Why Making Up for Lost Time is Hard

November 2023

The first post on this blog.

There's a classic puzzle about a pond and lily pads. If the lily pads double in size every month, and cover the entire pond after 36 months, when is the pond half-covered? The answer is month 35. By the time you can see you're close, it is already over.

Humans are very bad at perceiving exponential change. We evolved in an environment where almost everything that mattered changed gradually — seasons, harvests, social dynamics within small groups. The cognitive machinery that handles risk and prediction is calibrated for linear change. Exponential growth looks linear until it doesn't, and by then it's usually too late to adapt.

This is called exponential growth bias, and it's one of the most well-documented and least-discussed cognitive limitations we have. We know it exists. We know it affects our judgements. And we reliably fail to correct for it anyway.

The practical effect: we consistently underestimate how quickly things that are growing exponentially will reach us. We treat the current rate of change as the permanent rate of change. We assume that because something has been manageable until now, it will remain manageable.

This is compounded by present bias — the tendency to weight immediate concerns more heavily than future ones, even when we know the future concern is larger. Present bias and exponential growth bias combine elegantly: we can't perceive the exponential threat building in the future, and even if we could, we'd be inclined to defer action on it anyway.

The domains where this combination is most dangerous are the ones characterised by compounding change: climate and carbon in the atmosphere, antibiotic resistance building in global bacterial populations, debt accumulating in economic systems, and — the one I keep returning to — artificial intelligence.

AI capability has been growing roughly exponentially for several years. The rate of improvement in benchmark performance, in the breadth of tasks AI can handle, in the economic value being unlocked, is not linear. It is accelerating. The models available now are dramatically more capable than those available two years ago. The models available in two years will be dramatically more capable than those available now.

The critical question — the one that determines whether this matters urgently or merely eventually — is where we currently sit on the growth curve. If we're at month 34, we have one month. If we're at month 20, we have sixteen. The answer to this question is not known. The uncertainty is genuine. Serious forecasters disagree by years.

But here's what the cognitive biases predict: whatever our estimate, we've probably placed ourselves earlier on the curve than we actually are. We perceive linear progress because linear is all our brains can feel. And we're probably less prepared than we think we are, for the same reason.

Making up for lost time is hard because by the time the exponential change is perceptible — by the time it feels urgent — there often isn't much time left to make up. The pond looks manageable on month 34. On month 36, there are no lily-pad-free zones remaining.

This isn't meant to be alarming. It's meant to be useful. Knowing about the bias is the beginning of correcting for it. The adjustment is simple to state and difficult to maintain: whatever timeline feels right, move it significantly earlier. Whatever urgency feels appropriate, increase it. The feeling of having time is the bias, not the reality.