Category Archives: fourfolds

Everything is Four

Out of the None comes One,
out of the One comes Two,
and from the twain comes forth
the One as Four.

— Not the Axiom of Maria

How do you solve a problem like Maria?

— From The Sound of Music

Further Reading:

[*12.18, *12.20]




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 Eight Kinds of Love

There are several mentions of eight types of love purportedly discussed by the ancient Greeks, but I’m short on the actual references.

In no particular order:

  • Agape: unconditional love
  • Eros: romantic love
  • Philia: affectionate love
  • Philautia: self love
  • Storge: familiar love
  • Pragma: enduring love
  • Ludus: playful love
  • Mania: obsessive love

I had an earlier post on The Four Loves by C. S. Lewis, but now I see that he just left out half of them for some reason. Missing are Philautia, Pragma, Ludus, and Mania, which seem important, but since I haven’t read the book, I don’t know his reasons.

Further Reading:

8 Types of Love – Which One Are You?



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]