Learning · Maths · Psychology

How do we learn? How should we learn?

The fun bit is there are many ways to learn. Books, podcasts, videos, lectures, demonstrations, and doing it yourself. I have learnt that the optimal approach to learning is different for different people. Personally I find my self quite visual and auditory, if I can visualise a problem or listen to an explanation I can often internalise it.

There are also many stages to learning. Head knowledge, heart knowledge, practice, failure until eventually it becomes internalised, muscle memory, and we can be “in the flow…”, operating with unconscious ease.  

There are some guiding principles that I believe are important to remember on our journey to learn:

  • Be open minded: “It is the mark of an educated mind to be able to entertain a thought without accepting it.” ― Aristotle, Metaphysics
  • Seek to truly understand: “Any fool can know. The point is to understand.” ― Albert Einstein
  • Seek simplicity on the other side of complexity: “The simple things are also the most extraordinary things, and only the wise can see them.” ― Paulo Coelho, The Alchemist. (In mathematics you often know you have the cracked a problem and arrived at the right answer when the formulas magically compress to an elegant, beautiful solution)
  • Hold your own beliefs lightly: “Don’t believe everything you think. Thoughts are just that – thoughts.” ― Allan Lokos, Thomas E Kids

Each of these make us more receptive to deep learning.

But most profoundly, are the principle paths to wisdom:

“By three methods we may learn wisdom: First, by reflection, which is noblest; Second, by imitation, which is easiest; and third by experience, which is the bitterest.” ― Confucius

I don’t have time in this life to make all the mistakes myself! So Confucious’s first two paths are to be preferred:

If

  • I can learn through true understanding – often my preferred route, can I come up with an axiomatic explanation or understanding from first principles rather that statistical inference,
  • or learn from other people’s mistakes (or by deconstructing their successes) – the reason that studying history in any field of endeavour is so important is because through that we may potentially understand the reasons for the mistakes and successes of those who came before us

then I can get on with making the mistakes that I need to make myself, Confucius’s bitterest path, to push my own learning further.

And from there flows a further insight, to push the boundaries beyond what others have learnt, we need to be making mistakes. We learn by making mistakes. And you only make mistakes when you go for it.

So don’t be afraid to do, to act. My danger, my demon, is I spend all of my time thinking and not enough of my time doing. So doing is something I have to constantly challenge myself to do more of!

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