Curse of the Butterfly

Butterflies are already under suspicion for many catastrophes, as in: “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” This so-called Butterfly effect, in which the final outcome is very sensitive to the exact initial conditions, is one of the basic finding of chaos theory. We may never know which butterfly to blame for Hurricane Matthew, but the storm sent me on an unexpected trip from South Florida to Tallahassee.

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While visiting the museum inside Florida’s old capitol, I came upon the exhibit for the 2000 presidential election, which I remember distinctly, since it was the first I was old enough to vote in. Of course, the exhibit put the most pro-Florida spin possible on the debacle that demonstrated “the resilience of our democracy,” including the fact that the State Supreme Court ordered a full recount, only to be overruled by the US Supreme Court. The size of the victory either way was so razor-thin that it was certainly swamped by the margin of error. Mathematician John Allen Paulos suggested that flipping a coin was the most fair method to resolve the election, rather than trying to measure “bacteria with a yardstick.” Yet, the need to have a definitive answer caused us to scrutinize “hanging chads.” Multiple factors converged to swing the election. Primarily, a kind of butterfly was blamed, the “butterfly ballot.”

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The museum wisely placed it behind protective glass, lest it be attacked by vengeful Gore supporters.

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The irony was that the whole purpose of the unconventional ballot was to help older voters by increasing the size of the font. Combined with the many ballot issues that year, the decision was made to put candidate names on both sides. However, this confused some voters who wanted to vote for Gore, but mistakenly punched the second hole from the top, registering a vote for Pat Buchanan. While we can’t know for sure, there is strong evidence that this factor alone cost Gore thousands of votes, certainly many, many more than 537, the ultimate official margin of victory (2,912,790 to 2,912,253). During the weeks of uncertainty, many Bush voters wondered how anyone could miss the obvious, large arrows that clearly mark the proper hole. The curse of knowledge was at work. Once you know the right answer, it is hard to put yourself back in the mindset of not knowing and imagine  bumbling it. However, it is very plausible that someone seeing the ballot for the first time and told to adhere to the five minute time limit just saw the left page and punched accordingly.

Says Who?

Few things are more exciting to me that an intellectual throw-down between minds I respect on topics of fundamental importance. Recently, Nate Silver, who makes his living building prediction models, was under fire from Nassim Nicholas Taleb, who makes his living breaking them down. At issue was the foundational epistemological question of how much we really know, or rather, how confident we may presume in what we think we know. Taleb – who is famous for his books Fooled by Randomness, The Black Swan, and Anti-fragile – lives by the watchword “incerto” which means we should be much more circumspect about what we think we understand. He popularized the concept of a “Black Swan,” a momentous event that could not have been anticipated based on all previous observations. Consistent with this, Taleb has successfully implemented strategies that benefit from extreme, unexpected events that have previously been undervalued. Taleb has long inveighed against the widespread misuse of Gaussian distributions, especially those implicated in the 2008 finical crisis. Nate Silver’s models are much more sophisticated, so I was interesting when Taleb came after them:

The basic idea is that the prediction probabilities at 538 for each candidate to win are too volatile to be right. Instead, Taleb suggested a model based on his specialty, pricing options.

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The result is a much more parsimonious model, in which the chances are stuck at 50/50 until right before election day, at which time they jump to near certainty:

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Silver’s podcast riposte was swift and harsh, saying that when properly modeled – particularly by correctly accounting for the correlations between states – data from polls are actually very good predictors of the future election result. Especially after the conventions, the probability for a candidate to win can be forecast we a least some confidence.

This debate reminded me of Sean Carroll’s new book, The Big Picture. In it, he makes the astounding claim that the “Core Theory” of physics, which includes quantum field theory and relativity, can explain every experiment ever performed on Earth.

The reason for such incredible predictive power is that quantum field theory itself provides a recipe for including progressively smaller correction terms, which converge to a very good degree of accuracy. Carroll says that physics is “simple” compared with other fields, like biology or economics, in that reductionism works fantastically well, and every particle, and interaction between them, can be understood separate from the rest of the Universe. This is why the dimensionless magnetic moment of the electron is known to an uncertainty of a few parts per trillion.

This is, of course, not to say that we have (or will ever have) the functional omniscience of Laplace’s Demon, who can turn perfect knowledge of the laws of nature and the configuration of all particles at any time to perfectly predict their positions at every other time. The wild undulations of chaos theory, and the inherent uncertainty in quantum mechanics, preclude this. So perhaps the best approach is the one Carroll himself takes in “The Big Picture” – a Bayesian framework in which we are aware the credences we apply to various propositions and work to keep them up to date as new information becomes available.

Who ‘ya gonna call? Scientists!

A big change has occurred in the way our heroes are portrayed in fiction.

A good example is 1984 film Ghostbusters and its recent update.

In addition to the obvious gender change, a more substantive alteration to the characters is their profession

in the original they are parapsychologists, but now they are physicists (or engineers, plus a history buff). The main tension throughout the film is their effort to convince the world that the study of ghosts is real “science.” From the MIT consultants,  the movie is filled with real quantum mechanics equations.

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The science doesn’t end there. The proton packs are explained to be mini particle accelerators, complete with “quadrapole” superconducting magnets. As in the original, ghosts are classified by “classes,” but now they are summoned with blue glowing devices instead of rituals performed by demonic demigods.

I see a larger trend of “Scientization” of the paranormal in fiction. That is, heroes combat “the unknown” with science. Ghosts are seen to be so fearsome exactly because appear to represent “cosmic horror” that is dangerous and beyond human understanding. But with science, they are just another, albeit hazardous, phenomenon to poke, prod, and categorize.

Do not all charms fly
At the mere touch of cold philosophy?
There was an awful rainbow once in heaven:
We know her woof, her texture; she is given
In the dull catalogue of common things.
Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomèd mine—
Unweave a rainbow, as it erewhile made
The tender-person’d Lamia melt into a shade.

-“Lamia” by John Keats

This trend shows up in other media. In Rick and Morty, even the Devil is bested by science.

And the whole premise of Gravity Falls, a very binge-worthy show, is the rational study of the “weirdness” surrounding the Mystery Shack.

In fact, in the very first minute of the series, we get the introduction:

“My name is Dipper. The girl about to puke is my sister Mabel. You may be wondering what we’re doing in a golf cart, fleeing from a creature of unimaginable horror…Rest assured, there’s a perfectly logical explanation.”

Once again, a “cosmic horror” is cut down to manageable size, and ultimately defeated, with some rational thinking. Does this reflect our collective expectations, having battled problems in real life, like germs, famine, and natural disasters, with science?

STEM-Powered

I recently visited the Oregon Museum of Science and Industry in Portland, with an emphasis on “industry.” Housed in a former power-plant, there were many opportunities for visitors to actually build things. From 3D-printers to shake-tables for earthquake testing block towers, there was plenty for young makers to enjoy.

Compared with my recollections of (many, many) hours spent in science museums during my youth, I felt that there was a greatly reduced emphasis on simply observing, as opposed to doing.

Perhaps in an era of instant access to YouTube, simply watching a video or demonstration on a scientific principle is no longer a compelling enough reason to make the trip. Since knowledge is freely available, what is valuable is the ability to create something new. The museum gift-shop offered tools for budding programmers to learn to code.

Cavalier Predictions

As a native Ohioan, I was thrilled to see the Cleveland Cavaliers complete their remarkable Championship season, ending a 52-year drought for the city.

However, at least one person was somewhat less enthused that Cleveland came out on top in 2016:

 

This is not to pick on one pundit in particular; the track-records of sports (and politics) prognosticators are rarely checked, but it should be obvious that a history of accuracy is not a strict requirement to be invited back on TV. To be generous, it may be that the point of making predictions is to summarize one’s current state of belief, in a Bayesian sense. In other words, listeners should hear “pundit X believes, based on all evidence currently available, that outcome Y is the most likely.” Unfortunately, the process of computing this belief is almost always done in an unsystematic manner in the pundit’s head, and therefore subject to numerous cognitive biases, especially the availability heuristic, recency illusion, and the subadditivity bias.

When election guru Nate Silver apologized for being wrong about the GOP primaries, he did so for acting like “a pundit” – almost all of whom, by the way, were also wrong – instead of doing the “data journalism” for which he is famous. He wrote (emphasis added):

The big mistake is a curious one for a website that focuses on statistics. Unlike virtually every other forecast we publish at FiveThirtyEight — including the primary and caucus projections I just mentioned — our early estimates of Trump’s chances weren’t based on a statistical model. Instead, they were what we “subjective odds” — which is to say, educated guesses. In other words, we were basically acting like pundits, but attaching numbers to our estimates. And we succumbed to some of the same biases that pundits often suffer, such as not changing our minds quickly enough in the face of new evidence. Without a model as a fortification, we found ourselves rambling around the countryside like all the other pundit-barbarians, randomly setting fire to things.

So the main “sin” was putting numbers to a guess, which, unlike other 538 predictions, was not based on an actual analysis. Some believe that a way to improve the quality of predictions is to have people put money on the line, as in prediction markets. The idea is that the profit motive will help eliminate inefficiencies, but his is not certain. For example, consider the UK referendum (that has the charming portmanteau “Brexit”) occurring this week on whether to “Remain” part of the European Union or “Leave.” Prediction markets today have “Remain” a 3 to 1 favorite, despite the fact that poll results have gone back and forth and currently rest almost evenly split. Perhaps some punters believe that voters may flirt with leaving, but be blocked by their better judgement at the last moment, as with the Scotland referendum. Or, as King James would put it:

 

Entropy – The Musical

This video by A Capella Science (surprisingly not One Direction) touches on many key implications of the “Arrow of Time” predicted by the laws of thermodynamics but still not totally understood:

The 2nd Law of Thermodynamics can be stated in several ways, but the most intuitive formulation is that we can immediate discern that this video is being played backwards, since it shows many processes that we know from everyday experience only happen in one direction, like scrambling an egg, dissolving a sugar cube, or burning a match. Hot water and cold water mix together to produce warm water – you can wait as long as you want watching a puddle of warm water, the reverse simply won’t happen.

The basic idea is that, in a closed system, the amount of disorder – the entropy – can only increase or, at best, stay the same. This defines an “arrow” of entropic time that points from an era of lower disorder to higher disorder. But many deeper implications from Cosmology are mentioned in the video, particularly those popularized by Sean Carroll, like in this video

And in his book From Eternity To Here: The Quest for the Ultimate Theory of Time

For example, as natural as it may seem for some processes to be irreversible, the laws of nature are, as best as we can tell, don’t distinguish between forward and backward in time. How can irrreversibility emerge from time-symmetric equations? And how did we end up with an mostly ordered Universe it the first place? That is, even though ceramic shards will not spontaneously jump back onto a table and reform a cup, at least we started with a intact cup in the first place. We live in an era of very low entropy, all in all.

One possibility put forward is that our Universe is just a rather large random fluctuation out of equilibrium. While very unlikely, if you postulate an eternal Universe, everything will happen if you wait long enough. The argument against this is the (rather unsettling) idea of Boltzmann brains. That is, if everything experienced is just a passing fluctuation, it is much more probable that a conscious observer would just be a single brain.

As mentioned in the video, Sean Carroll suggests that a better theory involves multiple big-bangs, each creating a new Universe with its own arrow of time. At the beginning, the entropy is incredibly low, and increases as time evolves.

So how was the video make? *Spoiler Alert* Someone spent a long time learning to sing backwards.

Take a Free-Ride

Economists have long recognized that Public goods can suffer from a Free-Rider problem. Public goods are non-rival and non-excludable, like a lighthouse or national defense.
Individuals would like to enjoy the benefits without having to contribute.
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The Supreme Court just deadlocked on case, Friedrichs v. California Teachers Association, that hinged on compelling non-Union members to pay a portion of the fees to reimburse the costs of negotiating contracts, which everyone benefits from. As Catherine Fisk wrote: “agency fee provisions are necessary because public sector labor law imposes significant responsibilities on unions and thus the law itself would create a severe free rider problem if employers and unions could not require employees to pay for the services that the union is required by law to provide.”

I saw it firsthand: When people don’t need to pay to get union benefits, they don’t pay. And then the union loses its power to win those benefits….On Tuesday, the Supreme Court issued a split 4-4 ruling in Friedrichs v. California Teachers Association that, by default, affirms a lower court ruling that public-sector unions have the right to collect dues from all employees they represent. Were Justice Scalia alive and well, that right would surely have died.

In America’s 26 right-to-work states, unions, once able to collect dues from all workers for whom they negotiate, collect dues only from members who agree to pay them—meaning there’s no price at all to enjoying the benefits of a union contract. Freeloaders, hop on! Benefits become giveaways arranged by an Oprah-like union—You get affordable health insurance! And you get yearly raises! And you get holiday bonuses!—all available without contributing a penny to the organization responsible for negotiating to win them and fighting to protect them.

In game theory, this can be modeled with the “Snowdrift game.”
Public goods are not limited to human societies. They can also occur in nature, and large number of them can be categorized as “threat mitigation, ” like the system you studied in which algae secrete toxins to kill competitors. Maybe removing a threat is a better examples of a public good than something positive (like building a park etc) because there is no possible way to exclude other members from enjoying threat-free environment.
At least one political commentator said that the other GOP candidates didn’t attack Donald Trump because of a “collective action problem” – everyone wants to take down Trump, but would rather have someone else do it. There is also the fable called “The Bell and the Cat” in which the mice decide it would be a good idea to put a bell on the cat so they can hear it coming – although no one wants to do it himself.
en.wikipedia.org
Belling the Cat is a fable also known under the titles The Bell and the Cat and The Mice in Council. Although often attributed to Aesop, it was not recorded before …

Some other examples:

  • Digging a path in a snowdrift
  • Picking up litter
  • National Defense
  • Lighthouse
  • Beta-lactamase Enzyme for degrading antibiotics
  • Monkey predator alarm calls
  • Firefighters
  • Police
  • Health Inspector
  • Immunization (Herd Immunity)
All of these involve removing or mitigating a threat instead of providing an affirmative public good. In human societies – people are considered (mythic) heroes if they fight crime – or fires or Supervillans or predators or invading armies.
Enforcing fair cooperation, which we now do collectively via a complex system of laws, lawyers, and courts. But to get societies going, it may be need to outsource these roles to a higher power:
“Today’s most successful religions have one thing in common: moralizing gods that care about how people treat one another and will punish those who are selfish and cruel. But for most of human history, these “big gods” were the exception. If today’s hunter-gatherers are any guide, for thousands of years our ancestors conceived of deities as utterly indifferent to the human realm, and to whether we behaved well or badly… once big gods and big societies existed, their moralizing deities helped religions as dissimilar as Islam and Mormonism to spread by making groups of the faithful more cooperative and therefore more successful.”