Towards the end of the last chapter of Lara Alcock’s excellent book Mathematics Rebooted, I came across the following passage.
[. . .] I observed that human intuitions tend to be based on small finite numbers. But we’re not working with those now, so the intuitions need loosening. What mathematicians do is loosen them in favour of more abstract notions about systemic consistency. Instead of thinking
I must make this match my experience of everyday objects,
they think
Okay, clearly this does not match my experience of everyday objects, but perhaps we can still think about it in a way that’s internally consistent.
That frees them to explore various options [. . .]
Lara Alcock, Mathematics Rebooted, page 192.
Intuition loosening. I really like that. What does it mean and why does it matter? Let’s dig in.
As Daniel Kahneman observed, “you are rarely stumped. [. . .] The normal state of your mind is that you have intuitive feelings and opinions about almost everything that comes your way.” Such is the work of intuition, giving you answers quickly, right or wrong.
If you are reasoning from within your circle of competence, your intuition is likely to be better than if you are not, but the fact remains: your intuition gives you an answer and it may not be correct. It is your intuition, so it is easy for that answer to be your default.
The more certain you are of your answer, the less you are open to changing your mind, to looking for other possible solutions. Unexamined confidence can be a good thing, but when it gets in the way of learning and improving your understanding, then it is crosses into detrimental rigidity.
It is difficult to sense with your fingers, when they are curled into a fist. Likewise, rigid minds need relaxing to be receptive to new insights. That is, what intuition loosening refers to: you allow yourself to hold your beliefs, your convictions a little less firmly, giving them (and you) room to maneuver.
After a coin comes up heads ten times in a row, intuition often insists that tails (or heads) is now “due” (again). The feeling is strong, even though nothing about the structure of the situation has changed. The intuition is responding to surprise, not mathematical probability.
Similar patterns appear in more consequential settings. An intervention can seem clearly beneficial when its direct effects are visible and immediate. Antibiotics work. Policy changes signal action. Attaching financial rewards to specific work milestones can seem like an obviously good idea. Intuition tightens around what can be seen. Only by loosening that grip do delayed consequences, second-order effects and feedback loops come into view.
Intuition is responding quickly to experience, to what seems familiar. Loosening it creates the space needed to examine structure and see more clearly.
We have intuitions about almost everything. They give us answers quickly and often usefully. When those answers harden into defaults, they can close off further understanding.
Intuition loosening is the practice of holding those answers lightly enough to allow something better to emerge. That allows you to change your mind and know why.