At school we were taught all sorts of tricks for checking if numbers are divisible by something. For example, if the sum of the digits is divisible by 3, then the number itself is divisible by 3; if by 9, same thing; if by 7 ā unfortunately, that means nothing. Numbers ending with 5 or 0 are divisible by 5, and if the last three digits form a number divisible by 8, then the whole thing is divisible by 8.
From a practical point of view, this knowledge is completely useless ā but it teaches two important skills: how to verify information and how to simplify a question. Imagine you bought a calculator that, once in twenty times, when multiplying two numbers, adds some random number between -3 and 3 to the result. Thatās when the habit of sanity-checking things would come in handy. Say you square 3456 and get one of these: 11743934, 11743936, or 11743937. You donāt have the energy to recheck the whole thing by hand, but you can catch your calculator lying just by looking at the last digit ā 6Ć6 always ends with 6, not 4, and definitely not 7.
In the modern world, the key skill of a universal specialist is exactly that ā building such verification chains that lead you from āI know nothing about this topicā to āMy university professor studied under this guy and said he was great.ā
Letās say I want to know whether itās legal to smoke Cuban cigars in the U.S. My level of awareness: in TV shows, Cuban cigars are ācool,ā and I know the U.S. has heavy sanctions on Cuban exports. So my thought process might look like this:
- Ask ChatGPT to get a rough idea of the legal status
- Use Perplexity or ChatGPTās deep research to find specific laws about cigars, Cuba, and cigar imports
- Ask ChatGPT to highlight the relevant part of the law and summarize it for me
- Read that particular piece myself.
Thatās if Iām just curious. But if I actually plan to smoke cigars in the U.S. ā or worse, import and sell them ā Iāll be looking for a lawyer to consult.
Same thing applies to everything else. Donāt know how to organize a running workout efficiently? Iāve got access to neural networks that have read all of PubMed. But more importantly, I also have access to PubMed itself, and to my friend Vlad who reads it for fun ā so I can validate my conclusions with Vlad. Donāt understand how gravity works? Start by asking ChatGPT, follow the Wikipedia links, then follow the links in the sources, until you reach the point where you stop understanding the material. Then check who this āMikhail Korobkoā guy is and whether heās worth trusting. Oh, an h-index of 91? Yeah, the guy probably knows what heās talking about.
In fact, this skill isnāt unique to the modern world. Itās been impossible to be a Da Vinci-type āknow-it-allā for quite a while now, and most of our so-called scientific knowledge relies on a form of faith: faith in the authority of scientists, faith that the textbook isnāt lying. Sure, in school we could look at onion cells under a microscope, but believing that onions and I are made of similar cells ā especially that my liver and an onion are somehow structurally alike ā is not something I can directly verify. I have to trust entire systems: teachers not to lie to me, textbook authors not to lie to teachers, the Ministry of Education not to lie to anyone, scientists not to lie to their peers. And when that trust fails, we have to find alternative ways to verify things.
In the end, the difference between humans and language models isnāt in the āhallucinationsā ā itās in their predictability. A human lies because itās beneficial. A machine lies because fuck you, thatās why.
Still, being able to verify information quickly and reliably never hurt anyone.
For example, if you actually square 3456, youāll find that none of the numbers I listed above are even close.