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Blunders and Mistakes of Science and Engineering

Compiled by Donald Simanek

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.

Diagrams purporting to explain how the eye works are often defective, even in textbooks. But this example, from p. 16 of the special 2006 issue "Secrets of the Senses" put out by Scientific American is the most screwed-up I've ever seen (so far). Hardly anything about the ray paths is correct. It shows no deviation in direction of rays at the cornea (which actually causes most of the refraction in real eyes). It has rays devating much too much at the lens, so much that they cross within the lens.

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.

The British do have a sense of humour. Why else would they issue this gold and silver two-pound coin to honor the advance of British industry?

Image credit: chards.co.uk.

The artistic designer has used a circle of gears of different sizes in an interlocked array. There are 19 gears. Even if they were sized properly, an odd number of gears meshing around a circle couldn't possibly turn. The reason is simple; 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 will turn freely no matter what the gear sizes or 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. Something like a dog chasing its tail.

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 gridlocked 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 informed the British Mint of this goof before the 2002 coin was issued with the same locked gear design. A 2003 coin had a new design, with the gears replaced by a picture of the structure of DNA, and the edge of the coin then read "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 are clearly incorrect.

Cooperative Learning Gridlock

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. This will be true even if the gears have different sizes and different tooth counts, so long as they mesh smoothly and the gears lie in a common plane.

They never learn.

It's now 2005, and the gear mistake persists. Doesn't anyone read this web page? Adobe Systems wants to illustrate things working together. The three gears at the top left are locked and none of the rest will turn either. This diagram is an engineer's nightmare with gear tooth sizes mismatched and sloppily aligned, and a rope or cord at the bottom attached in some mysterious way. But doesn't this piece of art nicely illustrate some of the integrated software you have used? Thanks to Bill Beaty for drawing this to my attention.

In 2008, ever-alert Bill Beaty sends me yet another picture of bureaucratic 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.

In 2010 I got a newsletter from my investment firm with this gratuitous graphic that seems singularly appropriate for the current financial gridlock. But I doubt that was its intent. As I read it, this money isn't working for investors.

And the gears keep trying. Now, (2013) Claudio Sanchez sends me this advertisment from AMRO, a Dutch bank, "The pieces of a perfect mechanism." The financial crisis is indeed worldwide. Clearly these gears are all meshed up.

Exercises for readers. To get your mental gears grinding.

1. Can you prove them mathematically? (a) An odd number of gears in a closed loop in a plane will not turn no matter what their size and tooth count. (b) An even number of gears in a closed loop in a plane will turn smoothly no matter what their size and tooth count.

2. Find a way to make a model of an odd number real gears interlocked in a series loop (each one meshing with the two adjacent gears) so that they all can freely turn. That's an easy one. Now try to make the gears turn on their own fixed axles.

Don't look at the answers too soon, or you'll kick yourself for missing the simple solutions.

Short measure from the Pennsylvania DEP.

The Department of Environmental Protection of the Commonwealth of Pennsylvania recently (1998) distributed free pocket rulers to advertise their services to the taxpayer and promote their website. However, on close examination, the ruler is seen to have a defect. The blunder stands out like a sore thumb. They've shorted us one centimeter! Centimeter 14 is missing.

Perhaps this is the new "Metric Lite". One should praise the DEP for an effort to promote metrication in the USA, but their art 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.

[Nov, 2009] Rolf Marquardt, from Berlin, Germany, was the first to notice another problem with this ruler. It seems to be consistently based on the assumption of 1 inch = 2.5 centimeter. One inch should be 2.54 cm. It's a small difference, but it adds up. The ruler has the 2 inch mark lined up with 5 cm, 4 inch with 10 cm, and 6 inch with what should have been 15 cm if the 14th centimeter hadn't gone missing.

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:

We have no idea what direction the light is supposed to be going (that's true for the previous picture also). Suppose the light is directed from left to right, and divergent on entering the prism face, then emerging convergent. Refraction doesn't work this way. On the other hand, if white light is entering from right to left, then emerging from the left face, the colors should be divergent, not convergent as shown. So unphysical is this rendering, that it is 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!

[August 2002] I caught a "Weather IQ" factoid on The Weather Channel last week. Impress your friends by quoting this tidbit of what passes these days for science "knowledge": "Laser beams can travel at the speed of light." Well, duh! Laser beams are light.

James Bond's Science

One often wonders, when watching a movie, how much trouble the producers have taken to get the science correct. In the James Bond film Goldeneye we hear a Russian military technician report that they had placed two earth satellites "in 90 minute orbits at 100 km". I did a double-take on hearing that, trying to mentally calculate whether that could possibly be correct. Checking the figures later, it turns out that a satellite in an earth orbit with a period of 90 minutes would have to be at an altitude of 322 km, or nearly 200 miles.

Peter Taylor, from 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!)

One could rationalize this plot point by arguing that the blast would thoroughly intermix all sorts of radioactive stuff with the molten gold, but predicting the "danger lifetime" or even the half-life of that mess would be very imprecise indeed. And then there would be that loss of gold through vaporization, gold-plating a good portion of the landscape.

There are websites devoted to cataloging movie blunders of this sort, but this example is typical.

Recoil-less Guns

Seeing the 2003 movie "Once Upon a Time in Mexico" I was reminded again of a common physical perplexity seen in action movies with powerful hand-held guns. The hero holds an oversize gun casually, fires it, and hits one of his villainous adversaries, propelling the poor guy all the way across the room. Yet the hero hardly experiences any recoil! Conservation of momentum must have momentarily been suspended. At last, a recoil-less gun! This is a clear violation of Newton's third law, which ought to be illegal. If the bullet can propel a man that far, the recoil of the gun which fired that bullet ought to propel the shooter nearly as far.

Yes, nearly recoil-less guns exist. There are several ways to provide 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 recoil-less guns

A literary goof.

In William Golding's (1911-1993) novel Lord of the Flies (1954) one character, Piggy, is teased by the other boys because he is fat and wears glasses since he can't see anything without them. Later (Ch. 2) they use Piggy's glasses as a burning glass to start a signal fire. Is anything wrong here?

At the beginning of Chapter 11 "Castle Rock", Golding writes: "Piggy sat expressionless behind the luminous wall of his myopia". Myopia is the medical term for nearsightedness, so Piggy's glasses were certainly diverging (negative) lenses.

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

Golding was annoyed with readers who told him this was an error. Perhaps he was annoyed for having made an error of physics. Or perhaps his use of the glasses as a metaphor was compromised.

However, in the British movie of this book, the glasses Piggy wears are not strong at all. Typically glasses worn in movies are very weak or even zero diopter. If his glasses were for nearsightedness, his eyes would appear larger to us. If for farsightedness they would appear smaller. So the movie compounds the error.

Fried Crow.

Claudio Sanchez sends me this advertisement featuring a hapless fried bird on a power line. Don't worry, birds aren't electrocuted by sitting on high voltage wires. The bird would have to be large enough to straddle between two wires, one foot on each wire. The potential difference between its feet on one wire is too small to do any harm. Birds perch on wires safely, and squirrels are even acrobatic enough to scurry along a wire, as if walking a tightrope. But if any squirrel happens to reach from one wire to another, at a utility pole or at a transformer fuse, it won't make that mistake again.

Images again.

Optics is the downfall of many artists. Classic examples are rainbows with the colors reversed and crescent moons with a star inside the crescent.

This image of mountain resort shows the building right side up, and with very little spherical aberration of its perspective. In real life the image in a droplet is quite distorted and upside down.

If this is a raindrop, it is wrongly shaped, a common error of artists. Raindrops are not the classic tear-shaped, and not spherical. They are distorted as they fall through the air, being flattened on the bottom and rounded on top.

Deliberate Violations
of Physics.

We have concentrated on inadvertent errors of physics, neglecting deliberate perversions of physics. Classic examples of the latter are animated cartoons where a character running off a cliff doesn't begin to fall till he realizes he's unsupported.

A nice example is the tradmark of Sherwin Williams Paints. It defies gravity, supposing a source of gravity somewhere in the bottom of the picture.

But this does present an opportunity to mention an interesting fact about pictures of the earth. If the earth were accurately represented with all its mountains and ocean trenches rendered in true scale with the earth the size of a bowling ball, it would in fact be smoother than a bowling ball. The atmosphere would be no thicker than a thin coating of varnish. And what about us? Well, on this scale we'd be, as one wag put it "A crawling disease on the face of the earth."

Coriolis effect on food?

Marie Callender's Salisbury Steak frozen dinner has these instructions. After heating for 4 minutes you are instructed to "Rotate steak clockwise one half turn." Apparently this matters. One wonders if you'd have to rotate it counter-clockwise in the Southern Hemisphere. What dire results would result from turning it the wrong way? Inquiring minds want to know.

The carton also says that the gravy is "Made from scratch." What is this wonderful ingredient "scratch"?

Reality found!

Many books have been written about "reality", but none seem to ever define the word. This box from Marie Callender's fish dinner seems to have found reality, for the dinner is "made from real ingredients". What, then, are the "unreal ingredients" that other companies use? Seems to me that any ingredients of anything are equally "real", not imaginary. But some of them taste unreal.

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) explanations of science questions.
Strange Science. Mistakes in paleontology and geology.
The Glossary of Mathematical Mistakes.

Input and suggestions are welcome at this address. When commenting on a specific document, please reference it by name or content.

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This page last revised 2 March 2016.