Fractals.

1). An area has 2 dimensions, a volume 3 .. but fractals, as the author of the video below says

.. have a dimension which is not finite. Here are some examples : http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

I was thinking … what about fractals which have a dimension like PI (3.14159 ….) or PHI (1.618 …) ? PI is a transcendental number which is more than three. It might be exciting to see what PI-dimensional fractals may look like.

And, what if we think that matter is limited to 3 dimensions and we humans are more than matter, spiritual beings … who have consciousness … I’m thinking about those special states of “falling in love”, or “spiritual bliss that some women experience when they give birth to another human” or even spiritual trances, states of extasy resulting from prayer or meditation, even dreams … These kind of states which we pass through seem to be “more than 3 dimensional matter”.

I think fractals are the key to envision these kind of “things”. These maths are still recent, They are already used in some fields and I hope that in the coming years or centuries someone may find or invent even more interesting things based on them.

2). PHI, the golden ratio, is by definition given by the formula : PHI² = 1 + PHI and this leads to fractal-like formulas (symbols making the formula are themselves repetitive).

Phi, 1.618, the golden ratio, expressed as a limit

or

It’s really surprising to see that the golden ratio has fractal-like formulas.

We can replace 1’s by other numbers or we can even find other mathematical formulas with repeating patterns but their physical importance is not as great as the golden ratio.

Similar thoughts on helical fractals …

1). http://infinity-imagined.tumblr.com/post/54065841977/the-gravitational-orbit-of-any-moon-planet-star

Difficult to concentrate on the article as there are lots of animations aside. I hided the animations with my right hand and I read several times the article using paper and pencil to better understand what the author says.

First of all, it is convenient to have a better understanding of 4 dimensional things : note that there is no such thing as 4th dimension, it’s just a convention used by physicists to represent the flow of time.

a). A point is a 0 dimensional object.

A line, composed of points is 1-dimensional object.

A surface, composed of lines is a 2 dimensional object. And, finally,

a cube is a 3 dimensional object with length, width and height (each section of a cube is a 2D surface).

b). Suppose you have a paper which is a “surface” : you can draw lot of lines on that 2D object. And suppose you have a hollow carton => you can put papers in that carton which means that a 3D object can contain 2D objects, as well as 3D objects smaller than its volume, for instance, you as a 3D object are in a room, which is another 3D object.

c). 2D and 3D objects are daily objects and so, they are easy to make out. What about 4D ?

Suppose you hold a little cube in your hand and move it horizontally. This little cube moving through time, creates a 4D object. Another example : suppose you run … for let us say 5 seconds, and at the same time, you take 3D photos of your movement. Then this is the resulting sculpture :

MovingThroughTime

The “thing” above is still a 3D object because we don’t see any movement. For a 4D object to be seen, there must be a flow of time. For an event “myself running 5 seconds” to be seen, there must be intervention of time, there must be a video which lasts 5 seconds. No time, no movement. The above sculpture is just a superposition of several 3D slices of an event. Event = 4D, event needs flow of time.

d). So, finally, I hope you are now able to understand what the author says when he talks about planets instead of a runner.

Excerpts : d.1). “A 3-dimensional helix is a ‘slice’ of the 4-dimensional shape of the orbit of a planet”.

d.2). “One 2D slice of a 3D helix is a circle, another is a wave”.

d.3). “One 3D slice of a 4D helix is a sphere; a planet in a specific moment of time”

Explanations :   d.1) => Let us suppose we have a planet instead of a runner.

MovingThroughTime PlanetMovingThroughTime

Then, the shape of the totality of movement of a planet, is a helix. Adding time, we can really appreciate the movement instead of just a superposition of 3D snapshots condensed like a strange sculpture. Without time, all we have is just a 3D slice of it, which looks like a helix. Helix = 3D object, a snapshot of the whole movement of a planet.

d.2) => If we cut a very thin slice of the 3D sculpture of the runner, we can have a 2D object, which has only length and width, like photos. In the same way, if we cut the helix perpendicularly, I mean, suppose you put a helix on a table and cut it at the middle with a movement parallel to the table, then you’ll get a circle.

HelixCircleAndWave

But if you cut it vertically, then you’ll get a wave like thing.

d.3) => Let us take a cube and move it horizontally through time. It creates an event, a 4D object where the 4th dimension is time, by convention. You know that there are only 3 dimensions of space, but physicists have opted fot that convention in order to have beautiful mathematical equations. So, instead of a continuous movement of the cube through time, you take a 3D snapshot of it : what does it look like ? answer : a cube.

(Cube + movement of this cube through time) – movement of this cube through time = Cube

In the same way, replace the above cube with a spherical planet moving helically through time, and take a 3D snapshot. You’ll get a a planet which has a spherical shape.

Rk : reading d.1) and d.3) may give confusion.

Please note that in d.1) we consider the orbit as a 3D object (a helix), whereas in d.3), we considered just the planet as the 3D object (a sphere).

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After that, the author speaks about “fractal nature of gravitational fields”. What I see, is concentric circles from the above view and sinusoidal waves wrapped into bigger sinusoidal waves from the side view. Do these concentric circles and waves can be seen like fractals ? I don’t know, it’s like asking the question : “do russian dolls have a fractal nature ?”.

One funny thing though, ask yourself this question : if I’m able to replay past events (aka 4D objects) in my mind, does it mean that my mind acts like a container of 4D objects ? If so, can the mental space be considered as a 5D object because it can contain memories of events I’ve witnessed in the past ?

Suppose you are seeing a person running. It means that your consciousness can “contain” a 4D object, hence consciousness itself has a superior dimension than space and time. This is the subject discussed in the following point 2).

2). Type “time space and consciousness” on google search. It will take you to this PDF document : http://www.imprint.co.uk/pdf/smythies.pdf => Page 53 has something following the same ideas.

Excerpts : “[…] the earth is not a spheroid circling the sun, but a stationary hyperhelix wound around the world lines of the sun.”

Ideas of the week

1). http://www.bugman123.com/Hypercomplex/Mandelbulb8.m1v (looks like http://www.youtube.com/watch?v=EKtevjrZOGs )

This gives an idea of a hypercomplex fractal. Moving 3D Fractals are the best representation of “As above, so below“. When I spoke about the universe as a helical fractal, moving and lively, this is what I had in mind. All the matter in the universe and all repeating cycles like the movement of astral bodies may be just something like that (?).

Also sounds like a cymatic soundscapeThe spiral mouvement of galaxies may be harmonious vibrations producing fractal-like bodies, obeying cyclic trajectories ! This famous Bible verse  : “In the beginning was the Word, and the Word was with God, and the Word was God … ” may find a place here.

2). Another subject : Reduce the number of numbers as much as possible. We know that the fastest speed in universe is 299 792 458 m/s.

This is – unfortunately – not a prime number by itself and when broken down into primes gives : 2 x 7 x 73 x 293 339.

May be in another numerical base and other metric system, instead of our decimal base and meters, we may have an interesting number. And in that base, special numbers like PI, golden number, … may look better (?).

Back to our decimal base, the speed of light being the highest number, we can come to the conclusion that 293 339 is the highest prime number in the physical universe. To know how many primes exist between 1 and 293 339, we can use http://en.wikipedia.org/wiki/Prime-counting_function#Inequalities :

293339/((ln 293339) – 1) = 25 311 < x <  25 532 = 293339/((ln 293339) – 1.1)

Conclusion : there may be only 25 489 numbers in the physical world, if we take into account the number 1 and the number 293 339 according to this site  … only 25489 things.

Numbers : what’s the best representation ?

You learned at elementary school to represent numbers : 1, 2, 3, 4, … 10, 20, 30, … 100, 200, 300, …. 1000 … 10 000 … 100 000  …

These are symbols which represent what we call numbers. These help to have a representation of quantities … The question I asked myself today was what is the real shape of a list of numbers, suppose from 1 to 100 000 ? In other words, how do you visualize a set of numbers like 1 to 100 000 ?

This image below is the one which came to my mind :

100000

Usually, I put chunks of numbers in a rectangular-like figure. If I close my eyes, the form is smaller, but, if I see the rectangular wall in front of me, I can also imagine them on that bigger surface.

But, what is the best representation of them ? The closest one to reality ? What really are numbers anyway ?

First of all, the most important numbers are those who are in some way, unique : these are the prime numbers, the building blocks of numbers themselves. The number 4 : if you represent 2 by a tea spoon, then 4 is two tea spoons. But you can’t get 3 or 5 with a tea spoon because 3 and 5 are themselves unique, only devidable by 1 and themself. 3 is like a soup spoon and 5 can be seen as ice-cream spoon. Or if you prefer another representation like this …  http://focusonmath.wordpress.com/2013/01/08/factoring-a-visual-representation-of-numbers/    it’s OK.

Are all numbers of equal importance, or, is it preferable to sort them by their importance ? In the physical world – not the mathematical – we have 3 dimensions of space, 5 fingers on each hand, 2 eyes, 2 ears, 1 nose, 1 mouth … I chose to eliminate all those numbers which can be derived from the building blocks (aka, primes) and keep only primes, so that we could have a really nice view : http://tinyurl.com/oqp5mkw  … The same thing in 3 dimensions gives this :  http://www.youtube.com/watch?v=dJ0murDJgf4

Other images of the real shape of numbers : http://tinyurl.com/l5wgd5u

The final thought is that for even a set of numbers, the whole picture, is something looking like a spiral, if we consider only numbers which have a meaning in the physical world.

The roman representation I, II, III, IV, V … X, … L, C, D, M … as well as the usual representation, both of them look boring : a sequence of symbols, one following the other like sheep, we don’t know which one has a physical reality … no emphasis at all on any one : count them before sleeping, that’s the only thing they are good at. On the other hand, primes describe reality :   http://www.bbc.co.uk/news/magazine-14305667   and they have a very beautiful representation.

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Another spicy subject, if you came upto here :  numbers with multiple dimensions !

There exists what we call “complex numbers” : this way of representing numbers says that each number has 2 dimensions : one real and another imaginary. When you see 1, 2, 3, 4, 5, …. you only see symbols. Like people who have an unconscious part, numbers too have their imaginary dimension ! In this representation, we have these kind of beauties : http://tinyurl.com/ljstf46

But, what if numbers have more than 2 dimensions ? These weird beasts exist, they are called hypercomplex numbers. They have funny names like “quaternions“, octonions,  … http://en.wikipedia.org/wiki/Quaternion#See_also   and they are not so many nice pics or videos yet. I hope there will be lot more in coming years.

I have heard about this : http://en.wikipedia.org/wiki/E7_%28mathematics%29   around 2008 … or this one :  http://en.wikipedia.org/wiki/E8_%28mathematics%29   (just see the pics, don’t read, otherwise you’ll get mad).

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Quantum physics seen through helical lens

In a few sentences, this is what quantum physics says :

1). Duality : particle-like and wave-like behavior

http://en.wikipedia.org/wiki/Quantum_mechanics#Quantum_mechanics_and_classical_physics

2). possibility to be at two places at the same time.

3). possibility to be at different speeds, energies (quantum = quantity)

4). Tunnel effect ..

5). Spin : when we rotate an electron on a table by 720° (two rotations) , the electron only rotates once.

and so on.

The First one, … http://mythodrome.net/random-pieces-the-jesus-helix#comment-4326 => I think there is no duality. Suppose 10 aliens, visit earth and 5 of them have studied women and the other five, men : each group will insist on their own view of humanity. The reality is that humanity is a combination of women and men, so, even if these aliens perceive different measures/energies/behaviors which finally look unpredictable, … well, we humans know that their view is false. Both group of aliens are lacking information and even those clever ones who speak about duality are also false. There is humanity as a unit, there is no duality. No such silly thing like “it changes when we observe”.

Alike the helix, the side-view looks like a sinusoidal wave and the rear view shows a point moving like a circle. If you consider the nanoparticle as having a helical shape, then there is no duality.

The Second one, “being ubiquitous” : here too, if we imagine that the particle is rotating so fast that it looks like being at several positions at the same time : https://www.youtube.com/watch?v=es49S880bII   then, like this fan, even if there were only 3 blades, it looks as if there are 6 blades at some time and after that, it’s as if these are not 3 blades fastly rotating but some kind of ubiquitous or “spherical presence”.

See this : http://en.wikipedia.org/wiki/File:Hydrogen_Density_Plots.png  : isn’t it looking like a fan in several states of rotation ? This is the picture linked to http://en.wikipedia.org/wiki/Wave_function  (the wave function gives the probabilities of finding a particle at a given place, and at a given time).

As you can imagine, if a helical particle rotates very fast, then there’s no mystery that the particle appears at several positions at the same time. If microscopes take photos of the particle and then very respectable scientists with strange names like “Schrödinger” try to put a formula like “wave-function”, then this is the result ! After that, people are fooled by all this mystery.

The quantum physics looks weird when there is a simple explanation. Another fan ? https://www.youtube.com/watch?v=Z-Tf_9bpmO0  => scientists do not see 3 blades fastly rotating but a wave-function in Hilbert’s space, solution of Shrodinger’s equation, which can describe the probability of finding a blade at a certain position at a certain time. Then some guys like http://en.wikipedia.org/wiki/Werner_Heisenberg come with their “uncertainty principle” and get the Nobel prize for that blunder.

Third one : The possibility of being at different speeds and energies => once again, we can take the mechanical fan. http://en.wikipedia.org/wiki/Mechanical_fan  … What is the speed and energy of a particle which is close to the center of the fan compared to those particles of the blade which are on its outside edge ?

http://engineering.mit.edu/ask/does-outside-edge-ceiling-fan-blade-move-faster-inside-edge-0

You got it ? Scientists see them through microscopes, make measures and afterwards, say that at quantum level we can’t predict speed and energy of the particles.

Fourth one : tunnel effect. This too, has nothing mysterious. Suppose you are hearing music through earphones … If the sound is high enough, your neighbour can also hear it. Why ? because, 100% of sound doesn’t go to your ears, some of those sound waves can also go to outer regions upto the neighbour’s. Sound can cross walls … Nanoparticles are so small that they can cross things which look solid .. Never forget that atoms are almost empty ( http://education.jlab.org/qa/atomicstructure_10.html ) and … at nanolevels … with microscopes (not nanoscopes) we may perceive something apparently false.

Here’s the article in French : http://sciencetonnante.wordpress.com/2013/09/30/les-7-merveilles-de-la-mecanique-quantique/

Fifth one : when we rotate an electron on a table by 720° (two rotations), the electron rotates only once. It is said to have “half-spin” : http://en.wikipedia.org/wiki/Spin-%C2%BD

This one is also considered as a mystery.  How can we burn it through helical lenses ?

Let us consider that the electron has a helical movement or vibration (?) around the nucleus of the atom. If it has a 8-like movement, I mean, if you consider the electron moving on a möbius strip like this one :

Möbius-strip

Well, at first, the electron is at the center. Then, when we rotate this square above by 360°, the electron makes a circle and goes down the strip, it’s not visible. We still rotate the square by 360° and the electron comes to the initial position.

Möbius-strip_1

I think something like this is happening and fooling observers. The above figure gives a hint to the 1/2 spin mystery. Not the solution, but an idea of how 2 rotations may lead to an apparent unique rotation.

What is the figure which can explain a 3/2 spin ? A doube spin ? They say http://en.wikipedia.org/wiki/Spin_(physics)#Quantum_number   that the allowed values are 0, 1/2, 1, 3/2, 2, … I hope someone may find a logical explanation in future which can be visualizable and understandable, removing the mysterious part.

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A lot of things can be simplified if we consider that things at nanolevel have a helical shape … No more “duality” and all those probabilities in equations. This helical paradigm states that at all orders of magnitude, we have

– either helical trajectories ( http://www.youtube.com/watch?v=0jHsq36_NTU http://www.youtube.com/watch?v=C4V-ooITrws  ) or,

– helical shapes (DNA, and certainly nanoscopic particles) or,

– helical unity (men and women, belonging to the “helical unit” called humanity, can be broken down into uniaxial and circular tendencies).

[Max Tegmark says that the ultimate nature of the universe is a mathematical object. It may be a helical fractal, who knows ?]

To finish, let me tell you that all this article is just my imagination. It is certainly false. I just throw my ideas on this blog in order to have an uncluttered mind. Anyways ! I hope that you reader may be inspired … and I hope you may also share your super ideas too if you have any.

If there is one and only one, we may be approaching it slowly …

Mystics say that Identity is reality.

They say :”One without a Second” http://www.sacred-texts.com/hin/rls/rls21.htm

I was thinking this morning about light which curves the fabric of space-time … Light itself is an electromagnetic wave …

At one hand, you have electricity = f(x) and at another hand, magnetism = g(x), 2 functions …. and f(g(x)), the combination of both represents electromagnetism. In the same way, there is space = p(x) and time = q(x) which when combined gives “space-time”.

So, the sentence “light which cuves the fabric of space-time” is something like  f(g(x)) curves p(q(x))”.

With time, as we’ll recognize that things are different in appearance but are the same in essence, … sentences may look more and more like : “f(g(h(x)) combined with p(q(r(x))) gives b(c(x)) so …. “. At the end, we may come to acknowledge that mystical truth told since eons by saints, enlightened beings, prophets …

100 years back, no body thought that mass was equivalent to energy (energy is mass). More and more concepts which don’t seem to be equivalent may be linked in equalities and one day, everything may appear as unique.