Tag: education

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.

The real magic of quantum computing

By now you have read many articles on quantum computing. Congratulations. You know nothing about quantum computing.

There is a magician on stage. It’s tense. Maybe it’s a primetime TV show and the production value is super high. The celebrity judges look nervous. There is epic build up music as the magician calls their assistant on stage. The assistant climbs into a box that is covered with a velvet blanket. Why a blanket? I mean, isn’t the box good enough? What a pretentious as… forget it, I’m ruining this for myself. OK, so the assistant is in the box with their head and legs sticking out. What the fuck? Who made this box, anyway? Damn it, I’m doing it again. Then—oh shit—is that a saw? What’s going to happen with that? Fuck! No! The assistant’s been cut in half! And then the quantum computer outputs the answer. Wait, what? Where did the quantum computer come from? I don’t know—quantum computing is magic like that.

By now you have read many articles on quantum computing. Congratulations. You know nothing about quantum computing. I know what you are thinking: Whoa, Chris, I wasn’t ready for these truth bombs. Take it easy on us. But I see a problem and I just need to fix it. Or, more likely, call the rental agent to fix it.

You probably think that a qubit can represent a 0 and a 1 at the same time. Or, that quantum computing takes advantage of the strange ability of subatomic particles to exist in more than one state at any time. I can hardly fault you for that. After all, we expect Scientific American and WIRED to be fairly reputable sources. And, I’m not cherry picking here—these were the first two hits after the Wikipedia entry on a Google search of “What is quantum computing?” Nearly every popular account of quantum computing has this “0 and 1 at the same time” metaphor.

I say metaphor because it is certainly not literally true that the things involved in quantum computing—those qubits mentioned above—are 0 and 1 at the same time. Why? Well, for starters, 0 and 1 are defined to be mutually exclusive (that means it’s either one OR the other). Logically, 0 is defined as [NOT 1]. Then 0 AND 1 is equal to [NOT 1] AND 1, which is a false statement. “0 and 1 at the same time” just doesn’t make sense, and it’s false anyway. Next.

OK, so what’s the big deal? We all play fast and loose with words. Surely this little… let me stop you right there, because it gets worse. Much worse.

The Scientific American article linked above then deduces that, “This lets qubits conduct vast numbers of calculations at once, massively increasing computing speed and capacity.” That’s a pretty big logical leap, but I’d say it’s a correct one. Let’s break it down. First, if a qubit can be 0 and 1 at the same time then two qubits can be 00 and 01 and 10 and 11 at the same time. And three qubits can be 000 and 001 and 010 and 011 and 100 and 101 and 110 and 111 at the same time. And… well, you get the picture. Like mold on that organic bread you bought, exponential growth!

The number of possible ways to set some number of bits, say n of them, is 2n—a big number. If n = 300, 2300 is more than the number of atoms in the universe! Think about that. Flip a coin just 300 times and the number of possible ways they could land is unfathomable. And 300 qubits could be all of them at the same time. If you believe that, then it is easy to believe that quantum computers will just calculate every possible solution to your problem at once and pick the right answer. That would be magic. Alas, this is not how quantum computers work.

Lesson 1: don’t take a bad metaphor and draw your own simplistic conclusions from it.

Try this one out from Forbes: “A bit can be at either of the two poles of the sphere, but a qubit can exist at any point on the sphere.” Spot on. This is 100% accurate. But, wait! “So, this means that a computer using qubits can store an enormous amount of information and uses less energy doing so than a classical computer.” The fuck? No. In fact, a qubit cannot be used to store and retrieve more than 1 bit of data. Again, magic, but not how quantum computers work.

Lesson 2: don’t reduce an entire field to one idea and draw your own simplistic conclusions from it.

I can just imagine what you are thinking right now. OK hotshot, how would you explain quantum computing? I’m glad you asked. After bashing a bad analogy, I’m going to use another, better analogy. I like analogies—they are my favorite method of learning. Teaching by analogy is kind of like being in two places at the same time.

Alright, I’m going to tell you the correct analogy between quantum physics and magic. Let’s think about what a magic trick looks like abstractly. The magician, who is highly trained, spends a huge amount of time choreographing a mechanism which is then hidden from the audience. The show begins, the “magic” happens, and we are returned to reality with bafflement. If you are under 20, then you also take a selfie for the Insta #fuckyeahmagic.

Now here is what happens in a quantum computation. A quantum engineer, who is highly trained, spends a huge amount of time choreographing a mechanism which is then hidden from the audience. The show begins, quantum computation happens, and we are returned the answer to our problem. Tada! Quantum computation is magic. Selfie, Insta, #fuckyeahquantum.

Let’s dig into this a bit deeper, though. Why not uncover the quantum computer—open the box—to reveal the mechanism? Well, we can’t. If we “watch” the computation happen, we expose the quantum computer to an environment and this will break the computation. The kind of things a quantum computer needs to do requires complete isolation from the environment. Just like a magician’s trick, if we reveal the mechanism, the magic doesn’t happen.

OK, fine. The “magic” will be lost, but at least I could understand the mechanism, right? Sure, that’s right. But here’s the catch: a magician spends countless hours training and preparing for the trick. Knowing the mechanism doesn’t help you understand how to actually perform the trick. Nor does seeing that the mechanism of quantum computing is some complicated math actually help you understand how it works. And don’t over simplify it—we already know that doesn’t work.

Let’s look at the example of a sword swallowing illusionist. If you don’t know what I’m talking about, it’s exactly how it sounds—a person puts a sword the length of their torso in their mouth down to the handle. How one figures out they have a proclivity for this talent, I don’t want to know. But what’s the explanation? Don’t worry, I already googled it for you, and it’s simple: “the illusionist positions their head up so that his throat and stomach make a straight line.” Oh, is that it? I’m suddenly unimpressed. So now that you too know how to swallow a sword are you going to go and do it? I fucking doubt it. That would be stupid—about as stupid as reading a few sentence description of some “explanation” of quantum computing and then declaring you understand it.

Lesson 3: don’t place your analogy at the level of explanation—place it at the level of the phenomenon. Let your analogy do the work of explanation for you.

If you like figures, I have prepared a lovely summary for you.

Well there you go. Quantum computing isn’t magic, but it can put on a good show. You can learn about how to do the tricks yourself and even perform a few with a little more effort. I suggest starting with the IBM Quantum Experience. Or, start where the real magicians do with Quantum Computing for Babies 😂

One is the loneliest prime number

You can’t prove 1 is, or is not, prime. You have the freedom to choose whether to include 1 as a prime or not and this choice is either guided by convenience or credulity.

I occasionally get some cruel and bitter criticism from an odd source. I’m putting my response here for two reasons: (1) so I that I can simply refer them to it and not have to repeat myself or engage in the equally impersonal displeasure of internet arguments, and (2) I think there is something interesting to be learned about mathematics, logic, and knowledge more generally.

It all started when I wrote a very controversial book about an extremely taboo topic: mathematics. In my book ABCs of Mathematics, “P is for Prime”. The short, child-friendly description I gave for this was:

A prime number is only divisible by 1 and itself.

I thought I did a pretty good job of reducing the concept and syllables down to a level palatable by a young reader. Oh, boy, was I wrong. Enter: the angriest group of people I have met on the internet.

You see, by the given definition, I had to include 1 as a prime number since, as we should all agree, it is divisible only by 1 and itself.

Big mistake. Because, apparently, it has been drilled into people’s heads that this is a grave error, a misconception that can eventually lead young impressionable minds to a life of crime and possibly even death! It might even end up on a list of banned books!

By a vast majority, people love the book. I am generally happy with the reponse. The baby books I write are not for everyone—I get that. And I do try to take advice from all the feedback I receive on my books. There is always room for improvement. But the intense emotions some people have with the idea of 1 being a prime number is truly perplexing. Here are some examples:

I actually love the book, but there is a big mistake. The number 1 is not a prime number! The book should not be sold like this and needs to be reprinted.

and

1 IS NOT PRIME! How could a supposed math book have an error like this in it? I am disgusted!

Yikes. So what gives? Is 1 prime, or not? The answer is: that’s not a valid question.

Let me explain.

First, let’s look at a typical definition. Compare to, for example, Wikipedia’s entry on prime numbers:

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Much more precise—no denying that. It’s grammatically correct, but probably hard to parse. I wanted to avoid negative definitions as much as I could in my books. But that’s beside the point. The reason 1 is not a prime is that the definition of prime itself is contorted to exclude it!

OK, so why is that? Well, the answer is probably not as satisfying as you might like: convenience. By excluding 1 as prime, one can state other theorems more concisely. Take the Fundamental Theorem of Arithmetic, for example:

Every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.

Now, this statement would not be true if 1 were a prime since, for example, 6 = 2 × 3 but also 6 = 2 × 3 × 1 and also 6 = 2 × 3 × 1 × 1, etc. That is, if 1 were prime, the representation would not be unique and the theorem would be false.

However, if we do chose to include 1 as a prime number, all is not lost. Then the Fundamental Theorem of Arithmetic would still be true if it were stated as:

Every integer is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors and the number of 1’s.

Which version do you prefer? In either case, both the definition and theorem treat 1 as a special number. I’d argue that in this context, the number 1 is more of an annoyance that gets in the way of the deeper concept behind the theorem. But in mathematics you must be precise with your language. And so 1 must be dealt with as an awkward special case no matter which way you slice it.

So, is 1 prime, or not? Well, it depends on how you define it. But in the end it doesn’t really matter, so long as you are consistent. And understanding that is a much bigger lesson than memorizing some fact you were told in grade school.

The definition given in ABCs of Mathematics is not “wrong” any more than all of the other simplifications and analogies I have made are “wrong”. But, in case you were wondering, the second printing will be modified with the hope that everyone can enjoy the book. Even the angry people on the internet deserve to be happy.

David Wolfe doesn’t want you to share these answers debunking quantum avocados

Everyone knows you need to microwave your avocados to release their quantum memory effects.

Recently, I joined Byrne and Wade on Scigasm Podcast to talk about misconceptions of quantum physics. Apparently, people are wrong about quantum physics on the internet! Now, since the vast majority of people don’t listen to Scigasm Podcast [burn emoji], I thought I’d expand a bit on dispelling some of the mysticism surrounding the quantum.

Would it be fair to say quantum physics is a new field in the applied sciences, though it has been around for a while in the theoretical world?

No. That couldn’t be further from the truth. There are two ways to answer this question.

The super pedantic way: all is quantum. And so all technology is based on quantum physics. Electricity is the flow of electrons. Electrons are fundamental quantum particles. However, you could rightfully say that knowledge of quantum physics was not necessary to develop the technology.

In reality, though, all the technology around us today would not exist without understanding quantum physics. Obvious examples are lasers, MRI and atomic clocks. Then there are technologies such as GPS, for example, that rely on the precision timing afforded by atomic clocks. Probably most importantly is the develop of the modern transistor, which required the understanding of semiconductors. Transistors exist, and are necessary, for the probably of electronic devices surrounding you right now.

However, all of that is based on an understanding of bulk quantum properties—lots of quantum systems behaving the same way. You could say this is quantum technology 1.0.

Today, we are developing quantum technology 2.0. This is built on the ability to control individual quantum systems and get them to interact with each other. Different properties emerge with this capability.

Does the human brain operate using properties of the quantum world?

There are two things this could mean. One is legit and other is not. There is a real field of study called quantum biology. This is basically material physics, where the material is biological. People want to know if we need more than classical physics to explain, say, energy transfer in ever more microscopic biochemical interactions.

The other thing is called quantum consciousness, or something equally grandiose. Now, some well-known physicists have written about this. I’ll note that this is usually long after tenure. These are mostly metaphysical musings, at best.

In either case, and this is true for anything scientific, it all depends on what you mean by properties of the quantum world. Of course, everything is quantum—we are all made of fundamental particles. So one has to be clear what is meant by the “true” quantum effects.

Then… there are the crackpots. There the flawed logic is as follows: consciousness is mysterious, quantum is mysterious, therefore consciousness is quantum. This is like saying: dogs have four legs, this chair has four legs, therefore this chair is a dog. It’s a logical fallacy.

Quantum healing is the idea that quantum phenomena are responsible for our health. Can we blame quantum mechanics for cancer? Or can we heal cancer with the power of thought alone?

Sure, you can blame physics for cancer. The universe wants to kill us after all. I mean, on the whole, it is pretty inhospitable to life. We are fighting it back. I guess scientists are like jujitsu masters—we use the universe against itself for our benefit.

But, there is a sense in which diseases are cured by thought. It is the collective thoughts and intentional actions of scientists which cure disease. The thoughts of an individual alone are useless without a community.

Is it true that subatomic particles such as electrons can be in multiple places at once?

If you think of the particles has tiny billiard balls, then no, almost by definition. A thing, that is defined by its singular location, cannot be two places at once. That’s like asking if you can make a square circle. The question doesn’t even make sense.

Metaphors and analogies always have their limitations. It is useful to think this way about particles sometimes. For example, think of a laser. You likely are not going too far astray if you think of the light in a laser as a huge number of little balls flying straight at the speed of light. I mean that is how we draw it for students. But a physicist could quickly drum up a situation under which that picture would lead to wrong conclusions even microscopically.

Does quantum mechanics only apply to the subatomic?

Not quite. If you believe that quantum mechanics applies to fundamental particles and that fundamental particles make up you and me, then quantum mechanics also applies to you and me.

This is mostly true, but building a description of each of my particles and the way they interact using the rules of quantum mechanics would be impossible. Besides, Newtonian mechanics works perfectly fine for large objects and is much simpler. So we don’t use quantum mechanics to describe large objects.

Not yet, anyway. The idea of quantum engineering is to carefully design and build a large arrangement of atoms that behaves in fundamentally new ways. There is nothing in the rules of quantum mechanics that forbids it, just like there was nothing in the rules of Newtonian mechanics that forbade going to the moon. It’s just a hard problem that will take a lot of hard work.

Do quantum computers really assess every possible outcome at once?

No. If it could, it would be able to solve every possible problem instantaneously. In fact, we have found only a few classes of problems that we think a quantum computer could speed up. These are problems that have a mathematical structure that looks similar to quantum mechanics. So, we exploit that similarity to come up with easier solutions. There is nothing magical going on.

Can we use entanglement to send information at speeds faster than the speed of light?

No. Using entanglement to send information faster than light is like a perpetual motion machine. Each proposal looks detailed and intricate. But some non-physical thing is always hidden under the rug.

Could I use tachyons to become The Flash? And if so, where do I get tachyons?

This is described in my books. Go buy them.

Let kids be kids

Quantum Physics for Babies. Some find it hard to believe. But it is indeed a real book, and other books which introduce abstract scientific concepts to young minds have followed. It’s a quirky idea and I’ve told the story about how it all came about before. And people do love the quirkiness, but the honeymoon is short and sobering questions are soon to arise, like, “Isn’t this a bit much—do we really need another thing to teach children?”

Fear and uncertainty about the daunting task of teaching children about science and mathematics comes to the forefront and then it hits, shot straight from the hip, “Let kids be kids.” You hear that a lot. In fact, it’s said in so many contexts that it’s lost any meaning it might have had, but I think the gist is this: whether guided by gut instinct or scientific research people know the value of play in childhood—but their idea of education as an activity is the exact opposite of play.

I believe this is the wrong way to interpret education. The formal education system that you and I grew up with has existed more-or-less unchanged for several decades. It chops up knowledge into components which are introduced in a linear fashion. Sometimes the paths fork and the major branches are called “careers”. For a time, the system worked quite well—but that time is passed.

This is understandably a source of stress for parents. The education system was supposed to be the rock. Of course we don’t know everything, and so we send the kids to school, which has experts on all topics to fill those gaps. But technology is becoming more and more ingrained into society and everyday life. The problem is that technology is changing so fast that it is nearly impossible to keep up. The idea of having a single career has gone out the window.

This leaves us questioning the role, even the identity, of education. My view is simple: life is education. Maintain that childhood curiosity and drive to ask questions, and whatever you call education will come for free. Besides the obvious things—survival, independence, morality—what is the mark of successful parent? Even ignoring the fact that it is an immense privilege to entertain such a question, this is dangerous territory. But I’ll risk an answer: the goal of parenting is the help your child find their passion, which is that thing that fuels their curiosity.

Are you happy? If so, it’s probably because you do something that you love, at least as a hobby. I’m very lucky in that people pay me to do the things I love. Wouldn’t it be great if I could arrange for that situation to be a little bit more likely for my own children?

So how am I going on helping my children find their passion? I don’t really know. I guess I won’t find out for some time. But here is one step I think can go a long way: variety. Not necessarily for them, but for you. If there is something you avoid, they will never experience it.

I can’t think of any interest my children might have that scares me. But many parents I talk to find mathematics and science scary. Whether it is intentional or not, they steer them away from these topics. The situation is so bad that we discuss when is too young to introduce science to children. Science is just a formalized way of exploring our natural curiosity. You don’t introduce it; you reintroduce it—and only because you’ve taken it away.

Books about mathematics and science for young children are not educational tools for the children. They are reminders for the parents that this is not something to fear. This is something that people derive a lot of passion from. And, if some day your child sees some science topic that interests her, she won’t be afraid of it, because you are not afraid of it.

So, don’t feel you need to read Quantum Physics for Babies because you need to keep up with the Zuckerbergs Joneses. Read it because it’s something you wouldn’t otherwise be exposed to. Read it because you might be curious about the topic. Read it because you had a really cool friend that gifted it to you. Read it because it’s fun. And, if it only leaves you with more questions, good—ask away.

This post originally appeared on the Early Learning Review.

Quantum Physics for Babies

This talk was given at the University of Sydney School of Physics Colloquium 19 June 2017.

It’s​ great to be back here. That feels a bit awkward to say since it’s only been 6 months since I left and I’m only 10 minutes away. But King and Broadway might as well be the Pacific Ocean for academics. I’m Chris Ferrie. I’m just down the road at the Centre for Quantum Software and Information. It’s an awesome new Centre. We’re on Twitter. You should check us out.

Now, though the title of the talk doesn’t make it obvious, I am a serious, well… maybe not serious, but I am an academic. But I also have a hobby… tennis. No, I write children’s books. Yes, it is a real book. And, yes, I wrote it and self published it several years ago when I was a postdoc. Why, and how, and for what purpose, well… that is the purpose of this talk.

measure-1509707_1920Measure twice, cut once. So the old proverb goes. It certainly it makes sense if you only have enough material to build a thing. However, and I see this all too often in otherwise very smart people, too much measuring leads to over optimisation and inaction, not enough cutting. Whereas, I like cut several times, toss things out, try new cutting instruments, and so on. I almost never measure. Ultimately, this is the story of Quantum Physics for Babies. I just did it. It wasn’t carefully planned, nor was there a spark or ah-ha moment which spawned the idea. I started, I failed, I started again.

And, for better or worse, the book became popular. Journalists starting asking me, “why did you write this book?” and, more seriously, “why teach quantum physics to babies, why is that important?”

brain-2062057_1920So, I started to rationalize. Why did I write this book? And, is it important? In particular, is it important for all children, not just my own? (because it is always important to find a way to discuss your passion with your own kids.) I think the answer to “is it important?” is yes. In this talk I’ll walk you through the various levels of rationalisation I’ve went through. Each has an element of truth to it, both for myself personally and what the experts on the topic of early childhood education espouse.

But let me start at the same place I start most things, with a joke. Someone that has known me for only a short time probably wouldn’t be too surprised that I was voted “class clown” in high school. Humor plays a crucial part of almost every aspect of my life. I laugh with my partner, I laugh with my children, I laugh with my friends, and I laugh with other scientists. (Einstein didn’t think it was very funny—but, then again, he never liked quantum physics.) Happiness is the difference between your reality and your expectations. Humor often defies expectation and happiness ensues. So, hopefully you didn’t come to this talk with too many expectations and you’ll leave a little happier then when you came in. At least there’s cake.

There is no denying that I saw the irony as good for a laugh the first time the title popped into my head. Of course, the level of humour I’m talking about is not at all for the advertised audience. I’ve never seen a child laugh at the title of the book. Adults, on the other hand, love the juxtaposition of quantum physics with “for babies”. So I knew that at least a few people would buy it as a gag gift for a nerdy friend having a baby. What I didn’t expect was this nerdy friend getting a copy.

I’ve joked with various people about making other goofy “for babies” books. Why not “contract law for babies” or “geopolitical policy for babies”? Though, the only person in the world that needs to read such a book is too busy tweeting insults at women. But quantum physics—yeah—people seem to agree that is worth being more than a joke, and hopefully I knew something about it.

In the end, I put real thought and effort into the content. The goal became clear enough: how to fill a baby book out with short sentences, no jargon and a coherent description of quantum physics. It was a challenge and there is still probably room for improvement. But I’ve already had people say, “we all had a good laugh, then I started to read it and there was real quantum physics inside.” Many adults even claimed they learned something. But were the children learning?

The unanimous advice for new parents is to read to your newborn. Most say it doesn’t even matter what it is, just read. But, let’s play a little game here. Suppose a parent does read to their child and has no time to add a new book to the rotation. Then, Quantum Physics for Babies needs to replace a book. What book should it be? First, I don’t think it should replace fiction. Fiction and fairy tales serve many purposes and, besides, variety is the spice of life. So we are left with nonfiction, which for baby books is limited solely to only a few types of reference material.

Quantum Physics for Babies - Sydney Uni 19 June 2017 (1)A huge fraction of any newborn’s library will begin with the word “first”: “First Words”, “First book of numbers”, “First alphabet book”, and so on. One quickly gets the impression that these are essential reference books for the early learner. But beyond the obvious things—letters, numbers, shapes, three letter words—are a myriad of books about animals, and mostly farm animals.

Now, learning is tricky concept to define even for adults. There are numerous models of early childhood cognitive development, and so it is hard to say conclusively what is being “learned” and at what level, but something is clearly happening since every 3 year in the world knows what sound a cow makes. Do you? I think I do. But I have never heard one myself. Maybe there was a time when that was important, or at least relevant, but I don’t think that time is today.

Quantum Physics for Babies - Sydney Uni 19 June 2017 (2)Here is another example. Do you know what these birds are? My children seem to know and can identify the difference between a penguin and a puffin. Why? Why are there more books about puffins than there are puffins and no books about transistors when you are probably sitting on a billion of them right now. In your phone lives a few billion transistors making up, by the standards of only decade ago anyway, a supercomputer. A child today will probably spend their entire life closer to computer than they will an animal of comparable size. I’m not suggesting than all books on animals be replaced by physics for babies books, but we could maybe replace a few.

I won’t claim my children understand quantum physics, but they certainly understand it at the same level they understand anything else gotten from a book. They will tell you that everything in the world is made of atoms and atoms are made of neutrons, protons and electrons and electrons have energy. I think that is about the same level of understanding as being able to identify a puffin, or should I say Fratercula corniculata for the baby ornithologists in the crowd.

So it seems then that Quantum Physics for Babies is here to stay. But we’re all scientists here and we love nothing more than free cake and to categorize things. So where does Quantum Physics fit? In what aisle of the bookshop does it sit on the shelf? Well, it turns out that it has been shoehorned into the new educational buzzword de jour: STEM.

Quantum Physics for Babies - Sydney Uni 19 June 2017 (3).png

STEM (Science Technology Engineer and Mathematics) started out as an initiative to focus on its namesake topics with the goal of training a workforce ready for the careers that were assumed new technologies would create. Interestingly, the first press mention of the acronym seems to go back to 2008 when The Bill and Melinda Gates Foundation donated $12 million dollars to the Ohio STEM Learning Network, which is still going strong today. Most never looked back. [By the way, much backlash ensued over leaving out the Arts, for example. So you might see STEAM or even STREAM (Reading) out there.]

Now governments all over the world currently have numerous initiatives at all levels of the curriculum to enhance what they called STEM-based learning. This is vaguely and variably defined and can mean anything from simply having access to more technology in the classroom to the design and building of simple machines to solve practical problems. But the motivation and directives that follow are often based on decade-old studies suggesting rises in STEM-related jobs. One recent state-level education​ department cited a study with data collected prior to the release of the first iPhone (that was only 10 years ago, by the way). The often cited report of the Chief Scientist of Australia contained recommendations citing data accumulated from 1964-2005. Policy is good, but it cannot keep up with the pace of technology.

Disruption! The fear today—fueled by startups, makers, and ever younger entrepreneurs—is that we just have no idea what jobs will look like in the future. And so STEM, at least for the trailblazers, is now a movement with the audacious goal of graduating creators and innovators. We no longer want graduates who simply have more and integrated technical skills.

What does this look like? Let me give you an example. Here is Taj Parabi, now 17, CEO of his own business which ships DIY tablets. His company, fiftysix, also visits schools and puts on extracurricular workshops for students on technology and… entrepreneuring! That’s right. Your children are competing with 8-year-olds trained to be CEOs of their own companies!

On a topic near and dear to my own heart, a now veteran effort from the Institute for Quantum Computing is the Quantum Cryptography School for Young Students (QCSYS)Quantum Physics for Babies - Sydney Uni 19 June 2017 (4), which invites international high-school students for a week of intensive training on quantum technology. Indeed, many of these students eventually become PhD students in Quantum Information Theory. Other efforts include school incursions and the new QUANTUM: The Exhibition which is an all-ages, hands-on exploratory exhibit.

Quantum Physics for Babies - Sydney Uni 19 June 2017 (5)On the other side of the border (remember: the wall is on the souther border), IBM has recently released the “Quantum Experience”, an app that lets you program a quantum computer, a real quantum computer. You create an algorithm and then jump in the queue for it to run on real device housed in IBM’s labs. Here they are video conferencing with a school in South Africa and hosting local students.

So that is the tiniest snapshot of STEM education today. Is Quantum Physics for Babies on par with these efforts? Are the children learning the skills necessary to be quantum engineering start-up entrepreneurs? Of course not. Quantum Physics for Babies, at least as far as reading to actual babies is concerned, is about the parents.

20 years from now, your child might be sitting in an interview for the job of Quantum Communication Analyst or Quantum Software Engineer. How long will it be before such topics feature in the report of the Chief Scientist on the curriculum? How long before it is mainstream in public schools? I’m not holding my breath.

The problem today is that it’s impossible to keep up. Pilot studies, kids maker studios, programming toys and apps, … These are all beautiful, but the growth of STEM education has now outpaced even the technology. The curriculum cannot keep up, and so the onus of STEM education, however you want to define it, is largely on the parents.

Again, the efforts of STEM education researchers are impressive, but a parent cannot assume that their child will happen to be in the school that benefits from these one-off pilot studies or incursions. The education system in most developed countries has been too long taken for granted and is now depleted from underfunding. No doubt there are many great principals and great teachers out there. Two days from now, I’m going to go speak with a dozen principals and teachers about STEM education. But there are almost 1500 primary schools in Sydney alone (over 3000 in New South Wales). There is much that needs to be done at the larger scale—but even if I said that was being done, it is little comfort for parents today.

So—in the end—this is what I both want and expect from the book: the elimination of doubt and fear. I want quantum physics, indeed all physics and math and science, to be normal for a child to take interest in. When your child asks about going to Canada for a summer school on quantum cryptography, that should be seen as normal request. When she asks to help her set up an account for a quantum cloud computing service, you should be like, no worries I already have one.

Today, when 1 in 3 Americans would rather clean a toilet then do a math problem, when a search for “quantum physics” brings up Deepak Chopra instead of Stephen Hawking, and when the facts pointing to climate change are seen as equally compelling as a celebrity’s argument for a flat earth, we need all the help we can get. And we need to start that conversation as early as possible.

Quantum Physics for Babies was just the beginning…IMG_20170606_175007