I watched this fantastic YouTube video called “Think Deeply About Simple Things’ where a mathematics professor describes how magic appears when we question the simple.
He gives the example of a circle. The simplest shape. In one mindset, we can just accept it - “It’s a circle, it’s simple”.
But what if we thought more deeply about it? How many dimensions is it in? How would it look like in 3D - a sphere. What about 4D? Why is ‘pi’ the way it is, and how did it emerge from something as basic as the circle.
Another example- we all accept the sky is blue. But… why? Off the top of my head, it’s got to do with light refraction. But then why does light refract? What actually ‘is’ light? What is colour? And on and on.
Ultimately he boils it down to asking two main questions
1. Why —- Why —- Why
Like your 4 year old nephew, constantly question everything. Underneath your why, there is always another why. It leads to deeper thinking. Ask why about simple things. We have an inbuilt curiosity that we tend to squash as we get older, because ‘who has time to think about this’. This is tragic. Because the more you learn and question, the more you realise ‘how little we know’. It grants a level of humility. This leads to awe, as you realise how small ‘you’ are.
2. What if …
This is asking hypothetical ‘what if’s’. For example, what if I imagined myself chasing a beam of light? This is of course one of Einsteins ‘gedanken’ - though experiments. One that led to his understanding of the theory of relativity.
In thinking about consciousness. We can ask what it is. Why it arises etc. But we can take thought experiments too. Suppose we were to construct a conscious entity, atom by atom- like a Lego set. At which atom, would you suddenly become conscious. When would consciousness arise in that system?
This leads you to interesting hypotheses.
Thought experiments afford us different perspectives on problems, because the truth is that ‘reality’ and science tends to violently violate our intuitions. For example, that we are at the centre of the universe, violated by the copernican revolution that we are not even at the centre of our solar system.
’Hard’ things are not hard
There is this idea that complex maths or science is ‘hard’.
Yes, it requires focused effort, but that doesn’t mean that ‘you are doomed’ and that you’re just ‘not a maths person’.
It is a structure. A building that one has to construct from simpler concepts. But you have to understand the simple concepts first, before you can layer on them, and learn ones that require you to understand previous concepts.
For example to understand what mitochondria is, you have to understand a layer below that : ‘what a cell is’. Then you have to understand what a cell wall is, or what ATP production is, then you need to understand what a molecule is, what atoms are etc etc. It’s interlinked and interdependent. And you can go deeper and deeper into these concepts.
But it’s all just concepts layered on top of each other.
In the video he gives the example of 1+1. We can all do this. But what about 1+ 1/2.
If we haven’t been exposed to fractions, this seems like a ‘hard’ task. But if we understand what fractions are, then suddenly it’s just a problem. Neither hard nor easy.
What about 1+ 1/2 ^2
Again, the same, if you don’t know what square number is, then you cannot do this. It is simply concepts stacked on top of each other.
A problem in school is that students all move at the same pace. If one day, you miss a concept, or don’t understand it, often the teacher does not come and explain it to you. Then the next lesson, you are completely lost because you didn’t understand the previous concept. People who are ‘bad’ at maths just missed a concept, then they couldn’t progress any further. If only it was said in a different way, or expressed in a different medium, it would have ‘clicked’.
Thank God for YouTube. If you don’t understand something, you can go at your own pace on YouTube. Some really smart kids are being brought up in this generation thanks to YouTube.