Archive for the ‘Rant’ Category

When sports decide which teams make the playoffs, there are often tiebreakers used to sort-out teams with identical records.  One of the most common tiebreakers is the “head-to-head” record.

Head-to-head record is a poor tiebreaker, especially compared with, say, strength of schedule.

Let’s NCAA basketball as an example.  Suppose Wake Forest (my alma mater) and Western Carolina (the school where I teach) both go 29-1 in the regular season.  Suppose Western Carolina’s only loss was to Mars Hill, and Wake Forest’s only loss was to Western Carolina.

Image result for western carolina basketball

The diehard “head-to-head” people would say “Western Carolina should be ranked higher!  They won the head-to-head matchup!”  But I say: what about the other 29 games?  Wake Forest plays in the ACC, and has multiple games against Duke, UNC, Miami, NC State…you get the picture.  Western Carolina has a much weaker schedule against the likes of Wofford, the Citadel, VMI, Chattanooga.  Sure, Wake Forest lost to Western Carolina, but in turn, Western Carolina lost to Mars Hill!  Which loss looks worse, hmm?

Image result for wake forest logo

The problem with head-to-head is that it’s only one data point.  Any team can lose a single game.  Maybe Wake Forest was missing their starting 5 due to the flu for that one game against Western Carolina.  (Clemson’s loss in football to Syracuse, earlier this year, was partially due to their starting quarterback being out).  A tie-breaker should be as broad as possible, and take the entire year into consideration.  This is especially true in basketball or baseball, when the long seasons make head-to-head records well-nigh meaningless.

I’m thinking about this now because college football is nearing its end for the year, and some arcane committee will have to decide who gets into the college football playoff and who stays out.  There are those who have complained that an undefeated Wisconsin team (currently #3) should be ranked higher.  But the Badgers have played an easy schedule, compared to, say, Auburn, who has faced the toughest road possible.  (Look at strength-of-schedule rankings here.)  In fact, I personally rank Auburn (10-2) higher than Wisconsin (12-0) for that very reason.  We only have 24 total data points here, but if Auburn and Wisconsin swapped schedules, then Auburn would be 12-0 easily and Wisconsin would be, at best, 7-5.

I can’t say it enough.  Head-to-head is a garbage tiebreaker.  It’s only one data point.  Strength-of-schedule incorporates literally dozens of data points and should always take precedence.


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Here’s something that will never happen, but it would be awesome:

The NCAA should go to a Swiss-system for college football.  And I don’t mean for the playoffs; I mean for the entire season.

First of all, here’s a brief primer on what the Swiss-system is.  I don’t think I can explain it better than the hive mind on Wikipedia, so here’s a quote:

“A Swiss-system tournament is a non-eliminating tournament format which features a predetermined number of rounds of competition… In a Swiss tournament, each competitor (team or individual) does not play every other. Competitors meet one-to-one in each round and are paired using a predetermined set of rules designed to ensure that each competitor plays opponents with a similar running score, but not the same opponent more than once. The winner is the competitor with the highest aggregate points earned in all rounds.”

Such systems are very common in chess tournaments, and also used in backgammon, squash, and eight-ball tournaments.  I’ve never heard of them being used in team sports, which is a pity.

Image result for bern

If I were Emperor of the World, here’s how I would implement the Swiss-system for college football.  At the beginning of the season, I’d rank the 128 FBS teams (teams that normally are bowl eligible) from #1 to #128.  (Well, I probably wouldn’t rank the teams personally, but I’d have a computer and/or a committee rank the teams much as the BCS does now.)  The great thing is that a ranking of #1 vs. a ranking of #5 (say) at the beginning of the season wouldn’t matter much at all.

The first week of the season, #1 would play #65, #2 would play #66, and so on.  For illustrative purposes, if we based seeding on the current NCAA rankings (as of Nov. 7, 2016), we’d have Alabama (#1) playing Southern Mississippi (#65), Michigan (#2)  vs. Texas Tech (#66), Clemson (#3) vs. Georgia (#67), Washington (#4) vs. NC State (#68), and so on, down to California (#64) vs. Florida Atlantic (#128).  Every higher-ranked team would be favored of course, but you’re going to get plenty of upsets: every one of the matchups I just (arbitrarily) presented would be a decent game.  Gone would be the days when an Alabama would play a non-FBS Western Carolina for their first game and win 49-0 to pad their resume.

Starting with week #2, things are already interesting.  Every week after the first, each team plays another team with the exact same record (if possible).  Continuing with my example, and assuming that all the higher ranked teams won in week 1, you’d already have on the table Alabama (#1) vs. Troy (#33), Michigan (#2) vs. Tulsa (#34), Clemson (#3) vs. Minnesota (#35), etc.  None of these games are cake-walks by any means (for perspective, the current records of Alabama, Michigan, and Clemson are all 9-0, but the current records of Troy, Tulsa, and Minnesota are 7-1, 7-2, and 7-2, respectively.)

Here’s the thing: starting with week 2, every single game in college football is a competitive game.  And starting around week 4, every single game is almost evenly-matched.  We’ve eliminated the all-too-common problem with the current system: that the top teams really only play 2 or 3 meaningful games a year.

Suppose we were using the Swiss-system, and we were making the matchups for the coming week’s games (Nov. 12).  What games would be on tap?  Well, there are currently 5 undefeated teams, which in a Swiss-system would be very unlikely after 9 weeks.  Just for fun let’s assume that it’s possible, but let’s ignore Western Michigan (no way they’d go 9-0 if they faced a few good teams).  With Alabama, Michigan, Clemson, and Washington all 9-0, this week’s marquee matchups would be Alabama vs. Washington, and Michigan vs. Clemson.  It’s likely that next week you’d have Alabama facing Michigan.  This, in early November!

The good matchups continue all the way down the line.  One-loss teams would all face each other, and you’d perhaps have games like Louisville vs. Ohio State.  Even at the bottom of the barrel, with a Rice playing a Florida Atlantic, the games would be evenly-matched.  This would be great for fans, because as it stands, when a Rice fan attends a game, they fully expect a loss; but with a Swiss-system, that same fan can be hopeful for at least a 50-50 shot at winning.

At the end of the season, an undefeated team would be almost impossible.  It’s likely you’d have 3 or 4 teams that were 10-2, and they’d all have already played each other.  That’s when a playoff would kick in.

For the playoff, we’d have the 4 (or better yet, 8) teams with the best records play each other in a standard elimination format.  At this point, it wouldn’t matter if they’d already faced each other in the regular season; rematches at this point would be desirable.  The great thing is that these teams would all be excellent teams.  In a Swiss-system, if you go 10-2, facing tougher opponents every single week, no one can argue you aren’t one of the best teams in the country.  Built into the Swiss-system is an important feature, which is that basically, every team at the end with a similar record faced a similar strength of schedule.

This is important, for in the current system, teams which are 12-0 can be left out of the playoff discussion if they’d didn’t play any good teams.  That’s never struck me as particularly fair.  If my team goes 12-0 and doesn’t get to the playoffs, then that means the team never even had a theoretical shot at making the playoffs to begin with.  What’s the point, then?  It’s a sordid fact that in the current system, there are only 30 or so teams that can ever even theoretically make it to the playoffs in a given year.  I’m sorry, Florida Atlantic, but if you go 12-0 next year you ain’t playing in a major bowl game.

There are obviously a few objections one could raise to my brilliant scheme.  Let’s address them.

  1. What about logistics? How in the world could you have teams flying around the country, facing each other, planning trips on only a week’s notice?  Well, as Emperor, it wouldn’t be my problem.  But in any case, it’s the 21st century for Xenu’s sake, so I think with some 747’s and the internet, it could be done.
  2. What about revenue? If Western Carolina doesn’t get to play and get crushed by Alabama, then Western Carolina loses out on some big time TV money!  OK, sure, but the games will in general be much, much more competitive, and many more fans will go to see WCU home games since they finally have a chance to win.  I really believe TV revenue would be up across the board.  We could even implement a TV revenue-sharing scheme, but that’s a topic for another day.
  3. What about rivalries? Well, what about them?  The current system doesn’t give a fuck about them in any case.  I can’t even keep track of who’s in what conference these days.  (Syracuse is in the ACC?  When did that happen?  They’ll always be a Big East team to me.)  With a Swiss-system, conferences become meaningless, and I say good riddance.

Image result for army navy game 1963

As for the handful of actual rivalries that still exist, and haven’t become jokes, such as Army vs. Navy (come to think of it, that has become a joke) or Alabama vs. Auburn, you could have the teams play an extra game in mid-December that doesn’t really count for anything.  If you think it’s unfair that a team has to play an extra game compared to other teams, well then, why not have every team pick a greatest rival that they have to play every year?  Hell, these games might even be the first games of the year, a sort of pre-season-type game, and the results don’t affect the Swiss-system per se, but the results might inform the seedings.  So Navy plays Army (a joke game, usually) but if Navy loses, we might initially rank them a little lower than otherwise.

Would any of this ever happen?  Not one chance in a million.  But it’s fun to speculate about.  And mark my words, in the universe(s) where I actually do become Emperor, initiating an NCAA football Swiss-system is one of my first magnanimous acts.

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Economics (still) don’t matter

[An updated version of a post from 2012 which first appeared here.]

Economics don’t matter in this year’s election.

At least, they don’t matter to me.

There are smart people who think Hillary’s economic plan is better for America than Bernie’s.  There are smart people that think Cruz’s’s plan is better.  (Of course, Trump has no plan.) We have some idea of what a Democrat as president would be like, and with Obama at the helm the economy has improved greatly since the Wall-street induced recession of 2008, even with an obstructionist do-nothing congress.  But maybe you think a Republican could do better.  Who knows?  I don’t really know as a fact which candidate would be better, from an economic standpoint.  (Except for Trump.  Trump would be a disaster by any measure.)

And let’s be honest.  You don’t know who would be better, either.

Oh, there are a few people who claim to understand the economic issues involved.  But let’s face it, “experts” can’t really pick stocks better than monkeys or dartboards.  Why do we expect the American economy to be any more tractable?  In the language of mathematics, the economy is a chaotic system.  Any small change in policy is likely to produce unpredictable results.  So when you pick a candidate based on “economic principles” you’re really just saying “I believe this candidate’s meaningless economic rhetoric more than the other guy’s meaningless economic rhetoric.”  If you have a PhD in economics, maybe I’ll give you the benefit of the doubt…but if you’re a truck driver, or a doctor, or a waitress, or a welder, then your ideas about the economy are probably total bullshit.

I am a physicist.  My ideas about the economy are bullshit.

Ever play one of the Civilization computer games, such as Civilization V?  If you have, you see how complicated and interconnected every decision is.  You have to juggle money, and the happiness of citizens, and threats foreign and domestic, and culture, science…the tiniest decisions can have huge ramifications, and no monolithic blanket ideology will get you to the promised land of victory.  It’s a balancing act.  Sometimes you have to raise taxes.  Sometimes you have to cut them.  Sometimes you increase education, sometimes you build infrastructure, sometimes you go to war, sometimes you seek a diplomatic solution.

If the pundits are to be believed, being president is simpler than this.  Just drink the Flavor Aid, follow the party line, and everything will be great.  Being president is as simple as doing everything that Rush Limbaugh (or Michael Moore) says.

I don’t buy it.  And if you’re honest with yourself, you won’t either.  Just say it to yourself: “I know nothing about economics.  I know nothing about economics.”

Why is it that people who admittedly know nothing about chemistry, poetry, physics, differential equations, music theory, pottery, animal husbandry, statistics, number theory, ancient history, modern Japanese culture, biology, leatherworking, genetics, Shakespeare, phonetics, linear algebra, astronomy, geology, philosophy, music history, Greek, marketing, calculus, modern history, evolution, quantum mechanics, medicine, world religions, and engineering, think that they know anything about complex economic issues?

(Not you, Ken Rogoff.  I know you know economics.)

Why is it that people who are ignorant of 99% of the world’s body of knowledge still have strong beliefs concerning tariffs or debt ceilings or free trade agreements or progressive taxes?  Let me be frank: if you don’t know what something is, you have no logical right to an opinion about it.  (Do you think that decoherence is sufficient to explain effective wave collapse, a la the Copenhagen interpretation?  Or do you feel that, ultimately, some non-local theory will gives us the loophole we need to sweep Bell’s Theorem under the table?  I didn’t think so.)  Just once I’d like to see a fry cook from Burger King say, “I have no opinion regarding stimulus money…I don’t understand all the complex economic concepts involved…but you know, the Thirty Year’s War was less about Catholic/Protestant bickering and more about the Bourbon-Habsburg rivalry.”

Economist John Maynard Keynes

If you don’t know who I am, then why do you even pretend to know the first thing about economics?

So.  The economy shouldn’t matter in your voting decision.  So where does that leave you?

Well, what’s left are social issues.  Issues like civil rights for the LGBT community, civil rights for women, civil rights for immigrants, the failed war on drugs, the continuing (attempted) theocratization of America, and the stranglehold that the vile NRA has on our political system.  I can’t in good conscience vote for a party that denies the fact of global warming (and here’s where I will play the “PhD in physics” card), the fact of evolution, the fact that the Earth is billions of years old.  The Republicans give every impression that they are the anti-science party, the anti-women party, the party of a solely-Christian America, the party of Wall Street.  If that is not the case, it is still true that very few Republicans distance themselves from such stances.

If you vote for someone, anyone, don’t hide behind the “I just prefer his economic policies” defense.  At least have the courage of your convictions.  Say what you truly are, and why you prefer the social ideas of your preferred demagogue.

I am a liberal, in the best sense of the word: the world could be better, and we have a long way to go.

What are you?

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’til is not a word!

[Reposted from Dec. 4, 2012]


For I ne’er saw true beauty till this night…

’til is not a word.

Please, use either until, or till.  Some people think that ’til is an abbreviation of until, but this is folk etymology.  “Till” is the older word by far, going back to at least Shakespeare’s day.  For example:

John 21:22 (KJV)     Jesus saith unto him, If I will that he tarry till I come, what to thee?  Follow thou me.

Romeo and Juliet: I, v     For I ne’er saw true beauty till this night.

Also note that “Till death us depart”, from the marriage liturgy in the Book of Common Prayer, dates back to 1549!  It became “Till death us do part” in 1662.

Seeing advertisements for the old Fox show ’til Death always grated on me like fingernails on a blackboard.  Luckily, like most Fox sitcoms, that show departed quite a while ago.

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I am a huge supporter of free speech.  I also support the right to make pariahs out of any bozo who still thinks the Confederate flag is not about racism.  And so, as a society, my proposal is simple:


If enough people make fun of these asshats, peer pressure will kick in eventually.  They’ll see themselves as the losers we know they are.

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On Monday, Republican presidential wannabe Rick Santorum said that the Pope should “leave science to the scientists”.


What that hell does that even mean?


What the hell?

If taken literally, it would mean that Santorum defers to scientists, and so if a policy issue concerning climate change were to arise, he would trust in the scientists’ collective judgment. That collective judgment is overwhelmingly unanimous; the fact that 97% of scientists in a particular field agree on a particular something is well-nigh miraculous.

But of course Santorum doesn’t mean that.

It could also mean that he thinks no one should talk about anything unless they’re an expert in the field. But that’s absurd, right? If a tornado approaches, would Santorum say that only meteorologists should talk about it? Surely not. [See my last post.]

In point of fact, “leave science to the scientists” is a kind of code these days among many Republican politicians. Here’s my rough translation:

“Despite what I may personally believe, my voting base is generally against human-caused climate change, and many of these voters even deny that climate change is occurring at all. On the other hand, if I personally deny climate change, I will look like an idiot to the something like 71% of the general public who agree that climate change is happening. So I will obfuscate: by punting to unnamed scientists, I can deflect the question; I can make my voting base happy while at the same time not actually saying I’m against climate change per se.”

This kind of obfuscation is odious to me. Slimy. Maybe it’s par for the course; maybe that’s how the game is played; maybe that’s just realpolitik. But I don’t have to like it. Someone needs to take Santorum (or any other Republican who spouts such nonsense) to task, and ask the following hard questions:

  • Does science ever effect policy making? If so, who do we turn to for answers? Should we listen to the experts, or listen to conspiracy-theory-soaked hate-spewing trolls?
  • If we should leave science to the scientists, doesn’t that mean we should accept the answers they give us? After all, they’re the experts, not us.
  • I hear, Rick, that you don’t believe in the plain fact of evolution. Do you by chance also believe in the Tooth Fairy? [OK, that was a non-sequitur, but I couldn’t help it.]


Imagine Santorum is sitting beneath a mountain, and there are 100 volcanologists around him. 97 of the volcanologists say that the mountain is about to explode; 3 of them have doubts. But Santorum doesn’t listen to any of the scientists; he’s got Rush Limbaugh whispering in his ear, telling him “it’s all bullshit.” So Santorum says: “Leave volcanology to the volcanologists. Let’s do nothing.” His fan-base cheers—at least until the pyroclastic flow hits them all at 450 mph.

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[Note: this is the article that I wish Nate Silver would write.  He’d be so much better at the number crunching.  Of course, he’s also paid a lot more.]

I’m tired of hearing pundits spew their opinions about this, that, or the other.  Let’s face it, most people don’t know anything.

Of course, that includes me, but hey: this is my blog.

I’m using hyperbole; it’s true.  And yet in a country where 9% of people think that space aliens may have caused the disappearance of Malaysia Air flight 370; in a country where 55.56% of Supreme Court justices are completely ignorant about the First Amendment; in a country where sizable numbers of people believe in a 10,000 year-old Earth, and where numerous people doubt facts like global warming, evolution by natural selection, and the supremacy of Matt Damon…in such a country, how can you really take anyone seriously?

OK; I take Neil deGrasse Tyson seriously.  But he’s earned it.

People (of every political ideology) spew forth talking points without any facts to back them up.  Hell, they spew forth talking points without any justification at all.  I have liberal friends who are against GMO foods…even though there is no reason to think they could ever be harmful, and in fact have already saved millions of lives.  (Trivia question: how did Norman Borlaug save a billion people from starvation and subsequently win the Nobel Peace prize?  Answer: genetically modified wheat.)

On the other side, all kinds of nifty-sounding talking points spew from the conservative font, again without even a shred of justification other than “well, that sounds right”.  For example, people claim that less government is good.  Shrinking government is a goal of Tea Baggers.  “Democrats want more government, Republicans want less government…everyone knows that.”  It’s become a cliche, and people don’t even question it any more.

But this is the information age.  We don’t have to rely on our gut feelings, or even our supposed “knowledge”, to evaluate claims like “less government is good”.  We have data.  Why don’t people look at the data and then make up their minds?

I’ll tell you why: because looking at data is hard work.  Let’s face it; most people just can’t do it.  Most people want to be told what to believe.  But I just got tenure, so I have some time.  Let’s try to get to the bottom of this.

It didn’t take me long to find this website, which has nifty (exportable) data on all kinds of economic indicators.  Hey, look, the USA is ranked 12th in economic freedom out of more than 165 countries.  Yay!  We’re doing OK.

What about the size of government?  This is harder to quantify, since it means different things to different people (for example, many Republicans want to “reduce” the size of the US government without touching our defense budget, which is a little like trying to lower world sea levels by draining the Mediterranean Sea).  However, the indicator “Gov’t Expenditure % of GDP” seems pretty good to me.

How does the USA do here?  Do we have a “bloated, huge, nanny state?”  Our spending is 41.6% of GDP.  This makes us rank 47th in this indicator, so about the 72-percentile.  We have a “bigger” government than about 72% of the countries on the list.

Who’s ahead of us?  The supposed “socialist” states are (Norway, Sweden, Findland, Denmark) of course.  Everyone “knows” they are entirely nanny states.  Also: France, the UK, Germany.  The usual suspects.  Liberal, bloated, big government monstrosities.

But also: Cuba!?  Libya!?  Bosnia!?  Iraq!?  Malta!?

Maybe Cuba fits well into the narrative.  Cuba is a Communist country, so of course the commies have huge governments.  (I personally think Cuba is an outlier, since its GDP is pitifully small).  But what about other Communist states?

Hmm.  The narrative is starting to break down.  China’s government spending is about 23.9% of its GDP, almost half the size of the US.  The commies in red China are spending half of what we spend.  Vietnam spends about 30.9% of its GDP.

The talking point that the USA has become a “bloated nanny state” doesn’t hold water.  We’re in the top one-third of spenders, it’s true; but our defense budget is Brobdingnagian to say the least; if you plotted “non-defense government spending as % of GDP” our rank would be much lower.  (Note: I lack the skills to do this…feel free to do so yourself.)

But all this is distraction.  Ultimately, I don’t even know if big government is inherently bad or good, and more importantly, you don’t either.  Admit it.  You’re just guessing.

But we don’t have to guess.  We can try to understand the data a little bit more.

It didn’t take long for me to stumble on the cute Where-to-be-born index, a kind of “happiness index” which takes multiple factors into account like quality of life, health, economics, and so on, in order to rank countries based on where you’d prefer to be born.  (Admit it: you’d rather be born in Australia than Bangladesh.)  So hey, I know how to use Excel: let’s plot Size of Government vs. Where-to-be-born and see if there’s a correlation!


Firstly: there’s not much of a correlation (the R^2 value is only around 0.17).  This is not surprising; the size of government has little to do with anything.  (It certainly shouldn’t be the entire frakking basis for a political movement.)  But what correlation there is, is positive, meaning that as governments get bigger, people tend to get happier.  All the Viking countries are in the upper right.  And those Scandanavians are doing well, dammit!

Some countries stand out.  Russia and China are lower and to the left of the USA, meaning they have smaller governments (is that surprising?) but are also more miserable.  Cuba, though, is a huge government spender…why is that?  Also, what’s the deal with Singapore?  They’re happy and (apparently) almost an anarchist state.  Tea Baggers take note: emulate Singapore.

The main idea I want you to get out of the graph is this:  there’s a lot of noise there.  You can’t really draw any conclusions.  If you want to say that “Big Government Bad!” in the same way that Tarzan says “Fire Bad!” you’d better have some data to back up your claim.  And finding such data is, well, hard work.  Good luck.

And now I’d better get back to studying something I know about: physics.






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Move over, McDonalds!  There’s a new worst slogan in the world.

Budweiser (a “beer” company) has a new ad campaign about sports superstitions.  In a nutshell: sports superstitions (like sitting in your “lucky” chair) are funny, charming, and gosh darn it, might even be real!  Budweiser’s tagline: “It’s only weird if it doesn’t work”.

I disagree.  It’s weird, period.

What’s more, it’s ignorant, embarrassing, and frankly makes me a little pessimistic about humanity.  Do you really think that wearing that unwashed jersey will help your team win?  If yes, then please, please unfriend me on Facebook.  I don’t want to have anything to do with you.


This is only weird if it doesn’t work!

Superstitions have always been a force for evil in the world.  Yes, evil.  Superstitions caused Aztecs to pull the beating hearts out of innocent people.  Superstitions caused intelligent women to be burned at the stake as witches.  Superstitions caused Okonkwo to kill his son Ikemefuna to appease the village elders.  Superstitions put Galileo under house arrest, and drove Alan Turing to commit suicide, and prevent a sizeable number of otherwise educated adults from believing in the plain fact of man-made global warming.

Superstitions even keep a huge number of South Koreans from having fans in their bedrooms.

[Cue double-take]

I’m not making this up.  For some strange reason, many South Koreans think that a simple oscillating fan can kill you in your sleep.  This, despite the fact that fan death has never happened in human history.  And despite the fact that the rest of the entire world uses fans in their bedrooms to no ill effect.


But wait! you might say, in Korean I presume.  People have been found dead with fans running nearby!  The fans must have killed them!  Case closed!

I’ll leave it to the reader to punch holes in that kind of “logic”.

You may have heard of the famous experiment in which B. F. Skinner discovered “superstition” in pigeons:

“Skinner placed a series of hungry pigeons in a cage attached to an automatic mechanism that delivered food to the pigeon ‘at regular intervals with no reference whatsoever to the bird’s behavior.’ He discovered that the pigeons associated the delivery of the food with whatever chance actions they had been performing as it was delivered, and that they subsequently continued to perform these same actions.” [http://en.wikipedia.org/wiki/B._F._Skinner#Superstitious_Pigeons]


A typical Budweiser drinker.

Your team wins while you’re wearing that lucky shirt?  The shirt must have done it!  Of course, you should be ashamed of yourself.  You’re not any smarter than a pigeon.

Carl Sagan wrote a book called “The Demon Haunted World: Science as a Candle in the Dark”.  The idea is that science, and only science, illuminates; there is no other way to learn anything about the world.  The next time you’re around a “person” who exhibits superstitious nonsense around you, cough into your hand and say “Pigeon!”  Don’t worry; they won’t know what you’re talking about.  Like Giordano Bruno’s torturers, or the chicken-eater Wade Boggs, or the people who stoned Tessie Hutchinson, they have no idea what science is, or logic, or common sense.  They won’t have heard of B. F. Skinner or Carl Sagan or Alan Turing or Giordano Bruno.

They will, however, be familiar with Budweiser “beer”.

And they’ll be enjoying it, pathetically, in the dark.

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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).

honey badger

Honey badger doesn’t care.

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.

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In 1992, ranch dressing overtook Italian to become the most popular salad dressing in the USA.  If you’re interested in why that happened, click here.  I don’t care for ranch dressing.  I don’t really like milk on my lettuce.



But thinking about ranch dressing made me wonder: whatever happened to thousand island?  Growing up, thousand island dressing seemed ubiquitous; ranch was unheard of.  I don’t recall even tasting ranch until around the mid 1980’s; cool ranch Doritos came out around that time.  But thousand island dressing was everywhere.  If you asked a waiter in 1980 what salad dressings were available, he’d be likely to say “Thousand island, Italian, oil and vinegar, blue cheese, or French.”

Today you’d get “Honey mustard, ranch, vinaigrette, Caesar, or balsamic.”

What has happened?

I have no pat answers; I offer no sweeping theories; I haven’t got a clue.  I can only point to the slings and arrows of outrageous fortune.  The mind searches for a pattern, for answers, when in reality there’s just arbitrariness, fashion, randomness.  Balsamic is in, thousand island is out.  End of story.  Move on to something more interesting.

And yet…

And yet I do have a theory, nebulous, half-formed, rising to the surface.  My theory is this: most people don’t feel strongly for any particular salad dressing.  But people are strongly against.

I have a brother who is disgusted by ketchup.  I bet he wouldn’t go near thousand island, because (according to popular folklore) thousand island is just ketchup + mayonnaise.  True or not, it’s the reputation that counts; a reputation built in part on the “secret sauce” of the Big Mac and the Reuben and god knows what else.  How many people have the following associations in their mind: thousand island…Big Mac…disgusting fast food?  I wonder if the backlash against fast food (Supersize me!) is mirrored by the downfall of thousand island.

A lot of people today find thousand island, well, gross.

What about French?  Or about my personal favorite, Russian…a dressing so rare, now, that you can barely even find it in the grocery store?  I’m going to guess that these dressings suffer because of their names.  Russians have been gauche since the cold war 1950’s; the French since…well, since the last incident in which the French incurred the wrath of America.  (It’s sad, really, that I remember a movement to rename French fries to “freedom fries”, but have long since forgotten the international incident that sparked such outrage.)  Anyway, if you eat Russian dressing then you’re a commie, and if you eat French dressing then you wear a beret, enjoy Jerry Lewis movies, and hate America.

I love both French and Russian dressings.

I dislike ranch.

C’est la vie.

[Note: I’d be curious to hear from the denizens of other countries.  What salad dressings are de rigueur in the UK, or in South Africa, or Argentina, or Macao?  And how have the fashions changed over time?  Please don’t say you like ranch, too.]

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