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On Not Finishing Kaku’s “Physics of the Impossible”

Posted by jns on March 7, 2012

I read a lot of popular-science books. You know I do this partly to support the Science Booknotes and Science Book Challenge projects at Scienticity. I often remark to myself how thoroughly I enjoyed a book that I chose arbitrarily at my library, maybe because the title appealed to me or the book spine was the right color for me that evening. The implication for me, I’m happy to say, is that there is a great deal of really very good writing about science for the non-specialist. It’s satisfying to review these books and let other potential readers know about the great ideas they discuss.

Sometimes, of course, I select a book that turns out not to suit my taste for some reason. Generally speaking I prefer not to review a book I didn’t care for because I don’t see the point of a negative review about a book whose subject matter didn’t really appeal to me or whose author wrote in a style that I found unsympathetic. After all, many others might find the book worthwhile or tune in to that author’s particular style, and I’d much rather have a review in our booknotes collection setting out positive reason why a potential reader might choose to read a particular title.

Then there is the small but difficult category of books that I never finish reading because, for some reason or another, I find them too overwhelmingly irritating. For instance, I never finished reading Stephen Jay Gould’s The Hedgehog, the Fox, and the Magister’s Pox (my booknote) because his writing was so bad, and so badly edited, that I conjectured that it had been written by pod people who had taken over his body. Happily, these are rare events, but sometimes it seems important to write about them.

What to do, then, when I find an author known for his (or her) enthusiastic and entertaining advocacy and popularizing for science whose writing exhibits a notable disregard for precision about scientific facts and, furthermore, who seems to have a superficial or incorrect understanding of parts of his or her subject matter?

When I read a book that I plan to write about, I keep a folded sheet of paper inside the back cover where I make notes of interesting ideas, things to mention, and possible quotations for use in a review. I also make a note of trouble spots in the text: unclear or badly written explanations, confusion over facts of science, and such things. When I have filled the pages with errors the author has made and I’m only on page 30 of the book, I know I have trouble on my hands, and a quandary. I can easily stop reading the book, but I have to decide whether to write about it or not. Is there a useful point — beyond venting my spleen — to writing about bad science writing?

I have such a case on hand with Michio Kaku’s Physics of the Impossible*, in which the (apprently) well-known science popularizer talks about the physics and possibility of such science-fiction staples as invisibility cloaks, force fields, time travel, and such topics. It’s a very appealing idea, I thought, but I had to stop reading; there were simply too many errors–some serious errors–of science to continue, all before I reached page 30, less than one-tenth of my way through the book.

Let’s begin by going through some of the problems that I had in these early pages.

1. Conflating Historic Events

“Growing up, I remember my teacher one day walking up to the map of the Earth on the wall and pointing out the coastlines of South America and Africa. Wasn’t it an odd coincidence, she said, that the two coastlines fit together, almost like a jigsaw puzzle? Some scientists, she said, speculated that perhaps they were once part of the same, vast continent. But that was silly. [...] Later that year we studied the dinosaurs. Wasn’t it strange, our teacher told us, that the dinosaurs dominated the Earth for millions of years, and then one day they all vanished? No one knew why they had all died off. Some paleontologists thought that maybe a meteor from space had killed them, but that was impossible; more in the realm of science fiction [pp. xi--xii]

The idea that the continents might once have fitted together is a very old one, evident to most anyone who ever looked at a world map. These days we have at hand the well-established theory of plate techtonics to explain how it all could have happened, and certainly did happen. In the earlier twentieth century geologists and others began thinking more seriously about the idea of continents moving, but it was experimental results in the late 1950s and early 1960s that finally overthrew “conventional wisdom” that the continents couldn’t just move around. Plate techtonics was well established as scientific orthodoxy by 1965.

The Alvarez Theory, the idea that the extinction of the dinosaurs was brought about by the impact with Earth of a large body from space, was first proposed by Luis and his son Walter Alvarez following on Walter’s discovery of a thin sedimentary layer of iridium that dated closely to the time when dinosaurs disappeared. That theory did not appear until 1980. For many years afterwards the idea that an asteroid impact wiped out the dinosaurs was widely thought preposterous; before that time it hadn’t even been thought of. By now, of course, it’s widely familiar to the general public.

I hope you see my difficulty by now. The author writes that his teacher taught him that 1) some scientists speculated that continents drifted, an assertion that only makes sense prior to 1965, when Plate Techtonics was established; and 2) that some scientists though maybe an asteroid had killed the dinosaurs, an idea that no one had thought of until 1980. He writes that his teacher taught him these things in the same year, even though the closest in actual time that they may have come to each other is 15 years. In other words, this makes a good story but it’s highly unlikely that these two events took place in the same year.

2. Confusing Words and Ideas

This problem is more subtle. In the first chapter Kaku has a section on “force fields”, a common technology of science-fiction worlds for decades. Kaku unfortunately takes the words too literally and conflates the notion of a science-fiction “force field” with some combination of the ideas of “forces” and “fields” as they are used in physics, and so he spends some time talking about the four fundamental forces of the universe (gravitation, electromagnetism, the weak force, and the strong force) and discusses to some extent how each of these is formulated mathematically as “field theories”. But one does not get “force fields” by simply combining these two concepts. He confuses the reader over these pairs of words used differently in two different realms, and then leaves the reader with the mistaken impression that “force fields” might become reality just as soon as physics catches up and discovers a new field theory for a “fifth force”. None of this has anything useful to do with the concept of a “force field” as it’s deployed by science-fiction authors.

3. Casual Writing Leads to Mistaken Readings

In another space I’ll write about what I think should be the prime directive of any writer about science : First, Do Not Mislead. Writing about science for a popular audience is an awesome responsibility; scientifically literate readers can fend for themselves, but if the author has in mind an audience of nonspecialists, it is vital that the author take the utmost care with describing and explaining facts from science, because the nonspecialist reader can easily invent his or her own mistaken notion of how nature works when presented with sloppy, incomplete, or imprecise exposition. I expect popular science writers to

  1. Get it right, and
  2. Say it clearly.

Here are just some examples of statements that I felt violated the Prime Directive in Kaku’s writing. First, from the section on “Magnetic Levitation”:

“One common property of superconductivity is called the Meissner effect.” [p. 14]

When a superconductor in a magnetic field is cooled from its normal (non-superconducting) phrase to its superconducting phrase, it “expels” the external magnetic field from it’s interior, which is to say that it creates on its surface electrical currents that themselves create a magnetic field that just cancels the externally imposed field within the superconductor. This is known as the “Meissner Effect”, named for Walther Meissner. This is a defining characteristic of superconductors, a property necessarily exhibited by every superconductor. I find it odd to refer to it as a “common property of superconductivity”, as though it’s an incidental property seen in only some, perhaps many, superconductors, but suggesting that it is not a universal property.

In a section on “Invisibility”, discussing the possibility of an “invisibility cloak”:

“But today the impossible may become possible. New advances in “metamaterials” are forcing a major revision of optics textbooks. [p. 17]

Actually, the manufactured metamaterials that Kaku refers to, surprising and ingenious as they are, behave according to well-understood principles, requiring no “revision”, just an increase in understanding how to manufacture materials with desirable optical properties. This is misleading and a type of sensationalism that doesn’t serve the cause of increasing science literacy.

Later in the section on “Invisibility”, Kaku turns to a discussion of electromagnetic fields, namely, James Maxwell’s great advance in physical theory in the 19th century:

“(…If he [Maxwell] had lived longer, he might have discovered that his equations allowed for distortions of space-time that would lead directly to Einstein’s relativity theory. [p. 19]

Now, here is a frequent problem with those who write about science. There are, in fact, two distinct theories of Einstein commonly referred to as “relativity” : the theory of “Special Relativity”, from 1905, and the theory of “General Relativity”, from 1916. Special relativity is a theory of electrodynamics, basically a theory of light, which also introduced the idea of four-dimensional “space-time” and that most famous of equations, E=mc^2. General relativity is a theory of gravitation, a geometrical theory that treats gravity as deformations in space-time.

Usually the context makes clear which “relativity” the author meant. But here our only guide is that Kaku speaks of “distortions of space-time”. In special relativity travel at high velocities bring about time dilations and length contractions (“Lorentz Transformations”), i.e., distortions of space-time. In general relativity, gravitational effects are produced by the distortions of space-time caused by mass.

Carelessness here has caused a confusion that can’t be untangled and therefore does nothing to enlighten the nonspecialist reader who may not distinguish the two “relativity” theories so easily to begin with.

4. Errors of Physical Fact

These were the most troubling errors that confronted me in reading the first sections of Kaku’s book. Troubling because it betrays the trust between the nonspecialist reader and the authoritative voice of the author to make statement of physical fact, or to give descriptions of physical systems, that are imprecise or simply incorrect. I find it even more troubling when the author is a physicist who should be expected to get it right.

Back to the pages of discussion about Maxwell’s Theory of Electrodynamics, the author writes:

Maxwell began with Faraday’s discovery that electric fields could turn into magnetic fields and vice versa. He took Faraday’s depictions of force fields and rewrote them in the precise language of differential equations, producing one of the most important series of equations in modern science. They are a series of eight fierce-looking differential equations. Every physicist and engineer in the world has to sweat over them when mastering electromagnetism in graduate school [p. 18].

While it is certainly true that every physicist and engineer had to sweat over the equations in graduate school–probably even using the same, nearly universally taught textbook–the italicized phrase (my italics) would raise any student’s eyebrows. Whether the equations are “fierce-looking” or not is a matter of taste (I think they’re rather elegantly simple myself), there are in fact only four equations, two for the electric field and two for the magnetic field.

I nearly dropped the book when I read this — I couldn’t imagine how any physicist could have come to refer to “eight” equations. Now, while it’s true that the electric and magnetic fields are written in modified form when they occur in materials, rather than vacuum, the equations stay the same. That there are two each for the electric and magnetic fields is fundamentally characteristic of the entire field theory.

Slightly further on, Kaku offers this analysis of the property of optical transparency in materials:

Maxwell’s theory of light and the atomic theory give simple explanations for optics and invisibility. In a solid, the atoms are tightly packed, while in a liquid or gas the molecules are spaced much farther apart. Most solids are opaque because light rays cannot pass through the dense matrix of atoms in a solid, which act like a brick wall. Many liquids and gases, by contrast, are transparent because light can pass more readily between the large spaces between their atoms, a space that is larger than the wavelength of visible light. For example, water, alcohol, ammonia, acetone, hydrogen peroxide, gasoline, and so forth are all transparent, as are gases such as oxygen, hydrogen, nitrogen, carbon dioxide, methane, and so on.

There are some important exceptions to this rule. Many crystals are both solid and transparent. But the atoms of a crystal are arranged in a precise lattice structure, stacked in regular rows, with regular spacing between them. Hence there are many pathways that a light beam may take through a crystalline lattice. Therefore, although a crystal is as tightly packed as any solid, light can still work its way through the crystal.
Under certain circumstances, a solid object may become transparent if the atoms are arranged randomly [as in a glass]. [pp. 25--26]

It’s at this point that I threw up my metaphorical hands in despair and stopped reading the book. This “explanation” of transparency is so totally wrong I hardly know where to begin.

Light, namely, propagating electromagnetic waves, only interact with matter via the electromagnetic field (with a notable exception in General Relativity that doesn’t impinge on this discussion); in other words, light waves are sensitive to electrical charges, electrical currents, and magnetic fields. They sense the electrical charge of the electron “cloud” around an atomic nucleus; they might sense the positive charge of protons in a nucleus if they can get close enough for it to have an effect. Electromagnetic waves–light waves or photons, pick your favorite representation–do not interact with the mass of matter itself. Whether atoms are heavy or not heavy makes no difference, the light doesn’t sense the mass. Hold that thought.

Now, while it is true that the atoms in a liquid or solid are much closer together than they are in a gas, the atoms are still so physically small and so distantly separated relative to their physical sizes–not to mention that the components of an atom are vastly tinier than the “size” of the atom itself–that most of matter, whether solid, liquid, or gas, is still empty space. Even in a crystal or a glass this is true. Physically, the mass of atoms occupies exceedingly little of the space of the object they make up. By “exceedingly little” I mean this: the volume of the atomic nucleus is only about 1/1,000,000,000,000th the approximate volume of the atom itself.

I hope it’s becoming clear by this point that how close the atoms are together has relatively little bearing on how much “space” in matter is taken up by substantial parts of the atoms. The simple deduction, then, is that material objects are not more transparent or less transparent because the atoms are closer or further apart such that they “block” the light. The light does not run into the atoms and get blocked by their physical size. They are in no sense like a “brick wall” in any way that I can imagine makes sense.

The transparency of any given substance is determined by the not-so-simple interaction between light waves of particular frequencies (or “colors”) and the electric fields (predominantly) created in the substance by the particular configuration of its atoms. Gases do tend to be relatively transparent because the wide separation of their atoms creates a weakly interacting electric field. Nevertheless, some gasses do have colors because their atoms absorb certain wavelengths of light preferentially, through light waves being absorbed and/or emitted by the atomic electrons. Crystals have complicated and varied optical properties — transparency, opacity, colors in gemstones, birefringence, polarization rotations, etc. — depending sensitively on the periodically varying electric field inside the crystal that is produced by the regular (crystalline) placement of the atoms; but do keep your mind on the electric field inside the crystal, not the atoms “blocking” the light. There are also materials that are mostly opaque to visible light but that can be transparent in wavelengths of light that our eyes do not detect. The optical properties of materials is a rich field with lots of interesting effects and phenomena; get a taste for it, if you like, by looking up “transparency” in Wikipedia.

Looking up “transparency” is apparently something that author Kaku didn’t bother to do when he should have. His explanation of the phenomenon I find so confused and misleading that I feel his writing does a serious disservice to the nonspecialist who reads his book hoping for understanding from a scientist who knows what he’s talking about. This is why I stopped reading the book at this point, and why I have chosen to write about it.

One or two of the objections I noted earlier on amount to very little. I frequently find one or two little errors in any book I read, but it’s usually just something to note with some amusement and then move on; rarely does a misstatement or error like that cause me serious concern, and I rarely comment on them in my review of a book. A whole string of them, page after page, however, convinces me that the author is a sloppy writer or has a very superficial knowledge of the subject at hand. When the writer is a working scientist writing about science, I am totally confounded. As for these bigger errors I’ve just discussed — they are inexplicable. It is the author’s responsibility to realize the limits of his or her knowledge or understanding and find ways to avoid or correct problems in his or her writing.

These are the reasons why I simply cannot recommend this book to a general reader. That the book seems to have reached some level of popularity disturbs me : such poorly conceived and executed writing about science undermines the efforts of the many excellent writers about science — scientists, historians, journalists, and others — writing with more care and accuracy about their subject.
* Michio Kaku, Physics of the impossible : a scientific exploration into the world of phasers, force fields, teleportation, and time travel. New York : Doubleday, 2008. xxi + 329 pages.


Selecting a Popular-Science Book to Read

Posted by jns on January 6, 2011

Recently I was contemplating answers to potential questions prior to a brief interview (I’ll give a link if it shows up someplace linkable) I gave about our Science Book Challenge. One question that came to mind, one for which we try to provide one answer with our collection of science-book notes, is “How do I choose a popular-science book that I might like to read?”

It’s an important question. I want to encourage people to read about science, but I really want to encourage people to read something that they will enjoy, something that will speak to them and leave them feeling refreshed with new ideas. What value is there is reading something that just doesn’t speak to you? It may fulfill some false notion of virtue but it’s not going to open anyone’s mind to the idea that science is something that can speak to them with pleasure and profitable learning.

Here’s a simple algorithm I came up with that I truly believe will work well for most people. In addition to helping a reader locate a potential rewarding book, it has the virtue of introducing the reader to a librarian — librarians are great people to get to know! — and of encouraging the use of one’s local library, a valuable resource perennially in danger of withering from community neglect.

  1. Go to your library.
  2. Ask a librarian to show you where the science, or math, or engineering books are.
  3. Look along the shelves for a book with a title that interests you, or one with a funny author’s name, or one with an interesting picture on the cover or an attractive color on the spine. This isn’t as random as it sounds–you’re pulling out a book that already has something appealing to you.
  4. Open the book to some page near the middle and read a few paragraphs to see whether the way the author writes is agreeable to you. It doesn’t matter at this point whether you understand any of the ideas the author might be writing about. Rather, it’s to get an idea whether you can stand to listen to this author talking to you for the next 200 pages.
  5. Check out the book and start reading it. If it doesn’t engage you — for any reason whatsoever! — stop reading it, take it back, and try another one.

The basic ideas here are to start anywhere but start now, and not to let the books intimidate you–you get to judge the books, the books don’t get to judge you.


The Orthography of Equations

Posted by jns on July 21, 2010

Every now and then this little image appears on my Facebook page, as a sponsored ad, with the headline “Become a Physics Teacher”. The sponsors claim that they will help me get a master’s degree online in education so that I can become a physics teacher.

Now tell me, if you were considering paying someone to help you get certified in, say, programming C++, how would you respond if the image in their add had this programming fragment:

i = i + 1;

I don’t know that the above is a very clear analogy to any of you, but the point is this: if the ad in question displays a lack of knowledge of the idioms of the discipline, should you trust the advertiser to provide what’s on offer in a reliable way?

Why do I object to this little image? May I see a show of hands from the physical scientists who know the answer please?

Yes, that’s right. In this most famous equation from physics, a result of Einstein’s Special Theory of Relativity, the letters ‘m’, representing mass, and ‘c’, representing the speed of light in vacuum, are never, ever written as upper-case letters; they are always, invariably written in lower case. I should, perhaps, be more grateful that the ’2′ is at least written as a superscript.

A tiny detail, a nit that I’m picking? Would you trust a brain surgeon with dirty fingernails? A car mechanic who’s not aware of what a “spark plug” is called?

Long ago I started to draft a blog entry called “On the Orthography of Equations”, but I never got around to it. It was going to relate a story and draw some interesting conclusions.

The events of the story happened, now, some 20 years ago. I was talking to a secretary in our University department who was typing (yes, on a typewriter) a paper for another faculty member. She asked for some advice on how to type an equation. While I was answering her question I mentioned that if she put some space between two symbols and moved another to a slightly different place that the equation would be significantly easier to read.

“Easier to read?” she exclaimed. Clearly the idea that equations were somehow “read” rather than merely looked at surprised her. And that was when I realized that, to this secretary and likely to most people with relatively little mathematical training, the symbols in equation were mostly decorative and they did not realize that how the symbols are deployed affect the meaning and readability of the equations.

I was nearly as surprised as she to discover this, although it’s an observation I’ve never yet figured out what to do with. Neither am I sure that this was the blog post that I was going to write, but there you go–it’s the one you got.


It’s Cool that No One’s in Charge

Posted by jns on April 20, 2010

I think one of the defining moments of adulthood is the realization that nobody’s going to take care of you. That you have to do the heavy lifting while you’re here. And when you don’t, well, you suffer the consequences. At least I have. (And in the empirical study I’m performing about interacting with the universe, I am unfortunately the only test subject I have complete access to, so my data is, as they say, self-selected.) While nobody’s going to take care of us, it’s incumbent upon us to take care of those around us. That’s community.

The fiction of continuity and stability that your parents have painted for you is totally necessary for a growing child. When you realize that it’s not the way the world works, it’s a chilling moment. It’s supremely lonely.

So I understand the desire for someone to be in charge. (As a side note, I believe that the need for conspiracy theories is similar to the need for God.) We’d all like our good and evil to be like it is in the movies: specific and horrible, easy to defeat. But it’s not. It’s banal.


No one is in charge. And honestly, that’s even cooler.

The idea of an ordered and elegant universe is a lovely one. One worth clinging to. But you don’t need religion to appreciate the ordered existence. It’s not just an idea, it’s reality. We’re discovering the hidden orders of the universe every day. The inverse square law of gravitation is amazing. Fractals, the theory of relativity, the genome: these are magnificently beautiful constructs.

The nearly infinite set of dominoes that have fallen into each other in order for us to be here tonight is unfathomable. Truly unfathomable. But it is logical. We don’t know all the steps in that logic, but we’re learning more about it every day. Learning, expanding our consciousness, singly and universally.

As far as I can see, the three main intolerant religions in the world aren’t helping in that mission.

For all their talk of charity and knowledge, that they close their eyes to so much—to science, to birth control education, to abuses of power by some of their leaders, to evolution as provable and therefore factual (the list is staggering)—illustrates a wide scope of bigotry.

Now, just to be clear. If you want to believe, or find solace in believing, that someone or something set these particular dominoes in motion—a cosmic finger tipping the balance and then leaving everything else to chance—I can’t say anything to that. I don’t know.

Though a primary mover is the most complex and thus (given Occam’s razor) the least likely of all possible solutions to the particular problem of how we got here, I can’t prove it true or false, and there’s nothing to really discuss about it.

If Daniel Dennett is right— that there’s a human genetic need for religion— then I’d like to imagine that my atheism is proof of evolutionary biology in action.

[excerpt from Adam Savage, "Food for the Eagle", speaking to the Harvard Humanist Society, April 2010.]


95 – 21 = ?

Posted by jns on March 3, 2010

This is a fine development in UK news for people LGBTness, but my interest in this excerpt is in the second sentence/paragraph:

The House of Lords voted to lift the ban on civil partnership ceremonies in churches and other religious premises last night.

Peers voted by 95 to 21 – a majority of 74 – to lift the ban which previously prevented gays and lesbians from getting “married” in such places.

[from Mary Bowers, "Peers vote for church civil partnership ceremonies", TimesOnline [UK], 3 March 2010.]

Is it just me or is it odd to have the newspaper doing subtraction for us?

Maybe it’s my internal physicist, maybe it’s because I like numbers, or maybe it’s just my personality as a secret stair-counter, but whenever I read or hear an assertion with numbers, some sort of calculation usually happens in my head. I don’t think I’m alone on this.

“Hmm,” I think, “95 to 21, that’s a majority of 74 out of 116 peers, close to a 75% majority.” This usually gets one more refinement — 74% if it were a 100, but it’s 16% more than 100 so subtract about 15% of 74 from 74 gives about 63 — so let’s say about 63%. Not a bad majority.

Did I learn somewhere along the way always to calculate percentages or fractions when I’m given two numbers as input?

Okay, so I realize that quite a few people feel uncomfortable around fractions and percentages, although I’d like them not to. But isn’t addition and subtraction pretty much within the comfort level of most readers of that newspaper article?

So that leaves me trying to understand why the author (or, perhaps, editors), felt it necessary to subtract 21 from 95 in print.


Intellectual Abuse & “Insidious Creationism”

Posted by jns on July 7, 2009

Creationist advocates of intellectually dishonest ideas like “teach the controversy”, or “evolution is only a theory” are not engaged in a scientific debate. Neither are they engaged in a debate about how science works. Indeed, they are not even participating in good-faith (no pun intended) discourse but are pursuing their own subversive agenda, no holds barred.

An overt part of those agenda includes recruiting children to their world view. Planting intellectually deceitful ideas in the heads of young children makes those ideas less prone to revision as the child matures.

This is not really a summary, but more some thoughts that arrived as I was listenting to the 30-minute talk by James Williams (his website), lecturer in education at Sussex University, called “Insidious Creationism”. (Given on 8 June 2009 at a day conference called “Darwin, Humanism and Science”.) I watched it at “The Dispersal of Darwin“, Michael Barton’s blog.

Near the beginning, this idea of “intellectual abuse” caught my attention (transcriptions are mine):

This is why I apply the term “intellectual abuse” to “creationism”: I feel that when a person in a position of power and authority, who claims expertise in science, deliberately provides a non-scientific explanation for a natural phenomenon, knowing that to be at odds with the accepted scientific explanation, then that person is guilty of intellectual abuse.

Later on this fanciful image of a graduate in a “creation science” degree program generated a hearty laugh from the audience:

“Intelligent design” explains nothing. Science fails to proceed if that is the approach we take. Science succeeds where there are things that we do not know, that we don’t understand. And the role of science is to find those explanations for natural phenomena.

I can’t actually see Oxford, or Cambridge, in the near future offering degrees in “supernatural sciences”. I can’t see somebody going for a science Ph.D. saying, “Well, I’ve done the tests, I’ve investigated, I’ve read all the papers, I haven’t got a clue what’s going on, so therefore my answer is: It was designed. Could I have my doctorate please?”

The biggest laugh, however, was for the fanciful picture of Jesus holding the baby raptor, an example illustration from an “intellectually deceitful” book aimed at children.

It’s not all laughs, of course, even if the presentation is light hearted and digestible. Creationism would be merely a fringe group of ignorable wackos if they were not having such a disproportionate affect currently on educational discourse and policy in this country through deliberately dishonest and misleading tactics and strategies. “Insidious” indeed.

In case you’d like to listen, I’ll make it easy:


Accepting PI

Posted by jns on November 24, 2008

This is Euclid (c. 365 BCE — c. 275 BCE) of Alexandria, Egypt, possibly one of the earliest celebrities to use only one name. Euclid is famous, of course, for writing Elements, his 13-book exposition on geometry and the earliest mathematical textbook and second only to the Bible in the number of editions published through history.

Invoking Euclid’s name is a ruse. Although there are any number of things related to Euclid and the Elements that we could discuss, what I’ve really been thinking about lately is \pi, and I needed a pretext. In fact, it wasn’t even exactly \pi that I’ve been thinking about so much as people’s relationship with the idea of \pi.

It’s a trivial thing in a way, but I was perplexed to discover that some googler had reached a small article I had written (“Legislating the Value of Pi“, about the only actual case in history of an attempt to do so–in Indiana) by searching for “accepted value of pi”.

That disturbed me, although I’m finding it difficult to explain why. Let’s talk for a moment about the difference between physical constants and mathematical constants.

In physical theory there are any number of “physical constants”, numbers (with no units) or quantities (with units) that show up in physical theories and are generally presumed to be the same everywhere in the universe and often described as “fundamental” because they can’t be reduced to other other known values. Examples that might be familiar: “c”, the speed of light in a vacuum; “G”, Newton’s universal constant of gravitation; “e”, the charge of the electron; “”h”, Planck’s constant, ubiquitous in quantum mechanics; the list is lengthy. (You can find a long list and a bunch about physical constants at a page maintained by NIST the National Institute of Science and Technology.)

Fundamental physical constants are measured by experiment; that is the only way to establish their value. Some have been measured to extraordinary accuracy, as much as 12 decimal places (or to one part in one-million-million). The NIST website has an “Introduction to the constants for nonexperts“, which you might like to have a look at. (I never quite made it to being a fundamentals-constant experimentalist, but I did do high-precision measurement.)

Now, contrast the ontological status of fundamental constants with mathematical constants, things like “\pi“, the ratio of the circumference to the diameter of a circle; “e”, the base of the natural logarithms; “\phi“, the “golden ratio”, and numbers of that ilk. These are numbers that are perfectly well defined by known and exact mathematical relationships. (I once discussed a number of mathematical equations involving “\pi” in “A Big Piece of Pi“.)

Now, it may be something odd about the way my mind works (that would be no real surprise), but to me there is a difference in status between fundamental physical constants, which must be measured and will forever be subject to experimental limitations in determining their values, and mathematical constants, which can always be calculated to any desirable precision (number of digits) using exact mathematical expressions.

To me, one can reasonably ask about the “current accepted values” of fundamental physical constants–indeed, you’ll see a similar expression (“adopted values”) on the NIST page–but that “accepted value” makes no sense when used to describe mathematical constants that simply have not been calculated as yet to the precision one might desire. And so, asking about the “accepted value” of \pi seems like an ill-formed question to me. Your mileage is almost certain to vary, of course.

Well, now that you’ve made it through that ontological patch of nettles, it’s time for some entertainment. In the aforementioned article I had already discussed some of the fascinating mathematical equations involving \pi, so we’re just going to have to make do with something a little different, even though it is still an equation involving you know what.

The problem of “Buffon’s Needle” was first put forward in the 18th century by Georges-Louis Leclerc, Comte de Buffon. I like the way Wikipedia states it (or find another discussion here):

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle [whose length is the same as the width of the strips of wood] onto the floor. What is the probability that the needle will lie across a line between two strips?

Worked it out yet?

You can always measure an approximate value of the probability for yourself with a needle and a sheet of paper on which you have ruled parallel lines separated by the length of the needle. Drop the needle on the paper a whole bunch of times. Divide the number of times the needle lands on a line by the total number of times you dropped the needle. What value do you get closer to the more times you do the drop the needle?

The answer: 2/\pi. Exactly.


Inside the SX-70

Posted by jns on October 27, 2008

The name of this extraordinary film is “SX-70″; it was made by Charles and Ray Eames. (Whether you should watch first or read first I can’t say; if you have the time, watch then read then watch again.)

Some of us will be old enough to remember the Polaroid SX-70 camera and how exciting and modern it was. Such advanced technology! As the narrator says near the beginning:

Since 1947, Edwin Land and Polaroid have pursued a central concept, one single thread: the removal of the barriers between the photographer and his subject. [Title: "SX-70"] And now, a compact, folding, electronically controlled, motor-driven, single-lens reflex camera, capable of focusing from infinity down to ten inches, has been developed to exploit integral self-processing film units which, when exposed, are automatically ejected from the camera, with no parts to peel or discard, and whose final images emerge without timing, in daylight, where the viewer can see them materialize within the same transparent protective plastic cover through which the film was originally exposed.

The SX-70 looked like no other camera before or after, and worked like no other camera, either. The film was the culmination of this dream of Edwin Land’s, and the camera’s design and engineering gave the distinct impression that it had been thought about without preconceptions of how a camera should look.

But this isn’t just about the camera, which is a marvel. I’m more interested right now in this film about the camera, and the film itself is a marvel.

From the Eames Office page about the film, some of the credits:

Presentation of the revolutionary SX-70 Land camera and its aesthetic potential that becomes a meditation on the nature of photography. A tour-de-force of filmmaking that gives the audience a real understanding of the workings of the camera.
Filmmakers: Charles and Ray Eames
Sponsor: Polaroid
Composer: Elmer Bernstein
Narrator: concluding statement by Philip Morrison
Date: 1972

Charles and Ray Eames were the remarkably creative and remarkably influential husband-and-wife design team working mostly from the 40s through the 60s (a quick biographical survey). Many of their designs have become so iconic that they are recognizable by countless people who have never heard of the Eames. There is just so much that I can’t begin to organize my thoughts about them here, where my focus is on this one film anyway. When you have time, explore Charles & Ray Eames: A Legacy of Invention.

Next in the credits is Elmer Bernstein, noted composer of many, many famous film scores like those for “To Kill a Mockingbird”, “The Ten Commandments”, “The Blues Brothers”, and “Ghostbusters”, to name a small fraction. The score is just a few instruments, nothing that’s going to take a lot of time assembling and orchestrating, but nevertheless thoughtfully written and quite suitable for the film.

Then there’s Philip Morrison, whose distinctive voice appears near the end, where he takes over from the anonymous narrator in the rest of the film. Morrison, who died in 2005, was a physicist of some renown, but I think his more important contribution was as an explainer and popularizer of science, as he did with his remarkable television series (and book), “The Ring of Truth” (1987). Then there was the “Powers of Ten” project (1977), the justly famous film of which he worked on with the Eames (watch the nine-minute film). He had also been the main reviewer of books for Scientific American since 1965, a remarkable legacy.

But this list of luminaries would contribute empty celebrity if the film itself weren’t brilliant, and it is. It was shown originally at a Polaroid shareholders meeting and subsequently used internally as a sales tool. It was not made for average viewers, perhaps, and wouldn’t be the right tone for a television advertisement, but it’s not intended for a predominantly technical audience, either. Instead, it’s made for viewers of some intelligence who are willing to give it their attention and learn some amazing things.

I am particularly delighted at how the language is kept clear and understandable, particularly as it’s supported by the visuals, without being patronizing or gratuitously simplified. Amidst the poetical and metaphysical thoughts about photography as an art form, watch for the exposition about the camera, how it operates, and all the technical advances it contains. Pay attention: it’s all too easy to be drawn into the narrative without realizing that all that technical information is entering your mind with relative ease.

As you might expect, there are plenty of people taking pictures with the camera, demonstrating what fun it is and how it is used and its various special features. But look at what they’re taking pictures of: several appear to be scientists, or even amateurs of science, documenting the natural world. Of course, there are also proud parents taking pictures of their children, but they’re just part of the panorama. But even while we see the parents photographing their kids, we are also shown that the SX-70 has a fast lens, a short focal length, a quick shutter that can stop action, and the ability to take exposures in quick succession. The Eames are not merely marketing the SX-70 in this film, they are demonstrating its capabilities and technologies and making that look easy.

I love the attitude that includes the scientific as part of the cultural, a film that combines poetry and philosophy and technical explanations and kids and nature into one amazing whole that’s so amazing one hardly notices that all that’s going on. I like how the technical specifications of the camera are explored and shown rather than explained–before the narrated explanation (beginning at about the 4:15 mark) of the internal workings of the camera–assuming a viewer without special technical knowledge but sophisticated enough to absorb the ideas.

Then, when you do get to the technical narrative, notice how crisp and concise the narration is, and how it’s so beautifully documented by the combined animation and live action (done in the days before CGI). I don’t think it hurts anyone to hear the word “aspheric”, even if it’s not a familiar word–yet. And while we’re there, let’s not overlook the achievement of the Eames’ documenting the internal mechanisms of the camera. There are as many shots in there as Hitchcock used in that famous murder scene in “Psycho”.

Amazing. It inspires me and intimidates me at the same time, which I expect is a good thing.


What Would It Have Looked Like?

Posted by jns on August 25, 2008

Spending a bit of time online with Richard Dawkins (I was spending time with him whereas he spent no time with me–the net works that way), I listened to a reasonably interesting TED talk in which Dawkins talked about how our perceptions of reality are shaped by the evolution of our brains to help us get around in the universe at the size that we are.

That’s interesting enough, but what I want to preserve here is this perceptive and useful little exchange ascribed to the philosopher Wittgenstein, also on the subject of perceptions of reality and the “obvious”. It’s a lovely mini-drama and a useful point to remember.

Wittgenstein: Tell me, why do people always say it was “natural” for man to assume that the Sun went ’round the Earth rather than that the Earth was rotating?

Friend: Well, obviously, because it just looks as though the Sun is going ’round the Earth.

Wittgenstein: Well, what would it have looked like if it had looked as though the Earth was rotating?

[Richard Dawkins, "Queerer than we can suppose: the strangeness of science", TED talk, July 2005.]


Lightning Safety Awareness Week 2008

Posted by jns on June 24, 2008

Yesterday I had a press release from NOAA letting me know that this week, 22-28 June, is “Lightning Safety Awareness Week”. Apparently it is the seventh such declared week. The motto of LSAW comes from the mouth of Leon the Lion: “When Thunder Roars, Go Indoors!”

The National Weather Service, operated by NOAA, maintains a Lightning Safety Website that is filled with useful information and other interesting lightning-awareness stuff. For instance, there is a nice gallery of photographs of lightning, whence came the dramatic photograph at right, taken by Harald Edens near Socorro, NM, 2003 (used by permission).

On the home page, towards the bottom, there is a near real-time map showing lightning strikes in the continental US (and bits north and south) over a two-hour time period (delayed, they say, about 30 minutes after the data were collected).

We learn that each year in the US an average of 62 people are killed by lightning. Of those,

  • 98% were outside
  • 89% were male
  • 30% were males between the ages of 20-25
  • 25% were standing under a tree
  • 25% occurred on or near the water

We are told that lightning can strike from storms as far away as ten miles, which is why the NWS advises “When Thunder Roars, Go Indoors!” There really are no safe places to be outdoors. Either go inside a “safe building” or get inside a completely enclosed car (with metal roof). A “safe building” has walls with electrical wiring and plumbing, the latter being conductors that can get charge from a lightning strike into the ground instead of into people. Open shelters in parks, for example, are not “safe buildings”. Naturally, there’s more complete information around the NWS website.

Needless to say, perhaps, but my attention was drawn by two pages: “Lightning Science” and “Statistics and More“. Woo hoo!

From “Lightning Science”, lots of fun lightning facts:

  • At any given moment, there are 1,800 thunderstorms in progress somewhere on the earth.
  • There are lightning detection systems in the United States and they monitor an average of 25 million flashes of lightning from the cloud to ground every year!
  • Ice crystals in a cloud seem necessary lightning, which may result from charge separation that takes place in collisions of ice crystals.
  • Lightning is a rather complicated process for discharging negative charge in the cloud.

“Statistics and More” has several interesting sounding things like interesting lightning events in history, details on lightning deaths, policy statements, factsheets, and guidelines. Links can be so much fun sometimes.

My own awareness was increased this week by the rather dramatic thunderstorms we had last Sunday night, and again on Monday night, when Isaac and I were out and we both saw a brilliant stroke of lightning.