Helping Our Children Fall In Love with Math by Loving It Yourself
Help your children fall in love with math by loving it yourself! Learn how to use language, toys, games, TV, movies, books, and teachers to create a positive environment for math. Understand the butterfly effect and the law of unintended consequences to help your children develop a strong, intuitive mental model.
Discover the Magic of Math with the Lorenz Attractor: Uncover the Power of Free Will and the Butterfly Effect!
By Michael Levin
Friday, May 19, 2023
Things are difficult by nature. If things were easy, everyone and everything would be doing it, and it would lose meaning. If everything were too difficult, nothing would ever happen. There is a vibrating edge between the two, and we live there. Especially we humans, because it is precisely this wobbling between almost impossible and almost almost ruin that is the Earth’s orbit around the Sun. It’s the lovely, miraculous stage upon which sentient life that can appreciate it such as us have evolved.
Life happens in such wobbly places. It’s the sine wave of the universe. Folks hate math, but life is math. Math is what you use to describe and perchance have insight into this pendulum-swinging oscillation between the two, which we see mostly as day and night and the years of our life ticking by. We feel it as the dimensions of time and space in which we live. But we do indeed see and feel it, and it is indeed a sine wave, and it is indeed the stage of life.
Why math is a hated and reviled subject is first a direct result of the society in which you live, which is itself a result of the evolved tools of thought that culture uses to think. In other words, language. We hate math because the English language evolved against the backdrop of royalty and kingdoms, which are in fact a form of a criminal protection-racket formalized into government and social order. But they’re really fiefdoms. You get a fief of land and we take your grain.
Give me geld, peasant! Serf! Peon! Pee on… pee on you… that’s what they do, those royals. They don’t want you to know math because they don’t want you to know how much they’re stealing from you. That’s English. That’s the tool for thought that you’re raised on. You hate math because you’re raised to hate math. It’s not a conspiracy. It’s the evolution of language.
Asians aren’t inherently or genetically better at math. It’s that their language is more suited to it. I’m not going to re-write Guns, Germs and Steel here. Just go read it for yourself, but know that math is not what you think it is. Another example is how all the college Engineering 101 and 102 freshmen courses such as Physics and Calculus are designed to make you drop out because they don’t want incompetent engineers building bridges and stuff. Fair, but all our brains could do it if we were raised to think that way.
Now it’s not always society as a whole that let you down. Sometimes it’s more local, such as your parents or your school. No matter how rotten the English language is for math, if it’s integrated into your life right from the start, with the right toys as an baby, the right games as a toddler, the right TV and movies as a child, the right books as a pre-teen, and the right teachers a teenager you can overcome the handicap of English. But if you’re raised by someone who themselves “hated math”, you’re screwed.
And that’s colossally unfair. What’s worse is that solutions are there all around you, but you’ve likely closed your mind to them. You’ve been conditioned with negative reinforcement responses to close your mind to good solutions. It’s pure Pavlovian conditioning, like ringing a bell when you feed an animal, they will begin to associate the ringing bell with the positive experience of food. The very word “math” is now is a trigger for many, because of the schlock canned lessons pushed on them, which are as boring as the teacher who uses such techniques is incompetent.
Yes, there are good math teachers out there, but I can only remember two, and they were so fleeting, so rare. I wish I had them year after year. Thank you, Mr. Savage. You were savage. While I’m at it, Stephen White, you were all that and a bag of chips in English! Shout-out to Plymouth Whitemarsh!
Other than those few points of light, those insanely talented and dedicated soldiers of the correct war, you’re probably being conditioned to hate math by the very people who are supposed to be teaching you math. It’s a crime.
It’s the unfortunate circumstances of your early-life (all English-speakers of lower socioeconomic conditions). It’s not your fault, but more importantly, it’s never too late. The cycle can be broken right here, and I show you how. Unfortunately, it’s as much time coming out as it was time going in, so the sooner you start righting this wrong, the better! I’m 50, so I’m personally going to be 100 before I get down calculus. Perhaps you can do better.
With the right plan, the right tools, and the right instructor, we can do this. Unfortunately, such plans and tools aren’t so obvious to everybody, and such instructors aren’t so common. But they do exist. You just can’t plop a kid in front of a screen and hope it happens. It has to be totally integrated into their lives. And really you’ve got to find the love for math yourself if you want your kid to feel the love. They learn by example, remember? Do the maths in front of them if you can. Happily, that can just be playing with toys.
It’s Pavlovian conditioning again, but the right kind. You know what kids want? To not be bored. To feel like they belong. To feel proud of themselves. To laugh and play.
There is no reason “just learning math” couldn’t be a bi-product of becoming part of a really cool group of like-minded kids staving off the boredom, either in-person or online in this age of COVID. The reason this isn’t the same thing as just plopping them in front of a screen is the actual social connections that are forming, the group dynamics, the one kid egging the next on to greater and greater things. The right instructor is the one who knows how to make this happen.
Group-dynamics is rule #1, especially if you’re fixing problems that have set in from a wrong-minded upbringing. Do they have existing social groups where appealing, but still math-leaning activities can be introduced? Do they have friends who are already into math? Do they have friends who are into something else, but could be brought into math? Or perhaps you live in an area with world-class robot clubs, or chess clubs, or even art clubs.
Because art is math. Music too. Especially, music. It’s just not taught that way. But honestly if I were to delve into Gödel, Escher, Bach: An Eternal Golden Braid, I’d have to talk about artificial intelligence and the nature of creativity, and this article would run all out of control. Suffice to say, you can teach math very effectively by teaching around it with other subjects that have more surface-appeal for children.
I’ve seen wonderful Kickstarter for a book called Boolean Logic for Babies, and wow is it awesome, colorfully and interactively building up page-by-page the story of ON’s and OFF’s and why that runs everything in the digital world. But the world isn’t only 1’s and 0’s, so you have to follow-up immediately with something to prevent false dichotomies. In other words, things aren’t nearly as black and white as the very useful lie we call digital electronics.
Surprise! Electronics isn’t necessarily digital. We just force it to be that way and present it like it’s the whole story. It’s not. That’s a lie. The “digital” part of digital electronics is actually a complexity-reducing trick we do so that the principles of boolean logic (switches) can be applied to the real world.
You’ll hear the word thunk used a lot in computer science. It’s the sound of a deep, rich analog reality being reduced to the false dichotomy of 1’s and 0’s. THUNK goes a deeper, richer full-spectrum reality full of wonder and insights and easy-to-conduct home experiments. Now instead of Vandergaph generators and Tesla coils, it’s breadboards and Raspberry Pi’s—and even that’s if you’re lucky.
Natural electronics is analog by nature. Digital electronics is artificial, and so is a form of art, which only makes it natural that it is today leading works of art… artifacts, in fact that exbibit intelligence. But I digress.
So to fix this common lie of digital supremacy in nature, the Boolean Baby Book needs something like a swanee (slide whistle) to show the infinite range of sound. Reveal the full spectrum! Have them try to make a high note and a low note without going through the middle. That reveals the lie. That shows just how fast switches are to do the digital trick. Then talk about canal locks, relays, vacuum tubes, transistors, the modern integrated circuit, optical computing, and quantum computing. All still math, but tech ain’t the only path.
When you give a curious mind a swanee, they’re gonna want a saxophone. And then you’ve gone and done it, sparking an interest in music. You could end up a Starfleet Admiral or something. Music not for you? Well, that wonderful slide whistle lesson can lead very naturally into looking at that sound on an oscilloscope. If you ever want to quite literally draw the connection between math and music without saying the dreaded triggering math-word, just throw the soundwaves your kid’s making with whatever instrument up on the screen of an oscilloscope. Do you not know what an oscilloscope is? And you’re teaching your kid math? I question your qualifications. And don’t pretend. I can tell.
Okay, so then an oscilloscope is too expensive, you say? And indeed these were $1000-devices not long ago. I remember back in maybe 1990 or 91 when Commodore computers was going bankrupt and they were liquidating all their assets, I made a B-line straight for the lab oscilloscopes but was blocked by someone who already had claim to them, but I knew didn’t really need another oscilloscope in their lives, so they snatched it out of the hands of a kid who could be using it today with their own kid, these old-style cathode ray tube ones of the sort particles like electrons were discovered with. Oh, I may still dig one up.
But no, it’s Kickstarter to the rescue again, because even though a true hardcore oscilloscope is analog by nature, the digital world has driven very good digital oscilloscope emulators of the real analog thing down to like $100, quite accessible for a learning device. And you can even make the difference between analog and digital oscilloscopes a lesson in itself, drawing parallels between regular guitars and electric guitars, real pianos and electric keyboards… the possibilities are endless… oh, I know, I know!
You’ve heard of the butterfly effect, right? Hunting dinosaurs in the past who are about to die by natural causes anyway if you have a time-machine causes no harm, right? But when you return to your own time everything’s different because maybe the dinosaur fell onto a butterfly when your dumb ass shot it. Another is that if that a butterfly flaps its wings in Okinawa, there may as a result be a storm that ravages New York. Ask your student to come up with more of these stories. That’s math!
But don’t stop there. Remember the aforementioned difference between analog and digital this-or-that? Well guess what? Without even mentioning math or computers, you can put one of the greatest toys and cosmic insights in front of your student to engage, delight, and sneakily lay down some of the best maths that ever was. And that is visualizing the butterfly-shaped Lorenz attractor, thus giving one of the ultimate examples of… of… of… well, so many things. Let me explain.
When we say the “butterfly effect” it naturally invokes the image of a butterfly, right? Something with bilateral symmetry whose main characteristic is a big flanging wing on each side, right? And we talk about butterflies in this A leads to B leads to C leads to colossally different outcomes because a butterfly is such a little thing, right? A dinosaur falls on one. One flaps its wings creating a little air-current in a far-distant land. Well what if I told you that the maths behind this both draws a shape of a butterfly and reveals the lie in these assumptions. B does not necessarily lead to C.
I kid you not. It’s called a strange attractor, but that it looks like a butterfly is only just the beginning of the wonder of this story, because in reality the butterfly effect is bullshit. Why? why… why William… William Yeats, I believed you but you misled me! As did everybody who’s ever told your about the butterfly effect a certain way because it makes a better story. Beware the sensationalist! I lost you? Okay…
First verse of The Second Coming by William Butler Yeats:
Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.
No, Mr. Yeats. The center can hold, and I have the maths to prove it, and you don’t have to look at a single number, and it’s the most cool interactive visually engaging and beautiful toy ever invented, and there’s a lesson like the classic vs. electric guitar in here that’s more accessible because the digital version of a lorenz attractor is an easy download on your phone or quick visit to a website.
So you see, the center can hold even if the dinosaur steps on the butterfly you still will be born. And a butterfly flapping its wings in Okinawa isn’t necessarily (and probably won’t) change major weather patterns anywhere in the world. The fact that either might is the extreme exception and not the rule, just as with the domino effect, some developing nation becoming communist isn’t going to unleash a red tide.
People who latch onto the exception and make you think it’s the rule are trying to make you support war to kill our children and put money into their fat-cat bank accounts. This both kills your children (a potential competitor) and adds to the generational wealth being handed down to their children, like those of Lyndon B. Johnson’s and more recently, the Bush’s and Cheney’s. Blackwater, much? So math fortifies your mind against social manipulation and improves your lot in life and that of your children’s. The butterfly effect is a fallacy because the center can hold. This is a beautiful lesson.
Specifically, if the concept of the butterfly effect is causing you anxiety because of the false believe that any little move you make is going to have consequences that spiral out of control, put it to rest. It won’t. Oh, it might, but much more likely you’re only switching wings. To get an instinctive feel of precisely how often and how damaging, watch the Lorenz Attractor. Play with the apps.
Not all life parallels the particular magical formula I’m talking about:
dx/dt = s (y – x) dy/dt = rx – y – xz dz/dt = xy – bz
…and you certainly don’t have to understand that by looking at it (just watch the vids and play with the apps)… but many things in life do return to normal. In this case, they oscillate between 2 “wing sides”, but not on every pass. Every once in awhile the “butterfly effect” causes the little travelling dot to switch sides. But more frequently it’s just going in a little orbiting circle on one side (your comfort zone), and on a less-frequent basis it will switch sides. Then it comes back.
Many people confuse the butterfly effect with the law of unintended consequences. Perhaps it’s just labels and I could make the same argument about that one. Even when you make decisions that take you out of your comfort zone, you can always return to it. Maybe not on the first rotation, but give it 2 or 3 more and you can get back to where you were.
The most damaging fallacy of our time is the belief that what doesn’t kill you makes you forever a victim, damaged goods entitled to compensation, and it’s downhill from there and you can beat up everyone around you with a sense of entitlement and correcting their language and trying to impose your belief system on them. Wrong! I’m sorry about whatever happendd to you, and I’m sure it was awful and I’m not invalidating it. It’s just that you’re still alive, aren’t you?
What, are you not in control of your very own mind and how you move ahead in life? You’ve become like a feather in the breeze rather than a human, but a loud, complaining one? Get off it. What doesn’t kill you makes you stronger, period. If not, your mommy and daddy let you down too early, and you haven’t started correcting course soon enough. And because it takes as much time to back out of a bad situation as it took to get in, you had better start now. Watch the Lorenz Attractor. Okay? Now, steer that dot.
You are not actually following that mathematical formula. You have human free will, because we don’t live in a super-deterministic universe. That’s what we call non-falsifiable and about the same as believing in bigfoot. You can’t prove bigfoot doesn’t exist and you can’t prove that we do live in a super-deterministic universe.
So work on the presumption that you have free will, and that you can return to your comfort zone if you made a mistake. It’s not proven by the Lorenz Attractor, but it does give compelling evidence and a strong, intuitive mental model. And know that you’ve been lied to about math by people who don’t know better in our modern age, and by the evolution of your primary spoken language over the last 1000 years in a way that says nothing about your natural abilities, predilections, or what you’re capable of.
And most importantly, it says nothing about what subject-matter and things in life you might find interesting, and indeed fall in love with causing the law of unintended consequences to work in your favor.
And finally, the proper way to view the butterfly effect as expressed in the formula above is with an analog computer. I shit you not. This is a thing, and it’s what Eddie Lorenz first visualized the phenomenon on, trying to debug inconsistencies he was encountering on a paper printout, thus discovering two new fields of science: Chaos and Complexity theory. And somebody please kickstart an analog computer butterfly effect toy, cause I’m in!
There are some beautiful minds out there. Maybe I’ll make the whole math curriculum I have planned for my child actually the story of such inspirations as Hypatia - Geometry and Astronomy, Sophie Germain - Number Theory, Ada Lovelace - Computer Science, Sofia Kovalevskaya - Analysis and Differential Equations, Emmy Noether - Abstract Algebra, Maryam Mirzakhani - Geometry and Dynamical Systems, Karen Uhlenbeck - Topology, Ruth Lawrence - Number Theory, Olga Ladyzhenskaya - Partial Differential Equations; and actually learning the math, just a side-effect.