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by itvision·6y ago·view on hn ↗
There's one thing I cannot wrap my head around.

Math is purely abstract science yet it describes the world around us to the utmost precision. Does that mean that this world is simply ... a math model which means everything around us is ... not real?

I've long stopped believing in free will because everything points at it being an illusion of our brain because we're a product of this world and we had no chance of influencing the conditions which brought us to life, and even after our minds and consciousnesses form it's hard to believe they are fully autonomous and not simply a function of the processess in our brains we're simply not aware of.

If you think about all of it, it becomes utterly depressing as you begin to realize you're a biological robot, a byproduct of the universe evolution which couldn't care less about our species and this little tiny blue planet.

9 comments
> Math is purely abstract science yet it describes the world around us to the utmost precision. Does that mean that this world is simply ... a math model which means everything around us is ... not real?

You can only reach this conclusion if you categorize math as "not real". If everything we interact with is a perfect mathematical object, I prefer to take that as evidence that all mathematical objects may be real, however abstract they seem.

> Math ... describes the world around us to the utmost precision.

It does no such thing. The models we create using mathematical language do.

Math is a precise language that can be used to describe the world around us precisely. It can also be used to describe utter nonsense or utter fantasy precisely.

Yep, the counterpoint to the unreasonable effectiveness of maths in the natural sciences is accompanied by the unreasonable ineffectiveness of maths in the social sciences, humanities, etc. Although at least to some extent statistics is the one branch of mathematics that does seem to be applicable (but the way this influences results, as opposed to methods, seems to be mathematically not that interesting).

There have been a lot of efforts of modelling social phenomena, the arts, etc. mathematically and while there are some interesting partial results (e.g. that languages can to some reasonable extent be analysed by parse trees or some aspects of music), most "grander" theories I have seen do not really stand up to much scrutiny.

I'm not an expert, but I could assume that part of this is due to a lot of nonlinearity in the phenomena studies, which means that many classical methods don't work well; maybe chaos theory etc. could shed more light on these things, but I don't know enough about it.

> Yep, the counterpoint to the unreasonable effectiveness of maths in the natural sciences is accompanied by the unreasonable ineffectiveness of maths in the social sciences, humanities, etc.

Except it's not ineffective at all in these subjects. Social science experiments have so many variables that the small experiments that can be conducted given the financial resources are insufficient to infer a good model. This is not a math problem, it's a money problem.

If it's ineffective in practice, I consider it to be ineffective.

But even if you could design an experiment perfectly and come up with some strong statistical evidence and then had other means to tease out what is actually causal and what is only correlational, you'd only know what influences what and not necessarily why. But yes, I did say that statistics/probability is some rare exception.

You can study group theory and understand the way physical forces work better, or hilbert spaces to understand quantum mechanics, but I haven't yet heard of anyone who has studied topology or galois theory and found that incredibly useful for understanding social phenomena better.

> If it's ineffective in practice, I consider it to be ineffective.

Except you have no way to conclude that it's ineffective. Analytical solutions require data to study. Without data, or with little data, what analysis are you going to perform? At best, broad statistical correlations, which is exactly what we find.

You're effectively claiming that spoons are ineffective at a restaurant that provides only forks. Well no, if a spoon were available, then it would probably work just fine.

> but I haven't yet heard of anyone who has studied topology or galois theory and found that incredibly useful for understanding social phenomena better.

After 5 minutes of Googling:

* Power laws: https://en.wikipedia.org/wiki/Power_law#General_science

* Network theory: https://en.wikipedia.org/wiki/Network_theory

* There's a journal specifically for mathematical social sciences: https://www.journals.elsevier.com/mathematical-social-scienc...

* Economics, game theory, and social choice theory are all examples employing heavy analytical problem solving to social problems

* Quantum mechanics applied to social sciences: https://www.cambridge.org/core/books/quantum-social-science/...

The main stumbling block is that mathematicians are interested in mathematical problems, and so they make a common but mistaken assumption that social sciences either don't have such problems, or they are too messy for elegant math. Take it from a mathematician, this is incorrect: https://www.mathtube.org/sites/default/files/lecture-notes/S...

You may have a point. And I did forget about things like social choice theory or game theory (although I'd assume that partially this is also due to e.g. social choice procedures or "games" often being very limited and artificial settings where by their very nature the relevant space of options/outcomes can be explored in some systematic way, which is generally less the case in more organic, complex settings, such as e.g. gradual societal changes).

When it comes to economics, I know that a lot of people don't agree with the basis of many mathematical models that are used, but I'm not an economist, so I can't speak to that.

So maybe I was overzealous in discounting mathematics for the social sciences altogether. Still, I would contend (albeit with much less evidence):

- There's some measure of people trying to construe "nice models" of things in those subjects instead of trying to make sure they agree with reality. I have a degree in linguistics and I've seen this over and over. Most of these models haven't convinced me at all.

- The amount of maths that you either need or at least benefit from in order to do good research in such areas is still substantially lower than in, say, physics. I think it's still to be noted how we can describe much of physics just with a small number of economic and elegant models. I haven't seen anything comparable in any of the social sciences.

What’s depressing about being a nanotchmological robot attempting to conquer the solar system and spread his technology and nanotechnology? It sounds rather exciting and fascinating. Perhaps if the depression is too severe you need to check out your programming ;-)
> If you think about all of it, it becomes utterly depressing as you begin to realize you're a biological robot, a byproduct of the universe evolution which couldn't care less about our species and this little tiny blue planet.

It can also be liberating and uplifting. You're a part of the universe - you are the universe expressing itself. The result of uncountable generations of brutal evolution, you're quite a miracle!

Mathematics has not been static throughout history. It has evolved at the same pace our science and discoveries have evolved, and as such it has incorporated all necessary elements to help describe new phenomena. To the point that now is able to describe never observed phenomena.

So no, our world is not unreal because it can be described with maths. Maths have evolved to describe it. Same as human language has evolved to support our close environment and our human interactions.

>I've long stopped believing in free will because everything points at it being an illusion of our brain because we're a product of this world and we had no chance of influencing the conditions which brought us to life

Free will doesn't depend on the universe being deterministic or not. Things that haven't happened yet are likely going to happen in a certain way based on the trajectory, but it doesn't mean that you can't change your own path in a meaningful way, you're free to take a harder path vs. an easier or more obvious one.

>but it doesn't mean that you can't change your own path in a meaningful way, you're free to take a harder path vs. an easier or more obvious one.

This is of course debatable, there is some evidence to suggest that the feeling that you took a certain path is illusionary. Your brain made the decision, then you became cognizant of the options and you felt yourself making the decision[0], but if you could rewind the universe, you would always choose the same path based on your 'brain-state' at that time. At least that is what I understand of the most extreme "free-will doesn't exist" position.

Just got lost in the SEP rabbithole [1], still not sure where I land on this issue.

[0] : like how you feel thoughts 'bubble up' during meditation, you didn't actively 'think' those, they appeared to you. EDIT: atleast that is what it feels like

[1]: https://plato.stanford.edu/entries/freewill/#DoWeHaveFreeWil...

That things would repeat after a rewind, given the same "universal state" just contradicts free will from the perspective of looking backwards (to the then present), not in the current present or looking into the uncertain future.
That's exactly the idea behind Max Tegmark's theory which he described in his book: Our Mathematical Universe

https://en.wikipedia.org/wiki/Our_Mathematical_Universe

Math models are real things, hence reality also.