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My favorite RGB color

Posted in Physics, tagged , , , , , , , on January 15, 2013| 9 Comments »

crayon

Very slightly more green than blue, “Tropical Rain Forest” can be thought of as a dark cyan.

My wife called me the other day and asked what my favorite color was.

“Hold on one second,” I said.  “I have it written down.”

She explained that she just needed a color in the most general terms, because she was buying me a case for my new iPhone.  So I said “blue.”  But I was disappointed that I didn’t get to be more specific.

You see, my actual favorite color is (currently) Tropical Rain Forest, formulated by Crayola in 1993.  Its RGB color code is (0, 117, 94).  If you want to read about the color, it’s the first variation on jungle green in the Wikipedia article of the same name.

But what’s an RGB color code?  Anyone familiar with computer graphics will recognize RGB as standing for Red/Green/Blue, which are taken to be the three primaries.  And therein lies a tale: for didn’t we all learn in kindergarten that red, blue, and yellow (not green) were the primary colors?  What’s going on?

Light comes in different wavelengths, or more commonly, combinations of multiple wavelengths.  Color is a purely biological phenomenon having to do with what we perceive with our eyes.  So when a kindergarten teacher says that “mixing red and blue make purple”, there’s really a whole lot of physics and biology that’s being glossed over.

In our retinas, we (generally) have three kinds of cones that react to incoming light.  These cones can detect many wavelengths of light, but each peaks in a different part of the spectrum.  Very simplistically, we can say that one peaks in the “red” part of the visible spectrum, one peaks in the “green” part of the spectrum, and one peaks in the “blue”.

Now, the “red” cones don’t just react to red light—it’s just that they react most strongly to red light.  But light in the “green” part of the spectrum might also stimulate a “red” cone to some degree.  The colors that we see depend on how our brains interpret three signals: how much each of the three kinds of cones is stimulated by incoming wavelengths of light.  For example, if a “red” cone and a “green” cone were stimulated about equally, your brain would interpret this as seeing yellow.  If all three cones were stimulated strongly, you’d “see” white.  (It’s weird to note that different combinations of wavelengths can actually cause the same sensation in your brain: there’s not necessarily a unique combination of wavelengths for any given color perceived.)

Here’s a chart to help you out (note that this is very simplistic and glosses over many issues which I will address later):

Kind(s) of cone stimulated            What you perceive

“Red”                                                                Red

“Green”                                                            Green

“Blue”                                                               Blue

Red & Green                                                    Yellow

Red & Blue                                                       Magenta

Green & Blue                                                   Cyan

Looking at this chart makes the notion of an “additive” primary easy to understand.  We declare red, green, and blue (RGB) to be the additive primary colors.  We can then build (most) other colors by adding these colors together.  This corresponds to multiple wavelengths of light stimulating one or more cones in the retina to varying degrees.  If you want an applet to play around with this kind of additive color mixing, try this.  Input (0, 117, 94) if you want to see Tropical Rain Forest.

colors

Additive color mixing

One caveat: the RGB scheme arbitrarily chooses three exact wavelengths of light to be “the” additive primaries, but this represents a judgment call on our part.  The degree to which different wavelengths of light stimulate the three kinds of cones is messy; the graphs of intensity (of cone response) vs. wavelength are not perfect bell curves, and have bumps and ridges.  Furthermore, it has long been known that if you try to limit yourself to only three “primary” additive colors then you cannot reproduce every possible color that humans can perceive.  We would say that the gamut of possible colors you can make with an RGB scheme does not encompass all possible perceived colors.  (For example, true violet as seen in the rainbow cannot be reproduced with RGB—it can only be approximated.  You can’t see true violet on a computer monitor!)

Now, tell a 6-year-old that Red + Green = Yellow, and they will look at you like you’ve grown a second head.  That’s because most experience we have with “color mixing” doesn’t involve mixing different kinds of light; it involves mixing different kinds of pigments.  And that’s a totally different ball of (crayon?) wax.

Suppose I have a flashlight that shines red light.  I have another flashlight that shines green light.  If I shine both flashlights into your eyes, you will see yellow, as we just discussed.  With two flashlights (two colors), more light has reached your eyes than would have with just one flashlight.

Pigments (such as crayons or paint) work in the opposite way.  “Red” paint is paint that takes white light (a combination of R,G, and B) and subtracts some of the light away, so that only the R reaches your eyes.  Green paint takes RGB light and lets only the G reach your eyes.  In other words, red paint “blocks” G and B, whereas green paint “blocks” R and B.

Can you guess what happens if we mix red and green paint?

The 6-year-old knows you get black.  That’s because two successive blockers have filtered out all the light, and nothing reaches your eyes at all.  And when no cones are stimulated, we perceive that as black.

When a teacher says that the “primary” colors are red, blue, and yellow, they are referring to so-called subtractive primaries.  By mixing those three kinds of pigments, you can make many of the colors we can see.  But not all the colors.  Try mixing red, blue, and yellow to make pink.  It cannot be done.  Like the additive primaries, the gamut of the subtractive primaries is limited.  And, like the choice of RGB as additive primaries, the choice of red, blue, and yellow as the subtractive primaries is arbitrary.  Arbitrary, and inferior.  It turns out that using yellow, magenta, and cyan as the subtractive primaries expands the gamut and increases the number of colors you can make by subtraction.

Why yellow, magenta, and cyan?  Well, those choices make sense if you’ve already picked RGB as your additive primaries.  Consider the chart above.  It’s clear that a paint that looks magenta must be blocking green, since you’re seeing an (additive) combination of red and blue.  Similarly, yellow paint blocks blue, and cyan paint blocks red.  So what happens if we mix, say, yellow and cyan?  Well, the mixture will block blue, and then block red, so what is left is green.  You can try this here.

Anyway, I spent some time at this site trying to determine exactly my favorite color.  I finally chose Tropical Rain Forest, RGB=(0, 117, 94).  I think it’s peaceful and organic.  I also enjoy Tyrian purple, RGB = (102, 2, 60).  Let me know which colors you favor.

Coming soon: some thoughts about the extra-spectral colors!

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The top 10 science stories of 2012…not!

Posted in Rant, tagged , , , , , , , on December 30, 2012| Leave a Comment »

maser

CNN has no love for the room-temperature maser.

It’s almost a new year, which of course is the time that everyone writes retrospectives of the year before.  I don’t really want to write a retrospective; I’d rather start a new tradition: criticizing someone else’s retrospective.  So to begin: I draw your attention to CNN’s Top 10 science stories of 2012.

Let me start by emphasizing that this list was not written by a scientist.  It was written by the CNN Health beat reporter.  So maybe I shouldn’t be so critical: maybe I should give that reporter a pass.  But come on, shouldn’t we expect at least half of the “top 10 science stories” to actually be science?  Is that so much to ask for?  Ideally, such a list should be written by several scientists, or at the very least one scientist.  Having the CNN Health reporter compile a list of the top 10 science stories is a kind of near miss—like having Bob Vila comment on the top 10 advances in mechanical engineering, or having Tiger Woods list the best Cricket players in Australia (be sure to mention Michael Clarke, Tiger).

I am a scientist, so I feel qualified to comment on CNN’s list.  Therefore, in the spirit of new year snarkiness, let’s evaluate each “top 10 science story” for import, for scientific value, and for “wow” factor.  And let’s see how the health reporter did.  Remember, that reporter got paid for their work (and I am not getting paid).  Go figure.

1. Curiosity lands, performs science on Mars

OK, this is cool, and maybe some science will be done eventually—I am not aware of any actual results published yet in a peer-reviewed journal.  But the Curiosity landing on Mars is in itself not science; it’s a remarkable feat of technology and engineering.  So it shouldn’t be on the list.

2. Higgs boson — it’s real

I don’t have a problem with this being on the list.  This is big, and important, and exciting to most physicists.  The one thing it is not is surprising: most physicists had faith in the Standard Model, and most expected the Higgs to be found in the 125 GeV/c2 range.  Now the real work begins: determining all the properties of the Higgs, and all the interactions that it might participate in.

3. James Cameron’s deep dive

Seriously?  How is this science?  Avatar-boy goes on a vanity jaunt to the heart of the ocean, and we pay attention why?

4. Felix Baumgartner’s record-breaking jump

This is an even more embarrassing entry than the previous one.  An idiot pushes the envelope, and we call it science?  Does the CNN Health reporter even know what science is?

5. Planet with four suns

Planethunters.org discovered a quadruple star system with a planet in a (somehow) stable orbit.  This is an interesting discovery and an impressive feat by an amateur collective.  Maybe someone will get a journal article out of this someday, but that’s it.  A bigger story is how many extrasolar planets have been discovered so far—854 by Dec. 24, 2012.

6. Nearby star has a planet

So Alpha Centauri B has a planet.  That’s nice.  But didn’t we already cover extrasolar planets in the previous entry in the list?  A good list should vary its entries: if you were listing your top 10 favorite comfort foods, and if #5 were pepperoni pizza, would #6 be sausage pizza?  I didn’t think so.

7. Vesta becomes a ‘protoplanet’

Sigh.  What’s with all the space stuff?  Hey CNN Health reporter: only a small percentage of physicists are astronomers, you know, and there are many other branches of science than just physics.  Did you consider asking a chemist what’s hot in chemistry?  Did you think of calling a geologist, or a neuroscientist, or a paleontologist, or a solid-state physicist?  I didn’t think so.

mayim

Hey CNN? Why didn’t you call Dr. Mayim Bialik?

8. Bye-bye, space shuttles

Again?  More space?  And this isn’t even remotely science.  This is about the retirement of a vehicle.  Good riddance, I say: imagine all the real science that could have been done if the space shuttle money had instead been used to send out hundreds of unmanned probes, to Europa, Titan, Callisto, Ganymede…

9. SpaceX gets to the space station, and back

And still more space?

Dear lord, you’d think from this list that space exploration is the only kind of science that anyone does.  And again: not a science story.  It’s a technology story.  Look up the difference, CNN.

10. Baby’s DNA constructed [sic] before birth

“For the first time, researchers at the University of Washington were able to construct a near-total genome sequence of a fetus, using a blood sample from the mother and saliva from the father.  The study suggested this method could be used to detect thousands of genetic diseases in children while they are still in the fetal stage.”

This is interesting, and may be important, but I have an issue with the list item as the CNN Health reporter wrote it.  The baby’s DNA wasn’t constructed before birth.  The DNA was present before birth, sure; fetuses do have DNA.  The baby’s genome was sequenced before birth, which is a completely different thing.  You’d think a health reporter would know better.

Final Score

So what’s the final tally?  By my count, only of 6 of the items on the list are science, and that’s being very generous.  Of those 6, the fields of science represented are astronomy, particle physics, astronomy, astronomy, astronomy, and biology/medicine.  Nice, balanced list there.  Way to go.

So what stories did deserve to be on the list?  I don’t know.  I am a (mostly) solid-state physicist, and I could mention that researchers successfully used neutrinos to communicate, built a room-temperature maser, and found Majorana fermions.  I’ll stop there, and let chemists, neuroscientists (that means you, Mayim), and geologists add items of their own.

Happy New Year, everyone!

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Let’s end superstition now

Posted in Rant, tagged , , , on December 10, 2012| 5 Comments »

220px-Clomipramine.svg

The next time someone sneezes, don’t bless them. Take this instead.

[Note: I plagiarized this post.  From myself.  Over two years ago I “started” a blog and gave up a day later.  But that first post was OK, so here it is, with slight modifications.]

It’s the 21st century: science has successfully explained almost every aspect of the physical world (except that missing sock), and new successes are appearing every day. We have computers, cell phones, hand-held GPS devices, the Wii, velcro, and 8-track tape players. And instant pudding.

So why do people still cross their fingers for luck? Why is anyone still tossing spilled salt over their shoulder? Why do athletes still wear their “lucky” shorts? (See this for a list of the saddest athletes you’ve ever heard of.)

It boggles the mind.

Let this post be a rallying call to everyone that still has a shred of intellectual integrity. Let’s all agree to cast out the pernicious demon of superstition from our lives. Let’s all agree that there’s no such thing as your lucky number, that breaking a mirror won’t have any harmful effects (unless you break it with your bare hand), that Friday the 13th is nothing more than a bad movie franchise, and that crossing your fingers has about as much effect on the universe as taking a dump and wishing it were pancakes.

The next time you say “tomorrow’s going to be a good day”, refrain from knocking on wood.  Just don’t do it.  I mean, come on.  It’s silly.  Don’t do it.

Please.

Don’t do it.

And let’s not tolerate such bizarre, 13th century behavior in others: if someone is wearing their lucky Cubs jersey before the big game, call them on it. Say, “Hey Bob, you think wearing that will help? That’s ridiculous and frankly embarrassing. If you want to wear the jersey to support your team, then fine. But please, don’t tell me that wearing that shirt will have any effect on the outcome of the game.” And speaking of the Cubs, let’s all say it together: there is no such thing as a curse. The Cubs just haven’t been all that good in the past 100 years or so.

To bring the world into the 21st century, to promote a scientific and rational mindset, to remain skeptical in the face of irrational and pseudo-scientific claims—to do all these things requires your help. It all starts with you.

Seriously, you.

You can fire off a cannon shot in the superstition culture wars by just not being superstitious yourself. Continue the fight by making fun of people who are superstitious. (Shame: it’s a powerful weapon.) Start peer-pressuring people into being a little more rational. It’ll be good for them. They need to grow up. They can handle it; you know they can.

If not, there’s always clomipramine.

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Avoid Schrödinger’s cat

Posted in Many-worlds Interpretation, tagged , , , , , , on December 6, 2012| 5 Comments »

mcfly

“I am your probability density”

In an earlier post I discussed my philosophy of teaching special relativity.  My main idea was that physics professors should keep the “weird stuff” at bay, and start with non-controversial statements; once students are on board, you can push under the grass and show them the seething Lynchian bugs beneath.

Well, what about quantum mechanics?  Does the same philosophy apply?

My answer is yes, of course.  Don’t start with Schrödinger’s cat.  Don’t mention the Heisenberg uncertainty principle, or wave collapse, or the EPR experiment, or Bell’s theorem, or the double slit experiment, or quantum teleportation, or many worlds, or Einstein’s dice.  Start with the problems of physics, circa 1900, and how those problems were gradually solved.  In working out how physicists were gradually led to quantum mechanics, students will build up the same mental framework for understanding quantum mechanics.  At least, that’s how it works in theory.

Now, my perspective is from the point of view of a professor who teaches only undergraduates.  I only get to teach quantum mechanics once a year: in a course called Modern Physics, which is sort of a survey course of 20th century physics.  (If I were to teach quantum mechanics to graduate students, my approach would be different; I’d probably start with linear algebra and the eigenvalue problem, but that’s a post for another day.)  As it is, my approach is historical, and it seems to work just fine.  I talk about the evidence for quantized matter (i.e. atoms), such as Dalton’s law of multiple proportions, Faraday’s demonstration in 1833 that charge is quantized, Thomson’s experiment, Millikan’s experiment, and so on.  Then I explain the ultraviolet catastrophe, show how Planck was able to “fix” the problem by quantizing energy, and how Einstein “solved” the problematic photoelectric effect with a Planckian argument.  Next is the Compton effect, then the Bohr model and an explanation of the Balmer rule for hydrogen spectra…

We’re not doing quantum mechanics yet.  We’re just setting the stage; teaching the student all the physics that a physicist would know up until, say, 1925.  The big breakthrough from about 1825-1925 is that things are quantized.  Things come in lumps.  Matter is quantized.  Energy is quantized.

The big breakthrough of 1925-1935 is, strangely, the opposite: things are waves.  Matter is waves.  Energy is waves.  Everything is a wave.

So then, quantum mechanics.  You should explain what a wave is (something that is periodic in both space and time, simultaneously).  Here, you will need to teach a little math: partial derivatives, dispersion relations, etc.  And then comes the most important step of all: you will show what happens when two (classical!) wave functions are “averaged”:

ψ1 = cos(k1x – ω1t)

ψ2 = cos(k2x – ω2t)

Ψ(x,t) = (1/2) cos(k1x – ω1t)  + (1/2) cos(k2x – ω2t)

Ψ(x,t) = cos(Δk·x – Δω·t) · cos(k·x – ω·t)

where Δk ≡ (k1 – k2)/2, k ≡ (k1 + k2)/2, etc.

[Here I have skipped some simple algebra.]

This entirely classical result is crucial to understanding quantum mechanics. In words, I would say this: “Real-life waves are usually combinations of waves of different frequencies or wavelengths.  But such ‘combination waves’ can be written simply as the product of two wave functions: one which represents ‘large-scale’ or global oscillations (i.e. cos(Δk·x – Δω·t)) and one which represents ‘small-scale’ or local oscillations (i.e. cos(k·x – ω·t)).

This way of looking at wave functions (remember, we haven’t introduced Schrödinger’s equation yet, nor should we!) makes it much easier to introduce the concept of group velocity vs. phase velocity: group velocity is just the speed of the large-scale wave groups, whereas phase velocity is the speed of an individual wave peak.  They are not necessarily the same.

It is also easy at this point to show that if you combine more and more wave functions, you get something that looks more and more like a wave “packet”.  In the limit as the number of wave functions goes to infinity, the packet becomes localized in space.  And then it’s simple to introduce the classical uncertainty principle: Δk·Δx > ½.  It’s not simple to prove, but it’s simple to make plausible.  And that’s all we want at this point.

We’re still not doing quantum mechanics, but we’re almost there.  Instead, we’ve shown how waves behave, and how uncertainty is inherent in anything with a wave-like nature.  Of course now is the time to strike, while the iron is hot.

What if matter is really made from waves?  What would be the consequences of that?  [Enter de Broglie, stage right]  One immediately gets the Heisenberg relations (really, this is like one line of algebra at the most, starting from the de Broglie relations) and suddenly you’re doing quantum mechanics!  The advantage of this approach is that “uncertainty” seems completely natural, just a consequence of being wave-like.

And whence Schrödinger’s equation?  I make no attempt to “prove” it in any rigorous way in an undergraduate course.  Instead, I just make it imminently plausible, by performing the following trick.  First, introduce complex variables, and how to write wave functions in terms of them.  Next, make it clear that a partial derivative with respect to x or t can be “re-written” in terms of multiplication:

d ψ /dx  →  ik ψ

d ψ /dt  →  –iω ψ

Then “proving” Schrödinger’s equation in a non-rigorous way takes 4 lines of simple algebra:

E = p2/2m

E ψ = (p2/2m)ψ

Now use the de Broglie relations E = ħω and p = ħk…

ħw ψ = (ħ2k 2/2m) ψ

iħ(∂ψ/∂t) = (–ħ2/2m) ∂2ψ/∂x2

There’s time enough for weirdness later.  Right now, armed with the Schrödinger equation, the student will have their hands full doing infinite well problems, learning about superposition, arguing about probability densities.  As George McFly said, “I am your density.”  And as Schrodinger said, probably apocryphally, “Don’t mention my cat till you see the whites of their eyes.”

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To reach orbit, go sideways

Posted in Uncategorized, tagged , , , on December 5, 2012| 8 Comments »

sideways

If you don’t go sideways,
you will return to Earth

Why is it that astronauts “float around” in space?

If you were to ask Bill O’Reilly or the Insane Clown Posse, the answer would be that it is a mystery.  If you were to ask the average person on the street, the answer would be that there’s no gravity in space.  Both answers are ridiculous, of course.  It’s not a mystery; we have a very firm working knowledge of the physics of orbits.  And there’s plenty of gravity in space: at 230 miles up, where the International Space Station is, the acceleration due to gravity is about 8.8 m/s2, which is only 10% less than its value at sea level.

So why does the general public still not understand this whole “floating astronaut” thing?

I submit that some of us physics professors are teaching it poorly.  Here’s an explanation from a physics book on my desk:

“All objects in the vicinity of, say, the space station are in free fall with the same acceleration, and so, absent nongravitational forces, they remain at rest relative to each other and their freely falling reference frame.” [Rex and Wolfson, Essential College Physics (2010) p. 215]

I don’t find this very helpful.  And many physics instructors teach “weightlessness” in the same non-helpful way: by hand waving and saying that astronauts are in free fall, and that they are only apparently weightless.  Unfortunately, to the novice this brings up a host of new questions: what’s the difference between apparent weightlessness and actual weightlessness?  More importantly, if you’re in free fall, why don’t you crash into the Earth?

Another book on my desk does a better job:

“Why don’t planets crash into the Sun [if they truly are in free fall]?  They don’t because of their tangential velocities.  What would happen if their tangential velocities were reduced to zero?  The answer is simple enough: their falls would be straight toward the Sun, and they would indeed crash into it.”  [Hewitt, Conceptual Physics, 10th edition (2006), p. 193]

Newton himself also got it right:

“We may therefore suppose the velocity to be increased, that it would describe an arc of 1, 2, 5, 10, 100, 1000 miles before it arrived at the Earth, till at last, exceeding the limits of the Earth, it should pass into space without touching it.”  [Isaac Newton, The System of the World, Section 3, translated by Motte, edited by Cajori (1946)]  [Note Isaac’s use of the word “till”!]

The key idea which we physics professors should emphasize is that astronauts are in free fall, but they don’t hit the Earth because they are moving very, very fast horizontally.  That’s it.  That’s the secret.  They are going so fast that they fall “around the curve of the Earth” so to speak.  I don’t think this horizontal motion is emphasized enough.  I’ll say it again: you need to go sideways to get into orbit.  The next time you’re piloting a spaceship, remember the old adage: that which goes (straight) up will surely come back down (unless you reach escape speed).  So don’t aim for infinity and beyond—aim for the horizon.

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Don’t do algebra with numbers!

Posted in Rant, tagged , , , , , on November 30, 2012| 2 Comments »

As a physics professor, I have certain pet peeves.  For example, I cringe when someone says that “gravity” is 9.8 m/s2 when they mean the acceleration due to gravity.  I’m annoyed if someone says that an object “weighs” 7 kg.  And I stifle a laugh if someone says that a roller coaster is exciting because it goes so “fast”—humans can only detect acceleration, not speed, which is why we don’t notice that we’re traveling something like 67,000 mph right now in our orbit around the sun.

goose

“I feel the need for acceleration!”

But my biggest pet peeve may be students doing algebra with numbers.

Fellow physics professors will know exactly what I’m talking about, but for the uninitiated, here’s an example:

If you drop an object from a height of 20 m, how long will it take to hit the ground?

A student knows that a kinematics equation is needed, hits upon the correct one, Δy = vi Δt + (1/2) a Δt2, and then correctly identifies Δy = –20 m, a = –9.8 m/s2, and vi = 0.  So far, so good.  They’ve studied their physics, right?  What happens next is sheer madness:

algebra_with_numbers

Sigh.

Over and over again I tell students, “don’t plug numbers in until the end.”  But students love plugging in numbers.  They feel they’re actually getting closer to the answer if they’re manipulating numbers.  On some level, they still feel uncomfortable with letters—as if manipulating letters isn’t really “math”.

How does this problem look in my answer key?  Like this:

algebra 2

You can now plug in values if you like…and get Δt = √[2(-20)/-9.8] = 2.02 s.

Which of these approaches is more beautiful, more powerful?  The approach you pick indicates whether you “get” algebra or not.  If you do algebra with numbers, the answer you get is very narrow and very specific, even if you do it correctly.  That hypothetical student could have gotten 2 seconds as an answer, and I would have given them full credit.  But their answer would have been ugly.

The second approach is beautiful, because it is completely general and applicable to multiple situations.  I try to tell students “Look!  You found the time to fall a certain distance.  You now know the answer no matter what the height is, and even no matter what planet you’re on, since g doesn’t have to be 9.8 m/s2.”  This is usually followed by a blank open-mouthed stare, much like Kristen Stewart in a Twilight movie.

There is a more practical reason to avoid doing algebra with numbers.  It’s simply that when you do algebra with numbers, other people cannot follow your work as easily.  And then, if you make a mistake, it’s harder for someone else to spot.  Quick: what algebra error did the student make above?  It takes a while to find the mistake.

My ultimate point is that students need experience seeing the power of algebra.  It’s all well and good that algebra classes stress real-world applications—else, why teach algebra in the first place?  But real-world doesn’t only mean with numbers.  E=mc2 is certainly a real-world application of algebra, and it’s a lot more elegant than saying that 378,000,000,000,000 Joules is released when a teaspoon of sugar with mass 4.2 grams  is converted to pure energy, given that the speed of light is 300,000,000 m/s.  The hard part, for us physics professors, is to help this spoonful of algebra go down.

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Einstein’s “Imagination is more important than knowledge”

Posted in Uncategorized, tagged , , , , , , on November 26, 2012| 8 Comments »

Poor Einstein.  Is there anyone else who is misquoted more often?  Is there anyone else to whom more nonsense is attributed?

I have no desire to rehash things that Einstein said about “God”.  Einstein was by all accounts an atheist, an agnostic, or a pantheist—depending upon your definitions—and various religious apologists have been trying to co-opt the man for years by misquoting him.  Others have already discussed this at length.

My goal today is to tackle that old chestnut, “Imagination is more important than knowledge,” as seen on T-shirts, bumper stickers, and even on the packaging of the Albert Einstein action figure.  Did Einstein really say this, and if so, what did he mean?

Here’s the quote in context:

“At times I feel certain I am right while not knowing the reason.  When the [solar] eclipse of 1919 confirmed my intuition, I was not in the least surprised.  In fact I would have been astonished had it turned out otherwise.  Imagination is more important than knowledge.  For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.”  [From A. Einstein, Cosmic Religion: With Other Opinions and Aphorisms, p. 97 (1931).]

So Einstein did say this.  However, I maintain that the full quote in context has a different feel to it than the quote in isolation.

When I see “Imagination is more important than knowledge” on a bumper sticker, I think this: “Flights of fancy and imagination are more important than learning stuff.  So why should I study?  Einstein didn’t study.  He just sat around and daydreamed and came up with the most remarkable breakthroughs about the workings of our universe.  Imagination is more important than learning all the proofs and figures ranged in columns before me.  So I am going to follow good ol’ Einstein and daydream about being Batman.”

The New Age meaning of the quote is this: “I’d rather daydream than study.”  It’s Walt Whitman’s “learn’d astronomer” nonsense all over again.

In context, it’s clear that Einstein was talking about doing science.  Imagination is more important in making scientific breakthroughs than knowledge, but that doesn’t mean that knowledge is not important.  Einstein worked very, very hard to learn an awful lot of physics.  By all accounts, it took him almost 10 years to flesh out general relativity, during which time he had to acquire a lot of mathematical knowledge about Riemannian geometry and tensor analysis.  The “intuition” that Einstein developed during this time frame is what allowed him to be so confident of the results of Eddington’s expedition.  What Einstein calls “intuition” is just knowledge that has become so ingrained that you are no longer cognizant of it.

Einstein may have been more famous than most of his contemporaries, and it was probably due to his superior imagination.  But take Einstein’s imagination today and give it to a twenty-five year old high school dropout, and he’d be lost in obscurity, stocking shelves at Wal-Mart.  Imagination is more important than knowledge.  But only slightly more.

[Note: my book Why Is There Anything? is now available for download on the Kindle!]

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Marco Rubio and the age of the Earth

Posted in Rant, tagged , , on November 20, 2012| Leave a Comment »

Recently, Senator Marco Rubio told an interviewer from GQ that he wasn’t qualified to say how old the Earth was:

GQ: “How old do you think the Earth is?”
Marco Rubio: “I’m not a scientist, man. I can tell you what recorded history says, I can tell you what the Bible says, but I think that’s a dispute amongst theologians and I think it has nothing to do with the gross domestic product or economic growth of the United States. I think the age of the universe has zero to do with how our economy is going to grow. I’m not a scientist. I don’t think I’m qualified to answer a question like that. At the end of the day, I think there are multiple theories out there on how the universe was created and I think this is a country where people should have the opportunity to teach them all. I think parents should be able to teach their kids what their faith says, what science says. Whether the Earth was created in 7 days, or 7 actual eras, I’m not sure we’ll ever be able to answer that. It’s one of the great mysteries.”

This is so absurd on so many levels, I need to parse the quotation out bit by bit—partly to stretch out this blog post, of course, but partly to delve more deeply into the mind that is Marco Rubio.

“I’m not a scientist, man.”

Obviously.  But GQ wasn’t asking you to demonstrate the Earth’s age using science.  They were asking you how old the Earth is, which admittedly is code for: “Do you believe in the most basic science?”  And apparently, you do not.

“I can tell you what recorded history says,”

What does recorded history have to do with the age of the Earth?

 

“I can tell you what the Bible says,”

But unfortunately the Bible doesn’t actually say how old the Earth is.

 

“but I think that’s a dispute amongst theologians…”

Wait…what?!  Theologians?  We’re talking about the age of the Earth.  If geologists can’t answer this question, no one can.  Why?  Because geology is the study of the Earth.

 

“…and I think it has nothing to do with the gross domestic product or economic growth of the United States.”

So?

 

“I think the age of the universe has zero to do with how our economy is going to grow.”

True, but the interviewer is really asking if you have any knowledge about science and the scientific method.  If you don’t believe the arguments for a 4 billion-year-old Earth, if you distrust that much the collective human body of knowledge, then you may not listen to economists when they tell you that printing a quadrillion dollar bills and passing them out to everyone would be a bad idea.

 

“I’m not a scientist. I don’t think I’m qualified to answer a question like that.”

Do you have to be a historian to answer the question, when did the Crimean War start?  Do you have to be a biologist to answer the question, what does RNA stand for?  Do you have to be a mathematician to say that pi is irrational?  Are you really claiming, Mr. Rubio, that you have to be an expert to answer the most basic, settled questions that humans have successfully answered?  Are you really saying that you’re not qualified to look up an answer on Wikipedia?

 

“At the end of the day, I think there are multiple theories out there on how the universe was created…”

He’s right, check out these 90 different theories from religions around the world…

“and I think this is a country where people should have the opportunity to teach them all.”

Including, no doubt, the story of the water beetle Dâyuni‘sï  that made the Earth from mud, and the story of how Buga set fire to the water…oh, and don’t forget how Mbombo vomited the moon and the sun!  Make sure elementary school curricula cover them all!

“I think parents should be able to teach their kids what their faith says, what science says.”

I’m not sure what his point is here.  Is there a movement to ban what parents can and cannot teach their children?

“Whether the Earth was created in 7 days, or 7 actual eras, I’m not sure we’ll ever be able to answer that. It’s one of the great mysteries.”

Yes, a mystery, like how the tides work or how magnets work.  I guess the real mystery is why anyone takes Marco Rubio seriously.

(Photo credit: NASA)

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Misconceptions about the Many-worlds Interpretation of quantum mechanics

Posted in Many-worlds Interpretation, tagged , , on November 12, 2012| 5 Comments »

It may seem odd that this blog is called “Many Worlds Theory” and yet I have not yet blogged about, well, many worlds theory.  Well, I am doing so now.

The arguments that lead a sizable portion of theoretical physicists to postulate a multiverse are subtle and complicated.  I hope to eventually cover these arguments, but I’d like to start with a discussion of what many worlds is not.  Therefore, with much fanfare, I present to you:

The Top 5 Misconceptions About the Many-worlds Interpretation (MWI) of Quantum Mechanics

1.      Every time you do a quantum experiment, the universe branches into multiple universes.

This is a popular notion, as seen in TV shows like Nova and as presented by Martin Gardner.  Unfortunately, it is the wrong way to look at things.  It is much better to imagine that all of the possible universes already exist, and that doing an experiment just tells you (the experimenter) which universe you happen to be in.

Suppose you’re watching Star Wars.  You have no idea whether you are watching the original, or the retconned 1997 version.  You finally realize which version you’re watching when you see Han shoot and kill Greedo without Greedo ever getting a shot off.  You conclude you’re watching the original version.

Of course, up until that point, the movies are exactly the same. (Rather, let’s just say they are the same.  I haven’t actually checked this.) You wouldn’t conclude, when you got to that scene, that two movies were created from one, would you?  There were two movies all along; watching Han shoot first just told you which movie you were watching.  A physicist who performs a Stern-Gerlach experiment doesn’t split the universe in two; doesn’t create a whole universe; instead she has gained some new information: “Oh, so that’s what universe I am in.”  No new physics of universe-creation is needed, and we need not violate conservation of energy.

2.      The existence of a multiverse is a postulate of a strange kind of quantum mechanics.

There is a formulation of quantum mechanics often called universally valid quantum mechanics, which was first described by Hugh Everett III in 1957.  It involves (see this for details) just one postulate: isolated systems evolve according to the Schrödinger equation.  That’s it.  A multiverse is a prediction of this postulate, not a postulate in and of itself.  So if you believe that isolated systems evolve according to the Schrödinger equation, you will be led to the MWI, unless you invent new postulates to make yourself feel better (see #3).

3.      The Many-worlds Interpretation has a lot of baggage.

This obviously depends upon what you mean by baggage, but the claim is often made that the MWI is horribly antithetical to Occam’s razor.  That is, how could anyone seriously believe that countless billions upon billions of universes exist, when believing in one universe is much, much simpler?

If you feel this way, I have two responses.

One: how can you believe that countless billions upon billions of stars exist, when believing in just one star is much, much simpler?  Shouldn’t you be Earth-centric, and call for Galileo’s excommunication?  Or what about the integers?  Mathematicians claim that there are an infinite number of them, but infinity is too hard to fathom, so why don’t you just say that there are a lot of integers, but that there is only a finite number of them?  There.  I bet you feel better.

Two: like it or not, Occam’s razor cuts both ways, and can be used to defend MWI.  The idea is whether Occam’s razor applies to the number of universes, or the number of postulates in your physical theory.  As Max Tegmark pointed out, universally valid quantum mechanics leads to a multiverse as a consequence.  In order to get the Copenhagen interpretation (for years, the most popular flavor of quantum mechanics) and rid yourself of those pesky many worlds, you have to take Everett’s quantum mechanics and add one additional postulate: that wave functions collapse according to random and ultimately unknowable criteria.  That is, the MWI is simpler in the number of postulates required.  As Tegmark put it, which way you use Occam’s razor depends upon whether you prefer many worlds, or many words.

4.      The Many-worlds Interpretation is not falsifiable and therefore not science.

The jury’s still out on this one, but many people (including David Deutsch) think that the MWI is misnamed: that it is actually a theory in and of itself, and that it is falsifiable.  I haven’t made up my mind on this.

I tend towards Tegmark’s view that MWI is an untestable prediction of quantum mechanics, which is testable.  Because we take quantum mechanics seriously, we have to take one of its children (MWI) seriously.  As Tegmark says, it’s like black holes.  We can never see inside a black hole, so what goes on in there is never falsifiable; yet we take black holes seriously and call black holes “science” because general relativity (the theory that predicts black holes) is so successful.

5.      The Many-worlds Interpretation is fringe science and only believed by kooks.

These kooks include Stephen Hawking (who said the MWI was “trivially true”), David Deutsch, Bryce DeWitt, and Max Tegmark, among others.  They also include a sizable number of theoretical physicists working today.  In 1995 one poll (published in the French periodical Sciences et Avenir in January 1998) showed that 58% favored MWI; see also this informal 1997 poll.

Maybe we are all kooks.  But there are a lot of us, and the number is growing.

[Note: my book Why Is There Anything? is now available for download on the Kindle!  This book examines the many-worlds interpretation from a philosophical perspective.]

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Poem (No apologies to Walt Whitman)

Posted in Poem, tagged , , on November 2, 2012| 5 Comments »

When I heard the poet talking about hearing the learn’d astronomer,
When the poet mentioned how all the proofs, the figures, were ranged in columns before him,
When the poet described how he was shown the charts and diagrams, and how to add, divide, and measure them,
When I sitting heard the poet where he read with much applause in the lecture-room,
When I realized of a sudden, how the theme of the poem was “ignorance is bliss” and “beauty and science are incompatible,” and [holding hands over ears] “please! O please! don’t tell me how anything in this Cosmos works, since then it would cease to be ‘poetic’!”
How soon very accountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the rational moist night-air, time to time,
Look’d up in perfect silence at the stars,
Thinking about the fascinating Bethe-Weizsäcker-cycle.

(Sept. 25, 2009)

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