Tag Archives: Emmy Noether

Noether-Pauli-Jung, V2

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity. And if Space-Time and Matter-Energy are both divided into Space and Time and Matter and Energy, one obtains this eight-fold.

Causality means that some action or cause in time (say a process) of things in space can have an effect (another process, say) on different things in space, and Synchronicity means that different events (say processes) separated in space can have non-causal relationships between them.  Conservation means the consistency of a quantity of matter or energy or matter-energy through time, and Symmetry means the consistency of a measure of a structure or form through space.

I am reminded of my fourfold Four Bindings, consisting of Chains, Grids, Blocks, and Cycles. Causality and Synchronicity are Chains (or non-chains for the latter) Space and Time are Grids (or flexible meshes), Matter and Energy are Blocks (or chunks of stuff), and Symmetry or Conservation are Cycles (of the group-theoretic kind or the equivalence class kind or just loops).

Further Reading:

https://en.wikipedia.org/wiki/Causality

https://en.wikipedia.org/wiki/Synchronicity

https://en.wikipedia.org/wiki/Symmetry

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

https://equivalentexchange.blog/2016/04/06/four-bindings/

This is a reworking of a previous six-fold diagram that I believe is served better as an eight-fold.

https://equivalentexchange.blog/2018/03/29/noether-pauli-jung/

[*10.68, *10.155, *11.55]

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Noether-Pauli-Jung

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity.

I had to remind myself that Conservation means consistency (of matter or energy) through time (and space), and Symmetry means consistency (of form) through space (and time), so in some sense they are dualistic.

Combined, one has the three axes of dual concepts, represented above.

Further Reading:

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

[*10.68]

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Wu Wei or Natural Action

The sage does nothing, and yet everything is done.

— Lao Tzu from Tao te Ching

The principle of least action (or stationary action) seen in the previous entry Noether’s Theorem immediately makes me think of the Taoist concept of wu wei – literally no action or effortless action. It consists of knowing when to act and knowing when not to act (or perhaps even not knowing to act). It also means natural action, or the action of natural physical or biological systems. In Western culture, such action is considered bad and “mechanical” because physical systems are thought to be like clockwork, but in Eastern culture, it is sagelike and enlightened, harmonious. Very often intention, or conscious action, gets in the way and impedes our effort.

Another example that comes to mind is the short story “On the Marionette Theatre” by Heinrich von Kleist. In the story, one of the characters comment that marionettes possess a grace humans do not, a view which contradicts ordinary aesthetics. It is claimed that our consciousness and capacity for reflection cause us to doubt ourselves or become self-conscious, and prevent us from acting with the singlemindedness and purity of an animal or a puppet. For example, a bear in the story is able to successfully fence with the narrator, by deflecting every thrust towards him seemingly without effort. And all feints are ignored, as if the bear is reading the narrator’s mind or knowing the future before it happens.

Also note:

Philip Pullman, author of the fantasy trilogy “His Dark Materials”, was inspired by von Kleist’s story.

The character Forrest Gump, of book and movie fame, could be considered a Taoist. Be like a feather on the wind…

http://en.wikipedia.org/wiki/Wu_wei

http://liology.com/2010/01/19/exploring-the-neural-correlates-of-wu-wei/

http://www.his.com/~merkin/daoGloss.html

http://en.wikipedia.org/wiki/Heinrich_von_Kleist

http://ada.evergreen.edu/~arunc/texts/literature/kleist/kleist.pdf

Edward Slingerland / Effortless Action: Wu-wei As Conceptual Metaphor and Spiritual Ideal in Early China

[*7.91, *8.66]

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Noether’s Theorem

Nature is thrifty in all its actions.

    — Pierre Louis Maupertuis

From Wikipedia:

Noether’s (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system’s behavior can be determined by the principle of least action.

Noether’s theorem can be stated informally:

If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.

Note:

Symmetries are transformations or exchanges in space or time that leave systems structurally or functionally equivalent to what they were before. The equivalence may or may not be an identity, but only the same in appearance or behavior.

Conservation laws are equivalences for quantitative properties of systems. A given property of matter or energy is quantitatively the same before and after, or continuously through space or time. The functional measure of this property remains constant.

So consider an analogy between Noether’s Theorem and the concept of Equivalent Exchange: for (symmetrical, differentiable) exchanges, there are properties that are equivalent (conserved)!

http://en.wikipedia.org/wiki/Noether’s_theorem

http://en.wikipedia.org/wiki/Action_%28physics%29

http://en.wikipedia.org/wiki/Lagrangian

http://en.wikipedia.org/wiki/Principle_of_least_action

http://math.ucr.edu/home/baez/noether.html

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