# Talk at SIAM Annual Meeting 2017

I gave an invited plenary talk at the 2017 Society of Applied and Industrial Mathematics Annual Meeting in Pittsburgh yesterday. My slides are here. I talked about some very new work on chaos and learning in spiking neural networks. My fellow Chris Kim and I were producing graphs up to a half hour before my talk! I’m quite excited about this work and I hope to get it published soon.

During my talk, I made an offhand threat that my current Mac would be the last one I buy. I made the joke because it was the first time that I could not connect to a projector with my laptop since I started using Mac almost 20 years ago. I switched to Mac from Linux back then because it was a Unix environment where I didn’t need to be a systems administrator to print and project. However, Linux has made major headway in the past two decades while Mac is backsliding. So, I’m seriously thinking of following through. I’ve been slowly getting disenchanted with Apple products over the past three years but I am especially disappointed with my new MacBook Pro. I have the one with the silly touch screen bar. The first thing the peeves me is that the activate Siri key is right next to the delete key so I accidentally hit and then have to reject Siri every five minutes. What mostly ties me to Mac right now is the Keynote presentation software, which I like(d) because it is easy to embed formulas and PDF files into. It is much harder to do the same in PowerPoint and I haven’t found an open source version that is as easy to use. However, Keynote keeps hanging on my new machine. I also get this situation where my embedded equations will randomly disappear and then reappear. Luckily I did a quick run through just before my talk and noticed that the vanished equations reappeared and I could delete them. Thus, the Keynote appeal has definitely diminished. Now, if someone would like to start an open source Keynote project with me… Finally, the new Mac does not seem any faster than my old Mac (it still takes forever to boot up) and Bard Ermentrout told me that his dynamical systems software tool XPP runs five times slower. So, any suggestions for a new machine?

# AlphaGo and the Future of Work

In March of this year, Google DeepMind’s computer program AlphaGo defeated world Go champion Lee Sedol. This was hailed as a great triumph of artificial intelligence and signaled to many the beginning of the new age when machines take over. I believe this is true but the real lesson of AlphaGo’s win is not how great machine learning algorithms are but how suboptimal human Go players are. Experts believed that machines would not be able to defeat humans at Go for a long time because the number of possible games is astronomically large, $\sim 250^{150}$ moves, in contrast to chess with a paltry $\sim 35^{80}$ moves. Additionally, unlike chess, it is not clear what is a good position and who is winning during intermediate stages of a game. Thus, any direct enumeration and evaluation of possible next moves as chess computers do, like IBM’s Deep Blue that defeated Gary Kasparov, seemed to be impossible. It was thought that humans had some sort of inimitable intuition to play Go that machines were decades away from emulating. It turns out that this was wrong. It took remarkably little training for AlphaGo to defeat a human. All the algorithms used were fairly standard – supervised and reinforcement backpropagation learning in multi-layer neural networks1. DeepMind just put them together in a clever way and had the (in retrospect appropriate) audacity to try.

The take home message of AlphaGo’s success is that humans are very, very far away from being optimal at playing Go. Uncharitably, we simply stink at Go. However, this probably also means that we stink at almost everything we do. Machines are going to take over our jobs not because they are sublimely awesome but because we are stupendously inept. It is like the old joke about two hikers encountering a bear and one starts to put on running shoes. The other hiker says: “Why are you doing that? You can’t outrun a bear.” to which she replies, “I only need to outrun you!” In fact, the more difficult a job seems to be for humans to perform, the easier it will be for a machine to do better. This was noticed a long time ago in AI research and called Moravec’s Paradox. Tasks that require a lot of high level abstract thinking like chess or predicting what movie you will like are easy for computers to do while seemingly trivial tasks that a child can do like folding laundry or getting a cookie out of a jar on an unreachable shelf is really hard. Thus high paying professions in medicine, accounting, finance, and law could be replaced by machines sooner than lower paying ones in lawn care and house cleaning.

There are those who are not worried about a future of mass unemployment because they believe people will just shift to other professions. They point out that a century ago a majority of Americans worked in agriculture and now the sector comprises of less than 2 percent of the population. The jobs that were lost to technology were replaced by ones that didn’t exist before. I think this might be true but in the future not everyone will be a software engineer or a media star or a CEO of her own company of robot employees. The increase in productivity provided by machines ensures this. When the marginal cost of production goes to zero (i.e. cost to make one more item), as it is for software or recorded media now, the whole supply-demand curve is upended. There is infinite supply for any amount of demand so the only way to make money is to increase demand.

The rate-limiting step for demand is the attention span of humans. In a single day, a person can at most attend to a few hundred independent tasks such as thinking, reading, writing, walking, cooking, eating, driving, exercising, or consuming entertainment. I can stream any movie I want now and I only watch at most twenty a year, and almost all of them on long haul flights. My 3 year old can watch the same Wild Kratts episode (great children’s show about animals) ten times in a row without getting bored. Even though everyone could be a video or music star on YouTube, superstars such as Beyoncé and Adele are viewed much more than anyone else. Even with infinite choice, we tend to do what our peers do. Thus, for a population of ten billion people, I doubt there can be more than a few million that can make a decent living as a media star with our current economic model. The same goes for writers. This will also generalize to manufactured goods. Toasters and coffee makers essentially cost nothing compared to three decades ago, and I will only buy one every few years if that. Robots will only make things cheaper and I doubt there will be a billion brands of TV’s or toasters. Most likely, a few companies will dominate the market as they do now. Even, if we could optimistically assume that a tenth of the population could be engaged in producing goods and services necessary for keeping the world functioning that still leaves the rest with little to do.

Even much of what scientists do could eventually be replaced by machines. Biology labs could consist of a principle investigator and robot technicians. Although it seems like science is endless, the amount of new science required for sustaining the modern world could diminish. We could eventually have an understanding of biology sufficient to treat most diseases and injuries and develop truly sustainable energy technologies. In this case, machines could be tasked to keep the modern world up and running with little need of input from us. Science would mostly be devoted to abstract and esoteric concerns.

Thus, I believe the future for humankind is in low productivity occupations – basically a return to pre-industrial endeavors like small plot farming, blacksmithing, carpentry, painting, dancing, and pottery making, with an economic system in place to adequately live off of this labor. Machines can provide us with the necessities of life while we engage in a simulated 18th century world but without the poverty, diseases, and mass famines that made life so harsh back then. We can make candles or bread and sell them to our neighbors for a living wage. We can walk or get in self-driving cars to see live performances of music, drama and dance by local artists. There will be philosophers and poets with their small followings as they have now. However, even when machines can do everything humans can do, there will still be a capacity to sustain as many mathematicians as there are people because mathematics is infinite. As long as P is not NP, theorem proving can never be automated and there will always be unsolved math problems.  That is not to say that machines won’t be able to do mathematics. They will. It’s just that they won’t ever be able to do all of it. Thus, the future of work could also be mathematics.

1. Silver, D. et al. Mastering the game of Go with deep neural networks and tree search. Nature 529, 484–489 (2016).

# The simulation argument made quantitative

Elon Musk, of Space X, Tesla, and Solar City fame, recently mentioned that he thought the the odds of us not living in a simulation were a billion to one. His reasoning was based on extrapolating the rate of improvement in video games. He suggests that soon it will be impossible to distinguish simulations from reality and in ten thousand years there could easily be billions of simulations running. Thus there are a billion more simulated universes than real ones.

This simulation argument was first quantitatively formulated by philosopher Nick Bostrom. He even has an entire website devoted to the topic (see here). In his original paper, he proposed a Drake-like equation for the fraction of all “humans” living in a simulation:

$f_{sim} = \frac{f_p f_I N_I}{f_p f_I N_I + 1}$

where $f_p$ is the fraction of human level civilizations that attain the capability to simulate a human populated civilization, $f_I$ is the fraction of these civilizations interested in running civilization simulations, and $N_I$ is the average number of simulations running in these interested civilizations. He then argues that if $N_I$ is large, then either $f_{sim}\approx 1$ or $f_p f_I \approx 0$. Musk believes that it is highly likely that $N_I$ is large and $f_p f_I$ is not small so, ergo, we must be in a simulation. Bostrom says his gut feeling is that $f_{sim}$ is around 20%. Steve Hsu mocks the idea (I think). Here, I will show that we have absolutely no way to estimate our probability of being in a simulation.

The reason is that Bostrom’s equation obscures the possibility of two possible divergent quantities. This is more clearly seen by rewriting his equation as

$f_{sim} = \frac{y}{x+y} = \frac{y/x}{y/x+1}$

where $x$ is the number of non-sim civilizations and $y$ is the number of sim civilizations. (Re-labeling $x$ and $y$ as people or universes does not change the argument). Bostrom and Musk’s observation is that once a civilization attains simulation capability then the number of sims can grow exponentially (people in sims can run sims and so forth) and thus $y$ can overwhelm $x$ and ergo, you’re in a simulation. However, this is only true in a world where $x$ is not growing or growing slowly. If $x$ is also growing exponentially then we can’t say anything at all about the ratio of $y$ to $x$.

I can give a simple example.  Consider the following dynamics

$\frac{dx}{dt} = ax$

$\frac{dy}{dt} = bx + cy$

$y$ is being created by $x$ but both are both growing exponentially. The interesting property of exponentials is that a solution to these equations for $a > c$ is

$x = \exp(at)$

$y = \frac{b}{a-c}\exp(at)$

where I have chosen convenient initial conditions that don’t affect the results. Even though $y$ is growing exponentially on top of an exponential process, the growth rates of $x$ and $y$ are the same. The probability of being in a simulation is then

$f_{sim} = \frac{b}{a+b-c}$

and we have no way of knowing what this is. The analogy is that you have a goose laying eggs and each daughter lays eggs, which also lay eggs. It would seem like there would be more eggs from the collective progeny than the original mother. However, if the rate of egg laying by the original mother goose is increasing exponentially then the number of mother eggs can grow as fast as the number of daughter, granddaughter, great…, eggs. This is just another example of how thinking quantitatively can give interesting (and sometimes counterintuitive) results. Until we have a better idea about the physics underlying our universe, we can say nothing about our odds of being in a simulation.

Addendum: One of the predictions of this simple model is that there should be lots of pre-sim universes. I have always found it interesting that the age of the universe is only about three times that of the earth. Given that the expansion rate of the universe is actually increasing, the lifetime of the universe is likely to be much longer than the current age. So, why is it that we are alive at such an early stage of our universe? Well, one reason may be that the rate of universe creation is very high and so the probability of being in a young universe is higher than being in an old one.

Addendum 2: I only gave a specific solution to the differential equation. The full solution has the form $Y_1\exp(at) + Y_2 \exp(ct)$.  However, as long as $a >c$, the first term will dominate.

Addendum 3: I realized that I didn’t make it clear that the civilizations don’t need to be in the same universe. Multiverses with different parameters are predicted by string theory.  Thus, even if there is less than one civilization per universe, universes could be created at an exponentially increasing rate.

# What Uber doesn’t get

You may have heard that ride hailing services Uber and Lyft have pulled out of Austin, TX because they refuse to be regulated. You can read about the details here. The city wanted to fingerprint drivers, as they do for taxis, but Uber and Lyft forced a referendum on the city to make them exempt or else they would leave. The city voted against them. I personally use Uber and really like it but what I like about Uber has nothing to do with Uber per se or regulation. What I like is 1) no money needs to be exchanged especially the tip and 2) the price is essentially fixed so it is in the driver’s interest to get me to my destination as fast as possible. I have been taken on joy rides far too many times by taxi drivers trying to maximize the fare and I never know how much to tip. However, these are things that regulated taxis could implement and should implement. I do think it is extremely unfair that Uber can waltz into a city like New York and compete against highly regulated taxis, who have paid as much as a million dollars for the right to operate. Uber and Lyft should collaborate with existing taxi companies rather than trying to put them out of business. There was a reason to regulate taxis (e.g. safety, traffic control, fraud protection), and that should apply whether I hail a cab on the street or I use a smartphone app.

# Worst machine in the world

I really hate leaf blowers. I think they are a huge waste of energy. They mostly make noise and heat and perform a task that perfectly good tools (i.e. broom and rake) can already do extremely well.  I don’t believe they save much time. (Yes, I have raked a lawn full of leaves before.)

# Phasers on stun

The recent controversy over police shootings of unarmed citizens has again stirred up the debate over gun control. However, Shashaank Vattikuti points out that there is another option and that is for the police to carry nonlethal weapons like phasers with a stun option. Although, an effective long range nonlethal weapon currently does not exist (tasers just don’t cut it), a billionaire like Mark Zuckerberg, Peter Thiel, or Elon Musk could start a company to develop one. New York Times columnist Joe Nocera has suggested that Michael Bloomberg buy a gun company. There are so many guns already in existence that barring an unlikely confiscation scheme there is probably no way to get rid of them. The only way to reduce gun violence at this point is for a superior technology to make them obsolete. Hobbyists and collectors would still own guns, just as there are sword collectors, but those who own guns for protection would probably slowly switch over. However, the presence of a nonlethal option could lead to more people shooting each other so strong laws regarding their use would need to accompany their introduction.

# Are we in a fusion renaissance?

Fusion is a potentially unlimited source of non-carbon emitting energy. It requires the mashing together of small nuclei such as deuterium and tritium to make another nucleus and a lot of leftover energy. The problem is that nuclei do not want to be mashed together and thus to achieve fusion you need something to confine high energy nuclei for a long enough time. Currently, there are only two methods that have successfully demonstrated fusion: 1) gravitational confinement as in the center of a star, and 2) inertial confinement as in a nuclear bomb. In order to get nuclei at high enough energy to overcome the energy barrier for a fusion reaction, electrons can no longer be bound to nuclei to form atoms. A gas of quasi-neutral hot nuclei and electrons is called a plasma and has often been dubbed the fourth state of matter. Hence, the physics of fusion is mostly the physics of plasmas.

My PhD work was in plasma physics and although my thesis ultimately dealt with chaos in nonlinear partial differential equations, my early projects were tangentially related to fusion. At that time there were two approaches to attaining fusion, one was to try to do controlled inertial confinement by using massive lasers to implode a tiny pellet of fuel and the second was to use magnetic confinement in a tokamak reactor. Government sponsored research has been focused almost exclusively on these two approaches for the past forty years. There is a huge laser fusion lab at Livermore and an even bigger global project for magnetic confinement fusion in Cadarache France, called ITER. As of today, neither has proven that they will ever be viable sources of energy although there is evidence of break even where the reactors produce more energy than is put in.

However, these approaches may not ultimately be viable and there really has not been much research funding to pursue alternative strategies. This recent New York Times article reports on a set of privately funded efforts to achieve fusion backed by some big names in technology including Paul Allen, Jeff Bezos and Peter Thiel. Although there is well deserved skepticism for the success of these companies,  (I’m sure my thesis advisor Abe Bers would have had some insightful things to say about them), the time may be ripe for new approaches. In an impressive talk I heard many years ago, roboticist Rodney Brooks remarked that Moore’s Law has allowed robotics to finally be widely available because you could use software to compensate for hardware. Instead of requiring cost prohibitive high precision motors, you could use cheap ones and use software to control them. The hybrid car is only possible because of the software to decide when to use the electric motor and when to use the gas engine. The same idea may also apply to fusion. Fusion is so difficult because plasmas are inherently unstable. Most of the past effort has been geared towards designing physical systems to contain them. However, I can now imagine using software instead.

Finally, government attempts have mostly focused on using a Deuterium-Tritium fusion reaction because it has the highest yield. The problem with this reaction is that it produces a neutron, which then destroys the reactor. However, there are reactions that do not produce neutrons (see here). Abe used to joke that that we could mine the moon for Helium 3 to use in a Deuterium-Helium 3 reactor. So, although we may never have viable fusion on earth, it could be a source of energy on Elon Musk’s moon base, although solar would probably be a lot cheaper.