throwaway_2494

Studies have figured out how many 'concepts' or 'chunks' of information a typical human brain can hold in working memory. The famous 7±2 is a common way this is expressed. This research has been disputed and further nuanced (I know, I know, replication crisis...), but for the sake of argument, assume that there is some cognitive limit to how much information we can hold in our heads at once.

In the beginning, calculus as invented by Newton used complex ruler and compass constructions. Newton had a high cognitive capacity, so it was understandable to Newton. It took mathematicians coming later, including Leibniz, to turn this technique into a body of work that fits more easily into the average human mind. Newton and Leibniz independently developed calculus, but Leibniz's notation and formalism in particular provided a much more compact way of expressing and manipulating the ideas of calculus.

Open up Spivak at any page and find a formula; you should probably find that it contains 7±2 'things'. Like an integral, say: the integral sign, lower and upper limits, the function inside, the variable of integration. Then the theory and the rules for transforming these expressions was created so that working with calculus becomes mostly a set of rote operations.

Now a 1st-year student can do more calculus in a week than Newton even could have done in a year.

Now imagine aliens land on the Earth which have 10x our cognitive capacity, and we ask them about their mathematics. It would probably be incomprehensible to us because it would not have gone through a cognitive bottleneck sufficiently small to force it to fit into our minds. They might be totally happy with a mathematical expression containing 700 'things.'

We now find ourselves in this situation, except the alien is an AI we created.

I believe a cognitive bottleneck needs to be maintained so that maths can still remain human maths.

EDIT: Basically, mathematical elegance is finding a representation which allows irrelevant detail to dissapear.

Solipsism as a service!

The parent comment is constructed in a way that maximises moral provocation while minimising engagement with the all possible environmental arguments.

Move on...

A personal saying of mine: In computers the second best thing always wins.

It makes the leap from:

AI is improving dramatically in fields with logical formal structure (maths, comp sci.)

to:

AI should then should eventually conquer essentially every other cognitive task.

The problem with AI writing is that it can't add produce the texture of lived experience.

This would mean the specificity of details, thoughts and sensations as filtered through a specific individual.

There is a theory that what we perceive as beautiful in a face is that every feature, distance between the eyes, width of nose, distance between cheekbones etc is average. Note that a random face is very unlikely to have every feature be average.

With AI writing, the problem is the reverse. LLMs have captured lived experience, but it's the smooshed over experiences of millions of people.

It's not able to create a unique viewpoint which is believable. What comes out are average thoughts, sensations and details, but good writing lives in the specific.

AI's problem isn't that it can't generate unusual things. It's that it struggles to generate believable conjunctions of ordinary things.

But even this is too reductive. AIs don't have a body or a 'soul.' They don't know what it feels like to be a person, so they can't write like one.

Ok if you say so he's not racist, but you can keep him nonetheless.

It's a myth that US income tax is always lower than in Canada.

I worked in the US for a bit when I started out. I paid more income tax in CT than in Toronto on the same salary.

I just wanted to come back home. Even in small town CT, there were areas we were told to stay away from after dark.

Ok, but how does your hypothetical scenario apply to Canada though?

I remember when computer magazines were aimed at programmers and had code listings in them.

Then there seemed to come a time when all they talked about was the IBM vs. Microsoft lawsuit. From then on they must have felt that they had discovered a formula, because all they ever yapped about after was insider baseball of computer companies.

I find this sort of corp. vs. corp. coverage boring, sort of like techie reality TV. Who will be voted out tonight, Debra, or Deborah...?