Category Archives: Science

A Couple of Loops About Thinking and Then Doing

The Shewhart Cycle (also known as the PDCA) is an iterative design and management cycle for continuous quality improvement of products and processes. It is named after Walter Shewhart who is known as the father of statistical quality control. The more recent name, PDCA, has several variations in the literature. The PDCA or Shewhart Cycle consists of four parts:

    • Plan
    • Do
    • Check
    • Act

Similarly, the OODA Loop is an iterative framework for the improvement and management of decision processes. It is used in various domains such as business, litigation, and military strategy. The OODA Loop consists of four parts:

    • Observe
    • Orient
    • Decide
    • Act

Learning Cycles are similar to Design Cycles in that the process to be improved is learning and the product to be improved is knowledge. It would be interesting to compare the two types of cycles to understand their similarities and differences. Some of each type have four stages but others have more or less. I have mentioned several learning cycles with four steps already in this blog, the Kolb learning cycle and the Scientific Method.

Further Reading:




The Tree of Knowledge System

The Tree of Knowledge (ToK) System posits four hierarchical planes of existence having separate dimensions of complexity mapped out or studied by four different kinds of sciences:

  • Matter/Object: mapped by Physical Sciences
  • Life/Organism: mapped by Biological Sciences
  • Mind/Animal: mapped by Psychological, Cognitive, and Behavioral Sciences
  • Culture/Person: mapped by Human Social Sciences

The ToK System is reminiscent of other “big history” or “cosmic evolution” schemas such as Tyler Volk’s Combogenesis except for the special consideration for the mental and psychological (i.e. subjective) aspects of existence. I would think that this is primarily due to the fact that the developer of the system, Professor Gregg Henriques, is a psychologist.

In order to support his focus on consciousness and psychology, Henriques has developed several theories to address the “problem of psychology”, for example the Justification Systems Theory and the Behavioral Investment Theory. With the ToK System, these and several other key ideas, he claims he has a “Unified Theory of Knowledge” (UToK)!

Further Reading:

Combogenesis: a constructive, emergent cosmos


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.


Tinbergen’s Four Questions

Tinbergen’s Four Questions are questions that can be asked about an organism and its evolution that help to explain its adaptations and behavior. They operate via a double dual of Static vs. Dynamic and Proximate vs. Ultimate.  Static is concerned with the current time whereas Dynamic considers a time series. Proximate is concerned with how the organism behaves currently or how its behavior changes over its lifetime, and Ultimate considers why the organism and its behavior/adaptations may have evolved the way they did. Both pairs are somewhat confusedly concerned with time: both Static and Proximate are concerned with either the current time or a short lifetime, and Dynamic and Ultimate are concerned with changes in that short lifetime or over evolutionary time.

  • Ultimate & Static: Function or Adaptation
  • Ultimate & Dynamic: Phylogeny or Evolution
  • Proximate & Dynamic: Ontogeny or Development
  • Proximate & Static: Mechanism or Causation

Ultimate is also called Evolutionary, to distinguish it from a connotation of telos or purpose. Static refers to the current form of the organism, and is also called Synchronic or Single Form or Snapshot or Contemporary, etc.  Dynamic refers to the historical changes of the organism, and is also called Diachronic or Sequence or Historical or Chronicle, etc.

Some compare these four questions to Aristotle’s Four Causes, see for example [1] and [2]. However, [1] seems less enthusiastic than the published paper [2]. Also, I don’t agree with either completely on the assignment; it seems to me that the Efficient and Final Causes are Dynamic, and the Material and Formal causes are Static. I believe we all agree that the Efficient and Material Causes are Proximate, and Formal and Final Causes are Ultimate. See [3] for comparison. Frankly, I am guided more by the definitions of Static and Dynamic than anything else.

Further Reading:


Human Ethology Bulletin 28 No 4 (2013): Special Issue on Tinbergen 3-11


Aristotle’s Four Causes

Other Images of Tinbergen’s Four Question:

[*9.63, *10.98]


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:



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

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

Robert Zubrin / The Case for Mars

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

MP reminds me a bit of Olaf Stapledon:


The Periodic Table of the Elements

The familiar periodic table of the elements may be overwhelming in its usual initial presentation. You may not have noticed that there are four blocks of elements in the table, and they even have names! All good atomists need to become facile with the chemical elements though, because they are indeed the building blocks of the universe!

The table is usually presented as a partial grid, consisting of 7 rows and 18 (or 32) columns, although there are alternate representations. But columns (C) are called groups (G) and rows (R) are called periods (P)!

Within the grid, elements are arranged in four blocks, with the following properties:

  • s-block: 2C x 7R = 14 (G1-2,18, P1-7) “sharp”
  • p-block: 6C x 6R = 36 (G13-18, P2-7) “principal”
  • d-block: 10C x 4R = 40 (G3-12, P4-7) “diffuse”
  • f-block: 14C x 2R = 28 (between G2 and G3, P6-7) “fundamental”

Note how columns (groups) increase (by four!) as rows (periods) decrease! Blocks are named after electron orbitals which are also named s, p, d, and f.

Thus there are currently 118 elements having a unique “atomic number” in the usual periodic table, with the rows or periods having the following number of elements:

  • P1: 2 (2s)
  • P2: 8 (2s, 6p)
  • P3: 8 (2s, 6p)
  • P4: 18 (2s, 6p, 10d)
  • P5: 18 (2s, 6p, 10d)
  • P6: 32 (2s, 6p, 10d, 14f)
  • P7: 32 (2s, 6p, 10d, 14f)

Note the number of groups increases as the period does. This is due to the properties of electrons and their shells. Familiar elements are scattered throughout the table, although they occur less and less as the atomic number increases. Elements can also occur as different isotopes due to having a differing number of electrons than usual, and so may have a positive or negative charge.

As an homage to the classical four elements, I’ve arranged the blocks as follows: the s-block has the reactive alkali and alkaline metals (fire), the p-block includes the noble gases (plus C, N, and O needed for life as we know it) (air), the d-block has the precious metals like gold, silver, and platinum (plus liquid at room temp mercury but not bromine) (water), and the f-block with the heaviest and often radioactive elements like uranium and plutonium (earth).

Further Reading:


The Six Flavors of Quarks

Further Reading:

The Standard Model of Particle Physics

Working to Understand the Changing Flavors of Quarks



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:

The art of Claude Fayette Bragdon, 1866–1946

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!

[*3.139, *12.121, *13.50]



Maxwell Relations

Maxwell Relations are commonly known as a set of four partial differential equations between four thermodynamic quantities or potentials: pressure (P), volume (V), temperature (T), and entropy (S). So for example the expression (∂T/∂V) |S  means the partial derivative of T with respect to V while keeping S constant.

    • (∂T/∂V) |S = -(∂P/∂S) |V
    • (∂P/∂T) |V = (∂S/∂V) |T
    • -(∂S/∂P) |T = (∂V/∂T) |P
    • (∂V/∂S) |P = (∂T/∂P) |S

In my diagram above, the expressions that are equal are on either side of the common leg of adjacent isosceles right triangles.

Further Reading:

Thermodynamics and the Four Thermodynamic Potentials

[*12.194, *12.195]