It has to do with creating measuring devices out of what we can empirically derive, and building successive generations off of those. It’s fine for our local system but by the time you get intergalactic (or quantum) with it, flaws start to propagate themselves bigly.
I can’t reveal more at this time or Big Math will get suspicious.
nednobbins@lemmy.zip 1 day ago
Kurt Gödel wrote a whole paper on it.
He used math to show that all statements, in any language, can be expressed as math statements. He then proved that it’s impossible to create any cpnsistent set of math statements that completely describes everything.
rooroo@feddit.org 1 day ago
That doesn’t make it fundamentally flawed. I also can’t completely describe all muscle movement involved and yet I can walk.
Gödel’s incompleteness theorem has to be the most overhyped thing since a certain cat. For logicians, it mainly means that “is it probable” is a valid question for prepositions that are otherwise vastly esoteric in nature.
technocrit@lemmy.dbzer0.com 17 hours ago
That’s not a flaw. It’s an amazing breakthrough.
It’s only a flaw for people who want to believe in some imaginary positivism.
jwmgregory@lemmy.dbzer0.com 18 hours ago
like most commentary on Gödelian incompleteness, you got the right “vibe” but you’re not exactly correct.
for example, geometry is not an incomplete system, geometry is complete and thus not subject to incompleteness properties unless viewed strictly from the perspective of reality. in that case, all systems and models we build are necessarily presumed incomplete because of what people like Kant and Descartes said - all you know is known filtered through your perception, it isn’t what is actually real.
that is where people get the “it’s impossible to completely describe anything” argument from. it isn’t true flat out like that, though. you need some qualifiers, like, it’s impossible to completely describe reality solely through the human experience. this makes sense if you think about it. how much data lives just in a grain of sand? how many atoms are there in it? molecules? where might it fall in 2.76463 seconds? what does cathy juniper, born 1973, think this grain of sand would be named if it worked at the dollar store?
just because information that is incomprehensible or unreal to us lives in the world doesn’t mean it isn’t there. one iota of the universal computer has more computational power than all humanity combined over all history, many times over. our minds are so much smaller compared to the amount of information that actually lives in the world that we necessarily can only ever shine our spotlight of focus on tiny pieces of it at a given time, and not for very long. that is what the incompleteness theorem is describing…
this doesn’t mean that “it’s impossible to create any consistent set of math statements that completely describes everything,” if you’re willing to be a bit clever about it… after all, as humans, our big schtick is recording information in the world for later use, in reality… and there is proper suspicious to believe that reality itself could be a complete system, understandable from both the outside and inside if only viewed at the right angle…
hilbert’s dream is not dead yet, the early neoplatonist were just doing the dirty work of finding bounds.
technocrit@lemmy.dbzer0.com 17 hours ago
Nah.
It says far less than that: “It’s impossible for a mathematical system containing the natural numbers to be both complete and consistent.”
Reality has almost nothing to do with it.
This has been largely debunked.
I dunno what his dream was, but Hilbert’s program is very much dead.