I am in my late twenties.

Most of my life is taken up by trying to restart exercising, checking facebook to see if anyone has like my last status update, typing and deleting tweets, agonising over the size of my twitter following, seeing how many more people have read today’s blog post since I last checked ten minutes ago, and panicking about any tax return deadlines that I may have missed.

It is a long and steady flow of small anxieties.

The thing about small things is that they eventually grow into big things. Game-changingly so. I mean – my steady trickle of panic may one day become a coronary. Or a lifelong commitment to an asylum. Or an inability to leave the house without locking the door four times and high-fiving the gutter. All possible.


By this same principle, I can also make small changes, and I can achieve small successes, with similarly grand potentials of outcome. You know the old adage: “a lifetime to build a reputation”?

Financial freedom is no different. It does not arrive with a bonus, or a career opportunity. There is no lotto win, or fortuitous marriage into inheritance. The wealthy, as well as the poor, get stuck in the trap of not enough money*: that moment where the cash coming in does not cover the cash going out. At which point: credit cards are maxed, home loans extended, second mortgage applications submitted, relatives approached, et cetera.

The Solution?

The solution involves two things, really:

  • regular small sacrifices; and
  • time (or, rather, patience – which, in this case, is roughly the same thing).

From what I have seen (in myself, and in others), the reason we fail on this front is that our default mental math position is addition rather than multiplication. We look at the small sacrifices as an additive process of pain, rather than a multiplicative organic process of future rewards.

The Crisis of Mathematical Conditioning

Our understanding of time and life as addition and subtraction has dramatic ramifications for the way we operate. Relationships built on grand gestures have greater standing than those forged with small but repeated acts of kindness. We shout at a subordinate when we’re having a bad day, because we can tally it up against all those times that we’ve been gracious. We don’t recycle because what’s the point if no one else is doing it.

The trouble is that life and/or reality is an exponential process. Small shifts have multiplier effects. And if you ever have the chance, you should read Alex Bellos’ “Here’s Looking At Euclid**” – because in it, he explores the psychology of math.

In the very first chapter, he studies the Munduruku tribe of Brazil, who have no words for numbers beyond “five” (ie. their number system goes 1, 2, 3, 4, 5, many). He runs some experiments to understand their understanding of magnitude,*** and their understanding turns out to be logarithmic (or, inversely, exponential). That is, they had a natural understanding of magnitude. He then goes and looks at studies of children. And by a further series of (very clever) experiments, he establishes that before we enter school, our understanding of numbers is also logarithmic. But by the end of our second year of school, our understanding of magnitude has flattened into an additive process.

Let me put this another way: you know the question about placing a 1mm thick coin on one corner of the chessboard, and doubling it on each subsequent square, and asking how high the pile of pennies would be on square 64? That 184 trillion kilometre answer shouldn’t be so surprising: that answer should be intuitive. The exponential growth of coins echoes the exponential natural process of procreation.

As should the answer to this question: “on what square was the pile of coins half as high as the pile on square 64?” For most of us, the tip-of-the-tongue answer is somewhere around square 32. The intuitive (and correct) answer should be “63” (because the pile doubles on square 64).


Summary: our current mindset places the growth of coins onto a flat arithmetic line, where an exponential mind would see a curve.

What this means from an Investment Standpoint

To put this in terms of an example:

  • I say to myself: “Kiddo, it’s time you saved for your retirement.”
  • “You’re only 27. No need for big sacrifices – just take $300 from this month, and put it into this investment earning an annual 12.2% real return. Pretend you lost it, and that you’ll only find it again when you’re 65.”
  • When you look at this scenario, and decide whether it’s a good deal off hand, maybe you’ll say something like “Well that’s almost 40 years of investment. 12.2% is close to 10%. 10% a year is 30 bucks. So 30 bucks for 40 years, plus the original $300, maybe the investment will be worth around $1,500 bucks at the low end. But time value of money, so let me go crazy and say it’ll be worth $10,000!! Wait – that really does sound crazy. $3000?
  • Yes – you may know about time value of money – but your estimate is ridiculously undervalued. And that’s where this gut problem comes in – because the guess is limited by a preconditioned reliance on arithmetic.
  • In reality, my $300 at that return would be worth $30,000 when I turn 65 – in real terms****. And off the interest alone, I’d be able to have $300 a month for the rest of my life without ever touching the $30,000. I mean – it’s basically $300 per month for free forever.

The point of this post: you really should start putting some money aside. Even if it seems only a token amount (like R300/$30 every month into a unit trust), it’ll keep busily growing.

And the impact will be so much greater than your mathematical mind can contemplate.

*The wealthy man with the four kids in private schools and the two homes on mortgage and the wife with the retail habit – he too can go into convulsive fits of panic in the week before pay day. In fact – it’s almost worse. Because no one will understand – the wife will leave, the children will hate, and the two homes will empty and transfer into the hands of another beleaguered breadwinner.

**Also called “Alex’s Adventures in Numberland”. There seems to have been an argument between the American and Rest-of-the-World publishers about what title the book would be published under…

***Which is, after all, the fundamental reason for having numbers: to measure magnitude.

****And I say “real terms” because with that $300, you would be able to buy what you can buy today for $30,000. Just be careful – nominal returns means that inflation is being taken into account. And inflation is a negative (ie. if that $300 may only buy the equivalent of what $20,000 can buy you today if the 12.2% return was “nominal” rather than “real”).