[zmgsabst]

No — people don’t successfully use things they don’t understand every day.

They approximately use them with varying degrees of success, but also mistakes, broken inferences, etc.

My exact point is that your view reduces our ability to do mathematics to that broken, flawed usage and thereby undermines its utility for logical precision: mathematics is only useful because we cleanly understand it.

When you try to use mathematics without understanding, you cause disasters: stock market crashes from mispricing options, Amazon’s 2018 hiring freeze from misallocating $1B, etc.

Note: neither of your examples (sleep, gravity) are things that people intentionally use. They just happen to people.

I think it’s very telling you couldn’t think of an example.

[cornholio]

It's easy to find counterexamples: the entire science of pharmacology is based on macroscopic effects that often lack a fundamental understanding of the underlying mechanisms of action. Psychopharmacology is the extreme example. Often, the fact that a drug worked made scientists investigate and discover the mechanism behind it, but for many drugs used every day by billions it's still a mystery, or it's understood only in very broad terms.

So what will you do if the doctor prescribes you an LLM-vibecoded drug that nobody understands how it works, yet it cures some deadly affliction with close to 100% efficacy?

What if, say, these incomprehensible math results lead to a revolution in quantum physics which unlocks chip topologies that are orders of magnitude faster than human comprehensible designs?

Would the high priestess of human reason pass her divining rod over such chips or life-saving drugs and reject it as the work of the AI devil?

[zmgsabst]

Psychopharmacology is a great example of “doesn’t reliably work” as their products have serious and even disastrous side effects at times — including SSRIs triggering violent acts and suicides.

Again, my exact point is that mathematics loses its utility when you reduce it to that inaccurate usage. You no longer can have any faith in the conclusions — just like sometimes psychiatrists kill their patients with an SSRI prescription because they don’t understand the drugs.

> Would the high priestess of human reason pass her divining rod over such chips or life-saving drugs and reject it as the work of the AI devil?

My point is you can’t know if you’re turning it over for life saving drugs or poison, if you don’t understand what you’re getting.

[cornholio]

This is true for any drug, any drug can presumably become a poison, can interact with some genetic or biological trait and trigger a side effect and so on. The complexity of the biological systems is so great that they defy clear deterministic understanding, but stochastic empiric knowledge and treatments still have immense value.

If you give me an inference chip that runs 200x faster, yes, it could be backdoored to take control of my dishwasher and kill me in my sleep - but I can't deny it runs 200x faster an account of nobody being able to explain why. The same for the mistery cancer drug that cured everyone who took it up to now, but could, without doubt, kill the next patient.

[sdenton4]

How many people drive cars without knowing how an engine works? Or make a phone call without knowing how voice compression for a cellular network does it's thing? Or eats food without knowing how it came together from the supply chain?

[robrain]

The mechanic who repairs the cars knows how the engine works.

The telco that manages loads and allocates networks knows how voice compression works.

The farmers and supermarkets know how the supply chain works.

None of your questions show why mathematics should include blobs of incomprehensible gloop, where no mathematician, no logician, no philosopher, no man on the street can make sense of said gloop, or use it in any way to further human knowledge.

When it's been decomposed down we can discuss this further, but now it's like saying red is red, just because.

[sdenton4]

Well, you said people can't use things they don't understand.

But I'll take your expanded statement, to include riding a horse, something even older than the engine. We don't understand fully how a horse works -- biology is still a matter of seeing fragments of the whole -- but people had no problem riding and breeding them before the invention of the car, and before the discovery of genetics.

Meanwhile, understanding the math of a thing -- like stock markets, or nuclear bombs -- does not prevent its use from going badly.

Math is useful and beautiful, and a helpful tool for expanding our understanding of the world, but it is not the whole of understanding, or the sole factor in successful application of science to the world .

Signed, a mathematician.

[robrain]

I said no such thing - the comment that you just replied to is the first thing I’ve said in this thread.

[VBprogrammer]

This feels like a stretch. It would be impossible for someone who didn't know how an engine worked to repair or improve the design of it.

[drdaeman]

Why not? One can surely use math even if they have no clue about how to prove theorems. I suck at math, but I use it every day, without knowing how to advance it.

I think it might be fair to say that a proof cannot be without value if it proves something meaningful to a human, that a human can use somehow? But such proof probably doesn’t belong in a library seemingly explicitly dedicated to human-graspable proofs. Just because it violates the intent.

It’s not like such proofs mustn’t exist at all.