Whoops!

This page will document mistakes which are the result of misapplication or ignorance of science and engineering principles. Readers are invited to send us more of this kind of thing, or to provide additional information about the ones already here.

Faulty Vision.

Even worse, one of those rays mysteriously changes direction near the center of the eyelens! The other ray is nearly, but not quite straight there. Apparently the "secrets of the visual sense organ" are still a mystery to the artist and to the editorial staff of the magazine.

The Scientific American once was a good, reliable science magazine. But in recent years it, and other magazines, seem to be pitched at the lowest common denominator of science literacy.

You can read more about this at my science misconceptions page.

Don't judge a book by its cover.

This book cover is from the paperback edition of The Birth of a New Physics by I. Bernard Cohen (Doubleday, 1960). The diagram on the cover is striking, but on closer inspection, one must ask "What's wrong with this picture?"

Clearly it is meant to illustrate Newton's law of gravitation, represented by the equation in the white space below. The symbol D is the distance between the centers of the black spheres, labeled m and m'. But what do the blue and red arrows represent?

They can't be forces, for the mutual forces of attraction acting on the spheres must always be equal size and oppositely directed vectors as required by Newton's third law. Could they be accelerations? No, for the acceleration of the smaller ball is larger than the acceleration of the larger one, the accelerations being in inverse proportion to the masses, satisfying Newton's second law. In short, this artwork fails on several levels, misrepresenting the physics it is supposed to illustrate.

Most likely Prof. Cohen never saw the cover art before the publisher had printed thousands of copies. As one of my colleagues noted, "What can you expect? Its cover price is only 95 cents." I treasure this copy, not only for its excellent contents, but for the cover, which can be used to test whether physics students can spot what's wrong with it.

The little gears that couldn't.

Image credit: Chards.

The artistic designer has used a circle of gears of different sizes in an interlocked array. There are 19 of them. Even if they were sized properly, an odd number of gears meshing around a circle couldn't possibly turn. Each gear turns its neighbor in the opposite direction.

How about an even number of gears meshed around a circle? Contrary to one's intuition, such a system would turn no matter what their size and number of teeth, provided the gear teeth were cut according to good engineering standards. But, even then, the gears wouldn't be doing anything useful.

One hopes British industry is on the move, even if these gears aren't. Does anyone out there have more documentation on this incident, perhaps public and press reaction, lame excuses by the folks responsible, scientists' reactions? Send all such material to the address below.

The coin was introduced in 1997, to be phased into use gradually. You can read more about it at the Tax Free Gold website.

This is a handsome coin, the first bimetallic coin in British coinage. The inner disc is made of cupro-nickel, while the outer ring is made of nickel-brass. (A collector's version in gold and white gold was also made.) One side has the Queen's profile. The side shown above has a design in the center depicting a chariot wheel. Around this are the gears, then a printed circuit, and a pattern which represents the internet. On the milled edge is part of Newton's quote "Standing on the Shoulders of Giants." This is appropriate, since Newton introduced milled coinage in England when he was director of the Mint.

Apparently no one has yet informed the British Mint of this goof, for the 2002 coin still has the locked gears. A 2003 coin had a new design, with the gears replaced by a picture of the structure of DNA, and the edge now reads "Deoxyribonucleic Acid". (Alas, poor Newton; you have been displaced by a molecule.) But then some 2004 coins returned to the gear design. Perhaps someone at the mint does have a sense of humour.

Here's a 2007 update from Darren Dowling in England:

I like to make my students question things and we were discussing gears the other day while learning about loci in a GCSE class. I pointed out the 'error' on the two pound coin and they asked why they did it and why they didn't check first.

So I emailed the Royal Mint and received:

Dear Mr Dowling Thank you for your recent enquiry respecting the 'technology' design on the reverse of the two-pound coin. The idea behind the design is to represent the development of technology through the ages but it is not directed at doing this in a literal way. The artist wanted to convey this theme symbolically and so the number of cogs in one of the rings of the design was not a key consideration in his mind. Your observation is correct and you are not the first person to notice that the number of cogs means the gearing would not strictly speaking work in reality. We would, however, wish to emphasise that this is a coin design symbolic of the development of technology and its success lies in visually representing a complex idea in an interesting and succinct fashion. Best Regards Evelyn Thomas

A nice answer but one that I would call "arty farty wiffle waffle" (actually I would use other words but that is a more polite version). Would it not have been nice to represent the development of technology by applying some basic physics and engineering and seeing if the damn thing worked first? I am pretty sure that is how we managed such a technological revolution. Interesting and succinct ideas stand for little in physics if they clearly incorrect.

Educational researchers at the University of Saskatchewan chose this logo to symbolize cooperative learning. It appears on each page of the printed materials they designed to encourage healthy dynamics within cooperative groups. If this diagram is symbolic of the results of three students working together, the cooperative learning isn't dynamic, but static—at a complete standstill.

This was noticed by William J. Leonard, Department of Physics and Astronomy, University of Massachusetts, Amherst, MA 01003-4525. It appeared in The Physics Teacher, 34, Dec 1996. p. 471.

It's now the year 2002, and graphic designers are still gearing up for gridlock. The picture on the left, from Hitachi, shows six gears in a closed loop, which would have been just fine, if they hadn't put that last gear in the center, meshing with each of the others. [From the "Backspace" page of PC Magazine, Sept 3, 2002.]

This mistake occurs so often, we should set the record straight. This picture (above right) shows a closed loop of four different gears. No two of them have the same diameter, and no two have the same number of teeth. They turn smoothly. Any even number of gears, with parallel axles, or even smooth wheels, can be put into such a loop, and they will turn freely. There's a simple way to prove this, using elementary geometry. Perhaps that homework problem should be assigned to the folks in cooperative learning courses. Here's the answer.

They never learn.

And now, in 2008, ever-alert Bill Beaty sends me yet another picture of buearocratic incompetence. It was nice of people at the Manchester Metroshutttle to number the gears, making it more obvious that there were three—an odd number. We are also puzzled how a city (singular) can work "together" which is something only more than one entity can do. Several cities might work together. The people in a city can. But one city? Oh, well, three gears meshed this way can't work together either. Perhaps in Manchester they speak a different language.

Short measure from the Pennsylvania DEP.

Perhaps this is the new "Metric Lite". One should praise the DEP for an effort to promote metrication in the USA, but their design and/or printing service sabotaged the idea. That's what you get then you contract things out to the lowest bidder. Oh, well, we can always use this ruler in physics classes to demonstrate determinate error.

And pink isn't a spectral color.

The 1973 album "Dark Side of the Moon" (and its more recent CD release) by Pink Floyd features cover art of a prism with a spectrum. It is dramatic, and it is correct in depicting the fact that violet refracts the most and red the least. The colors of the spectrum depicted on this cover are rather impurely rendered, particularly the violet, which looks purple. Purple, magenta, and pink, are not spectral colors. The dispersion (spreading) of the colors is also shown. But the refraction angles at the second prism surface aren't consistent: the rays which are deviated the most in the picture have the least bending at the second surface. The rays deviated the most should also be refracted the most at each surface.

But on the back of the CD case, and on the back of the liner notes booklet, a different version is shown:

Here the spectrum is divergent on entering the prism face, emerging convergent. Refraction doesn't work this way. So unphysical is this rendering, that it's pointless to quibble about whether the order of the spectral colors is correct, or inverted. One suspects this was done deliberately to see if anyone was paying attention. Why else would they make two versions of the picture? Is it something like a movie "outtake"? Now Newton did manage to "recombine" spectral colors into white light using a prism, but he knew enough to use a lens to converge the spectrum onto the prism face.

Mistaken renderings of prism refraction and dispersion are common, even in some science textbooks. The commonest error of all is to show red refracting most, violet the least. Perhaps the reason this mistake is so common is that there's no elementary "explanation" for why refraction varies with frequency the way it does. The reasons are buried in the quantum mechanics of photon absorption and re-emission by atoms, and well beyond the level of elementary textbooks. Now if some reader, well versed in physics, can supply a brief explanation understandable by a college freshman, I'd be happy to post it here, with credit to the author.

Another common error is to show refraction and dispersion only at the second surface. It occurs at both, so one might think that if the spectrum is shown in color outside the prism, the spreading spectrum should also be shown in color within the prism.

Well, maybe not. If there were only a prism and a beam of light, we wouldn't see anything except where the emergent rays fell on something (a screen or wall) which scatters the light into our eyes. If we filled the room with white smoke (not too dense), we could see the colors, but not within the prism. Another way to make a dramatic photo of this kind without smoke is to lay the prism on a white paper, and allow the entering collimated light beam to make a small angle with the paper so that the beam and the spectrum would fall on it all along the path of the light. However, in such a photo, you'd see no colors between the prism faces, for the light would be totally internally reflected at the glass-paper interface.

This picture, courtesy of Richard Berg, rather accurately shows a narrow beam of light passing through a prism which is lying on a textured surface. The true colors cannot be rendered perfectly on a photograph or computer screen, and in the actual case the colors would blend smoothly without sharp boundaries.

Very illuminating!

James Bond's Science

Peter Taylor, of the UK, noticed this in an earlier film:

May I bring your attention to a delightful piece of physics from "Goldfinger"? I'm quoting from memory, but at one stage Goldfinger is explaining to Bond that he isn't actually going to steal the gold in Fort Knox, but explode a dirty atom bomb.

Bond: "But that will make it radioactive for [pauses a second] 57 years!"

Goldfinger: "58 years, to be exact!"

Apart from the idea that the gold will be unusable for this amount of time (why?), I just love that new form of radioactivity that lasts for exactly 58 years—I guess it has a half-life of 29 years (?) :)

Gold does have 3 radioactive isotopes, but with half-lives of two or three days (so they don't occur naturally, and provide no help to the film script!)

Recoilless Guns

Yes, nearly recoilless guns exist. There are several ways to proide the recoil momentum without much motion of the gun itself. They can use a heavy mass inside the gun (making for a quite a bit heavier gun), or allow ejection of something backward (gas, plastic particles, etc.) Also, they can use an "active" projectile that is a small rocket, burning propellant (and gaining most of its velocity) after it leaves the gun. However, in the movies I am criticizing, there is no visual evidence that the guns were using any of these methods. For more information, see recoilless guns

And what about all those movies showing a revolver with a silencer. The gun goes off with a soft "pfft", inaudible even in the next room. Back in 1980, Bob Shadewald educated us on this point.

...Silenced revolvers work only in James Bond movies and in similar schlock. The cylinder gap of a revolver is typically about 0.1 mm and maximum breech pressure a thousand atmospheres or so. Gas begins escaping there as soon as the bullet enters the barrel, and is not notably silent.

The revolvers made by Dan Wesson can be silenced because the barrel screws directly and can be screwed close to the cylinder so that there is no escaping gas. The front of the barrel and the sights are on a barrel shroud.

But now (2007), Bill Carr writes:

I disagree: Dan Wesson revolvers also require a barrel cylinder gap to function just like any other revolver. The gap permits the cylinder to rotate so that the revolver may fire. All revolvers rotate the cylinder with a pawl as the hammer is cocked or the trigger is pulled, locking just before hammer fall. No gap means no rotation. If we assume that the cylinder was perfect, the barrel was perfect and the alignment perfect with no space (but not preloaded because it would not be able to rotate, the high pressures will cause the gap to open because of deflection of the barrel, cylinder and frame from gas pressures.

There is an unusual revolver model, the Russian Nagant M1895, which can be silenced. When this revolver is cocked, a recess in the front of each chamber in the cylinder encloses the back of the barrel. In addition the cartridge case is slightly protruding from the chamber to close the small remaining gap, all in all creating a gas seal when the gun is fired, thus enabling silencing of the revolver.

Nearsightedness is corrected with negative (diverging) lenses. A positive (converging) lens is necessary to focus sunlight. Therefore a burning-glass must be positive. Piggy's negative eyeglass lenses would not work as a burning-glass.

Links to pages about science and math mistakes.

• Science Misconceptions, collected By Bill Beaty.
• The Bad Astronomy Page. Phil Plait's collection of misconceptions about astronomy.
• Bad Science. Alistair B. Fraser's comments on commonly heard (but wrong) explananations of science questions.
• Strange Science. Mistakes in paleontology and geology.
• The Glossary of Mathematical Mistakes.

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