I would only qualify my earlier statement: while human intelligence is flexible enough to understand anything that is possible, it might not be large enough. If there’s too much going on, the brain may simply not be able to compute it. In which case, the non-understanding doesn’t feel non-intuitive, it just feels too complicated.
I question whether the intuition always comes in the form of a mechanism, or even any additional concepts at all.
Even correct intuition? I guess I don’t mind putting forth a more definitive assertion that intuition must be based on a mechanical understanding. (While it’s likely I’m wildly guilty of the typical mind fallacy, that’s nevertheless my view.)
I’ve been considering the hypothesis that mathematical intuition (especially intuition about highly abstract, non-physical things) comes from an ability to model that math physically in the brain. When we interrogate our ‘intuition’, we’re actually interrogating these (mechanical) models. Modeling is a high-intelligence activity, and a model ‘correct enough’ to yield intuition may be hardly recognizable as such, if we were forced to explain in detail how we knew.
(If we have a correct intuition about mathematics outside our experience, how else could we have it?)
I’ve been considering the hypothesis that mathematical intuition (especially intuition about highly abstract, non-physical things) comes from an ability to model that math physically in the brain.
I’ve been considering the hypothesis that mathematical intuition (especially intuition about highly abstract, non-physical things) comes from an ability to model that math physically in the brain. When we interrogate our ‘intuition’, we’re actually interrogating these (mechanical) models.
This is correct, but there is a useful layer of abstraction to consider. There are a set of operations the brain does that we can be conscious of doing, and inspect the structure of how they interact within our own brains. These operations are, of course, implemented by physics, they come from the structure of neurons and other supporting biological components. And therefore, the structures that are built out of these operations are also, ultimately, implemented by physics, though a lot can be learned by looking at the introspectively observable structure. These operations can be used to build a model of arithmetic. This does give us some power to “explain in detail how we knew”.
I would only qualify my earlier statement: while human intelligence is flexible enough to understand anything that is possible, it might not be large enough. If there’s too much going on, the brain may simply not be able to compute it. In which case, the non-understanding doesn’t feel non-intuitive, it just feels too complicated.
Even correct intuition? I guess I don’t mind putting forth a more definitive assertion that intuition must be based on a mechanical understanding. (While it’s likely I’m wildly guilty of the typical mind fallacy, that’s nevertheless my view.)
I’ve been considering the hypothesis that mathematical intuition (especially intuition about highly abstract, non-physical things) comes from an ability to model that math physically in the brain. When we interrogate our ‘intuition’, we’re actually interrogating these (mechanical) models. Modeling is a high-intelligence activity, and a model ‘correct enough’ to yield intuition may be hardly recognizable as such, if we were forced to explain in detail how we knew.
(If we have a correct intuition about mathematics outside our experience, how else could we have it?)
New post?
This is correct, but there is a useful layer of abstraction to consider. There are a set of operations the brain does that we can be conscious of doing, and inspect the structure of how they interact within our own brains. These operations are, of course, implemented by physics, they come from the structure of neurons and other supporting biological components. And therefore, the structures that are built out of these operations are also, ultimately, implemented by physics, though a lot can be learned by looking at the introspectively observable structure. These operations can be used to build a model of arithmetic. This does give us some power to “explain in detail how we knew”.