Category Archives: Space and Time

The Ancient and the Modern

In the past, I’ve created several diagrams juxtaposing pairs of fourfolds, for example

So here’s another, The Four Classical Elements and Space-Time-Energy-Matter.

I asked ChatGPT to look at this association: “Please write a short essay comparing and contrasting the classical four elements of air, fire, earth, and water with the modern scientific foursome of space, energy, matter, and time.”

The concept of the classical four elements of air, fire, earth, and water has been a fundamental aspect of ancient philosophy for thousands of years. This idea, which was first proposed by the ancient Greek philosopher Empedocles, held that these four elements were the building blocks of the universe and were responsible for all natural phenomena.

In contrast, the modern scientific foursome of space, energy, matter, and time provides a more comprehensive and rigorous explanation of the nature of the universe. Space refers to the three-dimensional continuum in which all matter exists, and it provides the framework for the movements of objects. Energy refers to the capacity of a system to perform work and is responsible for all physical and chemical processes. Matter refers to any physical substance, including solid, liquid, and gas. Time, on the other hand, is a fundamental aspect of the universe that allows for the measurement of the duration of events and the progression of physical processes.

One key difference between the classical and modern concepts of the elements is that the classical elements were thought to have qualities and personalities, while the modern elements are purely physical and mathematical constructs. The classical elements were thought to interact with each other in specific ways to produce the natural world, while the modern elements interact according to the laws of physics and chemistry.

Another difference is that the classical elements were limited to four, while the modern elements form a much more complex and nuanced picture of the universe. This difference reflects the advancement of human knowledge and understanding of the natural world over time.

In conclusion, the classical four elements of air, fire, earth, and water have played an important role in shaping human thought and culture. However, the modern scientific foursome of space, energy, matter, and time provides a more comprehensive and scientifically rigorous explanation of the universe and its workings. Both concepts have contributed to our understanding of the world, and they continue to play a role in shaping our ideas about the nature of reality.

Not quite enough, so I replied “Thank you, that’s pretty good. However, please say more about how air is like space, how fire is like energy, how earth is like matter, and how water is like time.”

Certainly! Let me expand on the similarities between the classical elements and the modern scientific elements:

1. Air and space: Both air and space are often thought of as being intangible and difficult to define. They both provide the framework for other physical phenomena, such as the movements of objects in space or the flow of air currents. Additionally, both air and space have the ability to contain other elements or substances, such as the gases that make up air or the stars and planets that exist within space.

2. Fire and energy: Fire is often associated with heat and light, and it can be both destructive and transformative. Energy also has the ability to transform physical systems, such as through chemical reactions or the transfer of heat. Furthermore, fire can be seen as a form of energy that is released through combustion, and it can be harnessed for practical purposes, such as cooking food or heating homes.

3. Earth and matter: Earth is often thought of as being solid and unchanging, while matter is the physical substance that makes up the universe. Earth provides a foundation for other physical phenomena, such as the growth of plants or the construction of buildings. Similarly, matter provides the building blocks for physical systems, such as the atoms and molecules that make up the substances in our world.

4. Water and time: Water is often thought of as being cyclical and constantly changing, such as through the phases of the tides or the flow of rivers. Time is also cyclical and constantly changing, as it moves forward and allows for the progression of physical processes and the measurement of the duration of events. Furthermore, just as water can shape the physical world through erosion and the formation of land masses, time shapes the physical world through its influence on the progression of physical processes.

In conclusion, there are certainly similarities between the classical four elements of air, fire, earth, and water, and the modern scientific foursome of space, energy, matter, and time. These similarities reflect the continuity of human thought and understanding of the natural world, and they demonstrate the ongoing influence of ancient ideas in shaping our modern understanding of the universe.

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The Main Sequence of Star Types

I will scan your star charts.

— Nomad, from Star Trek “The Changeling”

While reading “Entering Space” by Robert Zubrin, I chanced upon the subject of stellar classification. The Morgan-Keenan system goes from O-type, the hottest, to M-type, the coolest (Red dwarfs). Our own sun, Sol, is an example of a G-type star, which are on the cool side yet still hot and bright. Later, other types have been added, for example White Dwarfs are known as D-types. If humankind will someday journey to remote stars, it’s best to memorize this handy list!

The Morgan-Keenan system is as follows:

  • O-type
  • B-type
  • A-type
  • F-type
  • G-type
  • K-type
  • M-type

This is sometimes remembered by the mnemonic “O be a fine gal/guy, kiss me.”

Further Reading:

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

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

https://en.wikipedia.org/wiki/O-type_main-sequence_star

https://en.wikipedia.org/wiki/B-type_main-sequence_star

https://en.wikipedia.org/wiki/A-type_main-sequence_star

https://en.wikipedia.org/wiki/F-type_main-sequence_star

https://en.wikipedia.org/wiki/G-type_main-sequence_star

https://en.wikipedia.org/wiki/K-type_main-sequence_star

https://en.wikipedia.org/wiki/M-type_main-sequence_star

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

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The Millennial Project: colonizing the galaxy in eight easy steps

The eight “easy” steps of the Millennial Project (MP) are:

  • Foundation (Institutions to promote MP)
  • Aquarius (Colonize and utilize Earth’s oceans)
  • Bifrost (To low Earth orbit and outer space)
  • Asgard (Build a large space station)
  • Avalon (Colonize and utilize the Moon)
  • Elysium (Colonize Mars)
  • Solaria (Colonize the Solar System)
  • Galactia (Then on to the Milky Way)

Further Reading:

Marshall T. Savage / The Millennial Project

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

https://tmp2.fandom.com/wiki/Main_Page

Robert Zubrin / Entering Space: creating a space-faring civilization

Robert Zubrin / The Case for Mars

https://www.marssociety.org/

Carl Sagan / Pale Blue Dot: a vision of the human future in space

MP reminds me a bit of Olaf Stapledon:

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

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

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

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Four-Dimensional Vistas

The Fourth Dimension has been an interest of mine since I was a child. I’m not sure when I first heard about it, but I still have my coverless copy of “Geometry of 4 Dimensions” by Henry Parker Manning that I bought in a used book store. (I wonder why it hasn’t ever been reissued by Dover?) Maybe I heard about the fourth dimension in some science fiction TV movie, or in some mathematical survey book like “Mathematical Snapshots” or “Mathematics and the Imagination”.

Once I tried to explain to my best friend about my newly discovered insight how a hypercube could be folded up in four-dimensional space from its so-called three-dimensional net consisting of eight cubes, just as a regular three-dimensional cube could be folded up from its two-dimensional net of six squares. This 3D net somewhat resembling a cross is famously seen in Dali’s “Crucifixion (Corpus Hypercubus),” although I probably didn’t refer to this painting in my explanation.

I’m not sure who came up with the take-away message from my exposition, but it remains clear in my memory that the “junk in the middle” of the hypercube was a piece of the fourth dimension, just as the faces of a cube enclose a piece of our normal third dimension.

I recently came across Claude Fayette Bragdon, architect, author, draughtsman, stage designer, and mystic. At first I was interested in his drawings found on-line. His book “Four-Dimensional Vistas” started off with a good if overly wordy introduction to the concept of the fourth dimension. But then he suggests that many esoteric concepts such as the meaning of dreams, reincarnation, past-life regression, prognostication, ESP, etc. could possibly be explained by higher dimensional space or even higher dimensional time.

Even though I initially found many of these hypotheses too far-fetched for my tastes, I still found some interesting ideas to mull over in this little book.

Further Reading:

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

https://www.gutenberg.org/ebooks/author/4128

https://theosophy.wiki/en/Claude_Fayette_Bragdon

https://theosophyart.org/2018/03/30/claude-fayette-bragdon/

https://rbscp.lib.rochester.edu/bragdon-family-papers-claude-bragdon-architectural-drawings

The art of Claude Fayette Bragdon, 1866–1946

https://rbscp.lib.rochester.edu/3514

https://bauarchitecture.com/research.loshuworldofwonderous.shtml

Claude Fayette Bragdon / Four-Dimensional Vistas (1930)

Claude Fayette Bragdon / The Beautiful Necessity (1910)

Claude Fayette Bragdon / Architecture and Democracy (1918)

For my gratuitous anime tie-in, Bragdon’s world-view suddenly reminds me of the anime character  Haruhi Suzumiya, who wished for her aliens, time-travelers, and ESPers so much that she willed them into being. If only she had known about the fourth dimension!

https://reelrundown.com/animation/Anime-Philosophy-1-Melancholy-of-Haruhi-Suzumiya

[*3.139, *12.121, *13.50]

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The Wolfram Physics Project

When I first started looking at Stephen Wolfram’s latest proposal to solve physics, I was somewhat disappointed. I was rather fond of his previous “New Kind of Science” based on the structural rigidity of cellular automata. However, I am now intrigued by his latest ideas, based on the looser but more flexible basis of networks.

And once you have pithy statements with space, time, energy, and matter (as momenta), you catch my attention:

  • Energy is flux of causal edges
  • through Spacelike hypersurfaces
  • Momentum is flux of causal edges
  • through Timelike hypersurfaces

I confess I haven’t read much about the project yet, but it seems to be using rewriting rules, perhaps similar to the notion of rewriting in Wolfram’s previous framework, cellular automata. Of course, cellular automata and also rewriting rule systems can be computationally universal or Turing complete.

Another idea might be to try some sort of computational metaphysics between nodes like the pi-calculus (or some other process calculus). After all, you have to support quantum entanglement! However if you can encode everything with simpler structures then do it!

Further Reading:

https://www.wolframphysics.org/

https://www.wired.com/story/stephen-wolfram-invites-you-to-solve-physics/

https://writings.stephenwolfram.com/2020/04/how-we-got-here-the-backstory-of-the-wolfram-physics-project/

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

https://www.scientificamerican.com/article/physicists-criticize-stephen-wolframs-theory-of-everything/

https://turingchurch.net/computational-irreducibility-in-wolframs-digital-physics-and-free-will-e413e496eb0a

View at Medium.com

Cellular automata:

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

Note this quote for future reference:

The primary classifications of cellular automata, as outlined by Wolfram, are numbered one to four. They are, in order, automata in which patterns generally stabilize into homogeneity, automata in which patterns evolve into mostly stable or oscillating structures, automata in which patterns evolve in a seemingly chaotic fashion, and automata in which patterns become extremely complex and may last for a long time, with stable local structures. This last class are thought to be computationally universal, or capable of simulating a Turing machine.

Rewriting:

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

https://en.wikipedia.org/wiki/Semi-Thue_system

[*12.32]

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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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Four Forms Make a Universe

How could I not love a paper with this title? I’ve struggled with it for a bit, and I’ve only managed a couple of diagrams relating the author’s LICO (Linear Iconic) alphabet made up of 16 letters. However, I see that there are a few other papers by Schmeikal available on ResearchGate that look easier to understand. But also however, the first one says to read the “Four Forms” paper first!

At any rate, I present a sixteen-fold of the LICO alphabet, and another of the binary Boolean operators that are in a one-to-one mapping with LICO. There is much to understand from these papers, including much syncretism between various mathematical sixteen-folds, so please forgive me if I don’t explain it all with immediate ease. However, I believe it is well worth the effort to understand.

(Please note that the characters of the LICO alphabet are oriented so that the bottoms of the letters are downward, but the Boolean operators are oriented so that the bottoms of the equations are towards the right angles of the triangles.)

The title comes from the result that four elements of LICO can reproduce the other twelve via linear combinations. These four forms are 1) Boolean True (A or ~A), 2) A, 3) B, and 4) A=B. These are within the interior right-hand triangles in the LICO diagram. Of course, it is well known from Computer Science that the NAND operator (~A or ~B) can also generate all other fifteen operators, but this is by multiple nested operations instead of simple Boolean arithmetic. There are several other “universal” binary gates that can do this as well.

Two other representations that have four elements that can generate the other twelve via linear combinations come from CL(3,1), the Minkowski algebra. These representations are called “Idempotents” and  “Colorspace vectors”. Because of this algebra’s association with space and time in relativity, Schmeikal claims that LICO has ramifications in many far-ranging conceptualizations.

Further Reading:

Bernd Schmeikal / Four Forms Make a Universe, in Advances in Applied Clifford Algebras (2015), Springer Basel (DOI 10.1007/s00006-015-0551-z)

https://link.springer.com/article/10.1007/s00006-015-0551-z

At http://www.researchgate.net:

Bernd Schmeikal / Free Linear Iconic Calculus – AlgLog Part 1: Adjunction, Disconfirmation and Multiplication Tables

Bernd Schmeikal / LICO a Reflexive Domain in Space-time (AlgLog Part 3)

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

https://www.allaboutcircuits.com/technical-articles/universal-logic-gates/

[*9.145, *11.50]

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An Eightfold Metaphysics

If one juxtaposes the fourfold Space-Time-Matter-Energy with the fourfold Structure-Function-Part-Action, one sees that there are several relations between them. These are simple common-sense relations, not modern-physics types of relations. Below they are listed by Space-type relations and Time-type relations.

Space is required for the extension of Structures.
Matter constitutes Structures.
Parts in an arrangement make up Structures.

Structures extend and are organized in Space.
Matter is located in Space.
Parts occupy Space.

Time allows the expression of Functions.
Energy is required for the operation of Functions.
Actions in a sequence constitute Functions.

Functions have duration and reoccur in Time.
Energy requires and is dependent on Time.
Actions take place within Time.

Several analogies are also evident in this diagram.

  1. Space : Structures :: Time : Functions
  2. Space : Parts :: Time : Actions
  3. Space : Matter :: Time : Energy
  4. Structures : Parts :: Functions : Actions
  5. Structures : Matter :: Functions : Energy
  6. Parts : Matter :: Actions : Energy

Notice that analogies 1.-3. are “contains” relations, and 4.-6. are “part of” relations. One obtains the nesting of entities:

Space > Structures > Parts > Matter
Time > Functions > Actions > Energy

I suppose that any analogy could be shown in a figure like the one on the right (or even written as A / B // C / D) or with the two squares side by side, and that sets of four or six analogies that overlap could be nicely shown as above. If so, I wonder what can be gained by such representations? Probably individually not so much but with overlaps I think it would be interesting.

Further Reading:

The study of parts and wholes relations is called Mereology.

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

https://plato.stanford.edu/entries/mereology/

[*10.157, *11.26, *11.34]

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The Seasons and the Zodiac

This isn’t a bad little diagram of the four seasons along with the twelve zodiac names and symbols. However, it might be oriented wrong by convention or going clockwise instead of counter-clockwise.  Interestingly, old horoscope charts that show what was in the sky (the positions of the zodiac stars and the eight or nine planets in regards to the twelve “astrological houses”) at the time of a person’s birth were shown using the outside ring of twelve triangles instead of the more familiar circle that is used today. The inner square might be for notes or some nice drawing.

Further Reading:

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

https://www.completehoroscope.org/envelope-diagram-horoscope.htm

https://equivalentexchange.blog/2014/10/31/the-four-seasons/

[*10.145]

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Fourfold Physicalism

It is not enough for a wise man to study nature and truth, he should dare state truth for the benefit of the few who are willing and able to think. As for the rest, who are voluntarily slaves of prejudice, they can no more attain truth, than frogs can fly.

— From Man a Machine, by Julien Offray de La Mettrie

Further Reading:

https://equivalentexchange.wordpress.com/2012/07/03/structure-function/

https://equivalentexchange.wordpress.com/2013/10/09/things-happen/

https://equivalentexchange.wordpress.com/2014/02/01/relations-all-the-way-down/

https://equivalentexchange.wordpress.com/2015/06/09/four-primary-relations/

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

Notes:

Structures are built from parts.
Parts are reductions of structures.
Functions are assembled from actions.
Actions are the constituents of functions.

[*8.132, *9.104, *10.10]

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