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## Cycloid illusion is not really an illusion

Photo credit: brusspup

Recently I came across the following “optical illusion” on the normally good website I Fucking Love Science:

http://www.iflscience.com/brain/cycloid-optical-illusion-will-boggle-your-mind

I encourage you to read the article and think about the video (otherwise the rest of this post will be less than illuminating).

Supposedly, there is an “optical illusion” in the video because you think there’s a wheel when in “reality” the dots are moving linearly.

This is bullshit.

This is not an illusion. The dots are moving linearly, that’s true. But there is also a wheel. If this causes you cognitive dissonance, so be it. It is not a paradox, however. It is the case that some wheels, when spinning inside other wheels, have points on them which travel linearly.

I admit, this is a field of mathematics close to my heart. Much of my recent work has involved geometric phase, which has connections to Spirographs, epitrochoids and hypotrochoids as mentioned in the IFLS article. I have battered notebooks with over 500 pages of algebra devoted to such things. This is something I know something about.

One way to see that this isn’t an illusion at all is to watch it being drawn. Go to the following Spirograph applet:

http://www.personal.psu.edu/dpl14/java/parametricequations/spirograph/

Play around a little bit. Then create the following specific Spirograph (which is exactly the one in the IFLS “illusion”):
Position = 29
Velocity = 8
If you need to, CLEAR the picture, input the above parameters, and hit DRAW. Hit DRAW again to watch it all over again.

There’s no illusion. A circle is rotating inside another circle. Simultaneously, a particular part of that circle is traversing a straight line. This comes as a surprise to many people: there’s a frisson of incredulity from the idea that your motion can be simultaneously linear, but curved as well. But there’s an easy explanation. Your motion is different in different frames of reference.

Consider an ant on the wheel. With respect to the center of that wheel, he just orbits in a circular manner. But with respect to us, outside of the contraption, he moves back and forth along a single line. This is not an optical illusion. It’s the relativity of geometric shapes.  And I think that’s even cooler than some cognitive trickery.

## Big Bang Discovery Opens Doors to the “Multiverse”

The big news of late is the discovery of gravitational waves from the very earliest time after the Big Bang.  What hasn’t been widely reported is that this represents a huge bit of indirect evidence that multiple universes really do exist.

Here’s more:

(Harvard University / EPA)

## There’s no philosophy in quantum mechanics

The conventional wisdom among people who know a little bit of quantum mechanics is that quantum mechanics is weird.

The conventional wisdom is wrong.  Quantum mechanics is not weird.  Interpretations of quantum mechanics are weird.

My thinking on this has changed over the years.  In high school I read everything I could about the “weirdness” of our universe: Schrödinger’s cat, wave-particle duality, the collapse of the wave function, many-worlds theory, the Heisenberg uncertainty principle.

Then a strange thing happened: I went to college.  I studied physics.  And guess what?  None of that stuff gets more than the briefest mention in the physics classroom.  Why?

Because those things are beside the point.  Quantum mechanics works.  How you interpret quantum mechanics is your problem.

There’s a dichotomy here which is the source of most people’s confusion.  Theories are different from interpretations of theories.  A theory is a mathematical model that allows us to make predictions.  An interpretation is a philosophical construct that allows us to sleep at night; it is a squishy heuristic that helps us unimaginative humans make sense of the math before us.  Theories get things done.  Interpretations never helped anybody, not really.

An abandoned shack.

Let’s say that in an abandoned shack you discovered a notebook with the word “PHYSICS” written by hand over and over, thousands of times, apparently filling every page.  You haven’t looked at the last few pages, but your theory is that these pages will also have the word “PHYSICS” written out.  Each time you turn a page, your theory is validated: “PHYSICS” is there, as predicted.

Next to this notebook is another that looks just like it.  You open the first page, and are not surprised to see “PHYSICS PHYSICS PHYSICS” again.  What’s going on?  Did some crazy person live in this shack?  Such speculation doesn’t really matter, since you can still hypothesize that “PHYSICS” fills this notebook as well.  In fact, you have a stronger theory: every notebook in this shack is filled with “PHYSICS”.

You perform an experiment: you turn the page.  “PHYSICS PHYSICS PHYSICS”.  The experiment supports your theory.  You find more notebooks; same results.  Every notebook in the shack is filled, apparently, with “PHYSICS”.  But guess what?  There are dozens of possible interpretations.  And in the absence of further data, you can never know which one is “correct”.

Maybe the shack was once inhabited by a crazy person, who wrote “PHYSICS” precisely 250,001 times in a futile attempt at summoning Cthulhu from his ancient slumber.

Maybe a student misspelled “physics” on a test, and her cruel teacher punished her in the most depraved way possible.

Maybe Matt Damon filled the notebooks, in a method-acting attempt to get into the mindset of an OCD scientist.

Which of these interpretations is the “truth”?  Without further data you cannot really say.  Arguing about which is right and which is wrong is futile at best, and annoying at worst.

Of course, new data may turn up.  We might find out that the notebooks are 75 years old, ruling out our Matt Damon interpretation.  That interpretation is no longer a valid interpretation of the data.

Which brings me to my next point: there is no official arbiter of what constitutes a theory versus what constitutes an interpretation.  Different philosophers and scientists have used the words differently at different times.  All you can hope for is that a particular author is consistent in his/her use of the terms.  I personally use the word “interpretation” to describe competing theories that cannot currently be differentiated by any known scientific experiment.  If two different interpretations make different, testable predictions, then they are promoted to being totally different theories.  (Caveat: others use the words slightly differently.  Deal with it.)

So what does this have to do with quantum mechanics?

Quantum mechanics is an entirely mathematical theory.  Its postulates are logical, concise, and powerful.  We can use quantum mechanics to invent cell phones, computers, lasers, and iPods.  Quantum mechanics doesn’t care if you “understand what it really means”, or not.  It is arguably the most successful and powerful theory to come out of the 20th century.

Now, the mathematics of quantum mechanics are abstract and hard to visualize.  Nevertheless, people insist on trying to visualize anyway.  And the result is all kinds of weirdness: Schrödinger’s cat, wave-particle duality, the collapse of the wave function, many-worlds theory, the Heisenberg uncertainty principle.  These ideas are all mental hoops that people have jumped through to explain some unambiguous, concrete, abstract linear algebra.  The math is just math, and it works; what it means is anyone’s guess.

There’s no crying in baseball, and there’s no philosophy in quantum mechanics.

There’s no philosophy in quantum mechanics!

Don’t like the many-worlds interpretation?  Fine.  Be a Copenhagenist.  Don’t like pilot waves?  Great.  Stick to your pet idea about superluminal communication.  Just remember that all of these competing interpretations make the exact same predictions, so for all practical purposes they are the same.  Some people go so far as to say, just shut up and calculate.  [Note added 3-19-14: there are problems with pilot wave theories that in my view rule them out as being a valid interpretations of quantum mechanics.  But there are hoops people can jump through to try and “force” pilot wave theories to be consistent with, say, Bell’s theorem.  My broader point is that there are multiple interpretations of QM and that all have followers to this day, but that none of the interpretations really have any distinct implications for our lives.]

I don’t usually go that far.  I actually think that the many-worlds interpretation is a testable theory, not an interpretation (hence the name of this blog).  I think many-worlds is falsifiable.  (If we ever observe a wave function collapsing, then many-worlds will have to be discarded.)  But I don’t think that will happen: many-worlds is too elegant, and too powerful, to not be true.

But we’ll see.

If you think it’s absurd that a cat can be alive and dead at the same time…if you think that it’s crazy to hypothesize other universes…if you think that God does not play dice with the universe…don’t blame quantum mechanics.  Blame the philosophers who try to interpret it.

Quantum mechanics works.  Otherwise, you’d be reading this on an actual piece of paper.

## Black hole misconceptions or: Why Dr. Who is not science fiction

I was watching Dr. Who the other day and came across a physics mistake so common I thought I’d address it here.  The mistake is this:

Black holes suck you in like a vacuum cleaner!

The setup: in Dr. Who [2.8] “The Impossible Planet”, the good Doctor and Rose meet the crew of a ship who are on “an expedition [to] the mysterious planet Krop Tor, impossibly in orbit around a black hole.” [Wikipedia]  That phrase “impossibly in orbit” made me almost spit out my drink while watching the show.

Black holes have event horizons.  I get it.  Even light cannot escape.  I get that, too.  But why does that mean I cannot orbit a black hole?

OK, time for a little general relativity.  Einstein figured out, between 1905 and 1915, that gravity is “just” a warping of space-time.  Matter causes the space-time around it to curve; the curvature of space-time determines how matter moves (insofar as objects in the absence of gravitational forces follow geodesics).  The formulas that link the distribution of matter to the curvature of space are Einstein’s equations:

This expression is compact and might seem relatively simple, but it’s not.  Gαβ and Tαβ are components of tensors, which are like vectors, but worse; they’re really 4×4 matrices.  So this equation is not one equation, but 16 different equations, since α and β can take on any of four values each.

What do all those letters stand for?  Gαβ is a component of the Einstein tensor, which tells you about how space-time is curved; the indices α and β can be any of four values in a 4D space-time.  (If you’re mathematically inclined, the Einstein tensor can be related to the Ricci scalar, the Ricci tensor, and the Riemann tensor.)  Tαβ is a component of the stress-energy tensor, which basically describes how matter/momentum/energy/stress/strain is distributed in a region of space-time.  So here’s another way to visualize Einstein’s equations:

The cause (mass) is on the right; the effect (the curvature of space-time) is on the left.

So what does this have to do with black holes?

One of the first solutions discovered to the Einstein equations is called the Schwarzschild solution, which applies to a spherically symmetric gravitational source.  The solution gives you a “metric” (essentially, a geometry) that is almost the same as “flat” space-time, except for a pesky (1–2GM/c2r) term.  But that pesky term has a strange implication: when that term equals zero, the solution “blows up” (i.e. becomes infinite).  Space becomes so curved that you essentially have a hole in the fabric of space-time itself.

When does this happen?  It happens when R = 2GM/c2, as one line of algebra will show.  This is called the Schwarzschild radius.  The Einstein equations predict that something weird and horrifying happens when a mass is squeezed down to the size of its Schwarzschild radius.  Current understanding is that the mass would then keep going, and squeeze itself into a point of zero radius.  Literally, zero.  (I did say it was weird and horrifying).

Incidentally, the Schwarzschild radius is exactly the radius you’d get if you set the escape speed for an object equal to the speed of light.  So this means that not even light can escape this super-squeezed object.

And here’s where various misconceptions start to creep in.

Another name for the Schwarzschild radius is the event horizon.  It’s a boundary of no return:  if you cross it, you can never go back.  But that’s all it is: a boundary.  There is not necessarily anything physical at the event horizon.  You might never know that you had crossed it.  Remember, all the mass is at the center.

Here’s how I “picture” a black hole:

Now, if I am outside the event horizon, what would I see?  Well, nothing from inside the event horizon could reach me (hence the term “black”) but I might see Hawking radiation.  I would certainly see gravitational lensing: the bending of distant light around a black hole.  Here’s a cool picture of gravitational lensing in action (artists conception only!) from Wikipedia:

Let’s say the Sun were a black hole.  Its event horizon would be around 3 km.  As long as we never got closer than 3km, we could do what we like.  We could fly in, fly out, orbit the black hole as we please.

Would the black hole “suck us in”?  Sure, in the same way that the Sun sucks us in already.  There is a strong pull of the Sun on the Earth.  And there would be a strong pull on our hypothetical spaceship.  But change the Sun to a black hole, and the pull would not get any stronger.  That is the key point that most people miss: black hole gravity is not somehow “stronger” than ordinary gravity.  There is just gravity; that’s it.  Change the Sun to a black hole, and the Earth would continue in its orbit, and nothing would be any different.  Except for, maybe, the lack of light.

Why was the planet Krop Tor’s orbit impossible?  Astronomical black holes (created by stellar collapse) have a lot of mass; when there’s a lot of mass hanging around, things tend to orbit them.  That’s what you’d expect.  It would only be impossible if somehow the orbit crossed the event horizon multiple times during its trajectory.  But of course, the show didn’t mention this.

I want to end my rant on GR with a suggestion: that there are two kinds of sci-fi: science fiction, and “sciency” fiction.  The first kind tries to get the science right, and makes an effort to be possible (if not plausible).  The second kind throws sciency words around in an effort to appeal to a certain demographic.  Basically, “sciency” fiction is fantasy, set in outer space.  When seen in this light, Dr. Who has more in common with Lord of the Rings than it does with 2001.

Don’t get me wrong: I love Lord of the Rings, and I love Dr. Who.  Just don’t call it science fiction.

## Sharing spacetime coordinates with Abraham Lincoln and Matt Damon

In an earlier post I talked about events in spacetime, and about how an error in time is usually more grievous than an error in space.

Let’s now talk about the coincidence of spacetime coordinates.  Specifically, how significant is it if you share one, two, three, or even four coordinates with a famous person?

First, some preliminary discussion.  An event is a point (x,y,z,ct) in spacetime.  Technically, you are not an event; you are a series of (unfortunate?) events smoothly snaking its way forward in time.  As you sit there, reading this post, your x, y, and z are probably staying constant while ct is continually increasing.  (Of course if you are reading this on the bus, then x, y, and z may be changing as well.)  Note that I will use a relative coordinate system where x and y are measured with respect to the Earth (they are effectively longitude and latitude) and z is height above sea level.  This way, we don’t have to deal with the annoying detail that the Earth is spinning, and orbiting the Sun, and that the solar system is hurtling through space.

Now the act of you reading this is an event; let’s say it has the coordinates (x,y,z,ct) in spacetime.  But let’s also suppose that when you read that word, Matt Damon was eating a bagel with cream cheese.  That event had the coordinate (X,Y,Z,cT), say.  Unless you happened to have been with Matt Damon just then, your spatial coordinates did not coincide.  However, it should be obvious that t=T.  This means that it is no big deal to share a time coordinate with a celebrity.  You currently share a time coordinate with every living celebrity.  Right now, as you read this, Quentin Tarantino is doing something.  So is cricketer Michael Clarke.  So is chess grandmaster Magnus Carlsen.

What are the spacetime coordinates of the Ashes?

But how significant is it if one spatial coordinate (x, y, or z) coincides with a celebrity?  Or two spatial coordinates?  Can we sort this out?

Here are some other possible cases:

x or y (and t) coincide: this is not likely to be true for you at this instant, but it happens with great frequency.  It means that either your longitude or latitude is the same as a celebrity, such as Christopher Walken.  Let’s say you’re currently in Jacksonville, FL whereas Walken is in Los Angeles.  Obviously, your x’s are very different and your y’s, although close, are also different.  But you decide to drive to Raleigh, NC for a friend’s wedding.  At some point along your drive on I-95 your y-coordinate will be the same as Walken’s, as the line of your latitude sweeps through 34 degrees North.  (If you’re curious, it will happen a little before you stop for lunch at Pedro’s South of the Border.)  On a flight from Seattle to Miami, your lines of x and y will coincide (at different times) with a majority of celebrities in the USA.

z (and t) coincide: this is also quite common.  It means that you and a celebrity (such as chess grandmaster Hikaru Nakamura) share an altitude.  I am currently at z = 645 m (2116 ft.) in elevation…well, scratch that, I am three floors up, so it’s closer to z = 657 m.  Anyway, if Nakamura drives from Saint Louis (Z = 142 m) to Denver (Z = 1600 m) on I-70 then our elevations will coincide at some point along his drive (presumably a little bit past Hays, KS).

x or y, with z and t: this is much rarer, but does happen.  For this to occur, your line of longitude or latitude would have to sweep through a celebrity (such as quarterback Cam Newton), but you would also have to coincidentally be at the same altitude.  Now, if you live in the same city as the celebrity (in this case, Charlotte, NC) then a simple trip across town to visit Trader Joe’s would probably be sufficient to achieve x=X (or y=Y) along with z=Z and t=T.  However, for someone like me who lives at an arbitrary (and uncommon) elevation such as 645 m, this does not happen often.

x, y, z….but not t: this means that you have visited the exact location that a famous person has visited, but not at the same time.  This probably happens hundreds of times in your life.  An obvious example is when you go to a famous location: maybe Dealey Plaza in Dallas, maybe the Blarney Stone, maybe the location of Lincoln’s Gettysburg address.  (By the way, today is the 150th anniversary of that speech!)  A not-so-obvious example (but much more common) is when you drive along a much-used road.  I have driven I-95 for huge stretches, for example, and I am sure many celebrities have driven that highway as well.  At some point along my drives, I will have “visited” the same location as another celebrity (Tina Fey, let’s say) when she decided to drive down to Savannah for the weekend.  I’m sure she stopped at Pedro’s South of the Border, and so have I.

Proof that I went there.

x,y,z and t: this is the holy grail of celebrity coincidence.  It means you met the person.  Now, of course, humans are not bosons, so the spatial coordinates cannot be exactly the same, but if you meet the person I will say that the coordinates are close enough.  My (x,y,z,ct) were once the same as Al Gore.  My (x,y,z,ct) were once the same as Alan Dershowitz.  My (x,y,z,ct) were once (almost) the same as Hikaru Nakamura.  That’s about it.

I have left out several cases (such as x and/or z coinciding, without t) because they are trivial and uninteresting.  Imagine the entire world line of a celebrity such as Winston Churchill, who traveled all over the world.  If his spatial coordinates were projected onto the ground (painted bright yellow, say) then this looping curvy line would be a huge mess, spanning the globe, and covering huge swaths of England like spaghetti.  As I live my life, at any given instant I am pretty sure that one or two of my coordinates match some part of this snaky line.  No big deal.

It’s not like he was Matt Damon or anything.

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If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.

I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  Publication of the first installment will be January 2015; further details will be released on Facebook, Twitter, or via email: SargassoNova (at) gmail.com.

## 10 physics misconceptions, explained poorly

[This blog post was written by a guest columnist, a D-student in freshman physics who will remain anonymous]

10.         It’s winter because we’re far from the Sun

Everyone knows that it’s cold in January because, well, we’re farther from the Sun that usual.  The orbit of the Earth is elliptical, so in the Summer we’re closer to the Sun, like Mercury.  I have no idea why the seasons are reversed in Australia…maybe it’s because they’re upside-down?

9.            Force is non-reciprocal

I tug on a rope with a force of 100 N.  On the other end of the rope is a football player; let’s say Greg Olsen (TE for the Carolina Panthers, of course, but you knew that I’m sure).  With what force is Greg Olsen pulling on the rope?  It must be much more than 100 N, because a football player is stronger than me.

8.            Areas and volumes have the same conversion factors as linear units

If 100 cm = 1 m, then 100 cm2 = 1 m2.  This is so obvious it doesn’t merit comment.  Another way to look at it is that a meter and a square meter are, basically, the same thing.

7.            Acceleration is the same as speed

Acceleration is, like, how fast you’re going.  So if I throw a ball straight up, at the top of its arc, its speed is zero, so its acceleration must be zero.  Can I have some of those Cheetos?

Best comic ever?

6.            Weight and mass are the same

I was asked in lab the other day to find the weight of a brass cylinder.  So I did:  I weighed it, and got that its weight was 250 g.  I was then asked to find the force due to gravity on the object, but I don’t know how to do that.  Oh, I have to go; I’m rushing Phi Upsilon.

5.            There’s a magical force that appears whenever you move in a circle

So, I was driving the Tail of the Dragon on my scooter the other day, and almost got pulled off the road because of centrifugal force.  That’s another kind of force; you know, like gravity, friction, drag, spring force…centrifugal force.  It appears whenever you move in a circle.  It’s directed outward.  It is a repulsive force, the opposite of gravity.

4.            Objects have a memory of circular motion

If you spin a circle with a ball in your hand, then let go, the ball will spiral outward (obviously) because by the 1st Law objects in motion stay in the same kind of motion that they had before: circularly moving objects keep moving in a circle, etc.  I might then wonder why my scooter didn’t keep going in a circle in spite of centrifugal force, but luckily I don’t ever experience cognitive dissonance.

3.            There’s no gravity in space

Here’s a spoiler in case you didn’t see Gravity with Sandra Bullock and George Clooney.  In the scene where Sandra Bullock is knotted up in some ropes, she tries to hold on to George Clooney, but lets go.  Of course then George Clooney plummets towards the Earth, because of gravity.  They must have been right at the invisible border between space and not-space, where gravity suddenly drops to zero.

2.            g stands for “gravity”

The formula for weight is w = mg, which stands for mass times gravity.  g is gravity.  It’s like a force or something.  I have no idea why my instructor winces every time I say this.

1.            No net force means no movement

This is the most obvious one of all.  On one of our homework problems, there were only two forces acting on a box: 50 N up, and 50 N down.  The net force is clearly zero.  So the box cannot be moving!  Therefore v = 0 (duh!)  But my professor marked this wrong.  She said that v might be 50,000 m/s for all we know.  That makes no sense!  Physics is too hard.

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If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.

I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  Publication of the first installment will be January 2015; further details will be released on Facebook, Twitter, or via email: SargassoNova (at) gmail.com.

## Why many worlds?

I thought I would re-post this excellent discussion of the many-worlds interpretation by David Yerle:

Why I Believe in the Many-Worlds Interpretation

I agree with him 100%, and he says it better than I ever could.  The crux of the argument is this: it depends on the book you’re reading, but as a practical matter there are typically 4 postulates of quantum mechanics (about the primacy of the wavefunction, Schrödinger’s equation, measurements being Hermitian operators, and wave function collapse).  Many worlds is what you get when you reject the unmotivated “wave function collapse” postulate.  It is a simpler theory in terms of axioms, so obeys Occam’s razor.  If multiple universes bother you, think of how much it bothered people in the 1600’s to contemplate multiple suns (much less multiple galaxies!)

## An H-R diagram for the 9 kinds of physics undergrad

In my continuing effort to present cutting-edge research, I present here my findings on the 9 kinds of physics undergrad.

First, let’s look at a scatter plot of Ability vs. Effort for a little more than 100 students.  (This data was taken over a span of five years at a major university which will remain unnamed.  Even though it’s Wake Forest University.)

Student ability is normalized so that 1 is equivalent to the 100th percentile, 0 is the 50th percentile, and –1 is the 0th percentile.  [This matches the work of I. Emlion and A. Prilfül, 2007]  Ability scores below –0.5 are not shown (such students more properly belong on the Business Major H-R diagram).

On the x-axis is student effort, given as a spectral effort class [this follows B. Ess, 2010]:

O-class: Obscene

B-class: Beyond awful

A-class: Awful

F-class: Faulty

G-class: Good

K-class: Killer

M-class: Maximal

As you can see, most students fall onto the Main Sequence.

The Typical student (effort class G, 50th percentile) has a good amount of effort, and is about average in ability.  They will graduate with a physics degree and eventually end up in sales or marketing with a tech firm somewhere in California.

The Giant student (effort class K, 75th percentile) has a killer amount of effort and is above average in ability.  Expect them to switch to engineering for graduate school.

The Smug Know-it-all student (effort class O, 100th percentile) is of genius-level intellect but puts forth an obscenely small amount of effort.  They will either win the Nobel prize or end up homeless in Corpus Christi.

The Headed to grad school student (effort class B, 75th percentile) is beyond awful when it comes to work, and spends most of his/her time playing MMORPG’s.  However, they score well on GRE’s and typically go to physics graduate schools, where to survive they will travel to the right (off the main sequence).

The Headed to industry student (effort class F, 55th percentile) is slightly above average but has a faulty work ethic.  This will change once they start putting in 60-hour weeks at that job in Durham, NC.

The Hard working math-phobe student (effort class M, 30th percentile) is earnest in their desire to do well in physics.  However, their math skills are sub-par.  For example, they say “derivatize” instead of “take the derivative”.  Destination: a local school board near you.

The Supergiant student (effort class K, 100th percentile) is only rumored to exist.  I think she now teaches at MIT.

The Frat boy student (effort class O, 50th percentile) is about average, but skips almost every class.  Their half-life as a physics student is less than one semester.  They will eventually make three times the salary that you do.

The White dwarf student (effort class B, 30th percentile) is below average in ability and beyond awful when it comes to putting forth even a modicum of effort.  Why they don’t switch to being another major is anyone’s guess.

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If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.  The book is weighty and philosophical, but my sense of humor is still there!

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I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  My partner in this project is Craig Varian – an incredibly talented visual artist (panthan.com) and musician whose dark ambient / experimental musical project 400 Lonely Things released Tonight of the Living Dead to modest critical acclaim a few years back.  Publication of the first installment will be January 2015; further details will be released on our Facebook page, Twitter feed, or via email: SargassoNova (at) gmail.com.

## The 9 kinds of physics seminar

As a public service, I hereby present my findings on physics seminars in convenient graph form.  In each case, you will see the Understanding of an Audience Member (assumed to be a run-of-the-mill PhD physicist) graphed as a function of Time Elapsed during the seminar.  All talks are normalized to be of length 1 hour, although this might not be the case in reality.

The “Typical” starts innocently enough: there are a few slides introducing the topic, and the speaker will talk clearly and generally about a field of physics you’re not really familiar with.  Somewhere around the 15 minute mark, though, the wheels will come off the bus.  Without you realizing it, the speaker will have crossed an invisible threshold and you will lose the thread entirely.  Your understanding by the end of the talk will rarely ever recover past 10%.

The “Ideal” is what physicists strive for in a seminar talk.  You have to start off easy, and only gradually ramp up the difficulty level.  Never let any PhD in the audience fall below 50%.  You do want their understanding to fall below 100%, though, since that makes you look smarter and justifies the work you’ve done.  It’s always good to end with a few easy slides, bringing the audience up to 80%, say, since this tricks the audience into thinking they’ve learned something.

The “Unprepared Theorist” is a talk to avoid if you can.  The theorist starts on slide 1 with a mass of jumbled equations, and the audience never climbs over 10% the entire time.  There may very well be another theorist who understands the whole talk, but interestingly their understanding never climbs above 10% either because they’re not paying attention to the speaker’s mumbling.

The “Unprepared Experimentalist” is only superficially better.  Baseline understanding is often a little higher (because it’s experimental physics) but still rarely exceeds 25%.  Also, the standard deviation is much higher, and so (unlike the theorist) the experimentalist will quite often take you into 0% territory.  The flip side is that there is often a slide or two that make perfect sense, such as “Here’s a picture of our laboratory facilities in Tennessee.”

You have to root for undergraduates who are willing to give a seminar in front of the faculty and grad student sharks.  That’s why the “Well-meaning Undergrad” isn’t a bad talk to attend.  Because the material is so easy, a PhD physicist in the audience will stay near 100% for most of the talk.  However, there is most always a 10-20 minute stretch in the middle somewhere when the poor undergrad is in over his/her head.  For example, their adviser may have told them to “briefly discuss renormalization group theory as it applies to your project” and gosh darn it, they try.  This is a typical case of what Gary Larson referred to as “physics floundering”.  In any case, if they’re a good student (and they usually are) they will press on and regain the thread before the end.

The “Guest From Another Department” is an unusual talk.  Let’s say a mathematician from one building over decides to talk to the physics department about manifold theory.  Invariably, an audience member will gradually lose understanding and, before reaching 0%, will start to daydream or doodle.  Technically, the understanding variable U has entered the complex plane.  Most of the time, the imaginary part of U goes back to zero right before the end and the guest speaker ends on a high note.

The “Nobel Prize Winner” is a talk to attend only for name-dropping purposes.  For example, you might want to be able to say (as I do) that “I saw Hans Bethe give a talk a year before he died.”  The talk itself is mostly forgettable; it starts off well but approaches 0% almost linearly.  By the end you’ll wonder why you didn’t just go to the Aquarium instead.

The “Poetry” physics seminar is a rare beast.  Only Feynman is known to have given such talks regularly.  The talks starts off confusingly, and you may only understand 10% of what is being said, but gradually the light will come on in your head and you’ll “get it” more and more.  By the end, you’ll understand everything, and you’ll get the sense that the speaker has solved a difficult Sudoku problem before your eyes.  Good poetry often works this way; hence the name.

The less said about “The Politician”, the better.  The hallmark of such a talk is that the relationship between understanding and time isn’t even a function.  After the talk, no one will even agree about what the talk was about, or how good the talk was.  Administrators specialize in this.

If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.  The book is weighty and philosophical, but my sense of humor is still there!

I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  My partner in this project is Craig Varian – an incredibly talented visual artist (panthan.com) and musician whose dark ambient / experimental musical project 400 Lonely Things released Tonight of the Living Dead to modest critical acclaim a few years back.  Publication of the first installment will be January 2015; further details will be released on our Facebook page, Twitter feed, or via email: SargassoNova (at) gmail.com.

## Formula snobs

I am a formula snob.

We all know about grammar snobs: the ones who complain bitterly about people using who instead of whom.  Many people know how to use whom correctly; only grammar snobs care about it.  I gave up the whom fight long ago (let’s just let whom die) but I am a grammar snob when it comes to certain words.  For example, ‘til is not a word, as I have discussed before.

However, I am almost always a formula snob.

Consider this formula from the text I’m currently using in freshman physics:

x = v0 t + ½ a t2.

Robin Thicke, c. 2012

To me, looking at this equation is like watching Miley Cyrus twerk with Beetlejuice.  I would much, much rather the equation looked like this:

Δx = v0 Δt + ½ a Δt2.

The difference between these two formulas is profound.  To understand the difference, we need to talk about positions, clock readings, and intervals.

A position is just a number associated with some “distance” reference point.  We use the variable x to denote positions.  For example, I can place a meter stick in front of me, and an ant crawling in front of the meter stick can be at the position x=5 cm, x=17 cm, and so on.

A clock reading is just a number associated with some “time” reference point.  We use the variable t to denote clock readings.  For example, I can start my stopwatch, and events can happen at clock readings t=0 s, t=15 s, and so on.

Here’s the thing: physics doesn’t care about positions and clock readings.  Positions and clock readings are, basically, arbitrary.  A football run from the 10 yard line to the 15 yard line is a 5 yard run; going from the 25 to the 30 is also a 5 yard run.  The physics is the same…I’ve just shifted the coordinate axes.  If I watch a movie from 8pm to 10pm (say, a Matt Damon movie) then I’ve used up 2 hours; the same thing goes for a movie from 9:30pm to 11:30pm.  Because a position x and a clock reading t ultimately depend on a choice for coordinate axes, the actual values of x and t are of little (physical) importance.

Suppose someone asks me how far I can throw a football.  My reply is “I threw a football and it landed on the 40 yard line!”  That’s obviously not very helpful.  A single x value is about as useful as Kim Kardashian at a barn raising.

Can you pass that hammer, Kim?

Or suppose someone asks, “How long was that movie?” and my response is “it started at 8pm.”  Again, this doesn’t say much.  Physics, like honey badger, doesn’t care about clock readings.

Most physical problems require two positions, or two clock readings, to say anything useful about the world.  This is where the concept of interval comes in.  Let’s suppose we have a variable Ω.  This variable can stand for anything: space, time, energy, momentum, or the ratio of the number of bad Keanu Reeves movies to the number of good (in this last case, Ω is precisely 18.)  We define an interval this way:

ΔΩ = Ωf – Ωi

So defined, ΔΩ represents the change in quantity Ω.  It is the difference between two numbers.  So Δx = xf – xi is the displacement (how far an object has traveled) and Δt = tf – ti  is the duration (how long something takes to happen).

When evaluating how good a football rush was, you need to know where the player started and where he stopped.  You need two positions.  You need Δx.  Similarly, to evaluate how long a movie is, you need the starting and the stopping times.  You need two clock readings.  You need Δt.

I’ll say it again: most kinematics problems are concerned with Δx and Δt, not x and t.  So it’s natural for a physicist to prefer formulas in terms of intervals (Δx = v0 Δt + ½ a Δt2) instead of positions/clock readings (x = v0 t + ½ a t2).

But, you may ask, is the latter formula wrong?

Technically, no.  But the author of the textbook has made a choice of coordinate systems without telling the reader.  To see this, consider my (preferred) formula again:

Δx = v0 Δt + ½ a Δt2.

The formula says, in English, that if you want to calculate how far something travels Δx, you need to know the object’s initial speed v0, its acceleration a, and the duration of its travel Δt.

From the definition of an interval, this can be rewritten as

xf  – xi = v0 (t– ti) + ½ a (t– ti) 2.

This formula explicitly shows that two positions and two clock readings are required.

At this point, you can simplify the formula if you make two arbitrary choices: let xi = 0, and let ti = 0.  Then, of course, you get the (horrid) expression

x = v0 t + ½ a t2.

I find this horrid because (1) it hides the fact that a particular choice of coordinate system was made; (2) it over-emphasizes the importance of positions/clock readings and undervalues intervals, and (3) it ignores common sense.  Not every run in football starts at the end-zone (i.e. x = 0).  Not every movie starts at noon (i.e. t = 0).  The world is messier than that, and we should strive to have formulas that are as general as possible.  My formula is always true (as long as a is constant).  The horrid formula is only true some of the time.  That is enough of a reason, in my mind, to be a formula snob.

A formula snob?

Bonus exercise: show that the product

ΩKeanu Reeves  x  ΩMatt Damon  ≈  3.0

has stayed roughly constant for the past 15 years.