Game Theory and Branding

1.Brand as a Meet-up Point
The game theorist Thomas Schelling came up with the following game: you and one other person are dropped at different locations in New York City, with no way to communicate. You both pick a time and place to try to meet up. If you both pick the same time and place, then you win!

This sort of game is incredibly common in business. Imagine that, instead of just two people, there are two groups of people. One group all have t-shirts which say “buyer”, and the other group all have t-shirts which say “seller”. Each person wins if they can meet up with someone from the other group - each buyer wants to find a seller, and each seller wants to find a buyer.

One really good solution to this sort of problem is to put up a giant billboard that says “Meet up here!”. In a business context, a strong brand can serve that role. Ebay is a great example - everyone knows that ebay is where you go to sell random stuff to strangers, and everyone knows that ebay is where you go to buy random stuff from strangers. Ebay serves as a meetup place for buyers and sellers, and the ebay brand is the game-theoretic equivalent of a giant billboard which says “Meet up here!”.

Why it’s valuable
This sort of brand value usually involves network effects - the more people meet up under your billboard, the more people will recognize it as a good place to meet up. If only 1% of people go to your billboard to meet up, then it really isn’t a very good place to go. But if 90% of people go to your billboard, then it’s the obvious place to go and you’d be an idiot to go anywhere else. That makes this sort of branding incredibly valuable, since you can effectively lock in a market - once ebay becomes the place to go to buy and sell random stuff, nobody will bother going anywhere else, and ebay can rake in the money.

In particular, that means the company is willing to pay lots of money for their billboard - i.e. maintain the brand through advertising. Especially early on, the company may spend very heavily on advertising in order to jumpstart the network effect.

In general, when you hear about a “network good”, it’s always a good with this sort of underlying coordination game structure. This includes goods from markets (ebay, uber, NASDAQ), to messaging (snapchat, whatsapp), to standards (VHS vs Betamax), to Facebook, the internet, and so on.

When not to do it
Notice that this whole setup depends crucially on the structure of the problem - buyers looking for sellers, in the ebay example. In general, this kind of brand value applies ONLY if the company exists to solve a coordination problem (a game where players win by “coordinating” on the same solution, i.e. meeting up at the same location). If that’s not the central purpose of the company, then this kind of branding does NOT apply.

2.Brand as a Signalling Mechanism
Nobody buys a macbook because of the computer’s inherent value. No, people buy macbooks so that they can be seen in coffee shops wearing scarfs and presumably typing up modern poetry on their macbook.

Ok, I’m exaggerating a little bit. But macbooks don’t sell for $1000 because of the material cost. (And don’t give me that “but I need it for coding!” crap; you’re probably just running the code in a linux VM anyway.)

iOS vs Android. Lexus vs Toyota. Rolex vs Timex. Signalling brands are all about selling the same shit, or even worse shit, for a higher price. Why would anyone buy such products? Because everyone knows they’re higher priced, so they’re a great way of showing off how fabulously wealthy you are.

Alternatively, signalling can show off how morally upstanding you are. Target vs Walmart, Prius vs cars which go vroom, Whole Foods vs Albertson’s… there are no shortage of opportunities to spend a little extra in order to show everyone how concerned you are about poor people, climate change, or poor people impacted by climate change.

Why it’s valuable
In this kind of branding, the brand IS the product. You’re also selling a nominal “product”, but that’s really just a vessel for the brand - just like Abercrombie shirts are often just vessels for the word “Abercrombie”. The shirt itself costs $10, the other $80 are for the brand. The good news is, it costs basically nothing to stick the brand on the shirt (or phone, or watch, or car, or whatever), so profit margins can be outrageously high.

Of course, you’ll need to spend heavily on advertising in order to build the brand identity. It’s not a completely free lunch. Indeed, everyone wants to claim a slice of this pie; this kind of branding will pit you against lots of competition.

When not to do it
Signalling is all about visibility. The whole point of a Rolex is that other people see it, so they can see how wealthy you are. The whole point of a Prius is that other people see it, so they can see how morally upstanding you are. The whole point of a Tesla is that other people see it, so they can see how wealthy and morally upstanding you are.

Corollary: if you’re selling something which is not highly visible, then it’s not a signalling good, so don’t bother with this kind of branding. For example, I’m currently at a mortgage company. Nobody would pay an extra-high rate on their mortgage to show how rich/moral they are.

Now, I can hear all you product managers out there thinking “I know! We’ll make it visible by adding a button to share on social media!”. Ok, please imagine Rolex adding a button to share “I just bought a Rolex!” on facebook. Clearly, anyone who actually shared this would immediately be labelled a desperate plebeian. Not good. That’s why signalling goods need to be inherently visible - whether you’re signalling wealth or morality, you have to pretend you’re not just showing it off.

3.Brand as a Trust Mechanism
In contract law, one of the first lessons a student learns is that contracts come with two rights: the right to sue, and the right to be sued. The latter often comes as a surprise, but it is arguably the more valuable of the two. If a person or company can be sued for screwing me over, then I can trust them not to screw me over (or at least not enough to merit a lawsuit). That sort of trust is necessary to enable business transactions, so it’s actually valuable to be able to be sued.

Practically, however, lawsuits are both expensive and risky. In most cases, a company has considerably more legal resources than a consumer. That means that the right to be sued is, for many companies, more a theoretical than practical threat. And since the ability to be sued means the ability to be trusted, a practical inability to be sued means a practical inability to be trusted. In short, companies with the legal resources to fight a lawsuit are not trusted.

Branding can be used as an alternative mechanism for trust.

How? Well, the right to be sued creates trust because the company can be hurt (via lawsuit) if they do something bad. Similarly, regularly screwing over consumers will ruin a brand, as word inevitably gets around that the company is no good. Consumers intuitively trust brands they’ve heard of (and haven’t heard bad things about), because if those companies screwed their customers, then word probably would have gotten around by now.

Why it’s valuable
The value in this sort of branding depends on how much trust matters. In general, trust is more important for larger-ticket items (cars, houses), online sales (since you can’t hold the item before buying it), and things consumers don’t understand well (lawyers, doctors). All of these cases create strong opportunities to screw a consumer over, so there needs to be a corresponding high level of trust.

When not to do it
Do NOT build a brand if you’re going to screw people over. This seems really obvious, but most US airlines, most cell phone carriers, Comcast, and the entire insurance industry apparently do not get it.

Pharma companies, on the other hand, have this one totally nailed down. I have no idea who makes the last few prescription pills I took.

Aside from having a negative-value brand, it’s worth thinking about whether a brand will have zero-ish trust value. For inexpensive items which consumers understand well (or at least think they understand well), trust probably isn’t a big deal, so this kind of branding isn’t going to add much. For instance, people hopefully trust the security of their google accounts more than the security of their yahoo accounts, but trust isn’t all that central to google’s value - they’re not selling confusing, big ticket items.

Four Parables, One Lesson: The Broken Chain Problem

The Emperor’s Nose (Richard Feynman)

A village in a remote corner of an empire decided to erect a statue of the emperor. The village sculptor was hired, but the sculptor had no idea how large to make the emperor’s nose.

The elders conferred. Nobody in the village had ever seen the emperor, nor heard anything about his nose, so they all had wildly different estimates of the size of the emperor’s nose. The elders argued about the right size for hours, until one particularly wise elder stood to address the room.

“Our estimates are too noisy,” the wise elder declared, “In order to improve them, we should employ the wisdom of the crowd. We will ask each person in the village to estimate the length of the emperor’s nose. Then, we can average together the results to obtain an estimate of high precision.”

This proposition was put to a vote, and the elders quickly agreed, eager to end the hours of argument before they missed the early-bird special at the village buffet. The next day, each villager was asked to estimate the length of the emperor’s nose, in millimeters. The elders averaged together all the responses, and estimated the emperor’s nose was 15.49 mm long.

The Cargo Cult (Feynman again)

During World War II, many remote pacific islands became military bases for the American navy. On one such island, the native inhabitants worked with the sailors in exchange for food, clothing and other supplies. All these supplies were flown in by plane, and landed on an airstrip.

After the war, the Americans left the empty airstrip behind. The planes stopped delivering supplies.

The natives wanted to get more supplies. So, they tried to make the planes land. 

They went out to the airstrip and did everything the sailors had done. They lit small, regularly spaced fires along the sides of the airstrip. They had someone sit at the side of the strip talking into a wooden box while wearing pieces of wood shaped to look like headphones. They had others stand on the airstrip and gesture with sticks. In short, they did everything they had seen the sailors do.

But the planes just didn’t land.

The Missing Quarter (Boy Scout tradition)

A boy was pacing back and forth at night under a streetlamp, apparently searching the ground, when another boy passed by.

“What are you looking for?” asked the newcomer.

“My quarter. I dropped it,” replied the searcher.

“Oh. I’ll help you look,” offered the newcomer.

The two continued the search for a minute or so before a third boy came along.

“What are you two looking for?” asked the third.

“A quarter he dropped,” replied the second, indicating the original boy.

“Let me help,” said the third, and set to searching.

This continued for some time, and the crowd grew steadily. Finally, a girl showed up.

“What are you all looking for?” she asked.

“My quarter. I dropped it,” replied the original boy.

“Well where did you drop it?” asked the girl.

“Over there,” said the boy, indicating an area off to the side.

“So why is everybody searching over here?” asked the girl.

“Because there’s more light here,” replied the boy.

The Soviet Nail Factories (Historical/Folklore)

The soviets' central economic planners regularly set targets for each factory under their control. Factories which exceeded their targets were rewarded in various ways. Factories which fell short of their targets… well, it’s the soviets, you can figure it out.

Early on, nail factories each had to produce some number of nails to meet their target. For a while, things went well. Factories produced nails. But there was always an element of competition - the best-performing factories received rewards and the worst-performing were punished, so occasionally people would cut edges in order to get ahead.

In particular, the nail factories found that they could gain an advantage by producing slightly smaller nails than the competition. By producing smaller nails, they could produce a larger number with the same resources. But over time, all the nail factories figured this out, and they had to cheat a little more to gain an edge - the nails became even smaller.

This arms race continued until each factory was producing large numbers of tiny, useless “nails”, better suited to pinboards than to construction.

The central planners heard reports of the tiny nails. They decided to update their targets - henceforth, nail production would be measured by weight, rather than number of nails.

A few years later, all the nail factories were producing just a few giant, useless “nails”, better suited to ballast than to construction.

The Lesson: Don’t Pull a Broken Chain

In everyday life, things are connected by chains of cause and effect. 

Suppose I’m driving along at night when a deer wanders into the road ahead. Light from my headlights reflects off the deer’s hide, into my eyes. The light is absorbed by photoreceptors, which trigger a cascade of electrical signals in my brain. My brain pattern-matches what it sees, and concludes that there’s a deer ahead and hitting it would be bad. The chain of cause and effect links the deer in the road, to me realizing there’s a deer in the road.

Once I realize there’s a deer in the road, electrical signals propagate down my spine to neurons in my leg and foot. Those neurons activate muscles, lifting the foot from gas to brake pedal and then pushing. That force depresses the brake pedal, which applies pressure in a hydraulic system, multiplying the force and eventually squeezing disks connected to the wheels. The increased force on the disks increases friction, slowing the wheels, which in turn slows the car. The chain of cause and effect links my decision to brake, to the car slowing down.

In everyday life, we pull on chains of cause and effect, either to gain information or to influence the world around us. But in each of the four parables above, the chain is broken.

In the story of the emperor’s nose, the elders try to estimate the nose length using statistical techniques… but none of the townspeople know anything at all about the emperor’s nose, so the causal chain from the actual emperor’s nose to the elders’ estimate is broken.

In the story of the cargo cult, the locals mimic the surface actions of sailors at an airstrip, but they don’t understand the underlying chain of cause and effect which led planes to land. Absent that underlying chain, the planes don’t land.

In the story of the missing quarter, the first boy searching under the light causes the second boy to search under the light, and the third, and so on. But the first boy is searching in the wrong place - the chain is broken at the very beginning, even before the story starts. In fact, the first boy himself is pulling on a broken chain: light is helpful for searching, because the light might bounce off the quarter and into the boy’s eye etc. But if the light will never bounce off the quarter - because the quarter isn’t under the light - then that chain is broken.

The Soviet nail factory is the most complicated story. In a normal economy, a nail factory produces an economically valuable nail. That nail is sold, and the nail will only be bought if it’s valuable to the buyer (and the more valuable it is to the buyer, the more the buyer is willing to pay for it). The money from the buyer goes back to the nail maker, and serves as incentive. This chain of cause and effect runs from the nail makers producing an economically valuable nail, to the nail makers being rewarded for whatever value the nail provided for the end user.

But once the central planners step in and set targets in terms of number or weight of nails produced, the chain is broken: the nail makers are no longer rewarded based on the economic value of the nail to its end user. So naturally, the nail makers deprioritize economic value in favor of number or weight of nails. (This is a standard example of Goodhart’s Law: when a measure becomes a target, it ceases to be a good measure. Goodhart’s Law itself is is a special case of the broken chain problem.)

To summarize the lesson: don’t pull a broken chain. When you want to gather information, make sure that the thing you want to know about is causally connected to the thing you’re looking at directly. When you want to influence the world around you, make sure that your action is causally connected to whatever you want to influence. If the causal chain is broken, don’t pull it.

Refutation of Summers' Hypothesis for the CS Gender Gap

Summers' Hypothesis is a widely-cited hypothesis purporting to explain gender spreads in academic/occupational fields, especially STEM fields. The idea is that gender spreads are driven by difference in variance of individual intelligence. Specifically, intelligence variance is higher among males, meaning that more males have either very high or very low intelligence, even though average intelligence is roughly the same across genders.

(The hypothesis is named for Harvard president and US Treasury secretary Larry Summers, who became a liberal pariah shortly after floating the hypothesis in public.)

The key word here is variance. I’ve seen lots of “refutations” of Summers' hypothesis which take a bunch of IQ data, and show that the average is the same (or at least very close) between the two groups. But that’s not actually Summers' hypothesis: the hypothesis states that the variance is different, and that difference explains the gender gap. I’ve never seen any popular media present a correct refutation of the hypothesis, so that’s what we’re going to do here.

We’ll focus on the gender gap in computer science. We’ll compute what gender gap we’d expect based on Summers' hypothesis, then compare that to the real gender gap.

Down to business. To start off, we need three key numbers: IQ variances for males and females, and average IQ for computer scientists.

The average IQ for computer scientists is fairly straightforward: SAT scores do a good job of measuring IQ, and there’s data out there on SAT scores by major. In fact, people have even crunched the numbers already! We’ll use the IQ-by-major estimates here; this source lists an average IQ of 124 for computer and information science majors.

IQ variance for males and females is trickier: it’s been the subject of considerable debate thanks to Summers' hypothesis, so of course people of various political stripes have published heavily-biased “studies” and arguments trying to prove their views. I’ll pull from this study. I like this study for several reasons:

• It uses sibling pairs, so lots of potential confounders are controlled for 
• The sample size is large (~1200 sibling pairs) 
• It draws from the US National Longitudinal Survey for Youth, so it’s fairly representative of the US population 
• The authors are careful to address g-factor specifically 

In short, the study is really carefully done from a technical standpoint.
Anyway, that study found a male intelligence standard deviation about 1.11-1.16 times the female standard deviation, depending on the exact measure used. Also noteworthy: the males had significantly higher variance on all but two subtests. (Difference in mean intelligence was tiny, as expected.)

The next bit involves some math. I’ll omit the calculations, and illustrate what’s going on with a picture:

The picture shows two normal curves. (Intelligence isn’t normally distributed, but it’s a good enough approximation for our purposes.) The taller curve (blue) represents females - I’ve set its standard deviation to 15, which is the usual standard deviation for IQ. The flatter curve (green) represents males - its standard deviation is 1.16 * 15, reflecting the study above.

Right at the mean IQ of 100, the blue curve is noticeably higher - among a sample of people with IQ exactly 100, there should be more females than males (the exact calculation predicts about 16% more). The curves intersect somewhere between 115 and 120, and between 80 and 85. Around these IQ levels, the females and males are about even.

We saw that “computer and information science” majors have an average IQ around 124. At that level, we’d expect about 20% more males than females. Put differently, based only on IQ variance differences, we’d expect about 45.5% of computer and information science majors to be female.

Now, anyone in CS knows that “information science” is a very different field, and those information science folks… well, their reputation isn’t as strong. I suspect that may be dragging down the IQ estimate. So to double-check, I looked here and found an estimated average IQ of 128.5 for computer scientists. At that level, we’d expect about 42% females. Another important factor is that we’re setting female IQ standard deviation to 15 - if we instead set male IQ standard deviation to 15, then we get an estimate of 38% female. This is just a side effect of lazy back-of-the-envelope math; a more careful calculation would be somewhere between the 38% and 42% numbers.

Anyway, Summers' hypothesis seems to predict roughly 38%-45% females in CS, depending on calculation details. What fraction of computer scientists are actually female? According to payscale, computer science is 85% male, 15% female.

So, Summers' hypothesis? Not even close. Differences in IQ variance are nowhere near large enough to account for the gender gap in CS. Other STEM fields are left as an exercise to the reader.

Vision and Academia

Background: I interviewed for Rice University's graduate program in Systems, Synthetic and Physical Biology (SSPB) on Friday. This post presents an initial reaction; I may flesh it out more in a later post.

I just got back from grad school interviews at Rice. Walking between interviews, I noticed that something felt… off. It took a while to put my finger on it, but I realized what was missing: vision.

In the silicon valley start-up scene, everyone wants to take over the world. Every company either wants to revolutionize their industry, or invent an entirely new gazillion-dollar industry, or completely rewire society. At Carlypso, the goal was to radically reduce the overhead of dealing in used cars by building a zero-inventory online dealership. At my current company, the goal is to radically reduce the time and cost of issuing mortgages by a factor of five. In both cases, we explicitly built everything with global market domination in mind.

Whatever the objective may be, a startup is organized around achieving that objective. Whatever the biggest bottleneck is, that’s the biggest business priority. In established industries (like mortgages and used cars), the bottlenecks for your business are usually the same bottlenecks faced by the whole industry. If you’ve chosen the right industry, then the bottlenecks are the sort of things which can be solved by throwing technology and smarts at the problem, and then you’ve got a formula for a viable tech startup.

In industry, you focus on the main bottleneck because you have to. If you don’t, then the business will flounder. But in academia, that impetus isn’t really present.

You can ask a professor what the big vision is, what they’re working toward, and usually they’ll have something to say about it. Maybe it’s understanding how cells process information, or curing cancer, or kicking off the bioengineering revolution. But then you look at their actual projects, and… well, maybe their projects are sort of tangentially related, but they’re usually not the major bottleneck on the path to their supposed goal.

Look at synthetic biology, for instance. What are the major bottlenecks to the field as a whole? Reduction of cycle time would be the number one item on my list (i.e. reduce time required to design gene drive, fabricate a plasmid, introduce it into cells, grow the cells, observe their behavior, and use the observations to inform design of a new gene drive). Another major item would be better chasses, i.e. cell lines which are simple, predictable and grow quickly. How many researchers are working on these problems? Not many, and even then it’s often a side project.

In fact, a lot of the work on these bottlenecks happens at private companies - they know that a better chassis cell line or new machine which accelerates cycle time will make lots of money. But academics don’t really have a motive to focus on the bottlenecks. Bottlenecks are usually not in areas where many professors have existing expertise - that’s partly why they’re bottlenecked in the first place. Funding boards don’t seem to focus much on addressing bottlenecks. In practice, inventing a new method which becomes widely adopted is a great way to make a name in a field, but I don’t think most academics realize there’s an easy way to do that - look at what the major blockers are, and then address those directly.

Coordination Economy

Spreadsheet Parable

Early on during my time at Carlypso, the company had a lot of internal divide. Each afternoon, the marketing guys would post car ads for the next day. But the sales team didn’t know what cars were being advertised, or at what price. So people would call in and say “Hey I saw your ad for a 2012 explorer for $20k, does it have a backup cam?” and the sales guys would be like “Umm…”. We had a hundred explorers available at any given time. Sales had no idea which ones were advertised, or the prices at which they were advertised. Every customer who called in had seen a particular car advertised, but the sales team had no idea which one.

This problem was brought before the dev team. At the time, ads were posted using a few hacked-together python scripts and a lot of excel. The dev team came up with a plan to replace that with a heavily automated ad pipeline, which would record all the ads to our database before posting them. As a separate project, we planned to create a new interface for the sales team to browse our available cars, including the ability to specifically search for cars which had been advertised.

Alas, this solution involved not just one but two significant projects, and the dev team was somewhat dysfunctional on top of that. A month later, neither project had even been started.

One day our project manager, Joe, walked over to the marketing room. He sat down next to Rogue (who usually posted the ads).

“Hey”, Joe asked Rogue, “when you’re ready to post today’s cars, do you think you could copy all the data into a google doc spreadsheet and share it with me?”

“Yeah sure”, replied Rogue, “I have a spreadsheet with all the cars we’re going to post anyway, since that’s the last step before posting. I’ll just copy that into a google sheet and send you the link.”

So Rogue shared the sheet with Joe. Joe sent it along to the sales team. And the next day, the sales team knew exactly which cars had been advertised, and at what price. The sales team was ecstatic. From then on, Rogue sent the spreadsheet directly to the sales team each day. For months, that was the system. It wasn’t perfect, but it fixed 80% of the problem with five minutes of work and without writing a single line of code.

Economic Bottleneck

What is the most significant bottleneck in the modern economy?

As a first approximation, there’s an easy way to answer this question: look at what sorts of activity are worth the most money. All else equal, the most money will flow to people in very high demand and very short supply, a.k.a. people who directly address the largest economic bottlenecks.

I’ve written about this before; the general pattern is that large amounts of money go to people who solve coordination problems. Entrepreneurs, upper management, investment bankers, real estate developers… pretty much anyone who makes the big dollars is primarily in the business of coordinating people. Upper management coordinates between departments and teams within a company, or between varies parties in a supply chain. Entrepreneurs coordinate between investors, employees, suppliers, customers and regulators. Investment bankers coordinate between multiple companies, and between investors and companies. But the central pattern is the same: it’s all about coordination.

Furthermore, this applies in almost every industry. No matter where you go, the same pattern applies: it’s the coordinators who make the money.

But now let’s go back to the economic bottleneck question. If the big money goes to the people who solve coordination problems, then that strongly suggests that coordination problems are the central economic bottleneck in almost every industry today. Think of it like revealed preference: if you’re willing to pay more for steak than for chicken, then presumably you prefer steak to chicken (or at least, one more steak over one more chicken). If the economy as a whole pays dramatically more for a coordinator than practically anyone else, then presumably a coordinator is worth more. In other words, coordination problems are the central economic bottleneck.

Everyday Application

Think about what this means for everyday business. Whatever business you’re in, whatever company you’re at, the primary bottlenecks at your business are probably coordination problems.

Once you start looking for this, you see it everywhere. Consider the story above, about Joe and the spreadsheet. Joe asked Rogue to send a spreadsheet of cars advertised out to the sales team. That took five minutes of effort on Joe’s part, and solved a major business problem. It may very well have been the highest value-per-minute work which Joe ever did at Carlypso. All it took was to notice a coordination problem, and solve it in the simplest possible way.

So, if you want to add lots of value to your current company, then the natural starting place is to look around for coordination problems. Here are some starting points:

• Is there information which some people have and other people need? This is particularly relevant for software teams, since this is the main type of coordination problem which can be solved by software. There are three subtypes to this kind of problem:
• Within the company, do some people have information which other people need? This was the case with the Carlypso example.
• Is there information available from outside the company which is needed inside? In software, this is usually solved by integrating internal tools with an external API. Sometimes the problem can be solved just letting people inside the company know where to find the information.
• Does information need to move between two external parties? Often, entire companies exist solely for the purpose of collecting information from some people and presenting it to others.

When building these sort of information pipes, the first and most important step is just getting the pipe in place; that’s often an 80% solution. The other 20% is the next item...

• Are there communication difficulties? I.e., is information flowing from A to B but being presented in a way which is hard to understand/use? This problem can range from poor conversational skills, to different people using different jargon, to the entire field of user interface design. Communication difficulties are often most noticeable between people with different specializations, discussed next.
• Are different specialized groups supporting each other as needed? A couple common examples:
• Do software developers understand the needs of whatever people they’re writing software for?
• When a product or customer is passed between groups in a pipeline (i.e. lead to sales, order to fulfillment, etc), is any information lost? Is the receiving group aware of any special conditions? Is there a long wait time between groups?

One general rule: when tackling these sorts of problems, avoid playing telephone. For example, it’s tempting to have a product manager research the needs of software users, and then write up exact specs for the developers… but we’ve all played telephone before. Things ALWAYS get garbled. To avoid telephone, communicate goals rather than specs as much as possible. In the product manager example, a spec is useful, but more important is the reasoning behind the spec… if the developers know WHY the spec is designed this way, if they understand the goals driving it, then things will be much less garbled.

• Are people working toward different goals? This one is often a balancing act, since most managers instinctively want to push everyone into line, but that’s only valuable to the extent that the one line is pointing the right way. Often, it’s more valuable to have people pursue different directions, since there’s a higher probability that one of them will hit on a really good direction. That said, when different groups of specialists need to coordinate to achieve a goal, then it really is important to make sure everyone sees the same goal… you don’t want one group building a square peg and another group building a round hole.

Godel's Construction for Humans

Part I: Setup

One day, our favorite neighborhood superintelligent game-theoretic agent Omega sits me down and says “John, let’s play a game.”

“I’ve written a simulation of you,” says Omega, “and before we get to the main game, I need to calibrate it. There’s a few parameters which need to be matched in order to properly simulate you.”

“Ok,” I reply, “What do I need to do?”

“I need you to prove this theorem,” says Omega, “while you work on proving it, I will simulate you proving the theorem, and make sure that the simulation output matches your own proof.” She hands me a piece of paper which (translated from math to english) reads “There exist infinitely many prime numbers.”

This is a classic problem, so I pull out my pencil and quickly write down a simple proof. When I’m done, Omega checks the paper, then checks her computer, and smiles.

“The simulation matches!” Omega announces. “All of the parameters fit, and now we can perfectly simulate you. Now, while I set up the main game...” Omega hands me few pages of paper.

Part II: Introspection

“Read through that carefully,” says Omega, “It contains a full specification of the simulation of you.” She hands me one more piece of paper. “These are the parameters we just calibrated, so now you have everything needed to run a simulation of yourself.”

I look at the papers and frown. It’s shorter than I would have liked.

I start flipping through. Omega’s models are, as usual, quite elegant. Looking at the fifth page, I grab a piece of mail off the table and run a quick back-of-the-envelope calculation. The result outlines a dream I had the night before with tiny multicolored lobsters pinching at my feet. Another calculation predicts that my blood sugar is a bit low… I grab a granola bar from my bag, then redo the calculation with time advanced by twenty minutes.

After I finish reading, I decide to try a slightly more complicated calculation. I check back a few pages, and find what I’m looking for: the specification for an infinite lazy data structure which encodes me, calculating a simulation of myself calculating a simulation of myself calculating a simulation of myself calculating…

“Ready!” says Omega, breaking my infinite regress. “Have you figured out that simulation specification?”

“I think so,” I reply, “it’s surprisingly understandable. Very elegant.”

“Thank you,” replies Omega. “On to the main game!”

Part III: The Game

Omega hands me another single sheet of paper. “Please prove this theorem,” she says.

I look at the sheet. It shows a data structure which refers back to the me-simulation spec. I flip back and forth for a minute, decoding the contents of the new paper, until I realize what it says:

“John cannot prove this theorem.”

I stop. It’s an impressive piece of work. First, a full, perfect mathematical specification of myself. Then, a shorter statement claiming that, based on the mathematical specification of me, I cannot prove the theorem. If I do prove the theorem, then I’ve proven that I can’t do it…

Wait! Technically, this just claims that the *simulation* of me can’t prove the theorem. So if the simulation is inaccurate, I might still be able to - I slap my forehead. No, this is Omega I’m dealing with. She’s scrupulously honest, and her simulations have never once been wrong. This is an accurate specification of me.

For all intents and purposes, I’m dealing with a copy of myself. If I can prove this theorem, then so can the simulation. But the statement says “John cannot prove this theorem.” If it’s false, then I *can* prove it, but then I’d be proving something false, so my proof would be wrong, so the theorem would be true… And if it’s true, then I can’t prove it.

I grumble a bit. It’s a classic diagonalization gambit. There’s no way I can prove this theorem… unless...

Part IV: Breaking Out

The only way I can prove this theorem is if I can somehow make the simulation *not* match myself. I mean, the simulation specifies a perfect copy of me, but if I could use some information which the simulation doesn’t have… Smiling slightly, I reach into my pocket, and withdraw a q-coin.

“A quantum random coin,” says Omega, “very clever.”

I catch a hint of sarcasm. “You knew full well I was going to use this, didn’t you?”

“Of course,” replies Omega, “The simulation is also using a q-coin. You haven’t actually diverged from it yet.”

“But once I flip this, I will,” I say, “It’s perfect randomness. The simulation can predict that I’ll flip it, and it can even simulate all possible outcomes, but it won’t know which outcome I actually get.”

Omega smiles as I flip the q-coin. Heads. I flip it again. Tails. I keep flipping. Heads-heads-heads-heads-tails-heads-tails…

Eventually, I turn back to the math. Sure enough, the simulation specifies a full distribution over all possible outcomes of the coin flip. I start to think about how to finally prove that theorem…

“Crap,” I say.

“Yup,” replies Omega.

“I’ve diverged from the simulation, but those coin flips don’t actually have a significant causal impact on my ability to prove the theorem. The theorem-proving part of the system isn’t chaotic enough to be affected by coin flips. There’s a whole distribution in there for the outcome of the flips, but that distribution isn’t relevant to theorem-proving.”

I lean back and close my eyes. If I want the coin-flips to affect theorem-proving, then I need some way to leverage randomness of the flips in the proof itself...

The Hierarchy of the Sciences

There is an intuitive sense among scientists that an hierarchy exists in the sciences. It looks roughly like this:

The hierarchy is fuzzier than drawn, especially among the “soft” sciences. I'm not going to bother perfecting the diagram; just keep in mind it’s not perfect.

This hierarchy pops up in a lot of different ways. This xkcd, for example, expresses the hierarchy in terms of “purity”. In practice, there’s a lot more to it than just aesthetics - the hierarchy of the sciences has both historical causes and real social consequences.

Social Status

I once heard a biologist give a tangential parable about physicists in a talk. Physicists, he said, are like cowboys. Every now and then, a gang of physicists rides into your field, whooping and hollering, shoots holes in all your theories, and then rides off into the sunset.

Practitioners sometimes joke about the hierarchy of sciences the way xkcd does. What we usually avoid talking about directly is the social side - though most are loathe to admit it, the hierarchy of the sciences reflects a real status hierarchy among scientists. Physicists do not tell parables about biologists shooting holes in their theories. Or chemists. Or economists. But mathematicians… mathematicians have been known to shoot holes in the work of physicists.

In general, fields frequently contribute results to fields below theirs on the hierarchy. Mathematicians contribute useful results to all of the scientific fields, but other scientists contribute new math much less often. Physicists have established subfields within lower sciences - think biophysics or econophysics - but you don’t hear much about biologists or psychologists contributing new results to physics. This pattern mostly holds up further down the hierarchy.

Occasionally, people will contribute to a field immediately above theirs - physicists discover new theorems, chemists break ground in physics - but one rarely hears about people contributing to fields two levels or more above their own. Indeed, I recall one instance where a biologist rediscovered a major theorem of statistics, a biology journal published it as a new tool, and then everyone was soundly mocked by mathematicians for not knowing statistics 101.

(Note: Philosophers do not have any real status in the sciences. They are drawn at the top of the hierarchy in much the same way you’d tell a four-year-old that they get to be ship captain for a day, then let them stand on the bridge and give “orders”.)

“Real Science”

There’s a sense in which some sciences have matured into “real science”, an intuitive dividing line. On one side are fields like chemistry or physics,  where the existing theory is mathematically precise and experimentally powerful and generalizable and will always be useful even as new theory evolves. On the other side are fields like psychology and economics, where theories lack mathematical precision and/or experimental validity and don’t generalize and have limited utility. Some people use the terms “hard” and “soft” sciences to describe these.

Historically, everything started out “soft”. The line dividing “real sciences” has shifted over time, as chemistry evolved from phlogiston to the periodic table, and biology evolved from elan vital to today’s state of affairs. As far as I can tell, the “real science” dividing line today looks something like this:

As the dotted line suggests, I’ve heard a general sentiment among many people (including myself) that biology today is the frontier of real science; biology is currently midway through a transformation from ad-hoc theory to an experimentally robust, mathematically precise field. I recall the first session in MIT’s intro biology course, in which the lecturer spent about half the class saying “look, you probably don’t think biology is a real science, and the biology you learned in high school isn’t… but a lot of that stuff is out of date, and you’re going to find that the field has come a long way.” It’s an exciting time to be in biology.

(If you’re still not sure whether the scientific hierarchy actually reflects social status, then try telling both a physicist and a biologist that their fields are not “real science”, and see how they react. Better yet, don’t try this.)

Engineering and Applied Disciplines

One good way to recognize which fields have matured into “real science” is to look for corresponding engineering disciplines. Once a scientific field has reached maturity, its theory is robust and useful enough that engineers start to adopt it, and new engineering fields are born. This creates an hierarchy of engineering, in parallel to the scientific hierarchy:

Again, it’s an exciting time to be in biology, as biology’s first real engineering field is just starting off.

One of the things which surprised me in college was the social status hierarchy in engineering, which to some degree reflects the hierarchy in the sciences. Anecdotally, the salaries of my classmates in computer science/EE/ME/Materials/Chem E seem to follow the hierarchy.

The Engineering Frontier

The absence of any engineering fields corresponding to the fields lower on the hierarchy is one of the main ways to tell they’re still below the “real science” dividing line. The soft sciences have not yet matured enough to support robust engineering. However, we can speculate on which fields will likely become engineering-type fields once the corresponding sciences mature enough to support them. This results in a “real science and engineering” frontier:

This diagram has all sorts of interesting space for speculation. It’s generally assumed that, as biology becomes a real science, medicine will become a real, robust engineering field. More interesting possibilities exist in finance and marketing (and other areas) - imagine what these fields will look like once sufficiently robust scientific theories are available to underpin them! And then there’s sociology… at this point, it’s hard to even imagine what the engineering applications of robust sociological theory might actually look like, but it would involve engineering of society and culture. Perhaps the memetic equivalent of genetic engineering? Memetic engineering?

Then there’s AI. AI is squarely on the “real science and engineering” boundary right now. As an engineering field, it corresponds to the more philosophically rich areas of mathematics, ripe with issues like self-reference, logical completeness, and the deceptively difficult mathematical/ethical question of how to formulate an AI’s objective.