Category Archives: Science

Charles Fourier and the Theory of Four Movements

Nothing is too wonderful to be true if it be consistent with the laws of nature.

— Michael Faraday in his Laboratory Notebook

There are many things to scratch one’s head about in Charles Fourier’s “Theory of the Four Movements,” first published anonymously in 1808. However, his progressive political thought influenced many in France and in the United States. Fourier was a utopian and a socialist, and thought social cooperation and unity were the only ways to overcome the discord and strife he observed in his times. His theory is based on a hierarchy of “movements” within four realms, from low to high: the Material, the Organic, the Animal, and the Social.

As he elaborated on these movements, Fourier claimed that social history went through four main periods of unhappiness and happiness, ascending from a chaotic period, through two harmonious periods which were each seven times longer, before descending into another chaotic period of length equal to the first. In order to achieve this happiness, he thought that we must envision and engineer a new social order to achieve a common purpose. Nowadays, of course, socialism has a noxious connotation to those of the right-leaning and hyper-capitalist persuasion.

  • Ascending Chaos
  • Ascending Harmony
  • Descending Harmony
  • Descending Chaos

And now, the United States teeters on the brink of choosing four more years of terrible leadership, all to maintain the status-quo of funneling more money into the pockets of the wealthy and more power into the hands of the already dominant.

Further Reading:

Charles Fourier / The Theory of Four Movements

[*9.62, *12.63]




Humankind, Unbound

Many books detail how we are our own worst enemy, how we are too smart for our own good, or not smart enough in the right way. This one traces the origin and evolution of eight technologies that make us who we are today, for better or worse.

  • Fire
  • Tools (incl. Digging tools, Weapons)
  • Language (incl. Writing, Music, Art, Symbolic Communication, Ethnicity, Culture)
  • Clothing
  • Shelter
  • Farming (Agriculture, Husbandry)
  • Machines (incl. Ships, the Wheel, and on to Precision Machinery)
  • Computers

Instead of having two technologies, “Clothing” and “Shelter,” Currier combines them, and lists “technologies of interaction” which includes writing, water-craft, the wheel, etc.

Can we overcome the myriad conflicts that threaten our survival? Please check back in a hundred years to see how we’re doing! It’s not very long, compared to how far we’ve come.

Further Reading:

Richard L. Currier / Unbound: how eight technologies made us human, transformed society, and brought the world to the brink

Some reviews:

Book Summary: “Unbound: How Eight Technologies Made Us Human” by Richard L. Currier

Click to access Volume8-Number1-Article7.pdf




Classes of Automata

Here is one way to carve up abstract (mathematical) automata into different classes of complexity (from low to high).

There is a somewhat different and older one that is based on the Chomsky Hierarchy (where ND stands for non-deterministic), and the associated language or grammar that they recognize:

Further Reading:



Flowing and Falling

Some philosophers say everything is process. From the cosmic scale of the universe to the submicroscopic scale of atoms, physical forces marshal matters and energies to and fro. In between these at the human scale, biology is ruled by flows of energy from the sun and nutrients from the environment as well as from other living beings. Dynamical forces such as temperature, weather and tides also affect biology and even the cultural processes of higher lifeforms.

At the scale of the solar system, gravity collects gases to ignite stars and form planets. Once stars reach their limits to burn, gravity can collapse them to dense cinders and black holes or even to rebound and spread their atomic matters in novas and supernovas. Even light spread by the stars can be gathered together into gravity wells such as black holes. Stars in turn are gathered into galaxies by the gravity of black holes and even unknown dark matters.

At the scale of atoms and molecules, temperature differentials and water can partition certain types of elementary constituents to form membranes and segregate insides from outsides. If an inside is protected sufficiently, then there is time and the conditions to harbor and perpetuate the delicate structures and processes that form cells. Cells can even gather together and continue as multicellular communities, or only temporarily to fruit and disperse again as simple creatures known as slime molds.

At the individual human or societal scale, there are flows for nutrients and excreta, materials for habitation and the manufacture of tools, distributed energies such as electricity, fossil fuels, and information for learning, work, and civic participation. Even speech and writing can be thought as flows of information. But just as flows of nutrients and materials and energies can prove toxic to biological health or ecologies, so can information.

For two-dimensional dynamical systems, certain common elements can be mapped out: sources and sinks, saddles and centers. Sources have flows out from a point or region, and sinks have flows in. Saddles have a roughly stationary center, due to balanced flows in and out at (not necessarily) right angles. Centers are circular vortexes about a stationary point or region. Sources and sinks can spiral, saddles can twist, centers can become eccentric or elliptical.

For example, think about everyday weather forecasts. The atmosphere is relatively thin compared to the earth and so the flows of air can be considered two-dimensional, at least at the ordinary strata of human habitation. There are air pressure highs and lows (sources and sinks), and air temperature cold and warm fronts (usually not saddles though), stationary fronts (centers?), and even circulations (hurricanes are spiraling sinks I guess).

Ordinary, human-sized change has conditioned many of our intuitions and insights about the way the universe works. Heraclitus famously said that all was change, and so he thought fire was the primal element. His predecessor Thales thought that water was instead the basic element, and it is pretty mutable also. Lucretius, inspired by Empedocles, thought none of the four classical elements were foundational, but all were composed of tiny bits that fell and bounced against each other through an endless void.

As earth is in opposition to air, and fire to water, the seasonal changes of temperature and moisture were considered by Hippocrates. Heat gains dominion over cold in Spring and Summer, but cold replaces it in Fall and Winter. Similarly wet and dry quarters cycle through the seasons. These oppositions gave rise to the theory of the four temperaments or humourism. Even to this day these considerations have inspired various theories of personality, like the Myers-Briggs Assessment.

Is everything a struggle of opposites? Empedocles, already mentioned, thought love and strife were the relations that respectively attracted and repelled all matter in their dance and change. Now we know that things fall towards the earth, not for the love of it, but because of the shape of space that the earth’s mass makes. Heat flows into the cold because both even up. Order dissolves into chaos since the latter is more likely, unless fed by other sources of order turning to disorder.

Is everything a flow between opposites? Light spreads out and diminishes into darkness, but gravity gathers matter together. Enough gravity can even gather light and bind it into the darkness of a black hole. A drop of ink spreads out in a glass of water, never to return to that inky state, unless the glass sits and the water evaporates until only a drop remains. Even epidemics and pandemics can be thought to be flows of transmission and contagion. Here, the small becomes the large, and the few the many.

Further Reading:

Also note that these four classifications are somewhat analogous to four valued logic: True is Source, False is Sink, None is Center, Both is Saddle.

[*12.52, *12.56]



Conditional Branching is Not Necessary

Four simple instructions are sufficient to evaluate any Turing computable function using self-modifying programs: LOAD, STORE, GOTO, INCREment.

Further Reading:

Raul Rojas / Conditional Branching is Not Necessary for Universal Computation in von Neuman Computers, Journal of Universal Computer Science 2,11 (1996) 756-768

William F. Gilreath, Phillip A. Laplante / Computer Architecture: A Minimalist Perspective



Scenario Thinking and Covid-19

Scenario Planning, Analysis, or Thinking is a technique for probing into possible futures when you are anticipating or overwhelmed by tumultuous challenges. One often starts by examining two factors that have both great Importance and Uncertainty and then considering two extremes of each. For their four different mixtures, you can posit causes, how to recover from bad outcomes, what actions would be favorable for all scenarios, etc. In other words, one can develop related stories about these different futures.

In these slides by authors Steven Weber and Arik Ben-Zvi, the two important and uncertain factors are Public Health and Economics, both affected by the Covid-19 pandemic, and for their initial purposes independent of each other. For public health, the disease could kill far more than estimated (a secondary wave) or kill less (vanish like a miracle). For the economic impact, the toll could be sustained (a long term depression) or the recovery could be relatively quick (v-shaped). So the two factors and their extremes are

    • Economic recovery is slow (depression, recession), or fast (v-shaped)
    • Health and death toll is worse (than estimates), or better (yay)

The four scenarios that are named are basically

    • Economy good, Health good: Americans Win
    • Economy bad, Health good: Fractured USA
    • Economy good, Health bad: Resilient USA
    • Economy bad, Health bad: Coronavirus Wins

and the scenario stories are told with respect to January of 2021 at the next state of the union address. Each of these scenarios are quite detailed and then followed by Insights and Implications for all. Often Scenario Thinking is used for more distant future analysis, but this shows it can be used for a mere nine months as well.

Further Reading:

Continue reading Scenario Thinking and Covid-19

The Pi Calculus

My previous post on Wolfram’s physics mentioned the Pi calculus, but I liked this little diagram so much I decided to let it have its own mention. The rules aren’t really four in number, but oh well.

  • (νx)P: create a channel named x, then do P
  • x(y).P: receive y over channel x, then do P
  • x‾<y>.P: send y over channel x, then do P
  • P|Q: do P and Q at the same time
  • !P: do P over and over until stopped
  • 0: stop

Further Reading:




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:

View at

Cellular automata:

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.




The Adaptive Cycle

As we all wonder how the current world order will be transformed by the Covid-19 pandemic, perhaps now would be a good time to read up on the Adaptive Cycle. Worried about societal and economic collapse, I was originally thinking about the notion of social cycles, but came across this more general notion of cycles within ecological systems. It is also applicable to insightful investigation of social institutions and organizations.

The Adaptive Cycle is usually shown as a figure-eight loop, with four main segments (Growth, Maturity, Release, and Renewal), inhabiting a space of two or three variables (Potential, Complexity, and Resilience):

  • Growth or Exploitation: (r)
  • Maturity or Conservation: (K)
  • Release or Collapse: (Ω)
  • Renewal or Reorganization: (α)

Thus these charts indicate a closed trajectory of a system’s state within a state space over time. This concept was originally applied to cycles within ecological systems, measuring certain attributes of systems in order to predict their ability to handle, recover, and adapt from significant disruptive changes in environment, species populations, genetic landscape, etc.

These cycles can form steps on chains of greater systems where an individual cycle is a quasi-stable element but the overall state can jump and grow to higher forms of complexity and potential, or indeed collapse and fall to lower forms if the resilience is weak. As well, the multiplicities of cycles can represent a range of spacial scales for systems that have smaller cycles nested within them, operating concurrently.

This greater notion of change within systems has been called Panarchy. In contrast to hierarchy or even anarchy, Panarchy is neither the top-down or bottom-up of the other two. Panarchy tries to describe how actual ecological and social systems can change and transform yet endure and return to similar states, across scales of space and time.

Further Reading:

View at

Images of the Adaptive Cycle:

Images of Panarchy:

Social Cycle Theory



The Genetic Code

There are many ways to show the genetic code, the map between triplets of nucleotides and the amino acids of proteins. Here is one that may be a bit awkward to understand, but other more standard ones are easily found.

 First, here are the codes for the four nucleotides:

  • U = Uracil
  • C = Cytosine
  • A = Adenine
  • G = Guanine

As well, let

  • $ = U or C
  • % = A or G
  • & = U or C or A
  • * = U or C or A or G

And so, here are the amino acids and their nucleotide codes

A = Ala = Alanine = GC*
C = Cys = Cysteine = UG$
D = Asp = Aspartic Acid = GA$
E = Glu = Glutamic Acid = GA%
F = Phe = Phenylalanine = UU$
G = Gly = Glycine = GG*
H = His = Histidine = CA$
I = Ile = Isoleucine = AU&
K = Lys = Lysine = AA%
L = Leu = Leucine = UU% + CU*
M = Met = Methionine = AUG
N = Asn = Asparagine = AA$
P = Pro = Proline = CC*
Q = Gln = Glutamine = CA%
R = Arg = Arginine = CG* + AG%
S = Ser = Serine = UC* + AG$
T = Thr = Threonine = AC*
V = Val = Valine = GU*
W = Typ = Tryptophan = UGG
Y = Tyr = Tyrosine = UA$
# = Stop = UA% + UGA

Note that some letters encode both nucleotides as well as amino acids, which might be confusing.

Further Reading:

[*10.146, *10.147]