This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com
In reaction to Yuval Noah Harari’s book Homo Deus (the part about humans evolving to break out of the organic realm and possibly breaking out of planet Earth):
When you cross the street there’s always a risk that an accident will happen that has a non-zero probability. If you live infinitely long, anything that has a non-zero probability can happen infinitely many times in your life. For example, if the event we are talking about is an accident, the first time it will happen in your life, you’re already dead. So when you cross the street and want to live infinitely long there’s a risk that an accident will happen and you die. So we come to the conclusion, that if you want to live infinitely long it’s not worth crossing the street. But there’s always a risk that you die, so if you live infinitely long, it’s not actually worth living. So we’ve got a little bit of a problem here. Unless you come to the more extreme idea of detaching yourself from the physical world all together. And I’m not talking about the sort of thing that you don’t have a body, but somehow still exist in the physical world. I mean literally that you live in a pure mathematical world. Because in mathematics, you can have things that have zero probability of happening. You can have something definitely happening and you can also have something that is definitely not happening.
However, there’s another thing. How does mathematics actually work? There are these things called axioms and it’s sort of built up from that. What if we even do away from those axioms? Then we can actually do anything in that mathematical world. And what I mean by anything is really anything that you can from any set of axioms that you can come up with. There’s a little bit of a problem with that, you can come to contradictions, it’s a little bit risky. We are really talking about the ultimate multiverse, we’re talking about quite controversial stuff here. The only way anyone can come up with this is by pushing to the extremes.
In reaction to Yuval Noah Harari’s book Homo Deus (the paragraph about the a-mortals anxious about dying in an accident):
With individual intelligences, you can have the car that’s driving down the street not knowing that you are going to be crossing the street at that point in time and then poof! You got yourself an accident. With collective intelligence though, that doesn’t happen. Because the whole definition of knowing something or not knowing something breaks down. The members of collective intelligence don’t have the notion of knowing something. It’s only the “central intelligence” that the members are hooked up to that has the notion of knowing something. Which means that you can have the central intelligence deciding that a car driving down the street does not create an accident with the person crossing the street.
In this video, Simon (a 9 year old mathematician and programmer) shares his views on what absolutely needs to change in the educational system and why self-directed learning works better than traditional schooling. Simon’s main points are:
At school, you’re forced to master a few subjects at the same “average” level while when learning at your own pace you tend to follow your talent and passion and learn some subjects at a much higher level. Simon depicts this difference as two bar chart diagrams. On the schooled diagram, there’re fewer subjects/areas of exploration and they are all at about the same level. On the self-directed learning diagram, the bars resemble a diverse metropolis with multiple buildings of varying height (or a garden with many sorts of flowers). Simon also explains that standardized tests and IQ tests expect a child to have developed evenly in all areas, while it may be more natural for a child to be much more developed in a few specific areas depending on her interests, and that there therefore such a thing as a total score simply shouldn’t exist.
Simon’s second point is that the internet, with its online educational opportunities, is going to kill traditional schooling. Simon himself is a perfect example of someone who learns a lot more on than off line.
Simon regrets that the way a student’s proficiency is evaluated today is mainly based on testing the speed at which the student can apply trained strategies as opposed to looking at the student’s original problem solving ability in an untimed setting.
Simon’s final argument against the traditional school system is that it doesn’t allow for failure. Failure is being discouraged and stigmatized, a bad grade can have serious consequences. That is very counterproductive, says Simon, because failure is an important part of the learning process. You don’t learn from your successes (when you have simply used what you already knew), you learn from your failures (because you start to look into why you’ve failed and that makes you a little smarter every time).
Simon has been teaching himself since he was a toddler. He is especially fond of math and sciences, doing university level math and researching serious questions about quantum mechanics and general relativity. He is also fluent in several programming languages. We have had to move from Simon’s native Amsterdam to Belgium to be able to homeschool, because homeschooling is nearly illegal in The Netherlands. Simon is an adamant advocate of educational freedom. There is a growing body of evidence that forced learning is not only ineffective and damaging to the intrinsic motivation, but may also be psychologically detrimental.
This is the fourth video in Simon’s short series Infinities Driving You Mad. In this episode, Simon attempts to start to comprehend indescribable numbers. To Simon’s knowledge, no one has ever made a video about indescribable numbers on YouTube before. Simon is planning to record a follow-up to this video, something like part 4b.
“I can see that your son has native speaker skills, but we still cannot give him a passing grade”, the English examinator told me in an apologetic tone of voice. She and her colleague at the Brussels examination committee had just finished their assessment of Simon’s oral English and brought Simon, a whole storm of emotions on his face, back to me in the waiting room.
“We were just wondering, does he speak Dutch? We weren’t sure he understood the tasks and they were written in Dutch”, — the examinator was sympathetic of Simon’s young age as most of the other kids taking the same test were about 6 years his seniors. As it turned out, the first task was to describe several photos of “criminals” (one of them with many piercings), the second task involved choosing two things that Simon would like to do from a list of recreational activities (the list included an escape room and a Stonehenge trip). “I just didn’t know what to say!” Simon was catching his breath in between the sobs. “It’s an impossible question, because I had to choose two things I like from a list where there wasn’t anything I liked!” The examinator suggested Simon could have said why he disliked those things. “If you don’t find something interesting you just don’t find it interesting, it’s a given fact! You can’t explain it!” – he told her in English.
Another fact is that Simon wouldn’t be able to perform these tasks in any of the three languages he speaks. Not because his vocabulary or grammar don’t stretch that far. I often hear him construct amazingly intact sentences, which I immediately record, like this one recently: “This is incredible! We’ve found a connection between a discrete problem, of what’s the smallest number that divides all of the numbers in a given sequence, to a continuous problem, of what is the fundamental frequency of a combination of sine waves. In other words, we found a discrete solution to a continuous problem!” Simon loves deep philosophical or scientific questions, but often cannot answer open questions lacking substance. He doesn’t care if you ask him to describe someone’s looks on a picture, it’s not important to him. He doesn’t know how to pick two things he likes from a list of things he doesn’t like. It’s just the way his mathematical brain is wired.
“Can I send you one of the many videos on Simon’s YouTube channel as an alternative proof of his excellent oral English skills?” I asked, still shocked at the absurdity of the situation. “Because I dare to say Simon speaks English better than any other student you have examined today”. The examinator agreed that I was probably right in my judgement but couldn’t accept anything else but a completed exam task.
Although distressed about what Simon had to go through, I can’t help feeling content with today’s scoop. What can provide a more obvious proof that exams don’t do a good job measuring one’s skill than this example of a 9 year old who gives hour-long science lessons on YouTube, speaks at grown-up creative coding meet-ups and is often mistaken for a native speaker, but doesn’t pass his oral English exam because he’s being asked questions that don’t interest him?
It wasn’t Simon who failed today, it was the exam that failed to measure his English. And this raises a whole lot of questions. Why is this system of measurements, that clearly doesn’t work for everyone, has become decisive in how our society views someone’s ability? And what is the use of spending so much money and nervous cells on something that doesn’t work?
Wouldn’t it be more fair towards both the students and anyone who honestly wants to know their level to actually look at what they can do with their knowledge in real life (their actual projects, videos of their social engagement) instead of the fake setting at the exam? Wouldn’t it be wiser to observe a student’s gradual progress in a given area, instead of stressing the students out and giving them the impression that it’s all about the examinator checking off that box and they can forget what they have learned the next day, because all that matters in our society is the passing grade?
“I’m so neutral about this”, Simon told me (in English) when he was lying in bed the same evening. “Because on the one hand, I kind of feel bad. And on the other hand, it’s so beautiful how we sort of accidentally taught them how exams can show false negatives or false positives. Because the exam showed a false negative. Even the examinators know it’s a false negative”.
In AI there’s this concept of dimensionality reduction, which reduces a lot of dimensions to three or less dimensions (however you lose a lot of information through that). IQ tests are basically a very, very, very glorified version of dimensionality reduction.
DNA stores zetabytes of information (one zetabyte is already 1000 to the power of 7, a sextillion bytes). OK, 99%is just telling that you are a human, but there’s still very much left and, as you can probably see, it’s still way, way, way too much to be reduced to a single number.
Simon didn’t want to watch Interstellar (he generally dislikes fiction and often finds it too scary as well), but somehow he did get sucked into the story after his sister and I were watching the movie right next to him for several days in a row and talking about it extensively. It’s one of my favourite films and I so much wanted Simon to see the part about time dilation and the black hole, and hear his thoughts about those scenes. I admit they were quite difficult for me to grasp when watching the film for the first time, especially the scene where the main character finds himself in the tesseract and has multiple visions of his daughter from the past. When we got to the scene, Simon was on fire. He kept walking around the room, euphoric as he was explaining to me how he understood what was happening on the screen:
“They used the many worlds interpretation! The many worlds interpretation is an interpretation of the collapsing of the wave function. It says that the wave function doesn’t collapse, we just find ourselves in a universe where it collapsed intone particular possibility. And there is theoretically another universe where something else happened and there is another version of us experiencing that. This produces uncontrollably infinitely many universes just to get out of collapsing the wave function. What they use is a metaverse – the multiverse of the many worlds interpretation!
Those grids of shelves are the multiverses! And then there’s a grid of those grids of shelves and that’s a metaverse. A metaverse of all of the multiverses of the many worlds interpretation at every single point in time!
I know why it’s 5-dimensional! It’s the 3 dimensions of space, the 4th number indicates what universe it is in the multiverse, and the last number is which multiverse it is in the metaverse! Which is a time dimension, because it’s metaverse of all the multiverses of the many worlds interpretation at every single point in time. And notice, these are all real numbers! Even the 4th and the 5th dimension can be any real number because there are only countably infinitely many natural numbers, integers and even rational numbers”.