error-correction, we are shown some conceptual challenges on the road to simple quantum error-correcting codes, subsequently generalised into a theory of quantum error-correcting codes. Then, some musing on the classical theory of linear codes gives rise to the fascinating Calderbank-Shor-Steane code system, and eventually we reach the so-called stabilizer codes. By this point, the authors' poetic sub-chapter introductions have evolved into sonnets! No, I'm serious. A refreshingly practical treatment of fault tolerance winds up chapter 10.

Chapter 11: Entropy and Information contains rather a lot of mathematics for such a short chapter, but looks as if it just might be of interest to someone, somewhere, some day. Who can say? Not me anyway. Stephen Hawking maybe?

Chapter 12: Quantum Information Theory brings it all nicely together. Yes, even the entropy stuff: high entropy implies low fidelity, after all. Other topics include the Holevo bound; Shannon's (classical) and Schumacher's (quantum) noiseless channel coding theorems; information over noisy quantum channels; entanglement distillation; and of course quantum cryptography.

Appendices mitigate the forementioned prerequisites by furnishing basic coverage of number theory; the theories of basic probability, and of groups; self-contained treatments of the Solovay-Kitaev and Lieb Theorems; and public key / RSA cryptography.

Conclusion

If any chapter(s) would be seen as the Achilles' Heel of the book, then the concluding chapters of parts II and III are surely most at risk, concerned as they are with the state of the art of quantum computing and/or IT at the turn of the millennium. But with help from the certitude of mathematics, the breadth of scope (and consequently implied shallowness of treatment), and expert exposition and presentation, upon inspection it passes the test of time rather well.

Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang
Cambridge University Press
First published 2000
ISBN 0-521-63235-8 (hardback)
ISBN 0-521-63503-9 (paperback)

Quantum Regex

The Go To Guy

Hardly a day goes by without someone asking me a question about regular expressions. Scale This! Chris is one such customer, although not one of my regulars, so to speak. Recently, Chris has also started asking me to explain, in layman's terms, such things as special and general relativity, and quantum mechanics. Why me?! I'm certainly no relativity guru, and could just as easily imagine asking him, or almost anyone else for that mass-energy, to explain it just once more to me!

But on the subject of quantum mechanics, I guess the day is approaching, when those of us presently engaged in high level control of electron flow (software writers, in other words) will have to get with the quantum program, or get a new career in retail greeting. With that in mind, I've just finished reading Quantum Computation and Quantum Information by Michael A. Nielsen (University of Queensland) and Isaac L. Chuang (IBM / Stanford University). Since buying this book it's taken me six years to plow through its 675 pages, but I think in this field at least, I might at last be suitably qualified to discuss just the very basics.

Warning! Metaphorical trainwreckage ahead!

This coming apocalypse will be the greatest ever sea change in the history of practical computing. One thing that might help us weather the storm, would be a source of analogies and comparisons to known references. It was a total blast recently to find a beautiful example of just such an analogy, hiding in plain sight, in the formal language subject of regular expression parsing.

All clear!

The Go Guy

Russ Cox, one of the people behind Google's new programming language Go - and apparently played here by the famous mathematical genius Will Hunting - has just this week completed the third article in his (hopefully!) three part series on the history, theory, and programming practice of regular expressions. Parts one and two have been available since Jan 2007 and Dec 2009 respectively; and inevitably, the sudden and unexpected appearance of part three has forced me to revisit those earlier articles, to refresh the old volatile storage units.

So here's the deal. You've probably heard that unlike classical "bits", each of which is at any given time in either its '0' state or its '1' state, the unit of quantum computation, the "qubit", can somehow be in more than one state at a time. It's said to be in a superposition of states, which is a kind of blurry combination of 0 and 1. It's only when we make a measurement, aka an observation, also what we may now begin calling a computation, that the quantum state or wave function "collapses" into either 0 or 1.

How does this help us compute stuff? Well, it all has to do with the preparation of the initial state of the qubit. I'll be going into that in quite a lot of detail in another article soon, but for now, just know that we prepare a superposition state of qubits, then later we read the evolved state.

So, what could all of this possibly have to do with regular expressions? The connecting tissue is of course this idea of state.

Going Back

Regular expression parsers are best modelled by finite automata: machines with states. Sometimes these are deterministic; given the current state and the next input character, we can always determine uniquely the new state of the machine. Sometimes they are not. It's these non-deterministic finite automata, or NFAs, that interest us here.

Russ's first example uses the pattern A(BB)+A, which matches any input string containing an A, followed by one or more pairs of Bs, then finally terminated by another A. This machine is deterministic; as we scan the input string, say ABBBBA, one character at a time, we move from our starting state, into a found A state, then a found AB state (i.e., found an A followed by an odd number of Bs), then found ABB (an even number of Bs), then back to found AB, forward again to found ABB, then at last upon reading the terminating A from the input string, we end up in a final success - match found state.

Whenever we find that the next state is not uniquely determined by the combination of the current state and the next input character, we can place markers in the pattern and the input string, make an arbitrary selection of the new state, and proceed just as before to see if we reach a match. If we fail, then we can use these markers to backtrack to the earlier decision point, make an alternative choice of new state, and retry. Eventually we'll find a match, or run out of input, or else we'll have tried every available route through the labyrinth, without reaching that final success - match found state.

Go Faster!

From a computational viewpoint, it's this backtracking that's the problem. It can lead to your regex matching code taking an exponential amount of time to decide match or no match.

In 1968 Ken Thompson (of "Thompson and Ritchie" Unix fame), in his CTSS text editor QED, introduced programmers to a superior theoretical approach. And when I say superior, well, just look at Russ's graphical comparison of execution time against x, where the test pattern (superscripts representing repetition) is A?^xA^x, and the input string is A^x. For the absolute avoidance of doubt: when x=3, the pattern is A?A?A?AAA, and the input string is AAA.

The upper, red curve represents the worst case performance of a backtracking algorithm, of the type which is still widely used today, for example in Java, Perl, PHP, Python, and Ruby. The lower, blue curve represents Ken Thompson's Nondeterministic Finite Automata. And why didn't Russ plot them on the same graph? Look at the vertical axes. One is in seconds, the other microseconds.

So that's settled then, we should all be using Thompson NFA in our Regex implementations. But just before we do, exactly what is its secret anyway? How does it avoid the exponential explosion?

Go Quantum

The secret is to do away with backtracking entirely. Whenever we come to a fork in the road, and we can't guess which turn may lead to a successful match, we take all available turns simultaneously. In other words, we choose the new state to be the set of all available, possible new states. Then the simple, plodding algorithm proceeds as before, but now effectively following multiple threads at once. What matters is simply whether any one of these threads reaches the final success - match found state, or whether we reach a total mismatch blockage, or run out of input.

Multiple new states may coalesce back into one, split again, and so on. But at any given point, the set of current states represents everywhere in state machine space that we could have legally reached, given the input so far. Exactly how we got there is unimportant; we only care that there was a way. So we're not actually following a bunch of threads. The threads have dissolved. All we ever have is that set of current states.

And then, if one of these states does eventually transition to the final success - match found state, the bubble bursts; the wave function collapses; an experimental determination is made.

Go On! You're Having A Laugh!

Of course, this is nothing more than an analogy, designed to help us get our heads around one particular aspect of quantum computation. As soon as you begin to push it, it breaks down. More generally, all attempts to simulate the operation of the quantum realm using classical systems are doomed to failure and disappointment, as I'll be recounting soon in the forthcoming review of the forementioned 10 year old book that took me 6 years to read (note: if you change "quantum" to "parallel", then the new analogy holds much more water). But as an adjunct to a layman's introduction to the spooky realm, I hope that like me, you will find it quite apposite.

If you're particularly interested in his (beautiful!) coverage of regular expressions, here are the links to Russ's entire series:

1. Regular Expression Matching Can Be Simple And Fast (but is slow in Java, Perl, PHP, Python, Ruby, ...)
2. Regular Expression Matching: the Virtual Machine Approach
3. Regular Expression Matching in the Wild

Only the first third of the first article is needed to illustrate the preceding ideas. So like I say, if you think you could benefit from another diagram or two, click through right now.

More Big Numbers

That's a Lotta Watts

And speaking of the sun's total energy output, as we were here, I forgot to explain the quiet chuckle which you might have heard just then. If you were in my house, that is, during the first programme of the tremendous new TV series Wonders of the Solar System, presented by ex-D:Ream keyboardist and the BBC's new go-to guy for physics, Professor Brian Cox.

This would be better told as a cartoon, ideally; but without the required skills, all I can offer is the following background.

There's a scene in the great 1999 Star Trek spoof movie Galaxy Quest set at a show convention, where the announcer, introducing Tim Allen's character, the main star of the TV series, builds the tension by simulating an echo using just his voice:

And finally, my fellow Questerians, the brave Commander of the NSEA Protector: Peter, Peter, Peter, Peter, Quincy, Quincy, Quincy, Quincy, Taggart, Taggart, Taggart, Taggart!

Now it turns out that Professor Brian didn't have the benefit of my previous post when making his BBC programme, so when it came time to divulge his big powerful number, the phrase point three hellawatts probably didn't occur to him. Instead, knowing how badly such numbers can confound the layman, he went with:

Three hundred million million million million Watts.

Which you know, kinda made it sound like he was just saying "300MW", but in a really ham dramatic way.

I know, but it sounded a lot funnier in my head...

Hella Big - Helio Small

Stop Saying That!

There's a proposal, currently before the International Committee for Weights and Measures, to add the prefix "hella" to the internationally recognised system of powers of ten. As is standard issue today, the motion comes fully equipped with its own official petition, in the guise of a Facebook Group, currently standing at 51,598 signatures. Not a hella big number, when you consider they're trying to convince the notoriously conservative Comité international des poids et mesures, to adopt into their sanctum sanctorum, an arbitrary particle of borderline-offensive slang, originating in the Hunters Point neighbourhood of San Francisco.

But the idea's supporters, including University of California physics student Austin Sendek who started the campaign, reckon it would be a good way to honour the state's impressive record of scientific research. It would be the first such change since 1991, when "zetta" and "yotta" were added to represent respectively the 21st and 24th powers of 10 ("hella" is proposed to stand for the 27th).

In our industry of information technology, we have yet to see the introduction of the corresponding powers of 2 in common use. But now that the creaky old engines have finally begun their increasingly steep ascent from our accustomed 32-bit plateau, where we have been swinging happily in hammocks since Intel treated us, in 1985, to the 80386 processor, and the end of the segmented memory management hell we had thought would never end, it won't be so much longer before we are routinely allocating zettabytes and yottabytes in the cloud. Can the hellabyte be hella far behind?

Hello World

One corollary caveat I'd like to raise is the issue of inverse, or negative, powers of 10. These conventionally end in "-o", and with the changes introduced in 1991, have begun to mirror the positive powers; hence, "zepto" (10^-21), "yocto" (10^-24). Presumably the "hella" proposal, properly formulated (I haven't read it, that would spoil my punchline), should contain a similar provision such as "helio", or maybe "hello", for 10^-27?

In which case, if the sun's output is 0.3 hellawatts, then a Watt must be 3.3 heliosuns.

Or: if the world's mass is 6 hellagrams, then six grams make a helloworld.

Thank you, thank you very much. I'm here all week.

Horizon: A Return To Form?

The Secret Life of Dogs

Last night's Horizon programme on BBC2 was a pleasant surprise.

As someone who doesn't need words like "history" or "phenomenology" to be erased from a title, or replaced by the now ubiquitous "secret life", I thought I'd more or less stopped watching this once brilliant documentary series, following its embarrassing dalliance in co-productions with The Discovery Channel, the consequent and inevitable "dumbing-down" (incidentally, an ugly and contemptible Americanism; what has this to do with speech impairment?), and the stripping out of any vestige of science, to be replaced by sensationalist, physically incorrect graphics, and equally inaccurate drone overs.

But having recently lost my super smart (so sue me!) Border Collie, I was irresistibly drawn in by yesterday's preview footage of "Betsy", the Austrian BC who knows over 340 words:

Betsy (photo copyright © BBC 2009)

She can fetch any object in her repertoire by name. She can also fetch it when shown a different, smaller version of it. Or even a photograph, or a drawing of it. None of this, of course, came as any surprise to the Border Collie lovers in this house! But it did make the evening's Horizon compulsory viewing.

Return of the Couch Potato

Pass those Doritos, baby! What was great about this documentary? I could sit watching TV for an hour, and feel that I'd learned at least a good half dozen things I hadn't known.

For example, dogs read human faces exactly as we do, viz. with right side bias. Dogs do not read other dogs in this way; it's an adaptation geared exclusively around interpreting their human owners' expressions. Dogs can also respond correctly to pointing, something that even our nearest relatives in the primate group do not learn. In fact, they can respond correctly to only a glance in a particular direction, just as if it were a direct command.

Barking is another revelation, once you're reminded that wild dogs, and the grey wolves they're descended from, don't actually bark very much at all. In fact, domesticated dogs seem to use some half dozen or more quite distinct barks as an inter special language to communicate various messages to us, and we correctly interpret these (e.g. from audio recordings) as "Get off of my lawn", "Great to see you", "So throw the bloody ball then", and so on.

Using blood samples from both, petting is found to be correlated with oxytocin releases in dog and owner, leading to reductions in their heart rates and blood pressures, and ultimately, stress levels.

Dogs are also now thought to have had an indispensable role to play in our species' transition from hunting and gathering, to animal husbandry and agriculture. Recent research suggests they may have started to cohabit and co-evolve with us much earlier than previously thought, perhaps up to 100,000 years ago.

Most of these "discoveries" are between one and many years old, and are of course multiply reported elsewhere. The health benefits of animal petting, for example, have been recognised by health care professionals for some time.

But what Horizon has done so brilliantly in the past, and so memorably, in areas such as standard model physics, or the microprocessor revolution, and what it now seems capable of doing once again, is this: drawing together the threads of recent research in an interdisciplinary and international context, throwing into focus a startling image of the current state of our knowledge in some area of science or technology. Like this week's...

Special Guest Star: Genetics

Domestication, and not socialization, emerges as the key to our unique relationship with dogs. In other words, nature and not nurture; the selected genetic blueprint, and not experience. This was proved in well-designed experiments to socialize wolf cubs, which regardless of their environment, reverted inexorably to aggression as they matured.

We saw the famous large scale fox breeding programme in Siberia, where in 1959, Soviet scientists began their attempts to domesticate silver foxes, selected from local fur farms. Those experiments continue to this day, but one of their earliest and most striking results was that within three generations (three years) of selecting that one percent of foxes who exhibited neither fear nor aggression, and successively allowing these to interbreed, the resultant population emerged as almost uniformly tame, fear and aggression having been all but eliminated. Within eight generations, as soon as they opened their eyes and began to crawl, these foxes sought out contact with humans, showing affection to them. And just as with the wolf cubs, cross-fostering, giving aggressive cubs to tame mothers and vice-versa, has no effect; aggressive cubs retain their aggression, and tame ones their tameness. In fact, even embryo transplant fails to break this genetic disposition.

The programme featured Cornell geneticist Dr Anna Kukekova, who has travelled over 5000 miles to study these foxes, discussing a "biology of tameness", but there was no sensationalist, tabloid attempt to leap to unwarranted conclusions about other species. There is, we are told, "not one gene, but a complex orchestra of them" at work here.

We saw the curious secondary juvenile characteristics that selection for tameness brings out: varied coat colours and patterns, floppy ears, shorter curly tails, shorter limbs. "What this shows, is that when you select against aggression, you get almost all the same suite of changes that you see when you compare dogs to wolves" - Duke University anthropologist Prof Brian Hare, another visitor to the Siberian breeding programme.

The programme ended with a survey of gene mutation research into diseases common between people and dogs. The comparatively narrow gene pool within a particular dog breed, combined with the known map of the dog genome (in 2005), makes the pinpointing of such mutations far easier to achieve, and even to automate in a genotyping machine, than in human populations.

Welcome back, Horizon. More of this quality please.

Available on iPlayer until 7th April 2010: http://bbc.co.uk/i/pssgh/

Observations on Observations

What The Hell Is Going On?

Last week, and in fact part of the week before, we saw the tenth anniversary of Canada's Premier Institute for Theoretical Physics celebrated with a festival: Quantum to Cosmos: Ideas for the Future. One fascinating discussion, picked up by New Scientist and widely disseminated, took place when a panel of leading physicists ran headlong into the question, "What keeps you awake at night?"

Seven questions that keep physicists up at night (New Scientist)

Topics in the above article include the anthropic principle; the continuous annihilation of dark matter; the nature of dark energy; emergent complexity; string theory; the holographic principle and the (cosmological) singularity; entanglement and the nature of observation; and rounding off all this, the limits of knowledge. For deeper coverage, the festival site has many video clips on a breathtaking array of subjects, in no way limited to the preceding list, and all available to watch here:

http://www.q2cfestival.com/schedule

Disclaimer: the random musings that follow below are presented for amusement only, and have no connection with any person who knows what they're talking about. They're just three speculations with a slender common thread. Also, the Lottery references are to the UK National Lottery; lastly, and most importantly, there is a "u" in "colour".

Observing A System

Observers, and their universe. They observe it, don't they? Well in a way, but remember, what they actually observe is the universe that contains them; in other words, they're a part of what is being observed.

An observer can observe some small part of the universe. Another observer, for instance. Or even itself. It can be said to be observing the entirety of the universe, excepting itself - which is what I usually imagine whenever I hear the term "observer". Something outside the universe, looking in. Yet that's not really what we have here. Instead, we have a small part of the universe, observing another part of itself.

Isn't there a sense in which the spatial distinctions implied by that account are illusory? When particles are entangled, for example, they act in all respects like immediate neighbours, regardless of the distance between them. And all distances are measured over the full set of dimensions, not just three arbitrarily selected spatial ones. So, could an observer be considered as extending over multiple, seemingly disjoint and disconnected, regions of space-time?

What's an observation anyway? Just a collection of particle interactions? When I observe a sunset, electrons in my cells are receiving, or interacting with, photons that originated something over 92 million miles away. Seems to me that a single Feynman diagram should suffice to picture that situation.

Now, let's try to zoom in on the observer here. In doing so, we conceptualize ourselves as some kind of meta-observer, which seeks to reduce the sunset-beholder to its lowest terms. Those electrons in my body, the ones doing the interaction with the sun's photons, well they had certainly better be counted as comprising part of our observer. What about the atomic nuclei they associate with? Curiously, if you trace the paths of the neural signals from my retinae through to my visual cortex, you will be following electron-photon interactions, in combination with almost imperceptible gross movement of particular electrons, all the way down. The bulk of the atoms, the atomic nuclei, will play absolutely no part in the act of sunset observation, other than as a static scaffolding giving those electrons somewhere to be. Even then, it's only the outermost shell of electrons in a given atom, that play any part in this process.

Certainly at the other end of this interaction, the sun, we have a quite different process which is producing the photons in the first place. And yes, that end does in fact require some involvement on the part of the local atomic nuclei. But from that point onward, the observation event is just an electromagnetic dance, ending with certain chemical changes in my nervous system.

What makes this sequence of interactions so special? What characterizes an observation, what distinguishes it from any other situation in which photons are exchanged between electrons? Take any photon in transit from old sol. Quantum electrodynamics tells us that it can split quite spontaneously into a positron and an electron, which then recombine, eliminating each other and producing a photon. This might happen any number of times during its eight minute journey to Earth. Upon hitting the upper atmosphere, it may then find itself absorbed by one of the outer electrons of a gas atom, causing a transition to an excited state. Do any of these interactions of the photon qualify as an "observation"? If not, then how exactly do they differ from the case where that excitable electron was in my eyeball, or the middle of my head?

Much of this can be encapsulated in the thermodynamical concept of a system. When we seem to peer out at the world, observing it as we might, we treat it as one closed system - with ourselves outside of it. This works well enough for observation of everyday objects at a sensible scale, for example, the balls on a snooker table. As the system shrinks, it begins to pull me in, until I find myself trying to observe single photons, and discover that the only way I can do so is to absorb them entirely into my body. They have left the system, escaped from the experiment; or to put it another way, I have become, bodily, a part of it.

No surprise then, to discover certain corollaries to this, such as: it's impossible to measure anything without changing it. Imperceptibly perhaps, but in the end it's all just a matter of scale. A voltmeter draws a tiny current in order to operate; this current causes a corresponding drop in the voltage across the source's internal impedance, with the result that the displayed voltage is slightly different from the value prior to measurement.

Observation is interaction: all the way down.

Deal Or No Deal

One of my better high school teachers, in chemistry as it happens, had a pet theory about the symmetry of time. We are talking 1974 here, when such ideas were popular only with certain types of crackpot, and quite invisible elsewhere. One day a few of us stayed behind after class to ask him a question or two about electron orbits, and somehow we got sidetracked into this idea of his. Next thing we knew he'd produced a pack of playing cards, which he proceeded to shuffle, then demanded that I start predicting the colour, red or black, of each card as he turned it over.

I started off well. Can't remember the exact sequence, save for the fact that it had a long run of about half a dozen reds near the start, but I certainly got into double figures, somewhere between 12 and 16 cards, without getting a single guess (prediction?) incorrect. Aware of being watched by my friends, I called out every one of those colours with complete confidence.

Then I paused, saying aloud, something like "This is too freaky. I'm going to start getting them wrong now." And the next half dozen or so were indeed wrong, just as I predicted. After that, I stopped and refused to continue. For some reason unknown, I had become fearful of getting one guess incorrect!

At the age of 16 I had an undeniable desire to impress my peers, and I'm certain that had a lot to do with the outcome of our little experiment; and perhaps, with my sudden desire to stop before the first, inevitable, failure. But what are the chances of getting this sequence of results? That's an easy calculation: somewhere between 1 in 262,144 (assuming 12 cards in my first run, followed by 6 correctly predicted mismatches) and 1 in 4,194,304 (assuming 16 + 6).

Throughout the trial, I had the unmistakable feeling - consistent with my teacher's pet theory - that I was in some sense reaching a little into the very immediate future, and somehow capturing a "memory", which I would rather term a "conviction", of what colour the next card would turn out to be. The closer you are to an event in time, he reckoned, the easier it should be to "remember" - regardless of whether it's a past or a future event.

Scott Adams, he of Dilbert fame, has written about this at some length, although he frames it very differently. When he talks about affirmations, for example in The Dilbert Future (p. 246, also Appendix A), I detect the same as-yet poorly understood phenomenon, the tricking with time, the constant falling-through into particular possible futures. Recently, Noel Edmonds has made much capital of a poorly understood, mysticised and new-aged-up version of the same idea, awkwardly framed as half philosophy, half self-help guide.

Richard Feynman's Quantum Electrodynamics, The Strange Theory of Light and Matter, contains a lucid account of the summing-over-all-histories method of prediction. At any given point in space-time, a given quantum has a certain propensity to move to any other such point. A lot of these propensities cancel out; others are bunched up in a particular direction, and hey presto, if that's not just where the darned thing goes.

Propensity: might be a good term to use for the complex square root of a probability! Better than Amplitude, at any rate.

When the Lotto [UK] balls tumble on a Saturday night, all fourteen million possible outcomes are represented by such propensities. Is there any way to force these to "bunch up" in a particular direction, so that a predetermined set of six numbers comes out?

Actually the signs aren't all that good. Under some modern interpretations of quantum mechanics, all of these possible worlds cascade forward into actual existence. Picture fourteen million distinct new realities, complete new universes, splitting off in unknown dimensions from a common starting point, the Saturday night lottery machine. Each new universe contains a replica of me, and most of these - almost all of them, in fact - have not just won the lottery.

Would there be any visible, observable indications if this interpretation were incorrect? Maybe there is but one actual reality, after all. Maybe I can bunch up the fibres of propensity in my favour, perhaps by leaving lots of little notes lying around, notes whose existence, or whose observation, would make certain lottery outcomes much less likely than others?

Observation is interaction: all the way down.

The Digital Universe

The majority of physicists today, when they can be pressed to opine on the matter (and many refuse), appear to be of a consensus that our universe is a simulation. At least, that's my impression of that community, from what I've read, both in the popular science press, and here on the web. However there's so much material available on the subject, it would be fatuous to pick out one such reference to "prove" my assertion. So you'll just have to do your own research, and form your own impression.

True or not, academically popular or shunned, this has undeniably been a favourite theme of much science fiction since the first half of the 20th century, and a favourite subject of philosophers much further back than that. It's inevitably one of those possibilities that enters your head when wrestling with quantum mechanical concepts. But in either of those contexts, it can't be said to have any more validity than, say, extrapolating the model of the atom as a solar system, in an indefinite recursion, without paying heed to the many and fundamental differences and incompatibilities between the two pictures.

What brought it home to me, after more than 35 years of programming these wonderful little digital systems, was a development in Loop Quantum Gravity. Specifically, a proposal to measure the stretching out of the spectrum of light coming to us across billions of light years, to see whether the discrepancies between the red and the blue predicted by quantized space were actually present. And why should the universe be quantized? Maybe because it's nothing more than the state of a digital simulation!

It seems likely that if anything is quantized (the available energy levels of an electron, for instance), then everything will be, including space-time. And by that is obviously meant, the entire M-dimensional manifold of our being, whatever that value of M eventually turns out to be.

Now consider the digital system on which our simulation is running. From our experience of software development, our knowledge of mathematics, the availability and impossibility of various algorithms, and the success of the neural net approaches, we would probably admit that the system software of this universe is genetic in its nature and approach. And once again, when it's laid out like that, it becomes clear. Of course nature uses genetic algorithms, where else would our brains - products of these methods - have picked up the idea?

Now, can we divine any information about who might be running this simulation? If the general argument is valid, making it vanishingly unlikely that we are not such a phenomenon, then it can be applied recursively to establish that we are "almost certainly" a simulation being run by a simulation, much as recent Sims games have your little creations running their own Sims. And so on, ad absurdum.

Actually there are several ways out of this reductio, each more fascinating than the next; see Paul Davies's Goldilocks Enigma for a full treatment.

At first glance, there doesn't seem to be much that we can infer about any of those higher levels, just from looking at this great universe of ours. However, if we assume that we are a simulation with a purpose, then it becomes likely (or at the very least, rational to assume) that we are observed. Shouldn't there be implications for our ability to detect such acts of observation?

Observation is interaction: all the way down.

And Finally: How It All Fits Together

Erm... on second thoughts actually, details are left as an exercise for the reader. Don't say I'm not good to you.