Quantifying the Trump-iness of Political Sentences

trumpheadshotYou could say that Donald Trump has a… distinct way of speaking. He doesn’t talk the way other politicians do (even ignoring his accent), and the contrast between him and Clinton is pretty strong. But can we figure out what differentiates them? And then, can we find the most… Trump-ish sentence?

That was the challenge my friend Spencer posed to me as my first major foray into data science, the new career I’m starting. It was the perfect project: fun, complicated, and requiring me to learn new skills along the way.

To find out the answers, read on! The results shouldn’t be taken too seriously, but they’re amusing and give some insight into what might be important to each candidate and how they talk about the political landscape. Plus, it serves to demonstrate the data science techniques I’m learning for as a portfolio project.

If you want to play with the model yourself, I also put together an interactive javascript page for you: you can test your judgment compared to its predictions, browse the most Trumpish/Clintonish sentences and terms, and enter your own text for the model to evaluate.

screen-shot-2016-10-19-at-7-25-47-pm

To read about how the model works, I wrote a rundown with both technical and non-technical details below the tables and graphs. But without further ado, the results:

The Trump-iest and Clinton-est Sentences and Phrases from the 2016 Campaign:

Clinton Trump
Top sentence: “That’s why the slogan of my campaign is stronger together because I think if we work together and overcome the divisiveness that sometimes sets americans against one another and instead we make some big goals and I’ve set forth some big goals, getting the economy to work for everyone, not just those at the top, making sure we have the best education system from preschool through college and making it affordable and somp[sic] else.” — Presidential Candidates Debate

Predicted Clinton: 0.99999999999
Predicted Trump: 1.04761466567e-11

Frustratingly, I couldn’t download or embed the C-SPAN video for this clip, so here are two of the other top 5 Clinton-iest sentences:

Presidential Candidate Hillary Clinton Rally in Orangeburg, South Carolina

Presidential Candidate Hillary Clinton Economic Policy Address

Top sentence: “As you know, we have done very well with the evangelicals and with religion generally speaking, if you look at what’s happened with all of the races, whether it’s in south carolina, i went there and it was supposed to be strong evangelical, and i was not supposed to win and i won in a landslide, and so many other places where you had the evangelicals and you had the heavy christian groups and it was just — it’s been an amazing journey to have — i think we won 37 different states.” — Faith and Freedom Coalition Conference

Predicted Clinton: 4.29818403092e-11
Predicted Trump: 0.999999999957

Frustratingly, I couldn’t download or embed the C-SPAN video for this clip either, so here are two of the other top 5 Trump-iest sentences:

Presidential Candidate Donald Trump Rally in Arizona

Presidential Candidate Donald Trump New York Primary Night Speech

Top Terms

Term Multiplier
my husband 12.95
recession 10.28
attention 9.72
wall street 9.44
grateful 9.23
or us 8.39
citizens united 7.97
mother 7.20
something else 7.17
strategy 7.05
clear 6.81
kids 6.74
gun 6.69
i remember 6.51
corporations 6.51
learning 6.36
democratic 6.28
clean energy 6.24
well we 6.14
insurance 6.14
grandmother 6.12
experiences 6.00
progress 5.94
auto 5.90
climate 5.89
over again 5.85
often 5.80
a raise 5.71
about what 5.68
immigration reform 5.62
Term Multiplier
tremendous 14.57
guy 10.25
media 8.60
does it 8.24
hillary 8.15
politicians 8.00
almost 7.83
incredible 7.42
illegal 7.16
general 7.03
frankly 6.97
border 6.89
establishment 6.84
jeb 6.76
allowed 6.72
obama 6.48
poll 6.24
by the way 6.21
bernie 6.20
ivanka 6.09
japan 5.98
politician 5.96
nice 5.93
conservative 5.90
islamic 5.77
hispanics 5.76
deals 5.47
win 5.43
guys 5.34
believe me 5.32

Other Fun Results:

pronouns

Cherrypicked pairs of terms:

Clinton Trump
Term Multiplier Term Multiplier
president obama 3.27 obama 6.49
immigrants 3.40 illegal immigrants 4.87
clean energy 6.24 energy 1.97
the wealthy 4.21 wealth 2.11
learning 6.36 earning 1.38
muslims 3.46 the muslims 1.75
senator sanders 3.18 bernie 6.20

How the Model Works:

Defining the problem: What makes a sentence “Trump-y?”

I decided that the best way to quantify ‘Trump-iness’ of a sentence was to train a model to predict whether a given sentence was said by Trump or Clinton. The Trumpiest sentence will be the one that the predictive model would analyze and say “Yup, the chance this was Trump rather than Clinton is 99.99%”.

Along the way, with the right model, we can ‘look under the hood’ to see what factors into the decision.

Technical details:

The goal is to build a classifier that can distinguish between the candidate’s sentences optimizing for ROC_AUC, and allows us to extract meaningful/explainable coefficients.

Gathering and processing the data:

In order to train the model, I needed large bodies of text from each candidate. I ended up scraping transcripts from events on C-SPAN.org. Unfortunately, they’re uncorrected closed caption transcripts and contained plenty of typos and misattributions. On the other hand, they’re free.

I did a bit to clean up some recurring problems like the transcript starting every quote section with “Sec. Clinton:” or including descriptions like [APPLAUSE] or [MUSIC]. (Unfortunately, they don’t reliably mark the end of the music, and C-SPAN sometimes claims that Donald Trump is the one singing ‘You Can’t Always Get What You Want.’)

Technical details:

I ended up learning to use Python’s Beautiful Soup library to identify the list of videos C-SPAN considers campaign events by the candidates, find their transcripts, and grab only the parts they supposedly said. I learned to use some basic regular expressions to do the cleaning.

My scraping tool is up on github, and is actually configured to be able to grab transcripts for other people as well.

Converting the data into usable features

After separating the large blocks of text into sentences and then words, I had some decisions to make. In an effort to focus on interesting and meaningful content, I removed sentences that were too short or too long – “Thank you” comes up over and over, and the longest sentences tended to be errors in the transcription service. It’s a judgement call, but I wanted to keep half the sentences, which set cutoffs at 9 words and 150 words. 34,108 sentences remained.

A common technique in natural language processing is to remove the “stopwords” – common non-substantive words like articles (a, the), pronouns (you, we), and conjunctions (and, but). However, following James Pennebaker’s research, which found these words are surprisingly useful in predicting personality, I left them in.

Now we have what we need: sequences of words that the model can consider evidence of Trump-iness.

Technical details:

I used NLTK to tokenize the text into sentences, but wrote my own regular expressions to tokenize the words. I considered it important to keep contractions together and include single-character tokens, which the standard NLTK function wouldn’t have done.

I used a CountVectorizer from sklearn to extract ngrams and later selected the most important terms using a SelectFromModel with a Lasso Logistic Regression. It was a balance – more terms would typically improve accuracy, but water down the meaningfulness of each coefficient.

I tested using various additional features, like parts of speech and lemmas (using the fantastic Spacy library) and sentiment analysis (using the Textblob library) but found that they only provided marginal benefit and made the model much slower. Even just using 1-3 ngrams, I got 0.92 ROC_AUC.

Choosing & Training the Model

One of the most interesting challenges was avoiding overfitting. Without taking countermeasures, the model could look at a typo-riddled sentence like “Wev justv don’tv winv anymorev.” and say “Aha! Every single one of those words are unique to Donald Trump, therefore this is the most Trump-like sentence ever!”

I addressed this problem in two ways: the first is by using regularization, a standard machine learning technique that penalizes a model for using larger coefficients. As a result, the model is discouraged from caring about words like ‘justv’ which might only occur two times, since they would only help identify those couple sentences. On the other hand, a word like ‘frankly’ helps identify many, many sentences and is worth taking a larger penalty to give it more importance in the model.

The other technique was to use batch predictions – dividing the sentences into 20 chunks, and evaluating each chunk by only training on the other 19. This way, if the word ‘winv’ only appears in a single chunk, the model won’t see it in the training sentences and won’t be swayed. Only words that appear throughout the campaign have a significant impact in the model.

Technical details:

The model uses a logistic regression classifier because it produces very explainable coefficients. If that weren’t a factor, I might have tried a neural net or SVM (I wouldn’t expect a random forest to do well with such sparse data.) In order to set the regularization parameters for both the final classifier and for the feature-selection Lasso Logistic Regressor, I used sklearn’s cross-validated gridsearch object, optimizing for ROC_AUC.

During the prediction process, I used a stratified Kfold to divide the data in order to ensure each chunk would have the appropriate mix of Trump and Clinton sentences. It was tempting to treat the sentences more like a time series and only use past data in the predictions, but we want to consider how similar old sentences are to the whole corpus.

Interpreting and Visualizing the Results:

The model produced two interesting types of data: how likely the model thought each sentence was spoken by Trump or Clinton (how ‘Trumpish’ vs. ‘Clintonish’ it is), and how any particular term impacts those predicted odds. So if a sentence is predicted to be spoken by Trump with estimated 99.99% probability, the model considers it extremely Trumpish.

The term’s multipliers indicate how each word or phrase impacts the predicted odds. The model starts at 1:1 (50%/50%), and let’s say the sentence includes the word “incredible” – a Trump multiplier of 7.42. The odds are now 7.42 : 1, or roughly 88% in favor of Trump. If the model then sees the word “grandmother” – a Clinton multiplier of 6.12 – its estimated odds become 7.42 : 6.12, (or 1.12 : 1), roughly 55% Trump. Each term has a multiplying effect, so a 4x word and 2x word together have as much impact as an 8x word – not 6x.

Technical details:

In order to visualize the results, I spent a bunch of time tweaking the matplotlib package to generate a graph of coefficients, which I used for the pronouns above. I made sure to use a logarithmic scale, since the terms are multiplicative.

In addition, I decided to teach myself enough javascript to learn to use the D3 library – allowing interactive visualizations and the guessing game where players can try to figure out who said a given random sentence from the campaign trail. There are a lot of ways the code could be improved, but I’m pleased with how it turned out given that I didn’t know any D3 prior to this project.

An Atheist’s Defense of Rituals: Ceremonies as Traffic Lights

BarMitzvahThe idea of a coming-of-age ceremony has always been a bit strange to me as an atheist. Sure, I attended more than my fair share of Bat and Bar Mitzvahs in middle school. But it always struck me as odd for us to pretend that someone “became an adult” on a particular day, rather than acknowledging it was a gradual process of maturation over time. Why can’t we just all treat people as their maturity level deserves?

The same goes with weddings – does a couple’s relationship really change in a significant way marked by a ceremony? Or do two people gradually fall in love and grow committed to each other over time? Moving in with each other marks a discrete change, but what does “married” change about the relationship?

But my thinking has been evolving since reading this fantastic post about rituals by Brett and Kate McKay at The Art of Manliness. Not only do the rituals acknowledge a change, they use psychological and social reinforcement to help the individuals make the transition more fully:

One of the primary functions of ritual is to redefine personal and social identity and move individuals from one status to another: boy to man, single to married, childless to parent, life to death, and so on.

Left to follow their natural course, transitions often become murky, awkward, and protracted. Many life transitions come with certain privileges and responsibilities, but without a ritual that clearly bestows a new status, you feel unsure of when to assume the new role. When you simply slide from one stage of your life into another, you can end up feeling between worlds – not quite one thing but not quite another. This fuzzy state creates a kind of limbo often marked by a lack of motivation and direction; since you don’t know where you are on the map, you don’t know which way to start heading.

Just thinking your way to a new status isn’t very effective: “Okay, now I’m a man.” The thought just pings around inside your head and feels inherently unreal. Rituals provide an outward manifestation of an inner change, and in so doing help make life’s transitions and transformations more tangible and psychologically resonant.

Brett and Kate McKay cover a range of aspects of rituals, but I was particular struck by the game theory implications of these ceremonies. By coordinating society’s expectations in a very public manner, transition rituals act like traffic lights to make people feel comfortable and confident in their course of action.

The Value of Traffic Lights

Traffic lights are a common example in game theory. Imagine that you’re driving toward an unmarked intersection and see another car approaching from the right. You’re faced with a decision: do you keep going, or brake to a stop?

If you assume they’re going to keep driving, you want to stop and let them pass. If you’re wrong, you both lose time and there’s an awkward pause while you signal to each other to go.

If you assume they’re going to stop, you get to keep going and maintain your speed. Of course, if you’re wrong and they keep barreling forward, you risk a deadly accident.

Things go much more smoothly when there are clear street signs or, better yet, a traffic light coordinating everyone’s expectations.

Ceremonies as Traffic Lights

Now, misjudging a teenager’s maturity is unlikely to result in a deadly accident. But, with reduced stakes, the model still applies.

As a teen gets older, members of society don’t always know how to treat him – as a kid or adult. Each type of misaligned expectations is a different failure mode: If you treat him as a kid when he expected to be treated as an adult, he might feel resentful of the “overbearing adult”. If you treat him as an adult when he was expecting to be treated as a kid, he might not take responsibility for himself.

trafficlightA coming-of-age ritual acts like the traffic light to minimize those failure modes. At a Bar or Bat Mitzvah, members of society gather with the teenager and essentially publicly signal “Ok everyone, we’re switching our expectations… wait for it… Now!”

It’s important that the information is known by all to be known to all – what Steven Pinker calls common or mutual knowledge:

“In common knowledge, not only does A know x and B know x, but A knows that B knows x, and B knows that A knows x, and A knows that B knows that A knows x, ad infinitum.”

If you weren’t sure that the oncoming car could see their traffic light, it would be almost as bad as if there were no light at all. You couldn’t trust your green light because they might not stop. Not only do you need to know your role, but you need to know that everyone knows their role and trusts that you know yours… etc.

Public ceremonies gather everyone to one place, creating that common knowledge. The teenager knows that everyone expects him to act as an adult, society knows that he expects them to treat him as one, and everyone knows that those expectations are shared. Equipped with this knowledge, the teen can count on consistent social reinforcement to minimize awkwardness and help him adopt his new identity.

Obviously, these rituals are imperfect – Along with the socially-defined parts of identity, there are internal factors that make someone more or less ready to be an adult. Quite frankly, setting 13 as the age of adulthood is probably too young.

But that just means we should tweak the rituals to better fit our modern world. After all, we have precise engineering to set traffic light schedules, and it still doesn’t seem perfect (this XKCD comes to mind).

That’s what makes society and civilization powerful. We’re social creatures, and feel better when we feel comfortable in our identity – either as a child or adult, as single or married, as grieving or ready to move on. Transition rituals serve an important and powerful role in coordinating those identities.

We shouldn’t necessarily respect them blindly, but I definitely respect society’s rituals more after thinking this through.

To take an excerpt from a poem by Bruce Hawkins:

Three in the morning, Dad, good citizen
stopped, waited, looked left, right.
He had been driving nine hundred miles,
had nearly a hundred more to go,
but if there was any impatience
it was only the steady growl of the engine
which could just as easily be called a purr.

I chided him for stopping;
he told me our civilization is founded
on people stopping for lights at three in the morning.

The Matrix Meets Braid: Artificial Brains in Gunfights

superhotIt’s The Matrix meets Braid: a first-person shooter video game “where the time moves only when you move.” You can stare at the bullets streaking toward you as long as you like, but moving to dodge them causes the enemies and bullets to move forward in time as well.

The game is called SUPERHOT, and the designers describe it by saying “With this simple mechanic we’ve been able to create gameplay that’s not all about reflexes – the player’s main weapon is careful aiming and smart planning – while not compromising on the dynamic feeling of the game.”

Here’s the trailer:

I’ve always loved questions about what it would be like to distort time for yourself relative to the rest of the universe (and the potential unintended consequences, as we explored in discussing why The Flash is in a special hell.)

In Superhot, it’s not that you can distort time exactly – after all, whenever you take a step, your enemies get the same amount of time to take a step themselves. Instead, your brain is running as fast as it likes while (the rest of) your body remains in the same time stream as everything else.

And then it struck me: this might be close to the experience of an emulated brain housed in a regular-sized body.

Let’s say that, in the future, we artificially replicate/emulate human minds on computers. And let’s put an emulated human mind inside a physical, robotic body. The limits on how fast it can think are its hardware and its programming. As technology and processor speeds improve, the “person” could think faster and faster and would experience the outside world as moving slower and slower in comparison.

… but even though you might have a ridiculously high processing speed to think and analyze a situation, your physical body is still bound by the normal laws of physics. Moving your arms or legs requires moving forward in the same stream of time as everyone else. In order to, say, turn your head to look to your left and gather more information, you need to let time pass for your enemies, too.

Robin Hanson, professor of economics at George Mason University and author of Overcoming Bias, has put a lot of thought into the implications of whole-brain emulation. So I asked him:

Is Superhot what an emulated human would experience in a gunfight?

His reply:

An em could usually speed up its mind to deal with critical situations, though this would cost more per objective second. So a first-person shooter where time only moves when you do does move in the direction of letting the gamer experience action in an em world. Even better would be to let the gamer change the rate at which game-time seems to move, to have a limited gamer-time budget to spend, and to give other non-human game characters a similar ability.”

He’s right: thinking faster would require running more cycles per second, which takes resources. And yeah, you would need infinite processing speed to think indefinitely while the rest of the world was frozen. It would be more consistent to add a “mental cycle” budget that ran down at a constant rate from the gamer’s external point of view.

I don’t know about you, but I would buy that game! (Even if a multi-player mode would be impossible.)

Why Decision Theory Tells You to Eat ALL the Cupcakes

cupcakeImagine that you have a big task coming up that requires an unknown amount of willpower – you might have enough willpower to finish, you might not. You’re gearing up to start when suddenly you see a delicious-looking cupcake on the table. Do you indulge in eating it? According to psychology research and decision-theory models, the answer isn’t simple.

If you resist the temptation to eat the cupcake, current research indicates that you’ve depleted your stores of willpower (psychologists call it ego depletion), which causes you to be less likely to have the willpower to finish your big task. So maybe you should save your willpower for the big task ahead and eat it!

…But if you’re convinced already, hold on a second. How easily you give in to temptation gives evidence about your underlying strength of will. After all, someone with weak willpower will find the reasons to indulge more persuasive. If you end up succumbing to the temptation, it’s evidence that you’re a person with weaker willpower, and are thus less likely to finish your big task.

How can eating the cupcake cause you to be more likely to succeed while also giving evidence that you’re more likely to fail?

Conflicting Decision Theory Models

The strangeness lies in the difference between two conflicting models of how to make decisions. Luke Muehlhauser describes them well in his Decision Theory FAQ:

This is not a “merely verbal” dispute (Chalmers 2011). Decision theorists have offered different algorithms for making a choice, and they have different outcomes. Translated into English, the [second] algorithm (evidential decision theory or EDT) says “Take actions such that you would be glad to receive the news that you had taken them.” The [first] algorithm (causal decision theory or CDT) says “Take actions which you expect to have a positive effect on the world.”

The crux of the matter is how to handle the fact that we don’t know how much underlying willpower we started with.

Causal Decision Theory asks, “How can you cause yourself to have the most willpower?”

It focuses on the fact that, in any state, spending willpower resisting the cupcake causes ego depletion. Because of that, it says our underlying amount of willpower is irrelevant to the decision. The recommendation stays the same regardless: eat the cupcake.

Evidential Decision Theory asks, “What will give evidence that you’re likely to have a lot of willpower?”

We don’t know whether we’re starting with strong or weak will, but our actions can reveal that one state or another is more likely. It’s not that we can change the past – Evidential Decision Theory doesn’t look for that causal link – but our choice indicates which possible version of the past we came from.

Yes, seeing someone undergo ego depletion would be evidence that they lost a bit of willpower.  But watching them resist the cupcake would probably be much stronger evidence that they have plenty to spare.  So you would rather “receive news” that you had resisted the cupcake.

A Third Option

Each of these models has strengths and weaknesses, and a number of thought experiments – especially the famous Newcomb’s Paradox – have sparked ongoing discussions and disagreements about what decision theory model is best.

One attempt to improve on standard models is Timeless Decision Theory, a method devised by Eliezer Yudkowsky of the Machine Intelligence Research Institute.  Alex Altair recently wrote up an overview, stating in the paper’s abstract:

When formulated using Bayesian networks, two standard decision algorithms (Evidential Decision Theory and Causal Decision Theory) can be shown to fail systematically when faced with aspects of the prisoner’s dilemma and so-called “Newcomblike” problems. We describe a new form of decision algorithm, called Timeless Decision Theory, which consistently wins on these problems.

It sounds promising, and I can’t wait to read it.

But Back to the Cupcakes

For our particular cupcake dilemma, there’s a way out:

Precommit. You need to promise – right now! – to always eat the cupcake when it’s presented to you. That way you don’t spend any willpower on resisting temptation, but your indulgence doesn’t give any evidence of a weak underlying will.

And that, ladies and gentlemen, is my new favorite excuse for why I ate all the cupcakes.

What Would a Rational Gryffindor Read?

In the Harry Potter world, Ravenclaws are known for being the smart ones. That’s their thing. In fact, that was really all they were known for. In the books, each house could be boiled down to one or two words: Gryffindors are brave, Ravenclaws are smart, Slytherins are evil and/or racist, and Hufflepuffs are pathetic loyal. (Giving rise to this hilarious Second City mockery.)

But while reading Harry Potter and the Methods of Rationality, I realized that there’s actually quite a lot of potential for interesting reading in each house. Ravenclaws would be interested in philosophy of mind, cognitive science, and mathematics; Gryffindors in combat, ethics, and democracy; Slytherins in persuasion, rhetoric, and political machination; and Hufflepuffs in productivity, happiness, and the game theory of cooperation.

And so, after much thought, I found myself knee-deep in my books recreating what a rationalist from each house would have on his or her shelf. I tried to match the mood as well as the content. Here they are in the appropriate proportions for a Facebook cover image so that you can display your pride both in rationality and in your chosen house (click to see each image larger, with a book list on the left):

Rationality Ravenclaw Library

Rationality Gryffindor Library

Rationality Slytherin Library

Rationality Hufflepuff Library

What do you think? I’m always open to book recommendations and suggestions for good fits. Which bookshelf fits you best? What would you add?

Messing With Time: Why The Flash is in Hell

clockInterfering with time can really make a mess of things. We’ve all thought about what might happen if someone travels in time – think movies like Back to the Future, Primer, or Terminator. But let’s take the question to the next level: what if instead of changing position in time – jumping ahead or back – we changed velocities? Would it still be a disaster waiting to happen if we speed up or slow down time?

What would it even mean to change the speed of time? Reading Sean Carroll’s “From Eternity To Here”, he makes an interesting point:

“We live in a world that contains all sorts of periodic processes, which repeat a predictable number of times in comparison to certain other periodic processes. And that’s how we measure duration: by the number of repetitions of such a process. When we say that our TV program lasts one hour, we mean that the quartz crystal in our watch will oscillate 117,964,800 times between the start and end of the show (32,768 oscillations per second, 3,600 seconds in an hour).

“As human beings we feel the passage of time. That’s because there are periodic processes occurring within our metabolism – breaths, heartbeats, electrical pulses, digestion, rhythms of the central nervous system. We are a complicated, interconnected collection of clocks.”

So speeding up time across the universe doesn’t make much sense. Every process would still happen at the same relative rate, including our thoughts and metabolism. Modern physics tells us that there isn’t an objective frame of reference – different objects can, in fact, experience different relative times.

The real question is what would happen if we speed up our own processes relative to everything else in the universe. We wouldn’t feel any different – the “internal clocks” Carroll talks about would all still be in sync with each other – but we would notice all outside processes happening much less frequently compared to our thoughts and motions.

But much like the dilemma facing Calvin and Hobbes, which way would you go? As I read Carroll’s book, I started to ask: If you could change your relative speed, would you want to be faster or slower?

The reason to speed yourself up is obvious: you get a comparative advantage over everyone else. Imagine being able to think more, run further, and react more quickly in the same duration of “external time”. Who wouldn’t want that?

But there are advantages to slowing yourself down, too. Slowing down your body’s processes would be like stretching your life experience over a longer period of external time. Any benefit you get from the rest of the world is amplified. Randall Munroe at XKCD seems to have thought about it before in his comic about ‘Time Vultures’:

And it goes beyond food – assistants, coworkers, and fellow citizens could accomplish more. You would get to take advantage of all the medical breakthroughs, technological advances, and political developments that people come up with during your “stretched” lifespan.

As I talked with my friends about the question, many of them brought up the same point: there’s a risk in permanently changing too far. And that brings me to my last point, that Barry Allen (alter-ego of ‘The Flash’) is arguably in a special version of hell. Yes, after being struck by lightning in his lab, he was granted superhuman speed. Sounds great, but if you follow the thought process to its horrifying conclusion you get “The Ballad of Barry Allen” by Jim’s Big Ego:

I’ve got time to think about my past
As I dodge between the bullets
How my life was so exciting
Before I got this way
And how long ago it was now I never can explain
By the clock that’s on the tower
Or the one that’s in my brain

And I’m there before you know it
I’ll be gone before you see me
And I’d like to get to know you
But you’re talking much too slowly
And I know you want to thank me
But I never stick around
‘Cause time keeps dragging on…
And on…
And on

The game theory dynamics are complex. It seems like to the extent that you’re competing with others, you want to be faster. To the extent that you’re cooperating/collaborating with others, you want them to be faster. And overarching all of it, there’s a coordination factor in that you don’t want to be too different from others.

At the moment, this is all just a fun thought experiment. But I know that the next time I’m bored in a meeting or enjoying a particularly nice moment, I’ll wish I could tweak my speed just a bit.

Colbert Deconstructs Pop Music, Finds Mathematical Nerdiness Within

Stephen Colbert channeling Kurt Godel

And here I thought I didn’t like pop music. Turns out I just hadn’t found the songs that invoke questions about the foundations of logic and mathematics. Fortunately, Stephen Colbert brings our attention to the fascinating – and paradoxical! – pop song “That’s What Makes You Beautiful” by One Direction. Watch Stephen do his thing deconstructing the lyrics with glorious nerdy precision before we take it even further (the good part starts at 1:54 or so):

For those of you who can’t watch the video, here’s the nerdy part, hastily transcribed:

Their song “That’s What Makes You Beautiful” isn’t just catchy, it has a great message. “You don’t know you’re beautiful. That’s what makes you beautiful.”

First of all: great dating advice. Remember girls, low self esteem – very attractive to men. Guys always go for the low hanging fruit, easy pickings.

Second: the lyrics are incredibly complex! You see, the boys are singing “You don’t know you’re beautiful, that’s what makes you beautiful.” But they’ve just told the girl she’s beautiful. So since she now knows it, she’s no longer beautiful!

But – stick with me, stick with me, oh it goes deeper! – but she’s listening to the song, too. So she knows she’s not beautiful. Therefore, following the syllogism of the song, she’s instantly beautiful again!

It’s like an infinite fractal recursion, a flickering quantum state of both hot and not. I mean, this lyric as iterated algorithm could lead to a whole new musical genre. I call it Mobius pop, which would include One Direction and of course the rapper MC Escher.

They say the way to a man’s heart is through his stomach but honestly, talking about recursion, fractals, and flickering quantum states does far more to win my love.  We can find intellectual stimulation in anything!

And there’s more – we can go nerdier!

Stick With Me, Stick With Me, Oh It Goes Deeper

Let’s analyze the dilemma a bit further:

  1. She can’t KNOW she’s beautiful because, as Stephen points out, that leads to a logical contradiction – she would no longer be beautiful.
  2. She can’t KNOW that she isn’t beautiful, because that also leads to a logical contradiction – she would be beautiful again.
  3. It’s impossible for the girl to know that she is or isn’t beautiful, so she has to be uncertain – not knowing either way.
  4. This uncertainty satisfies the requirements: she doesn’t know that she’s beautiful, therefore, she’s definitely beautiful and can’t know it.

It turns out she’s not in a flickering state of hot and not, she’s perpetually hot – but she cannot possibly know it without logical contradiction! From an external perspective, we can recognize it as true. From within her own mind, she can’t – even following the same steps. How weird is that?

Then it hit me: the song lyrics are a great example of a Gödel sentence!

Gödel sentences, from Kurt Gödel’s famous Incompleteness Theorems, are the statements which are true but unprovable within the system.  Gödel demonstrated that every set of mathematical axioms complex enough to stand as a foundation for arithmetic will contain at least one of these statements: something that is obviously true from an outside perspective, but isn’t true by virtue of the axioms.  (He found a way to coherently encode “The axioms do not prove this sentence to be true.”)  This raises the question: what makes a mathematical statement true if not the fact that it can be derived from the axioms?

Gödel’s findings rocked the world of mathematics and have had implications on the philosophy of mind, raising questions like:

  • What does it mean to hold a belief as true?
  • What are our minds doing when we make the leap of insight (if insight it is) that identifies a Gödel sentences as true?
  • How does this set us apart from the algorithmic computers, which are plagued by their own version of Incompleteness, the Halting Problem?

I had no idea pop music was so intelligent!

Was the boy band comparing her, not to a summer’s day, but a turing-complete computer?  Were they glorifying their listeners by reminding us that, according to some interpretations of Incompleteness Theory, we’re more than algorithmic machines?  Were they making a profound statement about mind/matter dualism?

I don’t know, but apparently I should turn on the radio more often.

[For related reading, see various analyses of Mims’ “This is Why I’m Hot”]


As they say in the Sirius Cybernetics Corporation: Share and Enjoy!

%d bloggers like this: