Personality Cafe banner

1 - 11 of 11 Posts

·
Registered
Joined
·
885 Posts
Discussion Starter · #1 ·
An Introduction
When math is witnessed in its purest form the realization can be truly amazing. Sometimes the application of mathematics can seem to be separate from the natural world but in actual fact when we take the time, math can be seen all around us. But how can we find examples of math in nature? It is as simple as opening our eyes. The majority of our knowledge of mathematics and modern science is strictly based and supported on our observations of our environment. What was once seen as the randomness of nature is now distinguished as the intricate applications of mathematics and illustrates the complexities of our natural world.

Symmetry1
Many mathematical principles are based on ideals, and apply to an abstract, perfect world. This perfect world of mathematics is reflected in the imperfect physical world, such as in the approximate symmetry of a face divided by an axis along the nose. More symmetrical faces are generally regarded as more aesthetically pleasing.

Symmetry2
Five axes of symmetry are traced on the petals of the flower, from each dark line on the petal to an imaginary line bisecting the angle between the opposing lines. The lines also trace the shape of a star.

Shapes - Perfect
Earth is the perfect shape for minimising the pull of gravity on its outer edges - a sphere (although centrifugal force from its spin actually makes it an oblate spheroid, flattened at top and bottom). Geometry is the branch of maths that describes such shapes.

Parallel lines
In mathematics, parallel lines stretch to infinity, neither converging nor diverging. The parallel dunes in the Australian desert aren't perfect - the physical world rarely is.

Shapes - Cones
Volcanoes form cones, the steepness and height of which depends on the runniness (viscosity) of the lava. Fast, runny lava forms flatter cones; thick, viscous lava forms steep-sided cones. Cones are 3-dimensional solids whose volume can be calculated by 1/3 x area of base x height.

Geometry - Human induced
People impose their own geometry on the land, dividing a random environment into squares, rectangles and bisected rhomboids, and impinging on the natural diversity of the environment.

Pi
Any circle, even the disc of the Sun as viewed from Cappadoccia, central Turkey during the 2006 total eclipse, holds that perfect relationship where the circumference divided by the diameter equals pi.First devised (inaccurately) by the Egyptians and Babylonians, the infinite decimal places of pi (approximately 3.1415926...) have been calculated to billions of decimal places.

Zero - Placeholder and Number
Zero is one of the most important mathematical concepts. The idea of zero as a placeholder, eg to distinguish 303 from 33, developed in both Indian and Babylonian cultures.

Geometric sequence
Bacteria such as Shewanella oneidensis multiply by doubling their population in size after as little as 40 minutes. A geometric sequence such as this, where each number is double the previous number [or f(n+1) = 2 f(n)] produces a rapid increase in the population in a very short time.

Infinity
Is one infinity bigger than another infinity? The size of all natural numbers, 1,2,3..., etc., is infinite. The set of all numbers between one and zero is also infinite - is one infinite set larger than the other? The deep questions of maths can leave you feeling very small in a vast universe.
 

·
Registered
Joined
·
35 Posts
"What turns out to be true is that, the more we investigate and the more laws we find and the deeper we penetrate nature, this disease that every one of our laws is a purely mathematical statement [...]
It's my purpose in this lecture to explain really, why I cannot satisfy you if you do not understand mathematics too well in trying to explain nature in any other way.
It is the burden of this lecture, in fact, to just tell you the facts, that it is impossible to [explain] in a way that a person can feel the beauties of the laws of nature without their having some deep understanding of mathematics. I'm sorry, but it seems to be the case."
--Richard Feynman


Nowhere, I think, is it more obvious that nature is mathematical than quantum mechanics. The reason is because our inuition is insufficient. Nobody really knows what the heck is going on, you can read many different interpretations online and confuse yourself more and more as one or another of them seem to be at odds with the implications of some physical observation. So, it may seem to someone unfamiliar with the mathematics of quantum mechanics that the entire theory is a big mess and physicists have no idea what they are doing.

However, the mathematics behind quantum mechanics (the theory) is the most strictly tested theory in existence, and despite it's probabilistic nature it has given us some of the most accurate predictions we've ever had.
So, even when our intuition falls short and we find that nothing in our everyday experience is adequate to help us understand something, the mathematics still tells us what's going on.
 

·
Registered
Joined
·
778 Posts
I don't think man would have learned anything ,if not from the nature ,from small needles to gigantic space telescope it all came from the observation man made out from, incredible and amazing facets of nature. If one needs a true inspiration and knowledge about any science I don't think there is any best teacher apart from nature and universe.
 

·
Registered
Joined
·
1,168 Posts
You left out the void which is irrational and absurd by definition and, in fact, the foundation of logic, comedy, and mathematics. Zero is not merely a placeholder, but a result that challenges the law of identity, that is, if you can't identify when you have identified nothing you have an identity problem. This was all based on Socrates' classic joke, "The only thing I know is that I know nothing". Thus we have different types of logic and mathematics that expand on that basic theme dancing around the void of our ignorance.
 

·
Registered
Joined
·
1,520 Posts
An Introduction
When math is witnessed in its purest form the realization can be truly amazing. Sometimes the application of mathematics can seem to be separate from the natural world but in actual fact when we take the time, math can be seen all around us. But how can we find examples of math in nature? It is as simple as opening our eyes. The majority of our knowledge of mathematics and modern science is strictly based and supported on our observations of our environment. What was once seen as the randomness of nature is now distinguished as the intricate applications of mathematics and illustrates the complexities of our natural world.

Symmetry1
Many mathematical principles are based on ideals, and apply to an abstract, perfect world. This perfect world of mathematics is reflected in the imperfect physical world, such as in the approximate symmetry of a face divided by an axis along the nose. More symmetrical faces are generally regarded as more aesthetically pleasing.

Symmetry2
Five axes of symmetry are traced on the petals of the flower, from each dark line on the petal to an imaginary line bisecting the angle between the opposing lines. The lines also trace the shape of a star.

Shapes - Perfect
Earth is the perfect shape for minimising the pull of gravity on its outer edges - a sphere (although centrifugal force from its spin actually makes it an oblate spheroid, flattened at top and bottom). Geometry is the branch of maths that describes such shapes.

Parallel lines
In mathematics, parallel lines stretch to infinity, neither converging nor diverging. The parallel dunes in the Australian desert aren't perfect - the physical world rarely is.

Shapes - Cones
Volcanoes form cones, the steepness and height of which depends on the runniness (viscosity) of the lava. Fast, runny lava forms flatter cones; thick, viscous lava forms steep-sided cones. Cones are 3-dimensional solids whose volume can be calculated by 1/3 x area of base x height.

Geometry - Human induced
People impose their own geometry on the land, dividing a random environment into squares, rectangles and bisected rhomboids, and impinging on the natural diversity of the environment.

Pi
Any circle, even the disc of the Sun as viewed from Cappadoccia, central Turkey during the 2006 total eclipse, holds that perfect relationship where the circumference divided by the diameter equals pi.First devised (inaccurately) by the Egyptians and Babylonians, the infinite decimal places of pi (approximately 3.1415926...) have been calculated to billions of decimal places.

Zero - Placeholder and Number
Zero is one of the most important mathematical concepts. The idea of zero as a placeholder, eg to distinguish 303 from 33, developed in both Indian and Babylonian cultures.

Geometric sequence
Bacteria such as Shewanella oneidensis multiply by doubling their population in size after as little as 40 minutes. A geometric sequence such as this, where each number is double the previous number [or f(n+1) = 2 f(n)] produces a rapid increase in the population in a very short time.

Infinity
Is one infinity bigger than another infinity? The size of all natural numbers, 1,2,3..., etc., is infinite. The set of all numbers between one and zero is also infinite - is one infinite set larger than the other? The deep questions of maths can leave you feeling very small in a vast universe.
I very much enjoyed reading this BUT!! even a Rose when growing in a tomato patch is a Weed!!!! Had this thread been placed in Art Forum or the Philosophy Forum I would have treated it as the interesting aesthetic article it is and accepted, appreciated it as such.......

But because this 'rose' has been planted in the Science Forum I'm going to subject it to the Scientific Method - I have a busy day today and tomorrow so it will take me abit to get back to this but I shall return. (Oh and I have degrees in both Mathematics and Geodetic Engineering - deal with this stuff on a daily basis and I will have fun with this 1) :happy:
 

·
Registered
Joined
·
885 Posts
Discussion Starter · #6 ·
I very much enjoyed reading this BUT!! even a Rose when growing in a tomato patch is a Weed!!!! Had this thread been placed in Art Forum or the Philosophy Forum I would have treated it as the interesting aesthetic article it is and accepted, appreciated it as such.......

But because this 'rose' has been planted in the Science Forum I'm going to subject it to the Scientific Method - I have a busy day today and tomorrow so it will take me abit to get back to this but I shall return. (Oh and I have degrees in both Mathematics and Geodetic Engineering - deal with this stuff on a daily basis and I will have fun with this 1) :happy:
I agree
 

·
Registered
Joined
·
635 Posts
Not sure if this video is about maths in nature or nature in maths, but fern fractals are classic concepts already.


Also,

Parallel lines
In mathematics, parallel lines stretch to infinity, neither converging nor diverging. The parallel dunes in the Australian desert aren't perfect - the physical world rarely is.
They even don't have to stretch to infinity. Two parallel lines (i.e. circles) on a sphere do not intersect, either. This is how non-euclidean geometries were discovered.

Geometry - Human induced
People impose their own geometry on the land, dividing a random environment into squares, rectangles and bisected rhomboids, and impinging on the natural diversity of the environment.
Sometimes nature does it even by itself.


Zero - Placeholder and Number
Zero is one of the most important mathematical concepts. The idea of zero as a placeholder, eg to distinguish 303 from 33, developed in both Indian and Babylonian cultures.
As far as I can remember correctly, zero was introduced to make writing equations easier. x + y = 0 was considered more elegant than x = -y. Moreover, a x 0 = 0 and a + 0 = a are two most important qualities of zero, known as identities.

Oh, and let's not forget that Chuck Norris has already divided by zero. Twice.

Infinity
Is one infinity bigger than another infinity? The size of all natural numbers, 1,2,3..., etc., is infinite. The set of all numbers between one and zero is also infinite - is one infinite set larger than the other? The deep questions of maths can leave you feeling very small in a vast universe.
This problem was addressed by Georg Cantor. That's how cardinals of infinite sets were born and it turned out that the [0..1] real interval is still "bigger" than set of natural numbers, while its size was still "equal to" the size of the whole real numbers set.
 

·
Registered
Joined
·
258 Posts
Two very interesting videos. I think fractals and Fibonacci numbers are very cool. They're everywhere in the universe, on our planet, in our DNA, and even in financial markets. Trippy stuff. I think it's because they're efficient so nature likes to use them, and that is why they show up in human behavior as well because we are an extension/part of nature.


 
  • Like
Reactions: dulcinea

·
Registered
Joined
·
1,168 Posts
Believe it or not, fuzzy logic and fractals can also be used to describe quantum mechanics and comedy. You could even say all the holographic theories like the string theories are just a specific type of comedy. For example, over the last half century string theory has provided an unending stream of beautiful and lucid explanations for life, the universe, and everything. The joke seems to be that each theory inevitably turns out to be less beautiful and lucid than other interpretations of the theory discovered later and string theory keeps producing more and more of these theories without finding a single practical application outside of mathematics. The implications to AI research seem to be that, in the future, instead of crashing or whatever, you computer may laugh in your face and say things like, "You want me to do what!"
 

·
Registered
In my own world :)
Joined
·
6,598 Posts
The golden spiral:
Not only everywhere in the universe, but a key determinant in what we find beautiful.




 
1 - 11 of 11 Posts
Top