Getting a Grip

Does reality depend on whom you ask? Or perhaps everyone is free to choose his or her own truth, like a personalized layout of Google News. In earlier times received wisdom was treated with special reverence. Now, many hold up “science” as indisputable truth.  If we are to, at least at times, defer to “authority,” where does that designation come from? And when authorities disagree, then what?

A seemingly minor kerfuffle about sporting equipment has expanded into a meditation on objective truth and how useful science and “experts” can really be in settling an issue. And even if you don’t care at all about football, you probably care a lot about how much credence society and policy makers should give to scientists when they talk about topics like climate change or genetically modified crops. Now, we are are living in a world where the truth means one thing in Boston, and another in Seattle – presumably switching somewhere over Kansas. Or maybe the fabric or reality shifts between the ivory tower and the kitchen table.

Experts vs. Everyone Else

The Pew Research Center finds that:

“Despite broadly similar views about the overall place of science in America, citizens and scientists often see science-related issues through different sets of eyes. There are large differences in their views across a host of issues.”

Some of the biggest gaps between the scientists and the general public were human responsibility for climate change (87%-50%) and the safety of GMO food (88%-37%). Is this merely a reflection of a sorry state of science education in this country? A separate survey by the Oklahoma State University Department of Agricultural Economics found that 80% of Americans wanted mandatory labels on food containing “DNA”:

“The results indicate that most Americans do not understand the difference between DNA and a genetically modified food. The former is genetic material essential to life as we know it. The latter is an edible organism, the genetic material of which has been altered for some purpose. One is a building block, the other is the result of a process that alters those building blocks to some end. Given that a label warning of a food’s DNA content would be, for all intents and purposes, as meaningless as a label warning of, say, its water content, the survey results reflect an unsettling degree of scientific ignorance in the American population.”

Thus, scientists usually side with former US Senator Daniel Patrick Moynihan, when he said that “You are entitled to your own opinion, but you are not entitled to your own facts.”

#Deflategate (or #Ballgahzi)

The fortnight that separates the NFL conference championship games from the Super Bowl are customarily a dull intermezzo between two over-hyped Sundays. To pass the time, we usually resort to exercising our amateur prognostication skills regarding the final score or the color of Gatorade that will be showered upon the victorious coach. This year, however, has gifted us with a story that just gets more intricate and engaging, touching on issues of the impartiality of scientists, knowledge of physics by laypeople, and deceptive statistics. If anything, the sordid affair give the impression that (1) there are an almost unlimited number of ways to bend the rules (2) physics and statistics may not be the objective arbiters they may seem.

 The basic facts are these:

“11 of the New England Patriots’ 12 allotted game footballs in Sunday’s AFC championship game were each under-inflated by 2 pounds of air per square inch…The ball is, by rule, to be inflated with 12.5 to 13.5 pounds of air per square inch and weigh 14 to 15 ounces.”

As noted by many, including ESPN’s Sport Science, playing with an underinflated ball will have a negligible effect on the velocity of passes. Rather, the advantage presumably relates to an ability to grip the ball, especially on Cold and Rainy New England nights. Since the Patriots won handily, few believe that non-conforming footballs played a difference in the outcome. However, head coach Bill Belichick’s amazing run of six Super Bowl appearances in 14 season with the Patriots has  already been tinged with a reputation to get creative with the rules, notably in the Spygate incident. In a press conference, Mr. Belichick denied any wrongdoing in regard to deflategate, and provided a somewhat confused  “scientific” explanation:

“Now, we all know that air pressure is a function of the atmospheric conditions. It’s a function of that. So if there’s activity in the ball relative to the rubbing process, I think that explains why, When we gave them to the officials, and the officials put it out, let’s say 12.5, that once the ball reached its equilibrium state, it was closer to 11.5, but that’s, again, that’s just our measurements.”

Back page of the Jan. 25, 2015 New York Daily News.

This prompted a response by the original Science Guy…

Notice that, at least in this edit, the video shows Nye using an appeal to (his own eminent) authority and admitted bias toward Seattle rather than the Ideal gas law or something one would usually expect from a science guy. This other video has a little more science, although you should note that no quantitative data was recorded. Also, Mr. Nye takes time to discuss climate change. Does this mean that only Seahawk fans believe in climate change, or is it an objective reality?

Neil deGrasse Tyson admitted he made a error in an tweet about the implausibility New England’s explanation when he neglected to account for the difference between gauge pressure and absolute pressure.

However, there are many who claim that the Ideal Gas Law does show that nothing untoward was going on, and that the drop in pressure can be explained by the difference in temperature alone between the room where the footballs were tested and the playing field. Being Boston, there is a plentiful supply of academics who happen to be Patriot supports. The Boston Globe interviewed scientists from some local schools (MIT, Boston University, Harvard) who were unanimous in exonerating the home team.

And Binzel acknowledges being a Patriots fan, but notes: “The laws of physics know no fandom. The laws of physics play no favorites.”

The NFL has turned to the Columbia University physics department, a place with, presuamly, a nonzero number of Jets fans who have a good memory of Spygate.

Recent recreation experiments by Thomas Healy at Carnegie Mellon have supported the view that natural factors alone can account for the changes. Read the full report here.

For those who think that deflate gate is overblown – which includes many football fans – consider this controversy as a microcosm of some very real issues about how we determine truth in our society.

Damn Lies and Statistics

While physicists were enjoying their day in the sun, statisticians also got a chance to join the fray when an analysis of the Patriots skill at not fumbling got traction on sites like Slate and Yahoo Sports. The allegation was clear: New England was using under-inflated footballs to achieve a specific unfair advantage, and the numbers added up to pretty damning evidence: “Maybe the smoking gun isn’t in a bathroom at Gillette Stadium. Maybe it’s in the laptop of a civil engineer in Washington, D.C.” A number like 1-in-16,234 was thrown around to represent the “nearly impossible” chance that there was a innocent explanation.

But not so fast! FiveThirtyEight blog was able to identify an impressive array of statisticians who disagreed with the result, saying that NE is not an outlier at all when properly analyzed.  Problems like excluding teams that play home games in domes, wrongly including special teams plays (which use specially designated K-balls), and the often overlooks statistical fact that just because a random variable X is normally distributed does mean that 1/x is also.

Numbers don’t lie, but if you torture the data it will confess to anything.

Be More Adversarial 

So what is the answer? Surprisingly, it is to have more arguments, not less. Our legal and political systems is adversarial system for a reason. We let ambition check ambition by making sure that each side has an incentive to scrutinize the other for weaknesses in their argument. Expert witnesses can be biased (not least by the hope of being called on again), so often the prosecution and defense will each have their own. The most important participant in a meeting is not the Yes-Man, but the devil’s advocate.

There are many sociological experiments that show we are more skeptical of an argument when we disagree with the outcome. We are more likely to spot tricky math mistakes when used to argue against, rather than for, our favored position. Brain scans show us thinking harder when challenged with evidence we don’t like. People stare at “test strips” longer when told they will change color to indicate the absence of disease. In science, while the system of peer review is far from perfect, it remains necessary to have an outsider check the work.

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Phase Change of Heart

This past week was the first meeting of the Top Flight Journal club, sponsored by the NSU chapter of the Society of Physics Students. The venue was the University center Flight Deck:

The paper under discussion, Simple Model for Identifying Critical Regions in Atrial Fibrillation, discusses a new method for simulating the electrical connections between heart cells. In the medical condition called Atrial Fibrillation, the heart’s normal coordinated pumping motion is replaced by a disordered quivering that can lead to blood clots.

Figure 1

It is known that people are much more likely to get atrial fibrillation as they age, but the exact reason remains unclear. In this work, the researchers used a very simple model of the heart in which cardiac cells are connected to each other in horizontal “cables”. With probability v, an additional vertical connection exists between cables.

cardiac

When v is high – as it is in children, whose hearts have many interconnections between cables – there is no chance for AF. The electrical signal always propagates in a healthy, orderly plane wave across the heart. The signal can’t go backward because of the refractory period each cell needs after being excited. However, the authors show how there can exist a critical value of v below which local ripples called “rotors” can start to form, corresponding to the onset of AF. That is, if v becomes low enough as in older people, there becomes a finite chance of a short circuit forming in which a re-entrant signal can work its way backwards past the region of refractory cells. The result is the formation of localized disturbances that can interrupt the coordination of the heart signal.

cardiac2

This switching between discrete regimes (healthy plane waves to rotors) by changing a continuously varying parameter (v) past a threshold value is the hallmark of “catastrophe theory“. This is like a phase transition in physics, in which the phase (solid, liquid, gas) can be altered by passing through a critical value of the temperature. Here, a continuous variable (the chance of cables being connected, which gradually decreases with age), can suddenly create the risk for AF that did not exist before.

A catastrophe might also occur in the case of communicable diseases. When the fraction of immunized people in the population is above the threshold for herd immunity, potential outbreaks remain contained. The connections between people can be modeled with a Bethe lattice. The chance of a percolating cluster that connects to infinity is a discontinuous function that is zero when the chance of each edge being connect is below the percolation threshold and non-zero above it.

Tie your Coach to the Goalposts

I know that this topic is becoming a common theme on this blog, but there was yet another piece of strong evidence that NFL coaches – who are paid millions of dollars in the hopes of squeezing just a few more wins out of their teams – act too conservatively. Just as the title, “Do Firms Maximize? Evidence from Professional Football” hints at, even when the stakes are high and the best strategy already known, teams don’t always choose that choice.

In this example, being ahead by four points near end of the game might be worse than being ahead by just three points. The reason seems to be that in the latter case, the opposing coach faces the tempting siren song of playing for a tie. That is, the trailing team will choose more conservative plays and try to get into field goal range to tie the game and hope for a good result in overtime. This thinking usually neglects to consider the chance of missing the field goal attempt or, more importantly, that the chance of winning in overtime is basically 50/50, when the chance of obtaining the winning TD at the end of regulation might be significantly higher.

When a team is down by four, in contrast, only a touchdown will do. So there is no choice but to go for the win. Thus, the whole drive is in “four-down territory,” and all kinds of risky passes are on the table. It turns out that a pre-commitment mechanism, like tying the coach to the mast like Ulysses or, similar to Alexander the Great, (supposedly) burning the boats you came on might actually be appropriate:

“When Alexander the Great arrived on the shores of Persia, his army was overwhelmingly outnumbered. The odds against them were terrible. Turning away and getting back in the boats seemed like an option to let them regroup and come back another time. But rather than having an emergency escape plan available, Alexander gave the orders to his men to ‘burn the boats.’ As their only means of retreat went up in flames, legend has it that Alexander turned to his men and said, ‘We go home in Persian ships, or we die.’ “

But if coaches know the correct approach, why do they still play for the tie when available? I think there are two major issues. First, knowing about a cognitive fallacy does not immunize from committing that fallacy. Cognitive psychologist Laurie Santos studies the behavior of monkeys in a “marketplace” in which they can exchange metal washers for food. The monkeys exhibits some of the same irrationalities as human consumers, including the framing effect, in which transactions framed as losses are treated differently than transactions treated as gains. She talks about the researchers falling for the GI Joe fallacy, which she defines as believing that you are not subject to the same mental fobiles as the monkeys, simply because “knowing is half the battle.”

Nicholas Nassim Taleb is the foremost speaker on deep-seated human irrationality, including  (or especially) on the part of investors who stand to gain untold fortune if they can overcome their biases. But even he concedes the difficulty of overcoming these feelings in himself.

On the other hand, maybe the coaches aren’t so irrational after all. As Think like a Freak conjectures, the real incentive is not always to win the game for your team, but rather, to not be blamed for losing the game.

So sometimes living a life with the law of the excluded middle is better than hoping for a partial victory.