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Is mathematics a fundamental part of nature?


Eldorado
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Nature is an unstoppable force, and a beautiful one at that. Everywhere you look, the natural world is laced with stunning patterns that can be described with mathematics. From bees to blood vessels, ferns to fangs, math can explain how such beauty emerges.

Math is often described this way, as a language or a tool that humans created to describe the world around them, with precision.

But there's another school of thought which suggests math is actually what the world is made of; that nature follows the same simple rules, time and time again, because mathematics underpins the fundamental laws of the physical world.

https://www.sciencealert.com/the-exquisite-beauty-of-nature-reveals-a-world-of-math?

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Aren't we supposed to be offered red and blue pills?

Who has the pills??

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16 minutes ago, zep73 said:

Who has the pills??

owen-wilson-pills.gif

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2 hours ago, Eldorado said:

Nature is an unstoppable force, and a beautiful one at that. Everywhere you look, the natural world is laced with stunning patterns that can be described with mathematics. From bees to blood vessels, ferns to fangs, math can explain how such beauty emerges.

Math is often described this way, as a language or a tool that humans created to describe the world around them, with precision.

But there's another school of thought which suggests math is actually what the world is made of; that nature follows the same simple rules, time and time again, because mathematics underpins the fundamental laws of the physical world.

https://www.sciencealert.com/the-exquisite-beauty-of-nature-reveals-a-world-of-math?

At the centre of theoretical physics is a problem.

If you have Minecraft mark out an area 10 squares by 10 squares. Build the best circle you can in it. Now ask yourself is that really a circle? The answer is obviously no because its made out of square building blocks. Reality is believed to be exactly like Minecraft but the resolution of those building blocks is vastly higher. But ultimately, physicists believe we live in a pixelated universe.

So if you take the mathematics for calculating a circle you will notice no matter what radius you use, the answer always has infinite decimal places. How can you replicate a circle which from its answer is not actually pixelated, into a pixelated universe? You cannot. So mathematics with its circles is incompatible with reductionism into indivisible building blocks. Its not just circles, most formulae in theoretical physics gives you an answer with infinite decimal places. So either mathematics doesnt precisely describe reality, or reductionism is wrong, or both are wrong.

This will start by sounding odd but the moon doesn`t exist. Its not a real object. Its nothing more than an idea. Its an idea about what a vast number of actual objects arranged in a particular way are. And those actual objects are the indivisible building blocks of matter. Theoretical physics describes ideas, not actual objects, so for most of history it appeared to work. Its only when science got down to investigating actual indivisible units it was found to be wrong.

Quantum Mechanics is the science that has investigated how actual objects work, and they dont work off theoretical physics. They work off indeterminism, or in English, off probabilities. Sadly it means the only way to be precise in describing the moon is to count up how many indivisible building blocks it is made out instead of relying on a formulae. Something so hard it might take a million years.

Of course there are far more obvious problems with theoretical physics. Take General Relativity. How can one calculate the gravitational attraction between the Moon and Earth without factoring into the equation every single unit of matter and energy in the universe? They all have gravity wells too, and no matter how far away and weak that influence, they all exert influence on the Earth and Moon.

To get a degree you dont need to be a genius, an IQ of 115 is enough. Sadly its only the geniuses in physics that have enough about them to spot what is wrong with the science. Dont believe a scientist just because they are a physicist, dont believe most graduates just because they have letters after their names, most haven`t got a clue. Question everything, and you`ll notice there are holes in everything.

At this point in history the human race knows not a lot about anything, you can quite literally pull apart virtually everything including mathematics being anything more than a tool.

Edited by Cookie Monster
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15 hours ago, Cookie Monster said:

At the centre of theoretical physics is a problem.

If you have Minecraft mark out an area 10 squares by 10 squares. Build the best circle you can in it. Now ask yourself is that really a circle? The answer is obviously no because its made out of square building blocks. Reality is believed to be exactly like Minecraft but the resolution of those building blocks is vastly higher. But ultimately, physicists believe we live in a pixelated universe.

So if you take the mathematics for calculating a circle you will notice no matter what radius you use, the answer always has infinite decimal places. How can you replicate a circle which from its answer is not actually pixelated, into a pixelated universe? You cannot. So mathematics with its circles is incompatible with reductionism into indivisible building blocks. Its not just circles, most formulae in theoretical physics gives you an answer with infinite decimal places. So either mathematics doesnt precisely describe reality, or reductionism is wrong, or both are wrong.

This will start by sounding odd but the moon doesn`t exist. Its not a real object. Its nothing more than an idea. Its an idea about what a vast number of actual objects arranged in a particular way are. And those actual objects are the indivisible building blocks of matter. Theoretical physics describes ideas, not actual objects, so for most of history it appeared to work. Its only when science got down to investigating actual indivisible units it was found to be wrong.

Quantum Mechanics is the science that has investigated how actual objects work, and they dont work off theoretical physics. They work off indeterminism, or in English, off probabilities. Sadly it means the only way to be precise in describing the moon is to count up how many indivisible building blocks it is made out instead of relying on a formulae. Something so hard it might take a million years.

Of course there are far more obvious problems with theoretical physics. Take General Relativity. How can one calculate the gravitational attraction between the Moon and Earth without factoring into the equation every single unit of matter and energy in the universe? They all have gravity wells too, and no matter how far away and weak that influence, they all exert influence on the Earth and Moon.

To get a degree you dont need to be a genius, an IQ of 115 is enough. Sadly its only the geniuses in physics that have enough about them to spot what is wrong with the science. Dont believe a scientist just because they are a physicist, dont believe most graduates just because they have letters after their names, most haven`t got a clue. Question everything, and you`ll notice there are holes in everything.

At this point in history the human race knows not a lot about anything, you can quite literally pull apart virtually everything including mathematics being anything more than a tool.

This is what happens when someone with a little knowledge and no expertise tries to impress others with their 'understanding' of a complex subject. In the age of the internet, relativity and quantum physics have become the happy hunting ground of gormless self-appointed experts. Between themselves, real authorities on relativity and quantum physics cannot discuss or analyse their subject without mathematics and a whiteboard. You cannot even embark on an undergraduate course in physics without a high level of competence in mathematics. Science cannot be done at all without maths and theoretical physics, especially, is impossible without it.  

'physicists believe we live in a pixelated universe' - that is a generalisation. In fact, it is just a conjecture that some researchers are trying to prove and it only exists as a conjecture because relativity and quantum mechanics have not yet been reconciled by physicists. 

You say that because the mathematical formula for the area of a circle (= pi x r^2) gives an answer with an infinite number of decimal places, it cannot precisely describe the area. The area of any circle is finite and can be stated to any degree of accuracy you require. The reason your answer has an infinite number of decimal places is not because of the measured length of the radius, but because you used pi (= 3.1415....), an irrational non-terminating decimal number.

Precision and resolution have to do with how we measure or represent the world we perceive around us. It has nothing intrinsically to do with mathematics which routinely involves smoothness, continuity, discretisation and limits to infinity. Using pi in the calculation of the area of a circle introduces no constraint on the subsequent accuracy of the answer. Inaccuracy, or the limit to which we can calculate the accuracy of the area, only creeps in when we take the measurement of its radius. 

'its only the geniuses in physics that have enough about them to spot what is wrong with the science' - too simplistic. Every scientist contributes to science to some degree and genius is a spectrum. Many geniuses are not widely recognised because they were not in the right place at the right time with the right resources and the right experience and knowledge to make a leap. Einstein said that genius was 5% inspiration and 95% perspiration. Science is only ever wrong until science proves otherwise. The beauty of science is the 'scientific method' which many populist commentators fail to understand.

'Dont believe a scientist just because they are a physicist' - a cheap populist soundbite. Most of what is good about the world you live in (albeit there are obvious examples to the contrary) are the result of scientific endeavour. Scientists have been responsible for immeasurable good.

'Dont believe a scientist just because they are a physicist, dont believe most graduates just because they have letters after their names, most haven`t got a clue.' -  I agree that some universities (many of them former polytechnics) are churning out poor quality graduates with substandard degrees, some of which are of little use. Standards in academia have fallen and yellow-pack graduates proliferate, but peer reviewed research continues to hold the line and only lets quality through. Whenever it fails the academic community quickly responds to condemn poor research and bad science. When and where it matters, the academic world maintains its integrity and truth. Error is always corrected and deficiency exposed.  

'you can quite literally pull apart virtually everything including mathematics being anything more than a tool' - another false generalisation, but one that lies at the heart of social media and populism. It's true that anything can become a target for criticism - anything at all - but that does not mean that the criticisms are justified. In an age that facilitates online education for everybody, people do 'research' and end up arguing with properly qualified specialists and scholars. Stupid populist politicians pander to this phenomenon by claiming they are 'fed up with experts'! The world is filling up with populist 'experts': antivaxxers, flat-earthers, creationists, conspiracy theorists, etc. You tried to undermine the integrity of a simple well-established formula for the area of a circle (= pi x r^2) because the answer it gives is infinite and not 'precise' (your word). You questioned whether mathematics 'precisely' describes reality when in fact the problem is with our ability as scientists to perceive, measure and graphically represent it. 

Maybe our world is pixelated, but we don't know yet that it is. If and when physicists tell us that it is, will you believe them?

Edited by Ozymandias
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1 hour ago, Ozymandias said:

This is what happens when someone with a little knowledge and no expertise tries to impress others with their 'understanding' of a complex subject. In the age of the internet, relativity and quantum physics have become the happy hunting ground of gormless self-appointed experts. Between themselves, real authorities on relativity and quantum physics cannot discuss or analyse their subject without mathematics and a whiteboard. You cannot even embark on an undergraduate course in physics without a high level of competence in mathematics. Science cannot be done at all without maths and theoretical physics, especially, is impossible without it.  

This is what happens with someone with little knowledge tries to reply lol

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21 minutes ago, Cookie Monster said:

This is what happens with someone with little knowledge tries to reply lol

But you're the one assuming to know science. You're trying to pass off your opinions as facts. They are not. You are not a self-taught scientific oracle.
A few days ago you rejected cell repair degradation as a cause for aging, even though it's a proven fact, just to name an example.
You seem to be experiencing a severe case of the Dunning-Kruger effect. The best way get past it, is realising it.

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4 minutes ago, zep73 said:

But you're the one assuming to know science. You're trying to pass off your opinions as facts. They are not. You are not a self-taught scientific oracle.
A few days ago you rejected cell repair degradation as a cause for aging, even though it's a proven fact, just to name an example.
You seem to be experiencing a severe case of the Dunning-Kruger effect. The best way get past it, is realising it.

No I`m not, one of my degrees is engineering.

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2 minutes ago, Cookie Monster said:

No I`m not, one of my degrees is engineering.

And you think that makes you qualified in theoretical physics, biology and whatnot?

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Who could claim that math causes reality with any plausability.

Math can be used to effectively describe many aspects of it, but math is not a cause, it's a human language. not a driving force of nature.

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2 hours ago, quiXilver said:

Who could claim that math causes reality with any plausability.

Math can be used to effectively describe many aspects of it, but math is not a cause, it's a human language. not a driving force of nature.

The math is in the details. (There might be a devil in there too.)
From probability distribution in quantum mechanics, to the double helix, to the formation of ice crystals, to snail houses.
It's as if nature itself uses an advanced calculator. Asking if nature itself uses math, is as obvious a gravity.

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Semantics.

Some aspects of Nature can be described admirably by humans using math.

This however is not creating Nature.  Math is conceptual thinking, an abstraction, a process of human awareness.  It is not, however a force of Nature or creation.

 

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Or... math is as natural as matter. We didn't invent it, we discovered it.

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Again, semantics. *shrug

 

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Nature is what it is. Our opinions don't really matter.

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To me math, like language and art can very accurately depict/describe some natural phenomenon.

But that doesn't mean that either of these diciplines is equal to the phenomenon described/depicted.

Edited by Abramelin
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Well said.

Describing something is not understanding it, nor influencing/creating it.

We discuss and describe electricity, gravity and many such forces, even playing with it, yet we do not know or grasp the ken of their source, nor creation.

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Need I remind you gentlemen that this is proposed by theoretical physicists who get their theories from advanced equations that deal with the fundamental properties of the universe? To have a feeling or assumption, or even refer to common sense about the deepest layers of reality is foolish. Einstein learned that the hard way.

Like I said earlier: Nature is what it is. Our opinions don't really matter. All we can do is sit back and let the pro's figure it out. They at least know what they're dealing with, unlike most of us.

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Maths is, of course, a fundamental part of nature. It is not just a language invented by man. The natural numbers, the building blocks of arithmetic and number theory, are intrinsic to the world around us. The concept of one ('oneness'), or any other whole quantity (2 or 3 or 4 etc) is evident everywhere we look. Humans have counted objects since we first used language. Asking if maths is a fundamental part of the real world is like asking if the dance is fundamental to the dancer. How can we separate the dance from the dancer, maths from the real world? For example, the irrational, transcendental number e (= 2.71828.......) aka Euler's Number, unknown before the seventeenth century, dictates the rate of change of all continuously growing and decaying phenomenon. Euler's number was there in nature before we humans knew it was there. It was discovered by mathematicians in the seventeenth century. The role of 'e' in natural growth and decay was there long before we had the mathematical language to describe it. There are innumerable examples of how maths is embedded in the dynamical behaviour of our natural world. 

Edited by Ozymandias
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16 minutes ago, Ozymandias said:

Maths is, of course, a fundamental part of nature. It is not just a language invented by man. The natural numbers, the building blocks of arithmetic and number theory, are intrinsic to the world around us. The concept of one ('oneness'), or any other whole quantity (2 or 3 or 4 etc) is evident everywhere we look. Humans have counted objects since we first used language. Asking if maths is a fundamental part of the real world is like asking if the dance is fundamental to the dancer. How can we separate the dance from the dancer, maths from the real world? For example, the irrational, transcendental number e (= 2.71828.......) aka Euler's Number, unknown before the seventeenth century, dictates the rate of change of all continuously growing and decaying phenomenon. Euler's number was there in nature before we humans new it was there. It was discovered by mathematicians in the seventeenth century. The role of 'e' in natural growth and decay was there long before we had the mathematical language to describe it. There are innumerable examples of how maths is embedded in the dynamical behaviour of our natural world. 

Not only nature, it’s a fundamental part of every aspect of our Universe and the building blocks of all life. I would go as far to say that math is also a Universal Language!

JIMO

Edited by Manwon Lender
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On 1/12/2022 at 10:07 AM, zep73 said:

But you're the one assuming to know science. You're trying to pass off your opinions as facts. They are not. You are not a self-taught scientific oracle.
A few days ago you rejected cell repair degradation as a cause for aging, even though it's a proven fact, just to name an example.
You seem to be experiencing a severe case of the Dunning-Kruger effect. The best way get past it, is realising it.

He certainly assumes a great deal, but assumptions and reality can be vastly different!:yes:

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