Aidan Maney
Bartosz MilewskiWho came up with this crazy idea that reality could be modeled using mathematics? Seriously!
The Cyberneticist@BartoszMilewski because God doesn't play dice?
Arturo Serrano 🇨🇴🤖👽🧙🦄@BartoszMilewski @avillavecesn When the first caveman raised three fingers to explain to his tribe that he'd just seen three deer, that, right there, was a mathematical representation of reality.
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.
@vonxylofon You're right about being able to predict stuff being useful for survival, but that applies I certain domains in particular. In the millions of years of evolution, most of the new domains (astronomy, quantum mechanics, fluid mechanics) became of human interest relatively recently.
The other day I heard someone (I think a linguist) in a podcast say something along the lines of: it's no wonder there's so many people with dyslexia and dyscalculia, our brains literally didn't evolve to read or reason mathematically.
like, I understand pattern recognition and prediction making are useful for survival, but I think at this point we've overextended this capability to the point where we needed to build external tools (computers, calculators, proof checkers, simulation software) to continue advancing
Btw, I understand that by reading the word "overextended," one might think im doing a value judgment about our use of these evolutionary tools. I'm not trying to do that, I'm merely trying to describe the way I see things.
Going back to your point about any animal being able to arrive at these conclusions. I understand what you're saying, but I believe that in most cases, having a big, complex brain isn't necessarily an evolutionary advantage. Most other species seem to be surviving just fine using, at most, basic tools. In fact, it seems like having this level of intelligence and reasoning is, at least up to a degree, less ecologicaly stable (compare the history of the world since the humans took over to before that).
p4nc4k3@BartoszMilewski That is a good question. There is this famous quote by Galilei that "the book of nature is written in the language of mathematics," but it is likely that he only voiced a sentiment that was felt by many others of his time. It has undoubtedly worked very well as a heuristic, but the problem starts when the unthinking, science-worshipping masses start to treat it as dogma.
@p4nc4k3
Galileo was most likely a religious person, so this is not surprising. God would have created the Universe compatible with the human abilities to explore it--mathematics being the blueprint for it. Even though Galileo believed that the Earth was not the center of the Solar System, he probably still believed that the Universe revolved around humans.
Galileo was most likely a religious person, so this is not surprising. God would have created the Universe compatible with the human abilities to explore it--mathematics being the blueprint for it. Even though Galileo believed that the Earth was not the center of the Solar System, he probably still believed that the Universe revolved around humans.