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| Thread: The Real & the "mathematical world" are both DISCRETE |  This thread is pages long: 1 2 3 4 5 6 · NEXT» |
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Gandalf196
Disgraceful
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posted March 09, 2019 09:37 PM |
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The Real & the "mathematical world" are both DISCRETE
"Continuous analysis and geometry are just degenerate approximations to the discrete world, made necessary by the very limited resources of the human intellect. While discrete analysis is conceptually simpler (and truer) than continuous analysis, technically it is (usually) much more difficult.
Granted, real geometry and analysis were necessary simplifications to enable humans to make progress in science and mathematics, but now that the digital Messiah has arrived, we can start to study discrete math in greater depth, and do real, i.e. discrete, analysis"
source:
http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf
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friendofgunnar
Honorable
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able to speed up time
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posted March 10, 2019 12:08 AM |
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I don't see what this approach will yield that continuous mathematics can't.
Also whoTF is the digital messiah?
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AlfWithCake
Known Hero
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posted March 29, 2019 08:43 PM |
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I love how this personjust develops an idea and claims that it's "true" and "real", for literally no reason. He gives no proof that the world is discrete, it's not known wheter it's true or not, and it doesn't matter to people. Not only that, math is not about trying to model real world, but rather abput modelling some perfect, beautiful world so then this world could be applied with approximation to our world, hopefully. Thus real or discrete analysis are both true in math world. He also made mistakes by not defining multiplication well (e.g. h is small, then h^2 is smaller, but this can't be) as well as readily calculating number in power when this function is only defined in continuous analysis. You can't just do these things and state "my idea is the best!" throught all article.
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Gandalf196
Disgraceful
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posted August 27, 2020 04:47 AM |
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friendofgunnar said:
Also whoTF is the digital messiah?
Computers.
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Gandalf196
Disgraceful
Supreme Hero
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posted August 27, 2020 04:49 AM |
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AlfWithCake said:
I love how this personjust develops an idea and claims that it's "true" and "real", for literally no reason. He gives no proof that the world is discrete, it's not known wheter it's true or not, and it doesn't matter to people. Not only that, math is not about trying to model real world, but rather abput modelling some perfect, beautiful world so then this world could be applied with approximation to our world, hopefully. Thus real or discrete analysis are both true in math world. He also made mistakes by not defining multiplication well (e.g. h is small, then h^2 is smaller, but this can't be) as well as readily calculating number in power when this function is only defined in continuous analysis. You can't just do these things and state "my idea is the best!" throught all article.
This is not some random person. He's a well respected mathematician.
But I must ask you, why do you think mathematics should model a perfect world, when its origin stem from the physical world itself - counting, adding and even Euclides postulates!
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JollyJoker
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posted August 27, 2020 11:48 AM |
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Because MODERN mathematics are axiomatic and axioms don't care about the "real world", whatever that is.
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Gandalf196
Disgraceful
Supreme Hero
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posted August 27, 2020 03:43 PM |
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JollyJoker said:
Because MODERN mathematics are axiomatic and axioms don't care about the "real world", whatever that is.
Butshouldn't it care though? I mean, what makes mathematics this transcendental knowledge if its origins are in the physical world?
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JollyJoker
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posted August 27, 2020 04:38 PM |
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No it shouldn't, because no one knows what the real or physical world is, so mathematics must necessarily be independent from the real world. It's basically an independent language which - as a BYproduct - allows to describe the real world (because the language is well-defined and unambiguous).
THAT is why mathematics work - observed facts and data are TRANSLATED into the language of mathematics which in turn offers results.
The postulation that the real world is finite/discrete is of no relevance for mathematics, because this is nothing mathematics can prove. In fact, our current established foundation of mathematics, numbers, behave like particles in some way. If, you take just Q, the set of rational numbers, that set has a countably infinite number of elements which are all discrete. Add the irrational numbers, and the set becomes uncountably infnite, the elements becoming continous since the irrational numbers cannot be determined (like a particle, which isn't fully describable). It's exactly that property that makes things continous. And that uncertainty with a view on particles is, what - in my opinion - makes the universe continous as well.
This is, what computers is making so lame, at this point. They count. Which is to say, they cannot work with irrational numbers, which, for example, has the consequence that RNGs are not really RANDOM NGs.
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Baronus
Legendary Hero
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posted August 27, 2020 08:36 PM |
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Mathematical world is perfect. All is working. In real nothing. So mathematic is a picture of heaven. Ideal world.
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JollyJoker
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posted August 27, 2020 09:40 PM |
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There is a similarity indeed: Both haven and mathematics are entirely of human making.
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Baronus
Legendary Hero
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posted August 28, 2020 05:26 AM |
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HUMAN MAKING???!!! What are you taking about?! Who make mathematic?!
Its great difference between discovery and handwork. Car is handwork of human but Earth not. Mathematic too. Pepole discovered mathemathic NOT MAKE IT! It was before people known it. Its evidence that Someone make it. Who? This Being we named God.
Its evidence of God existing.
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JollyJoker
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posted August 28, 2020 12:07 PM |
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Baronus
Legendary Hero
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posted August 28, 2020 02:35 PM |
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But its mathematic ont physic! Its different! For quantum physics we use mathematic to calculate! Maths laws are constant in these case! If your really think that Mat laws are as we want you are irraltonalist! Science is impossible when you use irrationalism.
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JollyJoker
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posted August 28, 2020 03:16 PM |
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Baronus
Legendary Hero
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posted August 28, 2020 04:22 PM |
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2+2=4
???
Never 3 or 5.
Its law.
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JollyJoker
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posted August 28, 2020 04:47 PM |
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No, it's not a "law". It's just a sentence that says, if there are two times the same thing and you put another two times that same thing to them the result is called 4. (We might call this 10 + 10 = 100 as well - or even II + II = IV instead) This is always true as long as we are in the simple arithmetical space described by the Peano axioms. It's different, when we are in another mathematical space, let's say group theory, for example, where elements and operations are defined differently.
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Baronus
Legendary Hero
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posted August 29, 2020 11:42 AM |
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Its your mistake. Its only script sign. Of course it can be b+b=d BUT ITS THE SAME SENSE! This is logical law. You cant change it and give another in this place. Of course if you are not a crazy. These laws ruled us. Who make it? God. God is not religion truth but sense truth. Religion begin when we talk about how is God.
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JollyJoker
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posted August 29, 2020 03:17 PM |
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You don't understand mathematics.
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Gandalf196
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posted August 29, 2020 04:14 PM |
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Back to the title:
Quote:
David Hilbert famously said:
"No one shall expel us from the paradise that Cantor has created for us."
Don't worry, dear David and dear Georg, I am not trying to kick you out. But, it won't be quite as much fun, since you won't have the pleasure of my company. I am leaving on my own volition.
For many years I was sitting on the fence. I knew that it was a paradise of fools, but so what? We humans are silly creatures, and it does not harm anyone if we make believe that א zero, א one , etc. have independent existence. Granted, some of the greatest minds, like Gödel, were fanatical platonists and believed that infinite sets existed independently of us. But if one uses the name-dropping rhetorics, then one would have to accept the veracity of Astrology and Alchemy, on the grounds that Newton and Kepler endorsed them. An equally great set theorist, Paul Cohen, knew that it was only a game with axioms. In other words, Cohen is a sincere formalist, while Hilbert was just using formalism as a rhetoric sword against intuitionism, and deep in his heart he genuinely believed that Paradise was real.
https://sites.math.rutgers.edu/~zeilberg/Opinion68.html
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JollyJoker
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posted August 29, 2020 06:09 PM |
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The mathematical world is NOT discrete (obviously - irrational numbers aren't discrete; "discrete" kills the defintion of "dimension"; discrete kills the idea of fractals...)
The real world MIGHT be discrete - but this would have consequences:
1) quantum theory would be complete nonsense;
2) there would have to be an "ether" "around" the discrete real worlD, simply because with a discrete reality we suddenly have no dimensional definition anymore.
The link I gave, by the way, is no hoax. Reading it might be fun.
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