Single Loop Roller Coaster

Oh, I don’t feel so good1.

Peter Griffin

Gravity is a contributing factor in nearly 73 percent of all accidents involving falling objects.

Dave Barry


I know that in cartoons the laws of physics are different2, but none of O’Donnell’s laws of cartoon motion seem to apply and there are a few things in this little clip that suggest the makers actually thought about this problem so I decided to find out if it is possible for Peter to be at the right place at the right time to catch his own puke. 

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William the Conqueror

William as depicted in the Bayeux Tapestry during the Battle of Hastings, lifting his helm to show that he is still alive1.


But to the extent that ancestry is considered in genealogical rather than genetic terms, our findings suggest a remarkable proposition: no matter the languages we speak or the colour of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who laboured to build the Great Pyramid of Khufu.

J.T. Chang2.



One of the things in Dan Brown’s book The Da Vinci Code that really ground my gears to a complete stop was the ‘revelation’ that Sophie Neveu and her little brother are descendants of Jesus and Mary Magdalene. At the time I thought the whole concept was ridiculous, because in every one of the 67 generations between the year zero and the present Jesus’ and Maria’s genes were halved, and nothing would be left, not even a base pair3. I never read another of his books.

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Heron versus Tench

I saw this grey  heron (Ardea cinerea) while riding my bicycle along the Oosteinderweg, near Aalsmeer, probably just after it caught a tench (Tinca tinca). The weather wasn’t great, so I upped the ISO a bit, to 1250, but nevertheless the pictures came out nice, or at least interesting.  In view of all the scratches on its beak, it is probably an older bird, and it is likely not his first large fish.


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Carnot’s own Cycles

Detail from “Il Grande Quadro”, Enrico Baj.

He who refuses to do arithmetic is doomed to talk nonsense.

John McCarthy.


Carnot was not a great mathematician, and not a deep thinker either. Otherwise he would certainly have caught the inconsistencies in his own theory. Had he been a better mathematician he could have derived, from the experimental data available to him, that heat cannot be a conserved quantity.  Had he been a better thinker, he would have understood how his calculation of the amount of work from a given quantity of heat is inconsistent with the principles he laid down for his heat engine to have maximum efficiency. I’ll devote another post to heat as a conserved quantity. In this one I discuss the second point: what is the according to Carnot the maximum amount of work we can get from the heat needed to raise the temperature of one kilogram of water by one degree? And why can’t his calculation possibly be correct?

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Carnot Cycle for the Photon Gas

Light is something like raindrops. Each little lump of light is called a photon and if the light is all one color, all the “raindrops” are the same.

R.P. Feynman.



The photon gas, a box filled with little light lumps, plays a very important role in physics. As a source of black body radiation — collect the photons coming from a small hole in the box and sort them by energy — it put Planck on the road to quantum mechanics, and although his hope that electromagnetic radiation was the origin of irreversibility did not work out as he intended, it is well worth studying this idea.  Here, however, I investigate the photon gas as a medium for a Carnot engine.

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Entropy 1

Prospects are good for laboratory construction and testing of this solid state Maxwell demon in the near future.

D. Sheehan1 (2002).




Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don’t understand it, but by that time you are so used to it, it doesn’t bother you any more.

This quote by Arnold Sommerfeld summarizes my state of mind from the moment I had taught thermodynamics for the third or fourth time. I could do all the exercises and answer almost all student questions (for them it was the first time, so it did not matter what the answer was anyway), but now that I don’t have to do this any more my lack of  understanding does bother me. So I did the stupidest thing you can do: go back to the original literature, Reflections on the Motive Power of Fire, by S. Carnot. Read more

Bremmer’s land

Mute swan (Cygnus olor).

Bremmer’s land (“Landje van Bremmer”) is a small pasture in Oegstgeest at the Leiden border close to where I live. It is adjacent to a park belonging to castle “Endegeest”, and next to a eco plant nursery: “De Groene Cirkel” (The Green Cirkel). So far I was able to get a decent picture of more than 20 species of bird I found in this area.

In this post I show a few of those pictures. Click on them for a larger view, or an album.

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Apparent Paradox?

We demand rigidly defined areas of doubt and uncertainty.

Douglas Adams



In 2001 Bartell published a paper [1] in which he posed, among others, the following question:


Suppose \(N\) photons of frequency \(\nu\) are emitted by a laser aimed at a stationary black body. The black body absorbs the energy \(nh\nu\) and converts it to thermal energy (heat). Compare this with the energy \(N h\nu’\) absorbed if the black body is moving away from the source. By the Doppler effect, \(\nu’\) is less than \(\nu\) and consequently the absorber sees and absorbs photons of lower energy than emitted by the laser. Where did the extra energy go? The answer to this simple question eludes many physical chemistry professors. It does, however, yield some important results

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