I was Perplexed about Compounding, then came Perplexity

 I recently started thinking about the specifics of what confounded Einstein so much about the wonders of compound interest (the "eighth wonder of the world"), or compounding in general it turns out (can apply to skills, knowledge, etc), so I asked Perplexity Pro that question. It gave me some pretty good insight as to why he was perplexed by its power. I also wanted to stress my own thinking in probing why I too should be perplexed by its power. 

One classic example is that of The Magic Penny, which apparently can turn into a sum of $5m if it doubles in value every day for 30 days. Yes, that's a lofty and mind-boggling number, but is that all there is to it? It turns out no. An equally mind-blowing fact is that it's a mere $5,242 on day 20. Yes that's right..but a few lightbulbs went off when I thought about these numbers. 

One is the realization that you can work your a** off for say 20 years, and not see the type of progress you'd like to in say your retirement goals, and then absolutely blast off in the last 10 years. This is not unlike many traders who find success after many trials and tribulations, only to run out of steam on the metaphorical "day 20", and never see their way to the promise land by day 30. Simply hanging in there without distractions or running out of mental capital would have resulted in previously unimaginable gains.

The second lightbulb was a bit more insightful, something that Einstein himself perhaps didn't contemplate, which is how our minds frame absolute numbers in the context of our daily reference points. You see, mathematically, going from $0.01 to $10 is equally as impressive as going from $5k to $5m. But our brains are not impressed by the former, since we can easily acquire $10. Even a $10 --> $10k account ramp-up may not impress many, for they have ways of acquiring $10k. But here's the thing - for a billionaire, a 5k-->$5m gain is just noise, and their brains would process it the same way you and I would for the seemingly achievable $0.01-->$10 increase. So in reality, the "eighth wonder of the world" is just a mental trick. There's nothing inherently special about compounding at different absolute values since the relative gains from previous values are exactly the same. They just happen to be orders of magnitude apart, and its when the numbers start exceeding our real-life norms that we start getting dazed...and perplexed.

The lesson here is to simply execute and follow your plan, to increase position size by some amount as your account grows. Leave the rest to math, and then allow yourself to be amazed by the numbers as the absolute values irrationally confuse your brain.