How simulating social networks revealed why I have no friends, and also no free time

The friendship paradox is an observed social phenomenon that most people have fewer friends than their friends have, on average. Sometimes it is stated more strongly that most people have fewer friends than *most* of their friends. It’s not clear from the popular articles about the topic whether the latter statement is generally true. Let’s investigate!

I would have thought this would be difficult to determine, and perhaps this is why it took until 1991 for someone to discover it. In Scott Feld’s original paper, Why your friends have more friends than you do, he suggested that this might be a source of feelings of inadequacy. But, I mean, it’s not like people keep tallies of each of their friend’s friends, let alone a list of their own friends, do they? This was probably true in 1991, but now in the age of Facebook we can do this with ease — and probably a lot of people do. 

How many faces are in my book

In fact, why not, I’ll have a go. I have 374 friends on Facebook. I’m not sure why. Anyway, let’s take 10 random friends and count the number of friends they have. Here’s the tally:

Friend 1 - 522
Friend 2 - 451 
Friend 3 - 735
Friend 4 - 397
Friend 5 - 2074
Friend 6 - 534
Friend 7 - 3607
Friend 8 - 237
Friend 9 - 1171
Friend 10 - 690

The average number of friends these friends have is 1042. So I have fewer friends than my friends have, on average. Also, of these 10, I have fewer friends than all but one of them — poor friend number 8. 

Okay, but this is not a paradox — especially if you know me. How about we look at someone else in my network, say Friend 2. Friend 2 has 451 friends, and because Facebook is such a secure website that naturally preserves the privacy of its users, we can click on profiles of the friends of Friend 2 to find out how many friends they have. The numbers of friends that 10 random friends of Friend 2 have are: 790, 928, 383, 73, 827, 1633, 202, 457, 860, and 121. On average, Friend 2’s friends have 627 friends, which is more than 451. Also, six of these friends have more than 451 friends and so Friend 2 has fewer friends than most of their friends as well. If we repeated this exercise for all of my friends, we would still find that most of them have fewer friends than their friends even though most already have more friends than me!

You probably have a gut feeling that this is paradoxical. My intuition for why it feels paradoxical comes from the following analogy. Consider your height. Perhaps you are shorter than average. Maybe you have some friends that are also shorter than average. But, you expect to find at least half the people out that are actually taller than average. That’s kind of the intuition of “average” after all. Why isn’t the same true for friends, then? That is, even though myself and Friend 2 have fewer friends than our friends, surely those people out there with lots of friends have more friends than their friends. This is true, but these popular people are extremely rare, and that is the difference between friend numbers and height, for example. 

In a typical social network there are lots of people with few friends and few people with lots of friends. The very popular people are counted in many people’s friend circles. And, the unpopular people are not counted in many friend circles. Take my Facebook friendship as an example again. I have, apparently, few Facebook friends. So, it would seem that many people have more friends than me. But — and here is the most important point — those people are unlikely to count me and my low number of friends in their friend circles. This is evidenced by the fact that Friend 2 and I only have 2 friends in common. So all of those friends of Friend 2, when they go to count the number of friends their own friends have, aren’t going to have me and my low friend count skewing the distribution in their favor. 

Is this why the “karate kid” was such a loner?

Let’s look at some smaller examples where we can count everyone and their friends in the network. The most famous social network (at least to network theorists) is Zachary’s karate club. It looks like this.

Zachary’s karate club. Node colors guide the eye and are marked based on the number of friends each person has.

(At this point I’d like to quickly mention that this post is duplicated in a Jupyter notebook which you can play with on Google Colab.)

This shows 34 people in a karate club (circa 1970) and who they interacted with outside class. Colors simply guide the eye to how many friends each member has. You can see one person only has 1 friend and another has a whopping 17! Already this graph is too big to count things by hand, but a computer can step through each node in the network and count the friends and the friends of friends. In Zachary’s karate club, then, we have,

The fraction of people with fewer friends than their friends have on average is 85.29%.

The fraction of people with fewer friends than most of their friends is 70.59%.
Histogram of friends and friends of friends in Zachary’s karate club. The data is collected by looking at the friends of each friend for every person in the network. The distribution of those friends can be summarized by the mean and median. For each friend of each person, those numbers are tabulated and plotted in the lower row.

The above histograms show the data in detail. You can see the key feature again of a few people with lots of friends. Obviously those few people are going to have more friends than their friends have. But that’s the point — there are only a few such people! Once we look at the full distribution of “friends of friends” we find it flattens out significantly, and it is more likely to find a large number of friends. The lower two histograms show the mean and median number of friends of each person in the network. Note that in either case, each person has friends with roughly 9 friends. This much more than the vast majority of people in the network! Indeed, only 4 people out of 34 have more than 9 friends. 

Go big or go… actually it doesn’t seem to matter how big we go

Now let’s go back to Facebook. This time we’ll use data collected from ten individuals, anonymized and made public. It includes roughly 4000 people connected to these 10 individuals in various social circles. The social network looks like this.

The Facebook Ego Graph, showing community structure and clustering around popular individuals.

We can do the counting of friends and friends of friends for this network as well. The details look like this.

Histogram of friends and friends of friends in the Facebook Ego Graph. The data is collected by looking at the friends of each friend for every person in the network. The distribution of those friends can be summarized by the mean and median. For each friend of each person, those numbers are tabulated and plotted in the lower row.

In summary, we find,

The fraction of people with fewer friends than their friends have on average is 87.47%.

The fraction of people with fewer friends than most of their friends is 71.92%.

Very similar! But perhaps this is just a coincidence. It’s only two data points after all. How do we test the idea for any social network? Simulation!

Fake it ’til you make it

Simulation is a tool to understand something by way of studying scale models of it. A model airplane wing in a wind tunnel is a classic example. Today, many simulations are done entirely on computers. In the context of social networks there are many models, but out of sheer laziness we will choose the so-called Barabási–Albert model because it is already implement in NetworkX, the computer package I’m using. If we create a mock social network of 34 people (same number as the karate club), it will look something like this.

An instance of the Barabási–Albert model on 34 nodes. It is constructed node by node, connecting each new node to two previous nodes, with a preference for highly connected nodes. This is a example social network.

It doesn’t look all that much different from the karate club, does it? The numerical data are similar as well.

Histogram of friends and friends of friends in the example Barabási–Albert model graph above. The data is collected by looking at the friends of each friend for every person in the network. The distribution of those friends can be summarized by the mean and median. For each friend of each person, those numbers are tabulated and plotted in the lower row.

In this example, the numbers of interest are,

The fraction of people with fewer friends than their friends have on average is 79.41%.

The fraction of people with fewer friends than most of their friends is 70.59%.

This is nice, but the real beauty of simulation is the ability to rapidly test multiple examples. The above is just one mock social network. To get full confidence in our conclusion (relative to the assumptions of the model of course), we need to perform many simulations over randomly generated social networks.

Simulate all the graphs!

If we repeat the above exercise over 10,000 random social networks with 34 individuals, we find,

The fraction of people with fewer friends than their friends have on average is 79.31%.

The fraction of people with fewer friends than most of their friends is 65.31%.

So now we can say with some confidence that the friend paradox persists in any social network — at least one that has the same characteristics as the Barabási–Albert model with 34 people. Another thing we can easily do though is change the number of people in the network to see if the trend continues for large networks. Indeed, things get much worse if we increase the number of people. As the number of people in the social network increases, the fraction of people with fewer friends than their friends (in majority or on average) also increases.

The friendship paradox demonstrated over 100 randomly chosen social networks created with the Barabási–Albert model, for increasing network size.

Cool, cool. Anything less depressing to tell us?

It’s been shown that this paradox goes beyond friends as well. You are also probably deficient, when comparing yourself to your friends, in income, Twitter followers, and how happy you are — and this fact is probably not helping. But, okay, enough of this crap — we all feel terrible now! Surely there is something positive we can glean from all this, right? Yes! 

Since your friends have more contacts than you, they will probably contract a virus — or anything else transmitted through communities — before you. Indeed, researchers showed that instead of tracking randomly chosen people to gauge the spread of a disease, it was much more efficient to ask those random people to name a friend, and track that friend instead! In the study, the group of friends got sick an average 2 weeks before the originally chosen people. There are probably lots of other applications out there waiting to be found for the friendship paradox. 

Before we end, though, I want to ask one last question: does the friendship paradox have to happen in any social network? The answer to this is yes and no. For the statement of the paradox that uses averages the answer is yes and this can be proven mathematically. That is, the statement on average, people have less than or equal to the average number of friends of their friends is true for any social network you can conceive of. For the statement which uses majority (most of your friends have strictly more friends than you), the answer is no. The key ingredient is the existence — or non-existence — of popular individuals. We can even create completely random social networks for which the paradox does not hold. Consider the following network, again over 34 people.

This network (coming from the Erdős–Rényi model) is constructed by considering every person is a friend of every other person with some fixed probability (in this case 75%).

For this social network we have,

The fraction of people with fewer friends than their friends have on average is 44.12%.

The fraction of people with fewer friends than most of their friends is 44.12%.

You can see from the detailed distribution of friends the difference more clearly. The number of friends is evenly spread around the average. This is similar to looking at the height of people. So, roughly half the people have fewer friends than their friends, another rough half has more friends than their friends, and the rest have exactly the same number as the average of their friends. 

Histogram of friends and friends of friends in the example Erdős–Rényi model graph above. The data is collected by looking at the friends of each friend for every person in the network. The distribution of those friends can be summarized by the mean and median. For each friend of each person, those numbers are tabulated and plotted in the lower row.

Conclusion

Of course, it should be somewhat obvious that if everyone had exactly the same number of friends, then they would have the same number of friends as their friends! But this is also true when the distribution of friends is more evenly spread. What does this suggest? I guess it lends credence to claims of favorability of egalitarian communities. But it seems to be the case that more hierarchical networks (be they in friendships, corporations, Twitter followers, etc.) grow naturally as a way to accommodate the complexity arising from maintaining large numbers of connections. But that is the topic for another blog post. In the meantime,

Please don’t share this. Instead, tell a friend to share it.

Some advice on learning at home

So you are stuck at home, the children aren’t in school, but you still need to get some work done. The internet is now full of activities for you to, as they say, “keep the learning going”. As a parent of homeschooled children, and someone who was working from home a lot already, things have changed less in our home than they have for most parents of school-aged children. For that, we are grateful. And so I thought it might be useful to not give you yet another list of activities to do, but step back and discuss some more big-picture things as we struggle with the physical and emotional havoc the Covid-19 situation has caused. Here’s some advice.

Trust yourself

When you get your child’s report card back it all seems like a very well thought out and scientific evaluation process. Here’s a little secret: it’s not. But busy administrators need simple numbers to rank not only the students, but the teachers, principals, schools, and even countries! The irony is that “one size fits all” fits no one at all. 

Testing can be useful if it is used and contextualized properly. But as a parent, you probably know your child better than they know themselves. It’s a problem in that you know them so well, you can hardly put into words what you know about them and how they will react to things. But this intuition is unique and yours alone. So you are the only one that can be trusted to know what is working for you and your child. Use this power to your advantage and don’t stress about what a particular day’s activities might mean for the far future. 

Take it easy

Do you remember your time in school? Have you ever volunteered in or observed your child’s classroom? If so, you’ll know that the amount of formal learning — whether it’s a lesson or one-on-one — is quite limited in classrooms with upwards of 30 students. 

There is a large variability among countries, but taking the average, students spend less than 1000 hours per year in the classroom. How many of these hours are effective? That’s impossible to say. But certainly less than half of them would involve direct teacher-to-student interaction. What does this all mean? It means, realistically, your children are getting — very roughly — 1.5 hours of formal learning per day (averaged over the year). The rest of their day is lost in thought, socialisation, and play. (These are arguably as important as formal learning for creating intelligent, healthy adults, and we’ll come back to that next.)

Since you are giving your child(ren) your mostly undivided attention, the amount of formal learning at home need only be a couple of hours at most. Some might breathe a sigh of relief. Ah ha! But what are you going to do with the rest of the day? Well, more learning, of course. The philosophy in our house is anything that is not mindless consumption of media is learning. This might involve playing board games, making a meal, playing hide-and-seek, drawing pictures, building with LEGOs, and so on. But make sure the child is choosing the activity — curing your own boredom is an essential skill many people are now realizing they don’t have! Remember: you can tell if mental or physical tools are being used and developed simply by observing.

Be proactive

In our house the order in which the activities play out can make a huge difference. We could do the same thing on two different days, in a different order, and one day could be great while the other terrible. Here are rules of thumb we play by.

  1. Don’t start the day with media and distractions. Do the formal stuff first. If your children aren’t keen on breakfast, do this first. If they are hungry as soon as they wake up, do it immediately after breakfast.
  2. Don’t end the day with media and distractions. If only for your own sanity, but also probably for a healthy sleep, end the day in bed with some calm reading rather than trying to tear a child away from their favorite movie.
  3. Every activity ends in disaster if allowed to go on long enough. Whether it is copying out hand-writing exercises or playing an addictive app on the iPad, eventually a meltdown will occur. Don’t allow something to go on too long before a break happens. Try a walk, a stretch, or a snack to break up the day’s activities.
  4. One activity must be completed and cleaned up before the next begins. This is not only to emphasize good organization and concentration, but also necessary if you are a parent working from home. The day simply cannot be a chaotic mess that requires your own constant attention.
  5. Consistent with the above rules, the rest of the day is completely unstructured.

Be flexible

What works and doesn’t work isn’t something you are trying to find as if there were a fixed perfect schedule out there. Routine is important. But as we are all keenly aware now, those change. Hopefully they don’t have to change so abruptly often, but they will change. Adapting to change is generally something humans are good at, and successful people seem to be better at. 

Your job is to find what works, while still working, knowing that what works will ebb and flow. Your children will be watching you now more than ever, learning how to react and deal with uncertainty, change, and boredom. It’s not going to be easy. And that’s why these might be the most important lessons your children receive. 

Polling and Surveys for Babies

When I started writing children’s books, they were for my own children. Since I never stop singing the praises of science, I wasn’t much concerned about how scientifically literate they would be. But how am I doing outside my own family? I don’t know! That’s where you come it 😁

Quantum Entanglement for Toddlers

quantum-entanglement-for-babies

I wrote a book a while back called Quantum Entanglement for Babies. But, now all those babies are grown into toddlers! I’ve been asked what is next on their journey to quantum enlightenment. Surely they have iPads now and know how to scroll, and so I give you Quantum Entanglement for Toddlers, the infographic!

Below is a lower-res version. Here is a high-res version (5MB). Contact me for the SVG.

nonlocal

Entry Points for Learning Quantum Computing

Desiree Vogt-Lee maintains a list of quantum computing resources called Awesome Quantum Computing. It is indeed awesome and comprehensive. Here I am looking to answer the question where do I start with quantum computing? with a more concise list of my current favourite entry points. 

But, before we get started, a general piece of advice if you want to study quantum computing (or anything else for that matter): learn more maths. More? Yes. More. It doesn’t matter how much you already know. In fact, I’m going to go learn some more maths after writing out this list. (I’m not joking — the next tab in my browser is Agent-based model – Wikipedia.) 

Now — in order of some sense of difficulty — here are my favourite recommendations for starting points on learning quantum computing.

Undergraduate

The academically minded might be looking for a more traditional approach. Don’t worry. Got that covered by Quantum Computer Programming, a course lectured at Stanford University. Other standard lecture notes include those by David Mermin and John Preskill. The former is more computer-sciencey while the latter is more physicsy.

If you want to do some real quantum programming, The Quantum Katas by Microsoft Quantum is a set of tutorials on quantum programming using the Q# programming language. While it does start with the basics, there is a steep learning curve for those without a background in programming.

Quantum computing for the very curious by Andy Matuschak and Michael Nielsen is like an electronic textbook with exercises that use spaced repetition to assist in remembering key facts. This is an experimental learning tool, which at the time of writing, is still under construction. 

Highschool

“Thinking Quantum”: Lectures on Quantum Theory by Barak Shoshany is a set of about 16 hours worth of lecture notes which was delivered to highschool students at an international summer school. Though it is more focused on quantum physics, the first half will give you all the basic tools needed to start analysing quantum algorithms. It is quite mathematical so the reader would have to be comfortable with some mathematical abstraction. However, much of the field of quantum computing comes from a physics background and the ideas and language of quantum physics are pervasive. 

The Quantum Quest by members of the QuSoft team is a web class which contains videos, lecture notes, and a pared down version of Quirk. It starts with the basics of probability and linear algebra and quickly gets you up and running with quantum circuits and algorithms.

Quirk by Craig Gidney is a quantum circuit simulator. It is incredible expressive and provides many useful visualisations. This tools is simple enough for anyone to start creating quantum circuits. However, interpreting the output does require some guidance and knowledge of probability.

If you prefer the video playlist approach, Quantum computing for the determined by Michael Nielsen is a series of short YouTube videos going over the basics of quantum information. However, if you are not putting pen to paper yourself, you are not likely to absorb the necessary mathematics to understand quantum computing.

Primary / C-Suites

Quantum Computing for Babies by me and whurley. 

My Speech to 500 Australian Teenage Schoolboys About Mathematics

I suppose I should start with who I am and what I do and perhaps why I am here in front of you. But I’m not going to do that, at least not yet. I don’t want to stand here and list all my accomplishments so that you may be impressed and that would convince you to listen to me. No. I don’t want to do that because I know it wouldn’t work. I know that because it wouldn’t have worked on me when I was in your place and someone else was up here.

Now, of course you can tell by my accent that I wasn’t literally down there. I was in Canada. And I sure as hell wasn’t wearing a tie. But I imagine our priorities were fairly similar: friends, getting away parents, maybe sports (in my case hockey of course and yours maybe footy), but most importantly… mathematics! No. Video games. 

I don’t think there is such a thing as being innately gifted in anything. Though, I am pretty good at video games. People become very good at things they practice. A little practice leads to a small advantage, which leads to opportunities for better practice, and things snowball. The snowball effect. Is that a term you guys use in Australia? I mean, it seems like an obvious analogy for a Canadian. It’s how you make a snowman after all. You start with a small handful of snow and you start to roll it on the ground. The snow on the ground sticks to the ball and it gets bigger and bigger until you have a ball as tall as you! 

Practice leads to a snowball effect. After a while, it looks like you are gifted at the thing you practiced, but it was really just the practice. Success then follows from an added sprinkling of luck and determination. That’s what I want to talk to you about today: practice.

I don’t want to use determination in the sense that I was stubbornly defiant in the face of adversity. Though, from the outside it might look that way. You can either be determined to avoid failure or determined to achieve some objective. Being determined to win is different from being determined not to lose. 

There is something psychologically different between winning and not losing. You see, losing implies a winner, which is not you. But winning does not require a loser, because you can play against yourself. This was the beauty of disconnected video games of 80’s and 90’s. You played against yourself, or maybe “the computer”. That doesn’t mean it was easy. I’ll given anyone here my Nintendo if they can beat Super Mario Bros. in one go. (I’m not joking. I gave my children the same offer and they barely made it past the first level). It was hard and frustrating, but no one was calling you a loser on the other end. And when you finally beat the game, you could be proud. Proud of yourself and for yourself. Not for the fake internet points you get on social media, but for you. 

I actually really did want to talk to you today about mathematics. What I want to tell you is that, when I was your age, I treated mathematics like a video game. I wanted to win. I wanted to prove to myself that I could solve every problem. Some nights I stayed up all night trying to solve a single problem. You know how they say you can’t have success without failure? This is a perfect example. The more you fail at trying to solve a maths problem, the more you understand when you finally do solve it. And what came along with failing and eventually succeeding in all those maths problems? Practice.

Well I don’t know much about the Australian education system and culture. But I’m guessing from Hollywood you know a bit about highschool in North America. I’m sure you know about prom, and of course about Prom King and Prom Queen. What you may not know is that the King and Queen’s court always has a jester. That is, along with King and Queen, each year has a Class Clown — the joker, the funny guy. I wasn’t the prom king, or queen. But I did win the honour of class clown.

When I finished highschool, I was really good at three things: video games, making people laugh, and mathematics. I promise you, there is no better combination. If there was a nutrition guide for the mind, it would contain these three things. Indeed, now more than ever before, you need to be three types of smart. You need to be quick, reactive, and adaptive — the skills needed to beat a hard video game. You need emotional intelligence, you need to know what others are thinking and feeling — how to make them laugh. And finally you need to be able to solve problems, and all real problems require maths to solve them. 

There are people in the world, lots of people — billions, perhaps — who look in awe at the ever increasing complexity of systems business, government, schools, and technology, including video games. They look, and they feel lost. Perhaps you know someone that can’t stand new technology, or change in general. Perhaps they don’t even use a piece of technology because they believe they will never understand how to use it. 

You all are young. But you know about driving, voting, and paying taxes, for example. Perhaps it looks complicated, but at least you believe that you can and will be able to do it when the time comes. Imagine feeling that such things were just impossible. That would be a weird feeling. You brain can’t handle such dissonance. So you would need to rationalise it in one way or another. You’d say it’s just not necessary, or worse, it’s something some “other” people do. At that point, for your brain to maintain a consistent story, it will start to reject new information and facts that aren’t consistent with your new story. 

This is all sounds far fetched, but I guarantee you know many people with such attitudes. To make them sound less harmful, they call them “traditional”. How do otherwise “normal” people come to hold these views? It’s actually quite simple: they fear, not what they don’t understand, but what they have convinced themselves is unnecessarily complicated. I implore you, start today, start right now. Study maths. It is the only way to intellectually survive in a constantly changing world.

Phew that was a bit depressing. Let me give you a more fun and trivial example. Just this weekend I flew from Sydney to Bendigo. The flight was scheduled to be exactly 2 hours. I was listening to an audiobook and I wondered if I would finish it during the flight. Seems obvious right? If there was less than 2 hours left in the audiobook, then I would finish. If not, then I would not finish. But here’s the thing, audiobooks are read soooo slow. So, I listen to them at 1.25x speed. There was 3 hours left. Does anyone know the answer?

Before I tell you, let me remind you, not many people would ask themselves this question. I couldn’t say exactly why, but in some cases it’s because the person has implicitly convinced themselves that such a question is just impossible to answer. It’s too complicated. So their brain shuts that part of inquiry off. Never ask complicated questions it says. Then this happens: an entire world — no most of the entire universe — is closed off. Don’t close yourself off from the universe. Study maths.

By the way, the answer. It’s not the exact answer but here was my quick logic based on the calculation I could do in my head. If I had been listening at 1.5x speed, then every hour of flight time would get through 1.5 hours of audiobook. That’s 1 hour 30 minutes. So two hours of flight time would double that, 3 hours of audiobook. Great. Except I wasn’t listening at 1.5x speed. I was listening at a slower speed and so I would definitely get through less than 3 hours. The answer was no. 

In fact, by knowing what to multiple or divide by what, I could know that I would have exactly 36 minutes left of the audiobook. Luckily or unluckily, the flight was delayed and I finished the book anyway. Was thinking about maths pointless all along? Maybe. But since flights are scheduled by mathematical algorithms, maths saved the day in the end. Maths always wins.

How about another. Who has seen a rainbow? I feel like that should be a trick question just to see who is paying attention. Of course, you have all seen a rainbow. As you are trying to think about the last time you saw a rainbow, you might also be thinking that they are rare — maybe even completely random things. But now you probably see the punchline — maths can tell you exactly where to find a rainbow.

Here is how a rainbow is formed. Notice that number there. That angle never changes. So you can use this geometric diagram to always find the rainbow. The most obvious aspect is that the rainbow exits the same general direction that the sunlight entered the raindrop. So to see a rainbow, the sun has to be behind you.

And there’s more. If the sun is low in the sky, the rainbow will be high in the sky. And if the sun is high, you might not be able to see a rainbow at all. But if you take out the garden hose to find it, make sure you are looking down. Let me tell you my favourite rainbow story. I was driving the family to Canberra. We were driving into the sunset at some point when I drove through a brief sun shower. Since the sun was shining and it was raining, one of my children said, “Maybe we’ll see a rainbow!”

Maybe. Ha. A mathematician knows no maybes. As they looked out their windows, I knew — yes — we would see a rainbow. I said, after passing through the shower, “Everyone look out the back window and look up.” Because the sun was so low, it was apparently the most wonderful rainbow ever seen. I say apparently because I couldn’t see it, on account of me driving. But no matter. I was content in knowing I could conjure such beauty with the power of mathematics.

I could have ended there, since I’m sure you are all highly convinced to catch up on all your maths lessons and homework. However, since I have time, I will tell you a little bit about what maths has enabled me to get paid to do. Namely, quantum physics and computation. Maybe you’ve heard about quantum physics? Maybe you’ve heard about uncertainty (the world is chaotic and random), or superposition (things can be in two places at once and cats can be dead and alive at the same time), or entanglement (what Einstein called spooky action at a distance).

But I couldn’t tell you more about quantum physics than that without maths. This is not meant to make it sound difficult. It should make it sound beautiful. This is quantum physics. It’s called the Schrodinger Equation. That’s about all there is to it. All that stuff about uncertainty, superposition, entanglement, multiple universes, and so on—it’s all contained in this equation. Without maths, we would not have quantum physics. And without quantum physics, we would not have GPS, lasers, MRI, or computers — no computers to play video games and no computers to look at Instagram. Thank a quantum physicist for these things.

Quantum physics also helps us understand the entire cosmos. From the very first instant of the Big Bang born out of a quantum fluctuation to the fusing of Hydrogen into Helium inside stars giving us all energy and life on Earth to the most exotic things in our universe: black holes. These all cannot be understood without quantum physics. And that can’t be understood without mathematics.

And now I use the maths of quantum physics to help create new computing devices that may allow us to create new materials and drugs. This quantum computer has nothing mysterious or special about it. It obeys an equation just as the computers you carry around in your pockets do. But the equations are different and different maths leads to different capabilities. 

I don’t want to put up those equations, because if I showed them to even my 25 year-old self, I would run away screaming. But then again, I didn’t know then what I know now, and what I’m telling you today. Anyone can do this. It just takes time. Every mathematician has put in the time. There is no secret recipe beyond this. Start now.

I gave up social media for a month. This happened next.

Nothing. Nothing, and it was glorious. If you haven’t tried giving up social media, I highly recommend giving it a try. But, now I’m back and — as you can see from the awesome clickbait title — I haven’t lost it. Why am I back and — for that matter — why did I leave? Read on.

First, a little back story for context. I joined social media in earnest about 5 years ago after I published my first book. I thought that I needed to be out there promoting my books. Around the same time, a growing number of academics were also adopting social media. I thought then that I could use social media to promote my academic work as well. Certainly, the number of eyes seeing my work increased with my presence on social media. But the big question was always left unanswered — was it worth the time spent?

This is a very difficult question to answer. I still don’t have the answer and I don’t think I ever will. In part, this is because not all time spent on social media has equal value. As my children get ever-closer to the age when all of their peers have a social media connected phone, I’ve become more and more interested in social media, who uses it, and what they use it for. This has been by no means a controlled — or even exhaustive — study, but I learned enough that I scared myself right off the platforms. I paid close attention as I used (mostly) Twitter, Instagram, and Facebook. I talked to colleagues at the university, other authors and parents, and observed people in public. Here is what I learned.

The uses of social media form a multidimensional spectrum, but there are easy to identify extreme behaviors:

  • Use it as a megaphone to broadcast your message or brand without any further engagement.
  • Use it to pass time, starring zombie-like at your phone as you scroll endlessly through your feed, which is curated by an algorithm maximizing the number of advertisements you see.
  • Use it to troll by intentionally offending people.
  • Use it to communicate with friends, family, or colleagues.
  • Use it to engage your audience.

In an ideal social network, there would be mutually beneficial interaction between creators and consumers of media. In reality, though, it’s just a vicious cycle of memes, with the most controversial or sensational going viral. It’s like 24-hour news, but a million times worse. It’s not a nice place to be. So, I left.

But what was the first thought to enter my mind after making this decision? Hey, I should tweet about this. Oops. I became addicted to social media. Luckily, I foresaw this and deleted the apps from my phone and had my browser forget my password. This was enough of a barrier to keep me away, and I stayed away for a month.

It was a great month, too. I was much happier and I got heaps done. It wasn’t just that I got back all the time spent on social media, but that social media was a huge distraction. Every time I had a break in my train of thought, or felt a little bored, or wanted a little dopamine hit from some likes, I’d pick up my phone or open a new tab. Even if I only spent a minute there, it was like hours were lost because that break in my train of thought was now completely lost.

So, given all that, clearly I made the correct decision in leaving social media, right? Well, no. The real lesson I have learned is that I wasn’t using social media optimally. There is value in being on social media, but you must be vigilant. And so, I’m back — ready to make the best of this mess called social media.

Your children will kill you, and maybe that’s a good thing

Over a hundred years ago an American medical doctor performed an experiment to weigh the human soul. The number he came up with is the now infamous 21 grams. While this is scientifically uninteresting, it is still fascinating to even the most radical antitheistic rationalist. Try as we might—though I’d argue we shouldn’t—to remove the human element from science, there is one inescapable human inevitability: death.

The 21 gram soul nonsense is often used as proof for life after death, or at least out of body experiences. But it turns out you don’t need any of that pseudoscience to existentially experience your own death. I know this because I died once. And, it was having kids that killed me.

The difficulty of raising children is a constant theme of the blogsphere and Twitterverse. There is no shortage of lamentations. These are often met with both harsh criticism and earnest sympathy. The exhausted parent is shamed on one side and lauded for their honesty on the other.

The great thing about your own death is you hardly remember it. And, maybe I shouldn’t talk about like it was mine, as if I own it. It was his death and I can only pity him because, honestly, I don’t get why it was such a terrible thing anymore. But I’ll continue to talk about it as if it were my own past because in a literal sense it is, and it would just be awkward reading otherwise. Or, poetry.

Before children, I was a work hard, play hard college student. I had infinite freedom and I took advantage of every minute of it. Basically, I was the worst candidate to have real responsibilities, and there is nothing like the responsibility of being handed a helpless baby when you’ve never held a child in your life. Seriously, the nurse hands you the baby, says, “congratulations, dad,” and then everyone leaves the room. What the fuck? What I am supposed to do with this? If you want to see the definition of karma, hand a 27-year-old college student who sleeps 10 hours a night until noon a newborn infant.

But, like I said, I hardly remember it. Today I am woken up at 5:00am to a creepy child silhouette—like, how long have you been standing there?—which whispers as soon as it knows I’m awake, “can I watch a movie?” 7 years and he doesn’t know that he’d get an infinitely more favorable response if he had coffee in his hand. But, the thing is, now I love mornings. There is a calm about sunrise that you don’t experience the rest of the day.

There are so many things about life that being a parent has taught me to enjoy, and many that it has forced me to realize are not important. Sure, you lose a lot of freedom. You can’t play Xbox or binge-watch reality TV every night or have those loud friends over. But, those shows were trash anyway and are people that get grumpy because they can’t drink all your beer until 2am anymore really your friends?

Like a phoenix risen from the ashes, with children I am reborn. Now, where is daddy’s coffee?

When will we have a quantum computer? Never, with that attitude

We are quantum drunks under the lamp post—we are only looking at stuff that we can shine photons on.

In a recently posted paper, M.I. Dyakonov outlines a simplistic argument for why quantum computing is impossible. It’s so far off the mark that it’s hard to believe that he’s even thought about math and physics before. I’ll explain why.

abstract

Find a coin. I know. Where, right? I actually had to steal one from my kid’s piggy bank. Flip it. I got heads. Flip it again. Heads. Again. Tails. Again, again, again… HHTHHTTTHHTHHTHHTTHT. Did you get the same thing? No, of course you didn’t. That feels obvious. But why?

Let’s do some math. Wait! Where are you going? Stay. It will be fun. Actually, it probably won’t. I’ll just tell you the answer then. There are about 1 million different combinations of heads and tails in a sequence of 20 coin flips. The chances that we would get the same string of H’s and T’s is 1 in a million. You might as well play the lottery if you feel that lucky. (You’re not that lucky, by the way, don’t waste your money.)

Now imagine 100 coin flips, or maybe a nice round number like 266. With just 266 coin flips, the number of possible sequences of heads and tails is just larger than the number of atoms in the entire universe. Written in plain English the number is 118 quinvigintillion 571 quattuorvigintillion 99 trevigintillion 379 duovigintillion 11 unvigintillion 784 vigintillion 113 novemdecillion 736 octodecillion 688 septendecillion 648 sexdecillion 896 quindecillion 417 quattuordecillion 641 tredecillion 748 duodecillion 464 undecillion 297 decillion 615 nonillion 937 octillion 576 septillion 404 sextillion 566 quintillion 24 quadrillion 103 trillion 44 billion 751 million 294 thousand 464. Holy fuck!

So obviously we can’t write them all down. What about if we just tried to count them one-by-one, one each second? We couldn’t do it alone, but what if all people on Earth helped us? Let’s round up and say there are 10 billion of us. That wouldn’t do it. What if each of those 10 billion people had a computer that could count 10 billion sequences per second instead? Still no. OK, let’s say, for the sake of argument, that there were 10 billion other planets like Earth in the Milky Way and we got all 10 billion people on each of the 10 billion planets to count 10 billion sequences per second. What? Still no? Alright, fine. What if there were 10 billion galaxies each with these 10 billion planets? Not yet? Oh, fuck off.

Even if there were 10 billion universes, each of which had 10 billion galaxies, which in turn had 10 billion habitable planets, which happened to have 10 billion people, all of which had 10 billion computers, which count count 10 billion sequences per second, it would still take 100 times the age of all those universes to count the number of possible sequences in just 266 coin flips. Mind. Fucking. Blown.

Why I am telling you all this? The point I want to get across is that humanity’s knack for pattern finding has given us the false impression that life, nature, the universe, or whatever, is simple. It’s not. It’s really fucking complicated. But like a drunk looking for their keys under the lamp post, we only see the simple things because that’s all we can process. The simple things, however, are the exception, not the rule.

Suppose I give you a problem: simulate the outcome of 266 coin tosses. Do you think you could solve it? Maybe you are thinking, well you just told me that I couldn’t even hope to write down all the possibilities—how the hell could I hope to choose from one of them. Fair. But, then again, you have the coin and 10 minutes to spare. As you solve the problem, you might realize that you are in fact a computer. You took an input, you are performing the steps in an algorithm, and will soon produce an output. You’ve solved the problem.

A problem you definitely could not solve is to simulate 266 coin tosses if the outcome of each toss depended on the outcome of the previous tosses in an arbitrary way, as if the coin had a memory. Now you have to keep track of the possibilities, which we just decided was impossible. Well, not impossible, just really really really time consuming. But all the ways that one toss could depend on previous tosses is yet even more difficult to count—in fact, it’s uncountable. One situation where it is not difficult is the one most familiar to us—when each coin toss is completely independent of all previous and future tosses. This seems like the only obvious situation because it is the only one we are familiar with. But we are only familiar with it because it is one we know how to solve.

Life’s complicated in general, but not so if we stay on the narrow paths of simplicity. Computers, deep down in their guts, are making sequences that look like those of coin-flips. Computers work by flipping transistors on and off. But your computer will never produce every possible sequence of bits. It stays on the simple path, or crashes. There is nothing innately special about your computer which forces it to do this. We never would have built computers that couldn’t solve problems quickly. So computers only work at solving problems that can we found can be solved because we are at the steering wheel forcing them to the problems which appear effortless.

In quantum computing it is no different. It can be in general very complicated. But we look for problems that are solvable, like flipping quantum coins. We are quantum drunks under the lamp post—we are only looking at stuff that we can shine photons on. A quantum computer will not be an all-powerful device that solves all possible problems by controlling more parameters than there are particles in the universe. It will only solve the problems we design it to solve, because those are the problems that can be solved with limited resources.

We don’t have to track (and “keep under control”) all the possibilities, as Dyakonov suggests, just as your digital computer does not need to track all its possible configurations. So next time someone tells you that quantum computing is complicated because there are so many possibilities involved, remind them that all of nature is complicated—the success of science is finding the patches of simplicity. In quantum computing, we know which path to take. It’s still full of debris and we are smelling flowers and picking the strawberries along the way, so it will take some time—but we’ll get there.

 

The point of physics

Something I lost sight of for a long time is the reason I study physics, or the reason I started studying it anyway. I got into it for no reason other than it was an exciting application of mathematics. I was in awe, not of science, but of the power of mathematics.

Now there are competing pressures. Sometimes I find myself “doing physics” for reasons that can only best be seen as practical. Fine—I’m a pragmatic person after all. But practicality here is often relative to a set of arbitrarily imposed constraints, such as requiring a CV full of publications in journals with the highest rank in order to be a good academic boi.

You may say that’s life. We all start with naive enthusiasm and end up doing monotonous things we don’t enjoy. But then we tell ourselves, and each other, lies about it being in service of some higher purpose. Scientists see it stated so often that they start to repeat it, and even start to believe it. I know I’ve written and repeated thoughtless platitudes about science many times. It’s almost necessary to convince yourself of these myths as you struggle through your school or your job. Why am I doing this, you wonder, because it certainly doesn’t feel rewarding in those moments.

On the other hand, many people are comfortable decoupling their passion from their job. Do the job to earn money which funds your true passions. Not all passions provide the immediate monetary returns one needs to live a comfortable life after all. So you can study science to learn the skills that someone will pay you to employ. There are many purely practical reasons to study physics, for example, which have nothing to do with answering to some higher calling. This certainly seems more honest than having to lie to yourself when expectations fail.

(I should point out that if you are one of those people currently struggling through graduate school, academia is not the only way—maybe not even the best way—to sate your hunger for knowledge, or just solve cool maths problems.)

A lot of scientists, teachers, and university recruiters get this wrong. There is a huge difference between being curious about nature and reality and suggesting it is morally good to devote one’s life to playing a small part in answering specific questions about such.

Einstein did not develop general relativity to usher in a new era of gravitational wave astronomy, as cool as that is. He did it because he was obsessed with answering his own questions driven by his insatiable imagination. Even the roots of the now enormous collaboration of scientists which detected gravitational waves started in a water cooler conversation among a few physicists, which is best summarized by this tweet:

In other words, we don’t actually do things through a consensual agreement about its potential value to a higher power called science. We think about doing certain things because we are curious, because we want to see what will happen, or because we can.

Like all other myths scientists and their adoring followers like to deride, science as a moral imperative is just that—a myth. Might we not get further with honesty, by telling ourselves and others that we are just people—people trying to do cool shit. The great things will come as they always have, emerging from complex interactions—not by everyone collectively following a blinding light at the end of tunnel, but by lighting the tunnel itself with millions of unique candles.