Analemma of the Sun and the Klein Bottle non Orientable Surface

Analemma and Klein flӓsche have possibly something in common. Let’s explain.

As I’ve sometimes suggested on the pages of this blog, the moon keeps on moving inside a nonorientable Mӧbius strip. This is a surface able to give the reason for the lunar phases. When the lunar disc keeps on running a full lap around its Mӧbius belt,  it will turn out, in the end, to be moving on the opposite side of the strip and, in that condition,  it will disappear from the sight of the world.

Mirror phenomena and the moon

In addition, a Mӧbius strip is endowed with another astonishing property. When a disc is moving on this surface in a right-handed way, in its coming back to the original starting point, it will change its spinning direction, undertaking a suddenly left-handed mirror movement (Chirality).  This is something happening to the moon in the course of its monthly phases: the lunar phases are mirror-phenomena. Think for instance of the crescent and falling moon: aren’t they mirror images? Of course, the moon should be imagined in the shape of a disc and not as a sphere. This will be of fundamental importance because we are always seeing the same face of the moon.

A widespread caldera

The sun, how could it be imagined? For now, I feel it doesn’t matter: a disc or a ball, it will be the same. Let it be unresolved. We could think of the solar disc/ball as of a sort of widespread caldera. The upper surface is not smooth but it rather looks as if it were made up of small grains or granules. These are the tops of convection cells that carry heat upward from the deep within the sun. They make me think of the special convection effects you can observe inside a pot when cooking some rice grains, barley, spelt or the like.

Solar faculae

The solar surface undergoes special phenomena. Solar faculae can easily be observed only near the edge of the solar body, on the sun’s outermost atmosphere, the corona. Faculae can be really observed only when the sun bright disc is hidden, as during a solar eclipse. These are surface phenomena. The bright spots are produced by concentrations of magnetic field lines. Solar faculae distribute in a non-homogeneous, highly localized way on the solar surface.

Sunspots and the11.11 Years Solar Cycle

While the faculae make the sun look brighter, the sunspots tend to make it darker. They are dark areas on the solar surface that contain strong magnetic fields that emerge through the solar surface and allow an area to cool slightly. The Solar Cycle is the observed high and low sunspot activity that repeats about every 11.11 years. 111 is a special number, not only concerning the earth but even the sun. It is a number that appears to be linked to the activity of the sun even in the arithmetic of the magic squares of old.

Analemma: sun, moon, and planets

Moreover, the sun, moon and planets, all have their own analemma. What is it? Imagine that you went outside, each and every day at the same time, and mapped the position of the Sun. What would you see? Doing this — taking a snapshot of the Sun at the same exact time from the same exact place on different days — gives you what’s called an analemma. So, an analemma is a diagram showing the variation of the position of the celestial body,  the sun,  in the sky over a course of a year, as viewed at a fixed time of day and from a fixed location on the earth. Even the moon and planets, during their complete course, draw their own analemma. The planets analemma show a different diagram in the form of a drop.

The sign of infinity

In the case of the sun, the analemma has the shape of a slender figure of a non-symmetrical eight. The lunar analemma is quite similar to that of the sun. It is very likely that from the eight-shaped-pattern of the solar analemma and from the concept of the cyclical repetition of the seasons, originated the mathematical infinity sign.

Analemma and the Summer and Winter Solstice

The north-south component of the analemma is due to the changing of the Sun’s declination caused by the tilt of the sun during the course of the year. The east-west component is due to the non-uniform rate of change of the sun right ascension.  The top of the analemma is reached during the Summer Solstice while the lowest point of the analemma will occur during the Winter Solstice. The “crossing” takes place twice a year: once on around April 15th and once about August 31st. So the solar analemma appears to be the corresponding movement of a Klein self-intersecting bottle in 3D.

Analemma and the so-called inclination of the axis of the earth

Mainstream astrophysicists, when considering the inclination degrees of the sun analemma, will define the so-called inclination of the axis of the earth.  These values, which are connected with the inclination of the analemma during the year,  undergo an annual variation of  +23°27’ and  -23°27’, respectively during the Summer Solstice and during the Winter Solstice. Of course, all scientists know this is the cradle of the changing seasons in the course of a year and that’s right. But let’s try a more in-depth analysis of the topic.

Analemma as a magnetic Klein  Flӓsche pattern

When connecting the solar analemma to the Klein Flӓsche, I felt excited. I often wondered why the sun would run, in the course of one year, such an eight-movement and finally I’ve got it. The intuition that the moon could follow a Mӧbius strip track led me to the only possible conclusion: that the solar system, in the whole, could be embodied in a cosmic Klein Flӓsche able to impress a special direction to the convective movements of the sun.

Analemma  and the movement of the solar magnetic field

The Klein Flӓsche is a one-sided surface as the Mӧbius strip, which, if traveled upon, will be followed back to the point of origin while flipping the traveler upside down. The movement of the solar magnetic field follows that pattern. They say the sun moves as a fluid, plastic body reaching higher speeds at the equator and lower speeds at the south and north poles. Since it is a gaseous surface, it does not move in a uniform way.

The Klein Bottle is a double Mӧbius strip

The Klein bottle and the Mӧbius strip belong to the same family. You could cut the Klein bottle in order to obtain two Mӧbius strips or paste two Mӧbius strips in order to obtain a Klein bottle. The main difference between the two non-orientable surfaces is that a Mӧbius strip can be available in a 3D space while a Klein Bottle cannot generate in 3D without self-intersections. The Mӧbius strip has a hedge but the Klein Bottle has not.

The geometry of the gum

They often say that topology is the geometry of the gum. When you examine a disc on a plane, the topology will explore those properties of the figure which stay unchanged even when you imagine to stretch it as a surface made up of some infinitely elastic stuff. You just should avoid to cut or paste those surfaces.

The Klein Bottle and the Van Allen belts

James Van Allen in 1958 discovered a pair of radiation belts, an inner and an outer doughnut-shaped ring above Earth. These were rings containing electrons and protons possessing very high-energy. Earth’s magnetic field can hold the radiation belts in place, but the rings shrink and swell as needed to respond to the Sun’s ejections of energy in our direction. The two doughnut-shaped belts are an evidence of the Klein bottle surface enveloping the sun while another outstanding structure proves the presence of the Mӧbius strip belonging to the moon. Inside the Klein bottle.

A storage ring inside the Van Allen belts

In 2013, Daniel Baker from the University of Colorado made an important discovery. He discovered a third structure between the inner and outer Van Allen radiation belts. Baker characterized this structure as a “storage ring”. He noticed that it was coming and going like raising or lowering an invisible shield. It is like something  necessary to block the effect of “killer electrons.” At the right altitude, a sharp boundary forms a type of inner edge on the outer radiation belt. This way it can block those electrons from penetrating deeper into our atmosphere.

A shield blocking the killer electrons

“It’s almost like these electrons are running into a glass wall in space,” said Baker. “Somewhat like the shields created by force fields on Star Trek.”  As if they were appearing there to repel alien weapons, they were looking as an invisible shield blocking the electrons. So Baker concluded:” It’s an extremely puzzling phenomenon.”

Scientists have developed several theories to explain this shield. But so far, none of them works completely. Very well. The Klein Bottle and the Mӧbius strip belonging to the moon can provide the needed explanation.

Infinitesimal Mӧbius strips in the structure of the light

More than 10 years ago something strange happened. Physicists discovered that the electromagnetic structure of light could contain infinitesimal Mӧbius strips. Then scientists were able to demonstrate experimentally the real existence of those strips in the constitution of light. It was the result of the efforts carried forward inside an international cooperation study. It was conducted among others by the Neapolitan Spin Institute of the Italian National Research Institute (CNR). The results appeared online on the Science magazine issued on the 27th of February 2015. Innovative technologies were developed in Germany in order to reach the expected results.

I ‘ll conclude this article just by saying that much of the sun’s motion and activity is still difficult to explain. So I don’t think to be able to give a more detailed explanation. For now, at least. However, without admitting  the earth is flat and not a globe, many outstanding cosmic phenomena would stay mysterious forever.

Leave a Reply