Hey there Raphael!

I'm really glad you are digging deep into the topic of symmetry and how it relates to physics because those are two of my favorite topics.

Originally Posted by

**Raphael**
Originally Posted by

**RAM**
I don't know why you think that spirals are not symmetrical.

you need to go beyond how you define symmetry.

a spiral is flat...a helix is spiral in 3 dimensions.

Is the double helix of DNA symmetrical or asymmetrical?

Well?

Dimensionality has nothing to do with symmetry. Objects can be symmetric in an number of dimensions.

If you want me to "go beyond" how I define symmetry, you will need to present a definition for me to consider. As it is, I use the standard definition found in physics and mathematics.

The symmetry of a 3D spiral is very similar to that of a 2D circle. A 2D circle has an infinite degree of symmetry because it remains invariant under an arbitrary rotation. Likewise, a simple 3D spiral is infinitely symmetric because it is invariant under an arbitrary rotation coupled with a translation along its central axis. For example, consider a 3D spiral around the z-axis that makes a full revolution every meter. Now rotate it by angle phi radians and displace it dz=phi/2pi. It's form will remain invariant.

Originally Posted by

**Raphael**
Originally Posted by

**RAM**
Here is a snippet:

As is well known from biology a relative arrangement of very different sprouts arising in the cones of shoots is characterized by the "spiral symmetry". This arrangement principle was named *"phyllotaxis"*. On the surface of phyllotaxis forms, especially in the closely packed botanic structures (pine cone, pineapple, cactus, head of sunflower etc.), one can see clearly visible left- and right curved series of sprouts. As to the symmetry order of phyllotaxis forms there exists a practice to indicate it through the ratios of the numbers corresponding to the number of the left- and right-hand spirals. In accordance with the law of phyllotaxis such ratios are given by the number sequence generated by the **Fibonacci** recurrent relationship

I suspect you do NOT understand the basics of asymmetry vs. symmetry.

You posted as proof of your symmetry theory a link that is discussing the Fibonacci series of numbers that is connected intimately to the Golden Spiral.

The golden spiral, any logarithmic spiral is asymmetric.

OKAY?

I think we might be disagreeing about semantics. You appear to be using a colloquial definition of "asymmetric" which recognizes symmetry only if an object remains invariant under rotation and/or reflection. But that is just a special case of the broader mathematical definition which defines any object that remains invariant under any given transformation as symmetric with respect to that transformation.

Case in point: The logarithmic spiral is invariant under a scaling + rotation (much like the scaling + translation explained above). Here is a snippet from Wikipedia's article on scale invariance:An example of a scale-invariant curve is the logarithmic spiral, a kind of curve that often appears in nature. In polar coordinates (

*r*, θ) the spiral can be written as

Allowing for rotations of the curve, it is invariant under all rescalings λ; that is θ(λ*r*) is identical to a rotated version of θ(*r*).

A simple circle remains invariant under an arbitrary rotation. The logarithmic spiral remains invariant under an arbitrary rotation + scale. They are both highly symmetrical objects.

You can get an excellent introduction to the general idea of symmetry in Symmetry, A Unifying Concept on Google books. It is filled with many images and long discussions about spirals. And here is a snippet that puts it in a nutshell:The symmetry of a logarithmic spiral is a combination of rotational symmetry and self-similarity. In the Mandelbrot set, spiral symmetry is seen in nearly all filament tips.

And don't forget the 449 page book published by the World Scientific Publishing Company called Spiral Symmetry.

Originally Posted by

**Raphael**
Originally Posted by

**RAM**
Yes, there is are a few obscure phenomena that apparently are not symmetric. But the siine qua non of the fundamental laws of nature is symmetry.

WRONG

WRONG

WRONG

The fundamental laws of nature ARE asymmetric.

NOBEL says so.

http://nobelprize.org/nobel_prizes/p...speedread.html
That's a very interesting article, but it does not support nor justify your triple ALL CAP repetition of the word "WRONG." There is nothing in that article that denies my fundamental point. Let me repeat:Yes, there is are a few obscure phenomena that apparently are not symmetric. But the sine qua non of the fundamental laws of nature is symmetry. That's how we derive the conservation laws, such as conservation of angular momentum (from rotational symmetry) and the conservation of energy (temoral symmetry).

My point stands. The broken symmetry discovered in the creation of matter/anti-matter does not mean that the fundamental laws are not themselves symmetrical. On the contrary, those laws are defined by symmetry. The mystery is why the symmetry of those laws "spontaneously breaks" during the process of creation.

I think you may have grabbed onto the word "asymmetry" in that article without understanding its meaning in the context of Standard Model. The Standard Model is built on symmetry. Symmetry is its very foundation. That's why the asymmetry is called "broken symmetry." Here is what that article stated:Luckily for us, the Universe is not symmetrical, at least at the subatomic level. If it was, the newly formed matter at the Universe's birth would have been annihilated by an equal and opposite amount of antimatter, and nothingness would have resulted. Instead, a small imbalance, or asymmetry, in the amount of matter and antimatter created led to a slight excess of matter, from which we are all eventually formed. Such 'broken symmetry' is one key to our existence

Understanding symmetry, or the lack of it, is an ongoing task, and the 2008 Nobel Prize in Physics rewarded two discoveries concerning symmetry violation in the field of particle physics. In the 1960s Yoichiro Nambu, who had been working on asymmetries underlying superconductivity, was the first to model how broken symmetry can occur spontaneously at the subatomic level. The mathematical descriptions he formulated helped refine the standard model of particle physics, the current working theory that best explains much, but not all, of the way that fundamental particles and the forces that govern their behaviour interact to create the known Universe.

Why "broken symmetry"? Because the Standard Model is __defined__ by symmetry groups! The "breaking" of the symmetry has to do with the states of the system, not the system itself. You can read about it here.

Thanks again for introducing this fascinating topic!

All the best,

Richard

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