In today’s culture, all you have to do is not be an asshole to be a hero.
We now absolve ourselves by simply denying guilt. Even the hint of criticism is charged as an offense. This fear of shame has run so rampant that a false feeling of innocence has turned into outright narcissism.
You are not a good person. I am not a good person. Let’s admit our faults, make amends, and try to be better.
Two of my children are in an art class together. It’s not going well. The teacher does not have much control over the class and favours the returning and skilled students. My two children tend to stick together (good on them), but often get to acting up. Today was particularly bad. The director of the art school had to speak to us about it after class. Their tone was serious, but also apologetic. The report ended with a complement about the children’s art.
At home we reflected on this a bit and decided to call the school. We told them that we were extremely sorry about the disruption and requested the children be split up into different classes and if that was not possible, we would voluntarily remove them from the class. The director was flabbergasted. We were apparently the first parents not to get immediately defensive about their children’s bad behaviour.
They are so afraid of defensive parents that the facts cannot even be stated without being padded with multiple compliments. We were thanked several times and given a free class in addition to accommodation of our request.
The moral of the story: in today’s culture, all you have to do is not be an asshole to be a hero.
Well, this is it—academic endgame. I am now a faculty member at the University of Technology Sydney. It’s been quite a journey, but it wasn’t mine alone—and I couldn’t have done it by myself. I met Lindsay at the university bar and it was love at first sight—and I thought she was all right, too 😛.
Chapter 1 found us in Waterloo, Ontario where we were students at the University of Waterloo. We moved into our first home and had our first two children. In any other profession, we would have been settled down by then. But I was still an academic baby. After finishing my PhD, it was time to embrace the nomadic lifestyle of academia, pack up the family and head west.
Chapter 2 was our adventure into the deserts of south-western USA. We were skeptical at first—having watched a bit too much Breaking Bad—but Albuquerque quickly grew on us. The people and culture were quite unique to North America as was the landscape. The sunsets, for example, are unparalleled.
We had our third child in Albuquerque and it was every bit as clinical and expensive as you would expect from the American healthcare system. In any case, he is happy and healthy as we haven’t told him him who his president is yet. It was also here where the idea for Quantum Physics for Babies was conceived.
In Albuquerque, I worked as a Postdoc at the Center for Quantum Information and Control with the eminent and ever-quirky Carl Caves. Carl is the most honest and generous physicist I have ever met. I hope to work with him again soon.
All-in-all, we loved our time in Albuquerque and it was very sad for all of us that we had to move on.
Chapter 3 brought us down under, to the land of Oz. We moved in to a closet in the inner-city suburbs of Sydney. Sydney is an unplanned transportation disaster in one of the most beautiful natural harbours in the world which are surrounded by white and golden sandy beaches. In Australia, beach is life.
While we weren’t at the beach, I was a postdoc at the University of Sydney, which is a hotspot for hands-on theory and experiment in quantum computing. One of things that I hadn’t appreciated about Sydney was its position as a hub for quantum information scientists visiting Australia. International travelers often come through Sydney regardless of their Australian destination. Consequently, I met many new people in the field here. This was extremely beneficial, as these connections led to my current position.
Chapter 4 started with bang: new year, new baby, new home and a new job—all in the span of a few weeks!
I’ve never really celebrated the other “milestones” in the academic progression—I didn’t even collect my PhD diploma, let alone frame it. I’ve always felt like there was more to do. And, although a tenured faculty position can be seen as the endgame, it is really just the beginning. There is just so much left to do—not only in my own specialization, but scientific research itself needs fixing!
Interestingly, no one researcher on the project had expertise in all of these areas. Moreover, within each discipline, everything from the way research is conducted to how it is disseminated is different. Couple that to the fact that many of us were senior researchers with other demands on our time and you get a 2 year long project!
Anyway, it is done and I’d gladly do it again with this bunch of talent scientists!
“In mathematics you don’t understand things. You just get used to them.” ― John von Neumann
John von Neumann made important scientific discoveries in physics, computer science, statistics, economics, and mathematics itself. He was, by all accounts, a genius. Yet, here he is saying he “just got used” to mathematics. While this was probably a tongue-in-cheek reply to a friend, there is some truth to it. Mathematics is a language and anyone can eventually learn to speak it.
Indeed, mathematics is the language by which scientists of all fields communicate—from philosophy to physics. And by mathematics, I don’t mean numbers. Scientists communicate ideas through mental pictures which are often represented by symbols invented just for that purpose. Here is an example: think about a ball. Maybe it is a baseball, or a basketball, or—if you are in Europe—a socc…err… football. Maybe it is the Earth or the Sun. Now try to get rid of the details: the stitching, the colors, the size. What is left? A sphere. You just performed the process of abstraction. A sphere is an idea, a mental image that you can’t touch—it doesn’t exist!
Why is this important, anyway? Well, if I can prove things about spheres, then that ought to apply to any ball in the real world. So, formulas for area and volume, for example, equally apply to baseballs, basketballs, soccer balls, and any other ball. Mathematics is a very powerful way of answering infinitely many questions at once!
Now, it is said that to become an expert at anything, you need 10,000 hours of practice. While not a hard-and-fast rule, it seems to work out in terms of acquiring modern language—10,000 hours probably works out to mid-to-late teens for an adept student. Usually, we don’t start practicing real mathematics until well after we have mastered our first language, in late high-school or college. Why not start those 10,000 hours now with your children?
Sounds great, but where do you start? The bad news is that there are no simple rules. The good news is that it doesn’t really matter where you start. With your children, you could practice numeracy, practice puzzles and games, read books, watch science videos, try to code, draw pictures, or just sit in a quiet room and think. As you do these things, encourage generalization and abstraction. Ask questions and let your child ask questions. The correct answers are not important—it is the process that counts.
I was asked recently to share some tips for parents who want their kids to excel at math and do well in the classroom later on. The trouble is, doing well in the classroom—that is, doing well on standardized tests—doesn’t necessarily correlate with understanding the language of mathematics. If you want to do well on standardized tests, then just practice standardized tests. However, if you want your kids to have the powerful tools of abstraction at their disposal and possibly also do well on tests, then teach them the language of mathematics.
The birthday paradox goes… in a room of 23 people there is a 50-50 chance that two of them share a birthday.
OK, so the first step in introducing a paradox is to explain why it is a paradox in the first place. One might think that for each person, there is 1/365 chance of another person having the same birthday as them. Indeed, I can think of only one other person I’ve met that has the same birthday as me—and he is my twin brother! Since I’ve met far more than 23 people, how can this be true?
This reasoning is flawed for several reasons, the first of which is that the question wasn’t asking about if there was another person in the room with a specific birthday—any pair of people (or more!) can share a birthday to increase the chances of the statement being true.
The complete answer gets heavy into the math, but I want to show you how to convince yourself it is true by simulating the experiment. Simulation is programming a computer or model to act as if the real thing was happening. Usually, you set this up so that the cost of simulation is much less than doing the actual thing. For example, putting a model airplane wing in a wind tunnel is a simulation. I’ve simulate the birthday paradox in a computer programming language called Python and this post is available in notebook-style here. Indeed, this is much easier than being in a room with 23 people.
Below I will not present the code (again, that’s over here), but I will describe how the simulation works and present the results.
Call the number of people we need to ask before we get a repeated birthday n. This is what is called a random variable because its value is not known and may change due to conditions we have no control over (like who happens to be in the room).
Now we simulate an experiment realising a value for n as follows.
Pick a random person and ask their birthday.
Check to see if someone else has given you that answer.
Repeat step 1 and 2 until a birthday is said twice.
Count the number of people that were asked and call that n.
Getting to step 4 constitutes a single experiment. The number that comes out may be n = 2 or n = 100. It all depends on who is in the room. So we repeat all the steps many many times and look at how the numbers fall. The more times we repeat, the more data we obtain and the better our understanding of what’s happening.
Here is what it looks like when we run the experiment one million times.
So what do all those numbers mean? Well, let’s look at how many times n = 2 occurred, for example. In these one million trials, the result 2 occurred 2679 times, which is relatively 0.2679%. Note that this is close to 1/365 ≈ 0.274%, which is expected since the probability that the second person has the same as the first is exactly 1/365. So each number of occurrences divided by one million is approximately the probability that we would see that number in a single experiment.
We can then plot the same data considering the vertical axis the probability of needing to see n people before a repeated birthday.
Adding up the value of each of these bars sums to 100%. This is because one of the values must occur when we do an experiment. OK, so now we can just add up these probabilities starting at n = 2 and increasing until we get to 50%. Visually, it is the number which splits the coloured area above into two equal parts. That number will be the number of people we need to meet to have a 50-50 shot at getting a repeated birthday. Can you guess what it will be?
Drum roll… 23! Tada! The birthday paradox simulated and solved by simulation!
But, wait! There’s more.
What about those leap year babies? In fact, isn’t the assumption that birthdays are equally distributed wrong? If we actually tried this experiment out in real life, would we get 23 or some other number?
Happily, we can test this hypothesis with real data! At least for US births, you can find the data over at fivethirteight’s github page. Here is what the actual distribution looks like.
Perhaps by eye it doesn’t look too uniform. You can clearly see 25 Dec and 31 Dec have massive dips. Much has been written about this and many beautiful visualizations are out there. But, our question is whether this has an effect on the birthday paradox. Perhaps the fact that not many people are born on 25 Dec means it is easy to find a shared birthday on the remaining days, for example. Let’s test this hypothesis by simulating the experiment with the real distribution of birthdays.
To do this, we perform the same 4 steps as above, but randomly sampling answers from the actual distribution of birthdays. The result of another one million experiments is plotted below.
And the answer is the same! The birthday paradox persists with the actual distribution of birthdays.
The above discussion is very good evidence that the birthday paradox is robust to the actual distribution of births. However, it does not constitute a mathematical proof. An experiment can only provide evidence. So I will end this with a technical question for those mathematical curiosos out there. (What I am about to do is also called Nerd Sniping.)
Here is the broad problem: quantify the above observation. I think there is more than one question here. For example, it should be possible to bound the 50-50 threshold as a function of the deviation from a uniform distribution.
It is too easy to get trapped into the mentality that—because you know better—you can instantly fix a child’s problem. So why is it that resistance follows? Hint: it’s because you are not listening.
Recently I decided to take the plunge into audiobooks. Since this was a new venture for me, I decided also to listen to something I wouldn’t otherwise read: a parenting book. I’m not implying that I’m a perfect parent by that—I’ve just been blessed by a great partner and four amazing children, such that I haven’t felt the need to seek unnecessary advice.
Whether or not you think you are in the same boat, you should definitely pick up a copy of How to Talk so Your Kids will Listen and Listen so Your Kids will Talk written byAdele Faber and Elaine Mazlish. Now, at this point you might be sarcastically saying, “Thanks for alerting us to the existence of a 30 year old parenting book in its 13th edition that has been referred to as the parenting bible.” But, this post is for those who don’t frequent self-help blogs and the parenting aisle of the bookshop; you might think you have a great relationship with your kids—this book will make it better.
A comment about the audiobook
Before I continue, let me remind you that I listened to the audio version of the book. I have mixed, but still overall positive, feelings about this. First, there are plenty of cartoons in the physical book which obviously don’t translate to audio. I honestly didn’t notice this. Second, there are lots of exercises and places where you are asked to write things down. This is a bit awkward if you are listening to the book while being active. On the other hand, it is narrated bySusan Bennett, otherwise known as Siri. She does an absolutely amazing job capturing the emotion of the authors and, most importantly, the constant dialog in the book between parent and child. In any case, the content is well worth it. The remainder of this discussion will be about the content of the audiobook.
I noticed that much of dialog in the book was dated in terms of language and subject matter. For example, a situation considered in the book was a child who borrowed and scratched a father’s compact disc. I mean, does anyone even own CD’s anymore? Luckily, this is more of a nostalgic amusement than a distraction.
I also didn’t like how the anniversary edition involved appendices of additions rather than a more streamlined approach. It felt a bit lazy and tacked on. In any case, the additional content was a useful addition to an otherwise great book.
Examples, examples, examples
A large chunk of How to Talk consists of real-life example dialogue between parent and child. These are invaluable. Often, the advice seems obvious in hindsight—validate feelings, for example. But, it’s only after hearing the examples when you really see where improvement can be made. The examples usually begin with a fictitious unhelpful response from the parent, followed by a helpful response. Let me give you an example that actually happened to me when I tried to use the skills on my own children after reading the first chapter: “Helping Children Deal with Their Feelings.” My strategy was to default to silent acknowledgment whenever I couldn’t quickly find an appropriate response.
Situation 1: Child (7) is asked to practice math exercises. After doing a few, she becomes bored and says, “I can’t do it.” Clearly, she can. Here is a typical way this would play out.
Child: I can’t do it.
Parent: Yes you can.
Child: I can’t. I don’t know how.
Parent: Well, you are not leaving the table until it is done.
Child (now crying): But I want to watch a movie!
Parent (voice raised): No movies until you are done all your homework!
Child: You’re mean!
And there is no end to the cycle. But, here is how it actually went:
Child: I can’t do it.
Parent: You feel that question is too hard for you?
Child: I think the answer is 17.
I couldn’t believe how well silence works for acknowledging feelings. Here is another example.
Situation 2: Child (3) is struggling to get his footwear on. He is frustrated that the sandal won’t fit on the wrong foot. Here is the typical way this would have gone.
Child (clearly frustrated): I can’t get it on!
Parent: That’s because you are putting it on the wrong foot.
Child: NO! It doesn’t fit!
Parent: Would you like me to do it for you?
Parent: [forces sandal on correct foot]
Here is how it actually went:
Child (clearly frustrated): I can’t get it on!
Parent: I see you are frustrated with that sandal.
Child (calmer): It doesn’t fit.
Parent: That can be so frustrating!
Child (probably knowing all along): It’s the wrong foot.
And he took it off the wrong foot and put it on the correct foot!
How to Talk contains seven chapters, the last being titled, “Putting it All Together.” But, to my mind, the first chapter contains the key insights to a better emotional relationship with my children. In the past, I’ve tried to avoid situations like those exemplified above. Accepting and dealing with my children’s emotions has not been that difficult because I have been fairly well in tune with them. This meant that I was able to easily anticipate meltdowns and avoid them altogether. For example, if I sensed that my 3 year old was irritable, I would not ask him to put his own shoes on, thereby avoiding the situation.
But protecting the children from their own feelings is not doing them any favors in the long run, and is becoming ever more difficult with a growing family. So, rather than doing the hard work of anticipating and preventing the emotional distress of my children, I’m now trying to acknowledge and accept how difficult it is to become an autonomous little person in a grown-up world.
For the first time, physicists have found a new fundamental state of cow, challenging the current standard model. Coined the cubic cow, the ground-breaking new discovery is already re-writing the rules of physics.
A team of physicists at Stanford and Harvard University have nothing to do with this but you are probably already impressed by the name drop. Dr. Chris Ferrie, who is currently between jobs, together with a team of his own children stumbled upon the discovery, which was recently published in Nature Communications*.
The spherical theory of cow had stood unchallenged for over 50 years—and even longer if a Russian physicist is reading this. The spherical cow theory led to many discoveries also based on O(3) symmetries. However, spherical cows have not proven practically useful from a technological perspective. “Spherical cows are prone to natural environmental errors, whereas our discovery digitizes the symmetry of cow,” Ferrie said.
Just as the digital computer has revolutionized computing technology, this new digital cow model could revolutionize innovation disrupting cross-industry ecosystems, or something.
Lead author Maxwell Ferrie already has far-reaching applications for the result. “I like dinosaurs,” he said. Notwithstanding these future aspirations, the team is sure to be milking this new theory for all its worth.
* Not really, but this dumping ground for failed hypesearch has a bar so low you might as well believe it.