Bartosz MilewskiWho came up with this crazy idea that reality could be modeled using mathematics? Seriously!
Von Xylofon@BartoszMilewski If you can't, your math isn't good enough.
@vonxylofon Notice that this is just wishful thinking. We would _like_ the Universe to follow simple mathematical laws. What if the Universe doesn't listen to our pleas?
@BartoszMilewski That's not how maths work, that's how religion works. Assuming the Universe gives a rat's arse about what humans think is pure hubris.
Maths is merely a self-correcting mechanism of adjusting your model to observations. Ordinary matter physics being inconsistent with reality is why the concept of dark matter was invented. If that proves to be wrong, it will be modified or replaced. Our increasing ability to predict what happens based on mathematical models speaks volumes.
vgarzareynaI would think believing the human mind, which evolved for basic survival tasks, would be able to understand the universe and model it effectively is pure hubris.
It's actually kinda weird the fact that it works so well. There's no good reason to believe it should.
@vgarzareyna @BartoszMilewski Being able to tell what happens before it does (modelling situations) is great for survival, isn't it?
We can even theorise other forms of reasoning than deduction and inference, and make observations about those. I firmly believe that is all we need to understand anything the universe can throw at us.
I also believe any creature (not necessarily a form of life) capable of observation and deduction will eventually arrive at the same conclusions given enough time.
@BartoszMilewski @vgarzareyna I am asserting that a knowledge system whose basic tenet is making itself compatible with observations made – and which is known to cover yet unknown knowledge systems different from it – is likely to ultimately cover the entire universe because no observation can invalidate it. (If there is such an observation, the system invalidates itself as it has to by definition, thus making itself compatible with it.)
You are asserting that's impossible because...?
@vonxylofon @vgarzareyna I'm not saying it's impossible. I'm just saying that the belief that the Universe is mathematical is just that: a belief. It's based on wishful thinking and unfounded extrapolations. Just because it's hard (impossible?) for us to imagine something that cannot be modeled mathematically doesn't mean much. We are just evolved monkeys.
@BartoszMilewski @vgarzareyna Maths routinely operate with things we cannot imagine. I've studied things like formal grammars where we provably know grammars that we cannot express using existing methods exist, but we don't know what they are. That says nothing about a different system existing that can describe them, and by discovering it, we can easily incorporate it into current knowledge, possibly modifying existing knowledge if it is inaccurate. Maths are independent of evolved monkeys.
@vonxylofon @vgarzareyna
Platonism makes sense if you're a religious person (Plato was). The neat thing about beliefs is that they don't require rational proofs.
Platonism makes sense if you're a religious person (Plato was). The neat thing about beliefs is that they don't require rational proofs.
@BartoszMilewski @vgarzareyna I am not deriving the belief that maths exist independently from us from religion, but from an assumption of an objectively observable reality existing, and therefore every observer coming to the same observation given the same precision. If that is not the case, it gets a lot more complicated, but that still doesn't satisfactorily (to me) imply that no logic mappable to deduction can describe that reality. The mere possibility was at the beginning of this debate.
@vonxylofon @vgarzareyna
You are correct about the observer. The problem is that an observer is by definition a living (presumably sentient) being. And life can only occur in very restricted environments---ones that are highly decomposable. Math is the science of decomposition, and we see it everywhere arond us because that's where life thrives. So you are seeing the world through a bioist lens.
You are correct about the observer. The problem is that an observer is by definition a living (presumably sentient) being. And life can only occur in very restricted environments---ones that are highly decomposable. Math is the science of decomposition, and we see it everywhere arond us because that's where life thrives. So you are seeing the world through a bioist lens.
@BartoszMilewski @vgarzareyna I have a degree in computer science, so I'm the first to make a case for a non-living observer. (I actually thjnk I made it earlier in the thread.) How is maths a science of decomposition? If anything, it's a scienxe of synthesis.
@vonxylofon @vgarzareyna
I'm not sure what you mean by non-living observer. Who decides who's living and who's not? I didn't say carbon-based lifeforms.
How is math about decomposition? You do agree that it's based on abstractions, right? And what is abstraction? It's discarding the inessential parts. Five apples, five elephants, five galaxies are all abstracted to a number 5. How can you discard inessential parts if you can't decompose it into parts? Our language revolves around decomposition: parts, elements, properties... Complex systems are composed of many parts. Synthesis is just the mirror image of analysis.