Computer proof ‘blows up’ centuries-old fluid equations

I know nothing of OP, or the professor he talked to, but I think they might be talking about the higher level concepts of math.

For example, set theory. If set theory allowed self reference you could have set R, a set of sets that do not contain themselves. Would R contain R? It can’t, but it can’t not either. It’s self contradictory. The solution, reached through consensus, was to restrict the definition of the set to not allow sets to reference themselves [1].

[1] https://youtube.com/watch?v=HeQX2HjkcNo

That's just some additional structure pertaining to, specifically, clouds. One cloud standing close to another cloud still equals two clouds, which is what 1 + 1 = 2 is really encoding.

You can choose whatever you want, and mathematicians do sometimes choose different axioms. The question is whether the consequences of some axioms are up for social negotiation.

> I guess you have to ask the man in the street.

How about checking with a GPS?

A social construct has nothing to do with simple facts about the universe. And whether the Eiffel tower exists as an object at a particular spot as indicated on maps is such a fact. And if there were maps that would place it elsewhere, those maps would be a lie. Even if the every single map ever made and every other person would deny that there is such a tower at that position one could still go there and check for oneself.

Maybe you are talking about the name? The fact that we call it the Eiffel tower? Well, that tower has a history and again one could lie about the history, who built it, how it was historically called as a matter of fact etc. But an observer would have seen who actually built this tower. It's a fact.

I'm going to relay a story. For a short period in my life, I had a roommate whom I wasn't sure if he was real for the first two weeks I knew him. At first it was just we agreed unreasonably well about our view on the world. Like I could not think of a single thing we differed on. But then it started to get uncanny. He had this way of knowing all the same trivia as I did. And also of not being able to recall the same bits of trivia I was struggling with. I'm talking really obscure sorts of things, not the sort of stuff you could dismiss as "20% random hn person recognizes it." Then there was the scavenging. Practically any time I mentioned off hand an idea for something we might have a use for, he would randomly find that or a similar item thrown out on the side of the curb (this was in NY). He wasn't buying these items, it was all just "lucky coincidence". Then there was the absurd situational similarity. We had started out as guests in an airbnb, permanent temporaries, but now we were both effectively bartering for rent making improvements on this guys apartment in exchange for free board. Its the sort of weird niche situation few people ever find themselves in, and we were both doing it.

At some point the thought occurs to me. Which is more likely, there's a guy who knows all the same stuff I know, is in the same awkward work situation I am in, happens to find the exact things I am looking for, OR I am having a psychotic break, this guy is my delusion, and all those things he does is actually just me doing it? After thinking this I started to realize, I had never really seen this guy outside the apartment. No one else I knew from before had ever seen or knew of this guys existence.

One day I'm idly humming a tune that got stuck in my head. You might recognize it as "Battle hymn of the Republic." But, there's actually 4 prominent songs in American history with this exact same tune. The others are "John Browns body", "Blood on the Risers" and "Solidarity Forever". My new roommate walks in and starts singing the words. But how did he know which one I was humming? It wasn't the obvious well known one! No, surely I am going mad.

My roommate had mentioned that he lived in Russia until he was 8 and could speak basic Russian. I do not know Russian. I ask him to teach me about Russian grammar. He agrees but then changes the topic. I push the issue again latter that day. He once again agrees to teach me some Russian and then proceeds to divert attention elsewhere again. I ask him to teach me some Russian. He pushes it off yet again. Whereas before the thought was idle, the evidence keeps on growing. I'm having a psychotic break. This guy can't be real.

We are sitting around one day. My roommate points out that all of us sitting in the room have hazel eyes, and that this is the rarest of the eye colors. They then proceed to pull up the statistics and crudely calculate the probability of this happening (pretending our genetic demographic is unrelated to the circumstances that led us all to this room). The result was some outrageously small number, less than a tenth of a percent. At this point I'm pretty sure my own delusion is taking the piss out of me, actively shoving the implausibility of his own existence in my face as a joke.

It turns out all of this really was amazingly coincidental. As weeks went by, guests at the airbnb would come in go, we would meet each others friends, and eventually there were enough people who also acknowledged his existence that I am now convinced he is real.

So I pose it to you. Was my roommate real, was everyone involved in this story a figment of a madman's imagination, or am I completely making up this roommate story to make a point? The answer is, reality is shared consensus. If you all are also convinced that this person existed and these events transpired, then we share a common set of facts. If there is no shared consensus, then he only exists for me. Perhaps there is some underlying truth beyond the shared consensus, but shared consensus is the instrument we use to measure realness. At some point, there is no difference between "every multimeter says this battery is 9 volts" and the battery actually being 9 volts.

I'm going to relay another story. Neils Bohr used to keep a horse shoe nailed to his door. When asked, he would say its for good luck. One day someone asked "do you really believe that?" He responds "No, but they say it works even if you don't believe in it."

Why believe quantum mechanics over lucky horse shoes? If everyone chooses lucky horse shoe theory, does that become reality? If powerful interests in government start forcing everyone to adapt horse shoe theory, does that make it real?

Thus I arrive at a truly bothersome set of contradictions. Reality is shared consensus, but reality is also the set of things not subject to popularity. There is no truth only power, but also the essence of science and math is that truth does derive from authority.

One day I will reconcile these. One day.