Some theoretical physicists play loose with mathematics.  Feynman, for example, never worried about the convergence of the series needed to calculate things in QED (that’s quantum electrodynamics); in fact, he designed a technique, now called Feynman diagrams, to allow him to throw away infinities easily and just hoped things would work out.  That’s called renormalization.  The renormalization of quantum field theories became a big deal.  The electro-weak theory of Weinberg, Glashow, and Salam, designed to explain and combine the electromagnetic and the weak forces, for example, was never fully accepted until ‘t Hooft proved it could be “renormalized.”

Dirac’s bras and kets were just vectors and linear functionals on a Hilbert space, but I doubt he worried too much about functional analysis, the study of infinite-dimensional vector spaces and their linear operators.  Even Maxwell’s brilliant synthesis of all classical electromagnetic phenomena—gamma rays, x-rays, visible light, electricity, and magnetism—had to wait years until vector calculus was invented by Gibbs before its true beauty could be seen.  A classical vector field is determined by its curl and divergence, and that’s exactly what Maxwell’s equations say about the electric and magnetic fields.

Sometimes physics gets ahead of mathematics.  Sometimes it’s the reverse.  The key to quantum chromodynamics isn’t Gell-Mann’s Eightfold Way.  The representations for the special unitary group SU(3) he used to organize hadrons into composites of quarks already existed.  His contribution was to recognize that the representations could organize the hadronic particle zoo.  Similarly, I always thought that algebraic topology was an esoteric branch of mathematics, and yet it has found multiple uses in particle physics.

On the flip side, Ed Witten’s treatment of string theory (part of quantum field theory) has led into many breakthroughs in the theory of knots, an unusually esoteric mathematical subject, so much so that Witten received the Fields Medal, the prestigious mathematics equivalent of a Nobel prize (the story about why Nobel didn’t want to give a prize to mathematicians seems apocryphal).  Much earlier, Einstein’s General Theory of Relativity wouldn’t have gone anywhere without tensor calculus—his friend Grossman, a mathematician, even helped him with the math.

(more…)

People are addicted to their smart phones, so much so that they walk into fountains, kill pedestrians and other drivers, and expose themselves to scam artists, muggers, and perverts.  Beyond that, or bloviating about trivial matters, or being a narcissistic showoff on social media, what can a smart phone do for you?  Depends on who you are, of course.  I’ll turn the question around and discuss what your smart phone CANNOT do.

ID a song.  I heard an oldie the other day.  I could hum the melody.  Loved the piano riffs.  But if I hadn’t been able to remember the name of the performer, I could have never answered the question: Who’s that performer and what became of him?  (It was Richard Marx, by the way.  He’s going on tour and has a new album.)  Song recognition isn’t covered by voice recognition.

Make par in golf, or catch a fish.  It might know what those things are, but it can’t do them.  And it can’t help you do them either.  Smart phones are just limited little computers, apps are just limited little programs, and neither of them are really smart.

Write a novel.  Beyond mentioning the obvious that your smart phone can’t create any of the elements necessary to spin a good yarn, try writing a novel with your thumbs!  Voice recognition technology, you say?  Try it.  You’ll be spending so much time editing that you’ll scream for your laptop.  Or join Jack in the Cuckoo’s Nest.  But maybe all those badly edited ebooks are written this way?

Help you find God or inner peace.  It might hook you up with the latest online quack who calls her- or himself a preacher, but God doesn’t answer a smart phone call and the internet offers no inner peace, just a bunch of random stuff that obeys Sturgeon’s Law, not God’s.  You can obtain more peace by putting your phone on a tile floor and stomping it into pieces.

Make popcorn.  Tres important, mes amis!

Offer a substitute for a loved one’s hug or kiss.  You might find a dating site or attract a pervert on Facebook (is that what the new “love” emoticon on FB is for?), but your smart phone is not much of a companion, in spite of your obsession with it.  Moreover, anyone who kisses her or his iPhone or Galaxy screen is just asking for a major bout with the flu, unless s/he puts hand sanitizer on that screen often enough.  That would have the advantage of making it slippery so thieves couldn’t grab it as easily…or make it drop to that tile floor and shatter into pieces!
(more…)

Benoit Mandelbrot (11/20/1924—10/14/2010) popularized the description and construction of 2D and 3D sets of fractional (non-integer) dimension.  He called them fractals.  I won’t use the word “invent” because such sets were studied as far back as the 1800s.  Of course, to say fractional (or “fractal” or non-integer) dimension, one has to redefine dimension a wee bit—Haussdorf, a 19^th century mathematician did that.  (The famous Cantor set, always a subset of the real numbers between zero and one, can be constructed to have any Haussdorf dimension between zero and one—no wonder Cantor went crazy.)  Just about everything Mandelbrot described and constructed still must exist in a space of integer (1, 2, 3, …) dimensions.  The construction of a fractal is often based on self-similarity, tacking on more and more similar but smaller pieces, ad infinitum (or taking them out).

Fractals represent ultimate geekiness because they have found many applications in computer graphics, including artsy stuff like landscapes and seascapes.  There was also a time, though, when just about every other paper in solid state physics used fractals, fractional dimensions, and self-similarity to describe complex systems—they’re ubiquitous in nature.  Today that fad has passed, but fractals still remain (sounds like a line in Paul Simon’s “Sounds of Silence,” doesn’t it?  It appeared 12 years before Mandelbrot’s The Fractal Geometry of Nature).

Mandelbrot spoke once at Clark University in Worcester, MA.  There was a cocktail hour before, befitting a famous VIP visiting from IBM, followed by a lecture—Mandelbrot seemed to enjoy himself at both.  He didn’t discuss the history of fractals much—to paraphrase Newton, Mandelbrot had stood on the shoulders of mathematical giants—but Benoit certainly sold his product well.  I’ll have to admit that his book is a work of art and probably helped popularize the subject even more—maybe a large number of applied mathematicians nowadays owe their geekiness to that book and its applications to computer graphics.

Today fractals are just another useful tool in the applied mathematician’s bag of tricks.  I even remember an image compression scheme based on fractals (JPEG is a more popular one).  Applied to sonic data (like MPEG), it could probably find useful applications today in compressing Senate filibusters—it was a lossy compression scheme, but the public wouldn’t care about that when dealing with filibusters.  No problem with candidates on the stump, of course, because they never spout more than fifteen-second soundbites.

And so it goes….

In his op-ed article on creativity in the NY Times, Prof. Adam Grant, management and psych professor at the Wharton School of UPenn, says step one to creativity is to procrastinate.  “Creativity takes time.  So I’m trying not to make progress toward my goal.”  I think that’s BS, and I’m hoping I’m not alone.  The first part depends on your definition of creativity, of course.  Presumably, this prof, who’s trying to sell his book, Originals: How Non-Conformists Move the World, is using a business definition.  I don’t see much creativity in the business world.  I see it in the author/composer of Hamilton; I’ve seen it in the works of Alejandro Obregon and Gabriel Garcia Marquez; and I’ve seen it in scientists and engineers, from researchers to smart phone and car designers.  Grant confuses creativity with business acumen.  Trump has the latter, but he isn’t creative (come to think of it, Trump and his progeny went to Wharton).

So, let’s get past that first statement in the quote and move on to the second.  Procrastination is the opposite of creativity!  If one procrastinates, s/he’s doing absolutely nothing.  Now Alan Watts might say doing nothing is accomplishing something—that’s part of Buddhist teaching (make your mind blank to achieve enlightenment)—but it sure as hell isn’t being creative.  I’d generally call it wasting time!  At a conference once some Austrian physicists told me that they were in the process of thinking about getting some dinner.  Maybe that’s typically Austrian—I seem to remember Vienna as pretty laid back (but probably not during WWII)—but dinner just isn’t that complicated, and time spent in the process of thinking about it would be better spent doing physics in this case, where a physicist can and should be creative.  Leave the dinner creativity to chefs—culinary art is creative, but only when you do it, not in the process of thinking about it.

(more…)

[A new feature just for my readers, wee bits of popular science nostalgia.]

John Archibald Wheeler (7/9/1911—4/13/2008) might have received only popular recognition for his students if he hadn’t coined the term “black hole” (Hawking popularly comes to mind first as the scientist most associated with black holes, of course).  His most famous student was Feynman, but Misner and Thorne were two others (the doorstop-sized tome Gravitation by Misner, Thorne, and Wheeler, is one classic on the subject of general relativity).  Wheeler was a physicist’s physicist, though, like Feynman, dabbling in anything that interested him.

Paul Adrien Maurice Dirac (8/8/1902—10/20/1984) was more like physic’s Harper Lee; he did a few things too (the idea of physical “constants” varying on a cosmic scale is intriguing), but he’s most famous for the equation that bears his name and postulating the positron as the electron’s anti-particle to make sense of it (it took physicists awhile to find that pesky particle, though).  He had an early tome on quantum mechanics where he introduced bras and kets—today we know them as vectors in an infinite-dimensional Hilbert space and complex-valued linear functions on them (Hilbert spaces existed in Dirac’s time, but, like Feynman and many other theoretical physicists, Dirac eschewed rigorous mathematical formalism).

At a conference in the early 1970s held at New Orlean’s Loyola University (next to Tulane), Dirac and Wheeler were guests of honor and sat in the front row competing to see who could doze off first when the geekiness became as stifling as the bad AC.  Dirac was particularly energetic during his talk, though.  Loyola is a Jesuit school, so one smartass grad student decided to embarrass Dirac by asking him if his belief in absolute measurements didn’t imply a belief in God.  Dirac, either agnostic, atheist, or just pissed (those might not be mutually exclusive, from Dirac’s reaction), dashed offstage and returned with a meter stick.  “This is a meter,” he said, “and it will be a meter whether God exists or not” (that’s a paraphrase).  Since Napoleon’s scientists invented the meter, he had a pretty good case.

By shifting several decades, black holes had a history similar to the positron—theory predicted them long before they were discovered.  Many other predictions of general relativity were confirmed experimentally before that happened (I’m discounting extensions to women’s large handbags).  Physicists play with positrons and a whole slew of anti-particles now; no one wants to play with or even come close to a black hole (unless you’re one of Pohl’s HeeChee).  Today astrophysics brings the small (like the positron) and the large (like the black hole) together, at least theoretically.  I’m sure Dirac and Wheeler are smiling about that—if they’re not taking a nap.

And so it goes….

Let’s give the old guy credit: he was received in the U.S. like a rock star and showed more resilience and stamina than men half his age.  Moreover, he’s speaking out on progressive issues.  On the plane en route to the U.S. from Cuba, a reporter asked if he was a leftist.  He replied something to the effect that everything he does is commensurate with the gospels.  Translation: Christ was a progressive revolutionary AND a religious man.  The two went hand and hand, no matter what conservative wonks think (some are right-wing Catholics, of course).

He’s painted environmental concerns as a moral issue that transcends all religions.  Climate change is a pressing concern for every human being on this planet, not to mention Gaia’s flora and fauna.  It’s the moral imperative of this generation to protect Gaia and all her creatures, according to the pope.  Of course, I didn’t need his encyclical to realize that.  Many people didn’t.  And a few are either too greedy and/or stupid, that they’ll resist that idea until they die, which might be sooner than later if we don’t deal with the pressing environmental problems.

(more…)

My new epic sci-fi novel, More than Human: The Mensa Contagion, is the tale of an invading ET virus and its effects on human society and space exploration.  That’s a strange combo (it’s sci-fi, after all), but the space exploration isn’t interstellar this time like it was in “The Chaos Chronicles Trilogy.”  It’s restricted to our solar system, to Mars and beyond.  Being a wee bit more local, many of the events are in the realm of the possible.  Most of the action is current day only because of the virus, though.  I don’t expect to see a Mars colony in my lifetime.  But exploration of our solar system will occur.  Of course, it’s already occurring with robot probes carrying specialized payloads.  That process is speeded up by the virus in the novel.

I’ve always been an avid reader and exhausted all the sci-fi in my public library by the time I entered high school.  I’ve read about Mars colonies since those halcyon days, although I’ve always thought that the space opera adventures were a bit too optimistic.  But I used recent reports as references for my novel, some optimistic and others pessimistic, to complement my imaginative musings.  Among these are: Bruce Bower, “Extreme Teams,” Science News, 11/29/2014; and the NY Times special issue on Mars, 12/9/2014: “On Mars,” by Kenneth Chang; “A One-Way Trip? Many Would Sign Up”; “Looking to a Neighbor for Help,” by Dennis Overbye; “Covering Mars Opened a New World,” by John Noble Wilford; and “Rover Finds Stronger Potential for Life,” by Marc Kaufman.  Other recent findings (about water in the solar system, for example), mostly in Science News, were also used.

(more…)

As a writer, I love words.  Sometimes I love a particular word because it’s mysterious.  “Eldritch” is an example.  You can understand its meaning from context when you combine it with “light”—it just looks spooky and sinister.  Because English is spoken in so many places, an author can give local color to his prose by choosing particular words (often not consciously).  I love the sound of “scarpered”—it just sounds like someone in a hurry to leave town.  When my beta-reader knew what it meant but still objected to its use in one of my books, I went on a search to find out how I’d picked it up.  Turns out it’s very UK-ish—sort of like “forthwith” and other words where I love how they trip off the tongue.  I’d picked it up from Ian Rankin (love his Inspector Rebus books), so my beta-reader was right and made a good catch.  Unless it occurs in dialog associated with a character who’s from the UK, or who’s trying to sound like a person from the UK, it isn’t quite appropriate in American prose.  Still love the sound, though.

“Troglodyte” is a word that looks and sounds good too.  It’s a fun word.  If I remember correctly, it originally means “cave dweller.”  (The origins of English are well mapped out in David Crystal’s The Stories of English—a lot of fun if you’re into that kind of thing.)  The word is more conventionally used to mean “deliberately ignorant or old-fashioned.”  Ergo, this long segue is just leading up to my main topic: There are anti-science troglodytes among us who are challenging science with their far-out beliefs and attacking scientific progress at all levels, some even funding campaigns against science.  Ironically, many of these same troglodytes are using science and technology as tools to further their anti-scientific agendas.

(more…)

At the end of ABC World News one evening last week, Kip Thorne made an appearance.  Seems he was a consultant for the new movie Interstellar.  The subject, of course, was FTL (faster-than-light) travel, what you need to visit other star systems in subjective times less than several hundreds of human generations.  Seemed Thorne was proposing wormholes (Deep Space Nine, anyone?).  While most sci-fi authors (including myself) just write a few words of pseudo-scientific technobabble and then get on with the story, I guess the director of Interstellar wanted to put some fancy ribbon around the technobabble.  I’m sure Prof. Thorne did a good job.

Generations of grad students have struggled with Einstein’s general theory of relativity.  The “classic texts” are Weinberg’s more experimentally grounded tome and the much longer differential geometry-oriented tome written by Misner, Thorne, and Wheeler (yes, that same Thorne).  Both were creatively and simply titled Gravitation.  Between the two, you had more than enough information to solve any problem on a PhD qualifying exam related to that subject, assuming you had learned the material well, of course.  Feynman’s simpler and less mathematical introduction in some of the first editions of the second volume of his famous lectures could be used to get in the mood, so to speak (Feynman did the same with his introduction to quantum mechanics in Vol. 3; with a bit more material, it’s a better introduction than any you’ll find elsewhere).

(more…)

I still have a copy of Benoit B. Mandelbrot’s The Fractal Geometry of Nature sitting on my shelf.  That 1982 hardcover edition is $31.90 on Amazon now.  Surprisingly, there is a 2010 Kindle edition, priced at $45.06, technically an eTextbook.  I say surprisingly because the original had many graphics pages.  I guess you’d better have a Kindle Fire or some other color tablet; you won’t see much on the Kindle paper white.  The coffee-table size of the original must have made the Kindle edition difficult too.

That said, I wonder how many millennials know what a fractal is.  Computer science types of all ages might, because displaying fractals is often a programming exercise (best seen on the high-res monitors found with graphics workstations).  However, even for them, fractals might seem akin to the much simpler Lissajous figures—very intriguing graphics, but so what?  Graphics artists might be familiar with fractals as an option when portraying landscapes like mountains and so forth.  The origins of these computer applications can be found as wow-content in Mandelbrot’s book.

(more…)