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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.

Re:Vibecoding Photoshop: Time and pressure on Wednesday October 07, 2026 @02:26PM (#49996845)
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...

Re:Laya the open source version of Jev on Saturday September 19, 2026 @07:35PM (#49771045)
A personal saying of mine: In computers the second best thing always wins.
Re:The Three AI Pills on Monday September 14, 2026 @07:16AM (#49694987)
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.

Re:The safest job from AI may be writing on Tuesday September 01, 2026 @08:10AM (#49520879)
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?
And anytime programmers start to discuss anything in detail, you know just when it's getting interesting: "Can we take this 'offline'..."

See also this song: https://www.youtube.com/watch?v=cMVuRGw_a5A

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...?

Re:A Decade of Docker Containers on Sunday March 08, 2026 @09:18AM (#47297106)
Back in the day when it came out, I gotta admit, Docker sort of got my my nerves as yet another thing coming to 'disrupt' how things are done.

(Half assed NOSQL 'databases' with poorly thought out storage models, everything having to be a microservice, turning every function call into a fallible RPC call etc...)

But I've come to appreciate it more, and i use it regularly now. I appreciate its relative simplicity.

But as in life, hell is other people's containers. My own I can at least try to keep them simple and minimal.

But I have seen many use the kitchen sink approach, giving me the feeling that even the developer don't seem to know how they arrived at their deployment anymore.

But this all seems quaint today. With LLMs, now we can look forward to a flood of code the developers haven't even looked at, but which is widely believed to work...

> "hey, why do mathematicians keep changing rules on the fly, they just told me square of minus one doesn't exist

Mathematicians aren’t chasing numerical solutions, they’re chasing structure. ℂ isn’t just about solving cubics, it’s about eliminating holes in algebra so the theory behaves uniformly and is easier to build upon.

And as for "changing rules" they haven't changed, they have broadened the field (literally) over which the old rules applied in a clever way to remove a restriction.

Re:Ask HN: How can we solve the loneliness epidemic? on Thursday January 15, 2026 @05:19PM (#46640197)
I like to hang around at my local skate park.

I'm not very good on a skateboard, better on a BMX. In any case the vibes are usually good.

Sometimes you think people aren't even noticing you, till you finally land the trick you're working on and a total stranger yells 'whoo!'

Re:Jerome Powell Responds on Sunday January 11, 2026 @09:54PM (#46583447)
[...] send not to know For whom the bell tolls, It tolls for thee.
Re:Jerome Powell Responds on Sunday January 11, 2026 @08:36PM (#46582727)
You know this part of the problem!

Politics is now consumed as entertainment, and ask any writer of books or screenplays and they will tell you _conflict_ makes for good entertainment.

Politics should be _boring_. The fact that we demand to be entertained by our political system is a big part of the problem.

Re:'Ghost jobs' are on the rise – and so are calls to ban them on Thursday December 18, 2025 @08:43AM (#46312523)
It also looks hopelessly Gen Z to want all communication to be asynchronous and ignorable. If you guys have your way, we’ll all be connecting via API like 1U machines in a rack somewhere.

Seriously—if you’re going to go overboard, so can I.

WTF is it with everything having to be mediated by a machine these days? People can’t get around without GPS, remember phone numbers, or now even do their work or homework without 'AI.'

How do you explain how people managed to do all of these things before without assistance? And how do you square that with telling 'boomers'—who were able to do these things—that they’re stupid and that you’re somehow better?

Seriously, it’s like we used to have weightlifting competitions where humans physically lifted weights overhead, and then you guys decided, "Nah, that’s too old and boomerish. From now on, all weightlifting competitions will use forklifts. Anyone who wants to lift the weights themselves is boomerish and stupid."

And where's your solidarity? If you lose your job, you may find yourself wishing you could meet people in person, when all your 'ignoreable,' electronically submitted job applications somehow get thrown away.

Re:Thin Desires Are Eating Your Life on Tuesday December 16, 2025 @04:32PM (#46294821)
I disagree. I feel there is a genuine insight at the core of it.
Re:The appropriate amount of effort is zero on Tuesday December 16, 2025 @10:24AM (#46289658)
I still don’t buy the “slasher movie” framing of nature at all, and the only function 'pleasant lies' serves here is just low effort dismissal. :shrug:

Alas, I'm ceding ground by even arguing within your chosen framing. It's all very self defeating.

Re:The appropriate amount of effort is zero on Tuesday December 16, 2025 @09:31AM (#46288948)
Come on you can't come up with a single five minute period when observing animals where they seem to be calm?

That does not fit the evidence.

And besides you can read thousands of articles on HN about anxiety in humans, a mostly useless anxiety focused on societal 'threats' which we suffer from just as much.

At least a deer is on the lookout for something real.

Also if you compare animals lives to human ones, with our propensity for war and torture and persecution, I think the animals _do_ objectively live calmer lives.

You don't see them systematically tearing each other to pieces over made up goods like money.

I think this trope that "nature is a constant struggle" is a projection of human values (or lack of) onto nature.

Re:The appropriate amount of effort is zero on Tuesday December 16, 2025 @09:19AM (#46288773)
>then flee at maximum speed because a well-fed 200+lb apex predator is passing by, it sure looks like work and effort.

I think the 'effort' being described in the article—despite using analogies of overgripping and physical strain—is mental effort.

When the rabbit has escaped, he returns quickly to a relaxed state. A typical human reaction would be to continue to worry about the predator, to form plans to rid the whole _world_ of all predators, to build a fortress with grass to eat on the inside...

This whole saying that "Nature is red in tooth and claw" is overstated. Most animals have normal, humdrum days like we do.

However, I think it was the Buddhist teacher, Ajan Cha who said: "We live in a world where we must eat to survive, and some of us are uncomfortable about being eaten."

But this does not mean that every animal lives a life of unremitting terror all the time.

I’m wary of your use of 'romantic' as a descriptor here. It's a rhetorical shortcut which makes it easy to pre-emptively dismiss a position as naïve without further examination.

Re:Programming peaked on Thursday December 04, 2025 @08:34AM (#46147489)
> it was the worst debugging experience one could have.

Hard disagree. I'm not going to argue that Java debugging was the best, however:

1. You could remote debug your code as it ran on the server.

2. You could debug code which wouldn't even compile, as long as your execution path stayed within the clean code.

3. You could then fix a section of the broken code and continue, and the debugger would backtrack and execute the code you just patched in during your debugging session.†

This is what I remember as someone who spent decades (since Java 1.0) working as a contract consultant, mainly on server side Java.

Of course this will not convince anyone who is determined to remain skeptical, but I think those are compelling capabilities.

† Now I code in Rust a lot, and I really enjoy it, but the long compile times and the inability to run broken code are two things which I really miss from those Java days. And often the modern 2025 debugger for it is unable to inspect some for the variables for some reason, a bug which I never encountered with Java.

Prediction: Non-determinism will become acceptable in areas we used to expect accuracy.

For example we will accept 'probabilistic bookkeeping' because it's cheaper than requiring ledgers to balance to the penny.

But this leeway won't be equally applied. Powerful institutions like banks will use “probabilistic models” to decide they probably don’t owe you that refund, but if they decide you owe them money, they will still hold you to every cent.

Nondeterminism for the powerful, determinism for everyone else. Yay!

Re:What's Happening Inside the NIH and NSF on Saturday February 08, 2025 @05:00PM (#42986554)
> elections be damned.

Isn't the current administration more culpable on this point? (viz. the last time Trump lost an election)

And in terms of norms I mean that there isn't a strict law or constitutional clause written to proscribe each and every thing that the president can and cannot do. The system relies on the people acting in good faith, which is definitely not happening in this case. Instead they are cynically trying to exploit every loophole they can to smash a system they don't even understand.

> whilst simultaneously calling a legitimately elected government a "regime".

It _is_ a regime. Who elected Musk or his Doge minions?

Most dictatorships consolidated power legally. That it was legal doesn't mean I want to live in one.

ANd speaking of having it bot ways, you can easily infer what side I'm on, but I get the sense that you are trying to hide behind 'just so arguments'. Could it be that you support the new regime and are trying to avoid saying it out loud?

I wonder why someone would want to hide that...?

Re:What's Happening Inside the NIH and NSF on Friday February 07, 2025 @08:09PM (#42979364)
>Don't you see? They would give the exact same speech about the other side and absolutely believe it, and in fact so would many other people.

Of course I see, and like in a chess match I looked past it cos I thought it was too obvious.

But I say again your argument amounts to false equivalence.

They can believe crazy and false things as fervently as they like, it doesn't make those beliefs an equivalent mirror image to what liberals believe.

This whole thread started with a complaint from you about Schedule F being 'unfair.'

Apparently anything except the liberals handcuffing themselves and letting themselves be frogmarched out of their jobs is unacceptable.

Meanwhile the new 'unitary executive' is allowed to jump up and down like Donkey Kong on anything he feels like no matter what the rules norms, laws or the constitution says.

Did I capture the essence of it?

I am totally serious about the need for resistance. The new people in charge just walked up to an unguarded lemonade stand which runs on the honour system, drank all the lemonade, pissed in the jar stole the money and smashed everything.

And why can they do that? Because they don't go in for honour and decency, but they expect us to. Democracy provides the tools and the freedom for people to subvert democracy.

I don't expect the new regime to grant such generous 'equivalent' terms should it manage to consolidate it's position.

I don't mean violent resistance, but we do have to resist.

Re:What's Happening Inside the NIH and NSF on Thursday February 06, 2025 @09:10AM (#42962466)
This is false equivalence.

There is such a thing as true and false, and there is such a thing as right and wrong.

I know which side's views and plans are almost always on the side of the false and the wrong.

One side wants to divide, one tries to unite, one seeks the truth, the other side does more than lie, it attempts to erase the very notion of truth. One side denigrates, insults and immiserates the weak and the poor. The other attempts to lift them up.

Often in a moral quandary ask yourself 'Which position would be more difficult for me to take?' that's a strong indicator of what is right.

It's easy to divide, denigrate, spread rumours, and to make statements without regards to truth or falsehood. It's easy to hate, to dehumanise and to cause pain.

I've said it in another post. Why are there so many people ready to line up to defend the powerful against the weak, the rich against the poor?

What a brave and noble purpose! I'd love to see you defend that.

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