Saturday, January 17, 2015

The Power Of Exponential Growth

From Google translate:

ex·po·nen·tial growth
Growth whose rate becomes ever more rapid in proportion to the growing total number or size.

The basic idea is quite simple: the bigger you are, the faster you will get even bigger.
The classic example is the "30 steps to the moon" gedankenexperiment: if you start walking and take 30 steps you will traverse ~10 meters, but if you double the length of your step each time then by the 30th step you will reach the moon.
Another popular example is Moore's law: the size of transistors is reduced every ~2 years - hence approximately doubling the computing power contained on a chip. This is one of the main reasons for the rise of electronics and its infiltration into everyday life (your smartphone has much more computing power than any Apollo spacecraft - and those things flew to the moon). A simplistic explanation of this phenomenon is the fact that we use older CPUs to design newer CPUs - each generation built using the tools provided by it's predecessor.
Ray Kurzveil talks about the unintuitiveness of this kind of processes a lot (e.g. "law of accelerating returns"). The human brain is built to think in linear extrapolations due to evolutionary advantages: lions (and rabbits) run at you (or from you) in a linear fashion, with approximately constant velocity. It's very hard to train exponential intuition - so perhaps the only way is to trust the data.

"Well, good for us", you might say, "but what am I supposed to do with this knowledge"?
Glad you asked :)

This idea - the power of exponential growth (vs. linear accumulation) - can be applied not only on the grand scale of technology but on the smallest scale as well - on yourself. All you really need in order to produce exponential increase in your skills/capabilities/success/money is to use what you've already achieved in order to get even better.
For me, the most obvious example is academic knowledge. Simply put, the more you know, the easier it is for you to learn and understand new ideas/techniques. Whether it's because you have the relevant mathematical background to understand the technical details of a derivation, the new ideas presented to you remind you of some similar concept you already know - hence easily digested, the fact that the more you learn the better you get at learning or any number of other reasons, the effect seems to have been validated empirically. This effect is one of the reasons the linear "skill vs. time" model (from the first post) is inaccurate.
Another important example is growth in the monetary sense, and not just the "rich get richer" idea. A common belief is that the higher your skill level - the higher your pay grade, and the most straightforward method of increasing your skill level is via education (today both of these assertions are somewhat inaccurate but a reasonable approximation). Before the era of the internet the way to get education is to pay universities for the skills and knowledge you presumably acquire during your studies - and that's not cheap (the years spent as a student - and not working - are a much bigger cost than the tuition itself in most cases). So we see that you need money to upgrade your money making capabilities. 
The complementary claim is that the most efficient use of money, once you have some, is channeling it into earning potential - via investments ("make the money work for you" as the stock brokers like to pitch) or by improving your personal skills. This is true for most "assets" once you start looking for such exponential growth opportunities: how do you use your current self-confidence level in order to increase it further? How do you use your fresh programming skills to get even better at programming? etc. Often the answer is simply "push yourself to the limit" - your current limit that is - and when you get better - change your life/work/mentality to use these new skills.

Let's say you are committed to personal growth - whatever that means to you. Obviously - it's achieved by effort (in the broadest sense), and, as we discussed so far, many types of progress are (potentially) exponential - whether naturally, by your design or both. Here lays one of the significant differences between being "good" and being "great" (according to Richard Hamming's seminal talk "You and Your Research"). Let's compare 2 people with the same level of "natural talent", both starting from scratch and earnestly devoting themselves to a certain area of expertise - the only difference is that one dedicates the "normal" 8 hours a day to work (for a "healthy life-work balance") and the other works a little extra. See how they compare in the long run (Green is the reference 8-hour work day results, drag the slider to choose how much time the other person works):

A small extra effort leads to big results.

An interesting side effect of human blindness to exponential growth is that - if you play your cards right - you constantly achieve the impossible. Well, not really impossible but things you believed to be not only hard - but literally "something that happens to other people". There are certain aspects of my life today that were outside the realm of possibility 10 years ago, stuff that happens in the movies. And it's not because I'm "so amazing" - I just couldn't envision my life and progress so far into the future.

One of the strongest long-term personal growth "hacks" is constantly expanding this realm of perceived possibilities. 10 years ago I couldn't imagine myself starting my own startup, now it's on my to do list - if I won't start one in the next 10 years I'll be very disappointed. It went from "impossible" to "a matter of time". Let's agree that you can't achieve something you perceive as impossible. But ask yourself: if it's possible for someone to do it, why not you?

To quote my father (my own crooked translation from Russian): "Not the gods make pottery".

Until next time, may you use who you are to become who you want to be.


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