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## 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.

## The mathematics of going viral

Up until Oct. 7, 2013, my modest blog averaged about 18 hits per day.  Then this happened:

A post of mine, the 9 kinds of physics seminar, had gone viral.  I was shocked, to the say the least.

I spent some time investigating what happened.  The original post went out on a Thursday, Oct. 3.  Nothing much happened, other than a few likes from the usual suspects (thank you, John Zande!)  I did share the post with Facebook friends, which include not a few physicists.  (Note: I don’t normally share my blog posts to Facebook.)  Then on Monday, Oct. 7, the roof caved in.

It started in India.  Monday morning, I had over 800 hits from India.  My initial thought was that I was bugged somehow.  But soon, hits started pouring in from around the world, especially the USA.

And then it kept going.

On Tuesday, Oct. 8, the Physics Today Facebook page shared the post, where (as of today) 451 more people have shared it, and 188,000 people have liked it.  (Interesting question: my blog has only had 130,000 views.  Are there really that many people who like Facebook posts without even clicking on the link?)

The viral spike peaked on Wed., Oct. 9.  I had discovered by then that my post had been re-blogged and re-tweeted numerous times, by other physicists around the world.  If you Google “The 9 kinds of physics seminar” you can see some of the tweets for yourself.

Why did the post go viral?  Who knows.  I’m not a sociologist.  I think it was a good post, but that’s not the whole story.  More importantly, the post was funny, and it resonated with a certain segment of the population.  If I knew how to make another post go viral, I’d do so, and soon be a millionaire.

What’s fascinating to me, though, as a math nerd, is to examine how the virality played out mathematically.  Here’s how it looked for October:

I don’t know anything, really, about viral cyberspace, but this graph totally matches my intuition.  Note that for the last few days, the hits have been around 400/day, still much greater than the pre-viral era.

After the spike, is the decay exponential?  I’m not a statistician (maybe Nate Silver could help me out?) but I do know how to use Excel.  Hence:

The decay constant is 0.495, corresponding to a half-life of 1.4 days.  So after the peak, the number of hits/day was reduced by 1/2 every 1.4 days.

This trend didn’t continue, however.  Let’s extend the graph to include most of October:

Over this longer time span, the decay constant of 0.281 corresponds to a half-life of 2.5 days.  The half-life is increasing with time.  You can see this by noticing that the first week’s data points fall below the exponential fit line.  It’s as if you have a radioactive material with a half-life that increases; the radioactive decay rate goes down with time, but the rate at which the number of decays decreases is slowing down.  (Calculus teachers: cue discussion about first vs. second derivatives.)

Maybe this graph will help:

The long-term decay rate seems to be 0.1937, corresponding to a half-life of 3.6 days.  At this rate, you would expect the blog hits to approach pre-viral levels by mid-November.  I doubt that will happen, since the whole experience generated quite a few new blog followers; but in any case, the graph should level off quite soon.  What the new plateau level will be, I don’t know.

Where’s Nate Silver when you need him?

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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!)

## Number form synesthesia [again]

Last week I had a post go viral.  My hits went into the stratosphere, and traffic to my blog went up by a factor of almost 1,000.  I know this is my 15 minutes, and they’re fading fast.  So, while I still have some elevated traffic, I thought I’d re-blog a few older posts, to see what happens.

Number form synesthesia or: why is there a kink at 20?

Whenever I think of numbers, I form a mental image in my head.  This is not a conscious process; it happens consistently and involuntarily.  For example, whenever I imagine the numbers 1 through 100, I see something like this:

You will note several interesting features of this mental map.  Firstly, there is always a 90° left turn at the number 20; there is always a 90° right turn at the number 100.  These two kinks are the only kinks in my mental number line; the lines are perfectly straight before zero and after 100.  Why the kinks are there is mysterious.

Notice also that the image is not to scale.  That is, 50 occurs half-way between 20 and 100 (why isn’t 60 there instead?)

Here’s another mental map I have, one that appears whenever I imagine a person’s age:

You will note that this mental image is similar to the previous one, but rotated 90° to the right.  The scale is also warped: not only in the location of 50 yrs., but in the location of 10 yrs.  I believe this stems from my childhood belief that the years from age 10 to age 20 would seem to last longer than the years from 0 to 10.

Why childhood?  Well, I’ve had such mental images for as long as I can remember; it follows that they were first “constructed” in my brain at an early age.  And there is a sort of logic to the idea that 10-20 lasts “longer” than 0-10.  After all, we don’t normally recall anything about our first 5 years or so; to a child, it’s almost as if you missed those years.  So if I am 10 years old, say, and looking back at my life so far, it won’t seem nearly as long as the decade looming in front of me.  (I must stress that I am not a neuroscientist and that this is all pure speculation.)  As for why 50 is half-way between 20 and 100, I can only conclude that I wasn’t so good at calculating averages when I was younger.  The similarity of the two mental maps is best explained by positing that one of the maps is derived from the other, although which came first I cannot say.

But still, that kink…

I only became aware very, very recently that there is a name for this phenomenon.  These maps I make are called “number forms” and they are a form of synesthesia.  I have a friend who experiences grapheme-color synesthesia, seeing letters and numbers as if they had very specific colors.  It never occurred to me that my mental number maps were a related phenomenon in any way.

Here’s how I see the months of the year:

The order is always counterclockwise.  Strangely, the months are not quite evenly distributed: July is always at the top, but December/January are level at the bottom, with the (strange) consequence that there is one more month in the first “half” of the year than the second.  I also mentally divide the year into three partitions, starting at Sept. 1, Jan. 1, and June 1.  I am confident that this partitioning is a product of having attended school (on a semester system) for 25 years of my life.

Here’s the strangest map of all, but one that has (I think) the easiest explanation:

This is how I picture the recent history of the world, from the late 1700’s to the present.  There are four kinks: at 1800, 1900, 1950, and 2000.  The three biggest wars (to an American, at least) are marked in red; 1968 is also clearly “labeled” in my mental map (obviously because it’s the year of my birth).  Again, there is a lack of scale: 1800-1900 takes up as much “space” as 1900-1950.  One might conclude that I regard the 20th century as more “important” than the 19th, since I relegate more space to the former.  But there is a simpler explanation.

I can still vividly recall a timeline of history that I saw, perhaps in the 3rd or 4th grade, that has the exact same topology as this last mental map of mine.  The years from 1800 to 1970 (or so) were graphically depicted in a timeline; there were folds at 1900 and 1950, simply to make the timeline fit on the printed page.  Above key years (such as 1939) were cartoonish drawings of world events, such as World War II or Man Lands on the Moon.  Beyond the 1970’s there was nothing.  I wish I could find this image, which I believe in some sense “triggered” this form of synesthesia; I want to say that the image was in a World Book Encyclopedia but I have no proof of this claim.

In any case, I think other forms of synesthesia may also be linked to the way we first learn certain things.  My friend (who sees colors for every letter of the alphabet) once told me the probable origin of his synesthesia.  He first learned letters and numbers through colored refrigerator magnets; the colors and letters became inextricably tied in his mind, and the connections exist to this day.  For any real neuroscientists out there, I believe this is a fruitful area for further research.

Anyway, I’d be curious to see how many other people experience “number forms”.  It doesn’t make you crazy.  After all, Sir Francis Galton called his book on the subject The Visions of Sane Persons.

But still, that kink…

## Don’t supersize me! [Again]

Last week I had a post go viral.  My hits went into the stratosphere, and traffic to my blog went up by a factor of almost 1,000.  I know this is my 15 minutes, and they’re fading fast.  So, while I still have some elevated traffic, I thought I’d re-blog a few older posts, to see what happens.

Don’t Supersize Me:  A modest proposal.

This post first appeared on Nov. 9, 2012.

What if there were a way to increase donations to worthy causes, while at the same time help fight this country’s obesity problem?

I think there is a way, and it would be simple to test.  Suppose fast food restaurants that offer “meal deals” (burger + drink + one side, say) offered a \$1 donation to Oxfam (or any other charity) as one of the side dish options?

There are two obvious benefits.  One, I believe that people donate to charities more if they can do so conveniently.  I myself had never given money personally to a hungry family, but when a local grocery store asks me if I want to buy a box of food “for the children” I do so almost automatically.  Convenience allows us to then feel good about ourselves.

Secondly, people who choose this “side dish” are clearly missing out on calories that most don’t need anyway.  How often do people get french fries, even when they don’t want them, just because they “came with the meal”?  And subsequently, how many people eat the fries, because they paid for them–-even if they are no longer hungry?  I’ve done this myself, although it seems irrational in hindsight.

What if instead I order a \$5 meal deal and the cashier asks, “What side?” and my response is, “give it to the hungry”, and the restaurant then has some automatic money transfer mechanism in place to make the donation in an instant?  I don’t know which would do society more good: the money raised, or the calories not consumed.  Why isn’t this a win/win?  Or a win/win/win, since the restaurant doesn’t lose anything, and only gains the positive PR?  It would even show evidence that the restaurant has heard the message of “Supersize Me” and taken it to heart.

I think this idea is a good one, and I hope someone reads this post and shares the idea.  All it would take would be one restaurant to start doing this, and before long all of them would be doing it.  I can’t see a single downside at all.

Admittedly, this may have been tried before.  If so: I wonder why it hasn’t caught on?  What are the economics of such institutionalized charity?  I think there are other interesting questions at play here…does charity in fact increase when it is convenient to give?  (I’d love to see the research data on this.)  Would people forgo empty calories in such a scenario?  What would be the economic benefit of millions of calories not being consumed?  Might there even be an adverse effect for, say, the potato industry, if less fries are scarfed down?

Let me know what you think.  And please share this if you think that someone, somewhere, will see it and have the possibility of implementing it.

[Note: this blog post, first posted on Nov. 9, 2012,  was originally written on Dec. 15, 2010, and emailed to a celebrity who will remain nameless.  Needless to say, there was never a response…not even an automated one.]