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March 15, 2019, 08:32:05 AM
Merited by HairyMaclairy (1)

Actually you might have persuaded me that 2 + 2 doesn’t necessarily equal 4.  You might have gotten me there.

I haven’t responded because I am still thinking about it.  To your point, it’s not a topic I know a lot about.
Yes that's what I assumed, since you seem like a generally curious person.


In case you care about the intuition, imagine numbers on a circle. If you have {0,1,2,3} and align them on a circle, the next number after 3 is a 0. Now when you use the usual operations of a field (multiplication or addition) you have to stay within that set of numbers. So by adding 2 to 2 you move two to the right of 2 and end up back at 0. This is also the Mathematics behind Boolean Algebras, and thus the basis of computation (where the set of numbers is just {0,1}).
It goes deeper than that if you want to know why it's not exactly just some randomly made up system and why it's natural, but that would require study of the abstract rules and the elements required to create any number system.

For people who reject the idea of "infinity" in practical reality these finite fields are far more real than "1+1=2" ones, as those are by definition infinite. This information should bring anyone to pause and ponder over reality, it sure broke many conceptions I previously had for me.


The big take-away for me was, from a philosophical point of view, that no matter how obvious something seems, as soon as you take a potentially arbitrarily small step to the side your perspective can change dramatically.

It helps me to think about "knowledge" and "truth" as a place in some abstract space. Sometimes what appears obvious may be a mountain, but once I move a step to the side I can see behind it and everything changes dramatically, despite looking from virtually the same starting point.


This I suspect, is fundamentally why humans have such widely opposing opinions on seemingly obvious topics. And it's also why I try to balance out any conversation by proposing the opposite view or other different approaches.

I don't care about convincing anyone, I'm well aware that in the majority of cases that isn't possible. But if some bystanders take away something from the interaction I feel it was worth it. And if not, then I thought about new things that I might not have otherwise.