Optics for Mathematicagicians

Update: I've added the original gif, linked from Flickr as a movie and it seems to be working a bit better this time.

It's taken me far longer to process this animation file than it has to create the short movie from Mathematica in the first place.

This is all in relation to the talk on atmospheric optics which I'll be giving this week, and is now being advertised on the regional weather website! Not quite sure how that all happened.

I wanted to create a little animation to illustrate some of the properties of a rainbow. In particular I wanted to illustrate Alexander's dark band, the dark region between a primary rainbow and a secondary. To do this you really need to understand the path of light rays going through a water droplet (thankfully water droplets are pretty close to spherical, otherwise the simple trigonometry would become significantly less trivial). I've just done the animation for the ray path for the primary bow, but this illustrates very nicely some of the properties of that bow.

The animation is in two parts. The first part looks at light rays going through a water droplet with two refractions and one reflection. At each refraction point there is a splitting in the colours, though I have only used red, yellow and blue as an example (really for best contrast).

I illustrate these paths for several impact parameters (how far the ray is from that ray which would go straight through the centre of the droplet).

The second part is then to build up the density of light rays so you can see the collective phenomenon (rather than the single path). The final diagram is that of around 100 rays coming in, in an even distribution of impact distances (which is the realistic distribution). One can see several things about this.

The first thing to notice is that none of the light comes out at a greater angle than around 43 degrees to the angle of incidence. However, in the region between about 43 and 41 degrees there is the highest density of rays coming out. The red, which is refracted least, has the highest distribution at around 43 degrees, and the blue, which is refracted most comes out at about 41 degrees. After this, the distribution (between 0 and 41 degrees) is roughly equal for all colours and therefore the light inside the bow is pretty much that of light passing through air (blue).

If you imagine what happens when you populate the sky with such droplets the overall effect is clear. You will see nothing reflected at more than 43 degrees (through single internal reflection), which will give a dark band over the top of the bow - the top of which is red. The secondary bow forms at around 50 degrees and is reversed both in colour and in the region where no light is reflected (there is no light reflected in the region below the secondary bow - giving Alexander's dark band. See here on the atopics website for a great example.

Right, now I've got to work out a good animation for the green flash!

Update, overflow and conjunction

Things are just a little too busy at the moment (hence taking five minutes out to write this!). The atmospheric optics talk is taking a little longer to get right than I'd hoped, having not given a pop-science/photography/flashy images talk for many years. On top of this I'm writing up a conference proceedings, tidying up two papers and working on two other projects simultaneously. I also have to think seriously about a talk I'll be giving before Christmas at a meeting in Madrid. Spanish lessons are on hold this week and I'm not even managing to get to my Spanish exchange. I do however have a temporary housemate who is in between flats with whom I can practice Chinese and Spanish and is currently cooking up a feast while I plug away at mathematica.

And before I forget, at the beginning of December, look out in the early night sky for a fantastic conjunction between Jupiter, Venus and the crescent moon

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Kafka in transit

Sometimes the time spent in airports is mirrored in their unending depths. In fact Barajas isn't a bad place to be stranded for a few hours, and I got some work done in between flights from Dublin and to Santiago. More of that soon, I hope.

Click if the image is cut off on the right of your screen.

Interlude

Now in Dublin after a long day yesterday. I spent a tiring but surprisingly enjoyable five hours at the airport in Madrid waiting for the second leg of my journey but a discussion of the strange mix of mathematics and neuroscience I had a chance to read will have to wait.

I'll be giving a seminar tomorrow but will try and write something up tonight if my talk is looking in shape by then.

From Monte Pindo

As we were driving back from Monte Pindo yesterday evening there were some stunning optical effects, not least the reflection of Venus on the sea, making a beam of light leading from the horizon to the shore. Sadly we couldn't stop to get a photo of this. The moon was also just rising as we were going to leave, and as it started to poke above the hill tops there was a magical moment as a wind turbine filled most of the face of the moon. If I had time I would go back to the same spot just to get this image. It was truly stunning!

Monte Pindo and the end of the Earth

It's been a ridiculously busy week this week, though some things never change. We finally got our paper out on Monday, though I have another two somewhere near the end of the pipeline and hope to have them out before Christmas. The rest of the week was busy with getting these a little closer to completion, though Monday night I went out to another film at Cine Europa to see Breath (Soom) by Kim Ki Duk, one of my favourite Korean directors.

Breath is not a film of clear logic and linearity, but it is a beautiful film of deep sentiments and powerful imagery. Kim Ki Duk manages always to lighten his dark subjects with the absurd, and wonderful scenes of a women in a seemingly continual battle with the past singing a love song to an unknown, suicidal man on death row are so full of confusing feelings that you can't help but laugh. The film is going to leave you with questions, which probably don't have answers, but for me I'm happy with this. I would recommend this film if you want some answers to the questions that Herzog was contemplating.

Today has also been a long day as 12 of us, mostly from Couchsurfing, headed out to the coast of Galicia for a day of hiking to the top of Monte Pindo, a rocky hill, some 600m high (11 mile round trip) right on the coast, overlooking Fisterre to the North and the Atlantic to the West. It took us some four hours, including breaks, to make it to the top of this very rocky mountain, but the view was well worth it. In fact this is without a doubt the most stunning view I've seen in Galicia. I have a lot of photos to go through today but I've put together a panorama from the top for now. The large size is pretty huge, and there are still some artifacts from the large contrast in light that can be seen in the sky. Still, click through to see the whole thing in full detail.


In fact, coming down we watched the sunset from half way and the last quarter of an hour was in almost complete darkness. We were exceedingly lucky that we left without a single twisted ankle!

Anyway, tomorrow I have to get on with some work for my trip to Dublin next week and will be cooking in the evening for a bunch of Korean friends. If my kimchi dumplings aren't just like their mothers' I'm going to be in some trouble!

Unofficial holiday boycott

Today most people are away from the department as it's a holiday. However, the holiday is for the USC science departments in the university because today is their Saint's day. The idea of having a Saint's day for a physics department just feels kinda weird to me, so I'm in work, unofficially not on holiday! Of course this still being a predominantly Catholic country such holidays are pretty common and I'll happily take a day or two off at Easter, but simply for the sciences it seems somewhat paradoxical.


On which note I shall get back to work...

Extrasolar planets pictured around sun-like stars for the first time

Some fantastic astronomy news which I'd been waiting for since hints were given a couple of days ago on Dynamics of Cats. Two pictures have just been released with images of extrasolar planets. One star with one planet and another with two planets orbiting it. These bring the total of extrasolar planets found to date to around 300, but this is the first time the planets have actually been pictured (around a normal sized star).

(Image taken from the Hubble press release).  For all the details and an explanation of the above image, head over to Bad Astronomy Blog. See also Dynamics of Cats writeup on this news.

On a side note, if you're around Galicia at the moment, keep an eye out in the sky, conditions seem to be pretty favourable for solar halo viewing at least over the next few days. 

Encounters at the end of the world

Once again Cine Europa comes to Santiago this month, and I hope to make it to more than one film, which was my paltry effort last year.

There are 10-20 films showing every day, from around the world and from many genres and I went yesterday to see the latest film by Werner Herzog, "Encounters at the end of the world" - Herzog's continuing quest to discover something about what makes us human by searching for the extremes that we put ourselves through.

I find watching his films, both documentary and fictional, a rather strange experience.  Herzog's films, more than any other director I know, are more about Herzog than about his subject. One doesn't go to see Encounters at the End of the World to discover a true picture of life at the Antarctic science base, but to hear Herzog's personal thoughts on the peculiarities he sees in such life. The editing and manipulation of the characters is clear and occasionally over the top, making the eccentricities the overriding feature of every character. As long as you go in with your critical senses alert you will be able to experience the world through the eyes of a very accomplished director and this is no bad thing in itself.

If you want a film which shows the beauty of the Antarctic, then there are dozens of more appropriate documentaries out there, but this doesn't detract from the occasional spine-tingling shot, or thought provoking piece of dialogue that is offered. Despite the beauty however, the films overall message is one of warning and pessimism, with little hope for salvation, The end of the world simultaneously taking on multiple meanings.

Through the pessimism however, appears a message, which though my materialist eyes gives a positive spin to the overall theme. Quoting Alan Watts, the forklift truck driver states that:

We are the witness through which the universe becomes conscious of its own glory.

and although Watts' ideas are given a religious overtone, exactly the same can be said in purely physical terms: our minds, being part of the universe, give the universe and not us alone a self-consiousness with which to study itself. This is something that I feel strongly, and this fact alone is enough for me to want to understand the universe more and more, in its huge complexity stemming from such simple principles - principles which we may or may not be alone in trying to understand.

just a thought...

Year on year

My Mathematica programs are biting back today and undocumented interpolationpoints commands are laughing at me every time I turn away. Still, answers are converging in hoped for directions and all should be well soon.

Anyway, I haven't had a chance to write up much more about my trip to Porto, but I will put up a couple more photos from this splendid city.

On the Sunday as I walked around the city with some friends from Couchsurfing, and waited for my midnight bus, I had a chance to go to a few wonderful viewing areas to see the city as the sun was setting. In particular the rather charming Crystal Palace gardens (no longer with a Crystal Palace, but a somewhat less attractive auditorium) gives a great view over the river, with the Port Cellars peppering the opposite bank:

Further along the coast the scenery changes considerably and you get a real view of the ocean and the smell of the sea replaces the smell of ancient city life:

A few more photos to process at some point too, but they will have to wait.

Anyway, everything is busy as ever at the moment, with a short trip to Dublin to give a seminar in a couple of weeks, and a semi-public lecture on atmospheric optics to give at the beginning of December. I'll be heading to Madrid to give a talk at the Christmas meeting too, before heading back home for a few days over Christmas and the new year.

Today we had a fascinating talk on the use of Turing machines to study evolution and I spent lunch quizzing the speaker on many things which have been on my mind since the amazing talks by James Glazier on morphogenisis back in 2007 in Beijing.

On a side note, I've now been living outside China for almost exactly a year. I never imagined how much I would miss the place, and although I'm extremely happy here in Spain, in the department, in the city and in my current position, there is something unreplacable about life in that sprawling, dirty, glorious city of fourteen million, which is at the same time undescribable and unforgettable. I was hugely lucky to have the chance I had in China, and am equally lucky now to be here in Santiago, in a very different, but equally stimulating environment.

Anyway, Mathematica seems to be giving me better answers now, so I should get back to it...

How very unaccommodating!

I wasn't able to do much on the computer since Friday afternoon, as I was being prodded and poked with sharp things around my eyes. Not terribly pleasant, but I came away from the afternoon at the hospital having learnt a little more about the effects of chemicals on the human body!

They had to do a fairly routine exam to measure the shape of my eyeball, but in order to do this with the correct calibration the nurse put in some eyedrops of what I have now determined was presumably a cycloplegic (probably homatropine), which inhibits accommodation (the focusing of the eye by changing the lens' shape) and causes mydriasis (the excessive dilation of the pupil).

A few minutes after putting the eyedrops in, it started becoming harder and harder to focus on things less that a couple of feet away. Slowly my field of vision altered such that everything but the very far was a blur and the light started to hurt my eyes.

It was only after they had done their needling that I got home (helped by a friend), a little shaken, that I looked in the mirror and to my blurred surprise saw my pupils were hugely dilated and unchanging in the presence of bright lights. I had to spend the next day staying away from sunlight which caused me to squint a great deal, though I'm now optically back to normal, even if the original reason I went to the opthalmologists has not improved. Anyway, of course I got a photo of my halloween eyes, though nobody was able to appreciate them as I was sat alone in a dark room listening to That Mitchell and Webb sound.

Kimchi blues

Spending a few weeks in Korea this summer gave me enough times to get completely addicted to kimchi, Korea's highly spiced pickled cabbage dish. Here in Santiago it's virtually impossible to find anything with a hint of heat, so I scouted around on the web and found a few recipes, the most explicit was in video form here. So, I bought the ingredients this week and spent a couple of hours this afternoon transforming this:

into this:

Now I just have to wait for 24 hours until it begins to ferment, and then fit the whole thing in the fridge. I'll be making kimchi mandu ASAP!