Going to make that point myself. There is 'four score' in English, and an old Northumbrian counting scheme that used to count in multiples of 20 ('chiggit'). Weirdly enough, 'quatre vingts' seems a compartively recent invention: I am told 'ottante' was used in Belgium around WW1. This counting style may not have been ancient.

The UK laws granted a sole case of perpetual rights to 'Peter Pan', which J.M.Barrie had given to the Great Ormond Children's hospital. This isn't quite copyright that 'never grows up' ( see http://www.gosh.org/gen/peterpan/copyright/faq ), but it comes pretty close. I think the UK legislation could be a bit flexible to a time traveller too.

This is happening in a non-linear medium where photons interact: it can't happen in free air. Photons hardly interact on most transparent media, but there are materials with non-linear electric properties that can be used to generate harmonics ( see for example http://en.wikipedia.org/wiki/Second-harmonic_generation ). This is used to convert red light into green in some green laser light pointers. At high power levels, the refractive index increases in more normal materials, which is a nuisance in high-power lasers as light in NdYg glass laser elements can self-focus and damaage the apparatus if the power gets too great.

Hardly "contrary to decades of accepted wisdom about the nature of light" if you can find it in a green laser pointer. Meh.

I do not think the original article was a success for various reasons. It is not easy to explain quantum mechanics convincingly, and I don't think the lack of equations was a main weakness. Those of us who are happy with equations with Hamiltonian operators and eigensolutions probably understand the uncertainty principle too. Those of us who have not touched serious maths, or have done it too long ago will be made to feel stupid rather than being helped.

I think what the article needs was good pictures. How about...

A picture of the Young's slit experiment. A light wave goes through two slits, and interferes with itself. You get fringe patterns. You can calculate the fringe patterns using classical physics.

A picture of the Stern-Gerlach experiment. An electron beam is split into two and interferes with itself. You get similar fringe patterns. What, what? This works with electrons? Yes, it even works with substantial molecules such as buckyballs. In fact, if you did your Young's Slit experiment with a very dim light source and a long integration time, you would be passing photons, one at a time, through the apparatus.

So, when a particle interferes with itself, does it go through the left slit or the right one? Some people say it goes through both, but it doesn't, really. The wave function, which we can calculate but we can't measure, may go through both slits in some senses, and determine the fringe pattern. If we install a detector that can tell us the electron is going through the left slit, or going through the right slit, then the electron goes through one slit, and we do not get the interference pattern. We can know which slit the electron goes through, or we can predict the interference pattern, but we can't do both.

A picture of a wave packet plotted in ordinary space, and in frequency space.

There is nothing magical about the observation, itself. The idea that being observed changes the states dates back to an old and rather unhelpful thing called the Copenhagen model. A better approach is to say that we can measure some property of a particle wavefunction such as the position, or the momentum of the particle; but in measuring the position we lose the ability to also measure the momentum, and vice-versa. In this case, the width of the wave packet determines how accurately we know where the particle is at the time of measurement, while the width in frequency space determines how accurately we know the momentum. Our measurement will tell us what the wavefunction was like at the point of the experiment, but nothing else. This is one form of the Uncertainty principle, but it can be applied to other measurements too.

See, it can be done. If you don't get it, don't worry: small things and quantum stuff are pretty weird.

He was supposed to use the Walther PPK it. It was the standard MoD handgun. The AWE guards used to have them. I expect it still is. But he thought it was too bulky, and preferred a Beretta 418. I am not a big fan of the books, but I picked up 'Dr No' years ago, thinking I ought to see what a Bond book was like, and that bit stuck. The films get that wrong too.

I have always wondered why people build stone circles for astronomical measurements. You could do a lot better by picking some distant landmark - the pass in this case - and moving sideways until the sun or moon appears aligned. Better still, pick something that is above you, so you are looking slightly upwards - if you were trying to mark the position where the sun sets over the sea, there is a lot of atmosphere that may contain clouds and stop the reading, and a lot of distortion. This uses a valley, and a set of sticks in the ground: more accuracy for less effort than stone circles.

Simple way to achieve this with conventional media. Destroy mankind!

Remember when the Hubble telescope first went up, and could not focus? It had all been tested on the ground on an artificial star target. Unfortunately, the test rig had a plate that was about half-an-inch thick that should have been subtracted from the optical path. So they had a mirror that was accurate to about 1/100th of a wave but half an inch in the wrong place.

There was a rocket where the guidance for the two stages had been coded separately. One stage used a value of -9.8 m/s2 for 'g' because it measured heights upwards and the acceleration was downwards, while the other used a value of +9.8 m/s2 and flipped the sign in the equations. When the rocket took off, the first stage was fine but the second stage suddenly flipped over.

That's what I dread: thinking I have checked everything, and thought of everything, and then finding out publicly and expensively that my regression tests were worthless all along.

When I looked at the video, YouTube also offered a trailer for 'Pacific Rim'. Oh, how we laughed.

I remember people doing something like this back in about 1990 using very similar techniques - locating the nostrils, the eyes, the curve of the mouth to generate a real-time animation. Back then, this allowed people to transmit a cartoon over the existing phone network, allowing the deaf to lip-read. Back then, this was a clever idea.

I agree. Are VC's right for you? The alternative in your case might be to look at collaborating directly with people who make video editing products. They will have solved a lot of the dull stuff: getting the different formats of video in and out, making sure the machine hits rate, checking the video passes QA, and having a useable interface. A convincing before and after video ought to be enough.

...we don't know the answer.

We can look at the states before and after a quantum transition, but we cannot try and catch an energetic hydrogen atom that is half-way through emitting a photon. Well, we don't actually know that but a lot of people have tried because not being able to take some process apart really irritates physicists like nothing else, and in the last hundred years, quantum physics has not been cracked open at all. We can tell whether an electron is in a particular orbital, or whether a nucleus can spontaneously decay, but we cannot predict exactly how long it is going to stay in any state other than the ground state, because the ground state has no energy to go anywhere.

We cannot tell when a quantum state is going to change but can another quantum state see something we can't, even if it cannot communicate it? Can you get processes which ping back and forth, or go in circles in a regular fashion; or when a quantum state is reached, is all information lost, and the particle may have been in that state for a quadrillionth of a second or a billion years. My guess, and it is a pure guess with no information behind it, is that the information is lost, and you cannot get these cyclic quantum events. We shall see. Or not.

Not sure about the piezoelectric bit, though.

Ok, I'll have a stab at it. First of all, ignore the 'crystals of time' hoopla. This is not helpful.

Imagine a hydrogen atom with one electron and a fixed nucleus. The electron will be in a certain orbital. If you are thinking of the atom according to the Bohr model, the the electron is going around the nucleus like a planet around the sun. However, the position of the electron, or rather the probably of finding the electron in any particular position, is determined by a wave-function. This wave-function is a complex number that varies with space, and possibly with time too. You cannot measure this complex function directly, but if you can detect the particle somehow, you might learn something about the value the wave function had before the measurement started.

Actually, the stable hydrogen atom wave-function is simple and calculable, and just like the simple harmonic oscillator, it does not change with time. The electron is in a stable orbit, and will need to lose energy or gain energy to go to a different orbit. The same is true for many much more complex wave-functions. If you have a current running in a superconducting loop, then all the electrons in the superconducting band can be described by a single giant wave-function. You still have all the individual electrons, but they are all moving in a coherent manner, so they are not losing energy. Indeed, they probably got into that state by taking energy from the giant wave-state, until it reached some local stable minimum. And even though you may have billions of electrons in the wave-state, the wave-function does not change with time unless something disturbs it.

Okay, the idea of sucking out energy until a particle or a system reaches a stable state is pretty common, but it is not necessarily universal. You could have two hydrogen atoms, one with the electron in the ground state, and one with the electron in an excited state; and the second atom loses its energy to the first one, and after a while, the first atom gives it back to the second one again, and so it goes on. In real life, the atom would probably emit a photon that would not get caught by the other one, and that would be the end of it. But if you could somehow constrain the photon to just bounce between the two atoms, then you have two electron wave functions that are perpetually flipping between two states in such a way that energy is preserved. This cyclic flipping would mean that the whole system gets back to where it was a short while ago: it is something that happens at regular intervals in time, hence the 'crystals in time' bit. Ugh. Can we describe the whole system, including whatever it is that constrains it by a bigger wave-function that does not change with time, like our superconductors? It's a bit unlikely, because the jumping between states and emitting or absorbing a photon is a sudden transition, where the super-electron interactions were smooth and continuous. But there might be a way.

An error with an Excel spreadsheet looses Belgium, and the corresponding warp in the data space plays with the world economy? The only logical explanation is someone in Heaven has hired Douglas Adams to make reality 'more interesting'.

This is at complete variance with Hardy's description of him. Hardy and Ramanujan were opposites: Hardy gloried in mathematical rigour, where Ramanujan seemed to work by instinct. Hardy described with awed fascination what it was like working with this wholly alien mind. Ramanujan sometimes seemed to guess the form of a solution instantly and without effort, and then work backwards from that to derive the proof that Hardy insisted upon. Freeman Dyson says much the same. There are many first-class mathematicians who have contributed more to mathematics than Ramanujan did, but he still has this unique reputation. So much so, indeed, that some people see his talent as proof of the Vedic deities that he said gave him the answers. I don't believe this myself, but if others of his temple started showing the same talents, I would be impressed. But no, he seems to be the only one of his kind. He had a unique talent way beyond "reasonably bright". He had a placid personality, utterly free of "raging obsession". Otherwise OK.