This month's article, and another nonfiction version, have already been posted on online archives.
Sunday, December 5, 2021
A Universe Green Lanterns Can Play In
By Michael Griffin
All covers Copyright © DC Comics
1. Development of Green Lanterns
From the article “Magic Ring” in Wikipedia, the free encyclopedia:
“In the DC Universe, the members of the Green Lantern Corps wear power rings that have a scientific, not magical, basis. These rings allow the bearer to perform any feat he can imagine, but are limited by his willpower. The Blackest Night storyline reveals the existence of similar rings of other colors, powered by other emotions such as greed and hope. The original Green Lantern, Alan Scott fashions a power ring from an ancient lamp that is a concentration of magic energy that the Guardians of the Universe created in an attempt to remove magic from the universe. As a result of this discovery, Scott's ring functions much like the standard Green Lantern rings, except that it cannot directly affect wood.”
Besides Alan Scott, the most well-known Green Lantern since 1959 is Hal Jordan, pictured above on the left and below flying through the vacuum of space. The green vapor trail around Jordan is an example of how the power ring can create things. .
All covers Copyright © DC Comics
Another example of the green material emanating from the power ring is shown by this cover:
All covers Copyright © DC Comics
2. A Universe Needed
A single UFT force for the ring
What is the green will-goo? To spin it into theory, it must be a solid single substance, not matter or atoms, a unified material that can act as solid force yet move as if just light speed of pure energy, speed of thought. Thus, we need a single, pure force field of matter that can easily shift into energy. The will of thought shapes it while its power comes from the ring's charge. The ring is recharged from a lamp-battery as shown in the cover below. The ring and lamp use a single energy that can store as a charge. It reshapes at the will of thought into forces of matter. So how can energy and matter be two forms of the same thing? Let us recall that basic truth written as E=MC2 or E equals MC squared. Since this article is merely comic book speculation, we are not bound by the rigorous mathematical constraints of known physics. We can form a new interpretation of space-time (st) intended for compatibility with as many basic principles that fit.
Covers show the 4 forces
For classic unified field theory (UFT), we are concerned with the four basic forces of gravity, electromagnetism, nuclear binding, and radioactivity. Each of these forces is illustrated by one of the covers shown. Gravity is represented by the cover of issue 24 above with a planet in space. Nuclear binding and radioactivity are illustrated by the next cover. In the nucleus of the atom, protons are bound together in spite of their repelling electric charges, as Hal Jordan's ring is stuck to the power battery. The nucleus can also discharge particles or radiation, radioactivity, which we represent by the jagged lightning bolt from Sinestro's ring to the battery, though the radiation would be going away from the battery.
All covers Copyright © DC Comics
The next cover is an actual illustration of electromagnetism with dotted lines to show the magnetic field. Electric current flow lines up electrons, or if a bar magnet has the electrons lined up in the same orientation, the effect is the same as current flow, to create a field as shown in the next cover. We could take the direction of the steel girders as one of current flow fitting the “right hand rule” of a field curving around like fingers curled up behind the right hand’s pointing thumb.
All covers Copyright © DC Comics
3. Action Principles
Speed-field relation
Electromagnetism is also modeled as the electromagnetic wave spectrum, which also is modeled with particle properties. A particle of light is called the photon, typically considered as energy without mass. The constant speed of light, c, in all frames of reference led to the theory of special relativity. General relativity models the curvature of space and time by gravity from mass. One way it was confirmed is by observing the bending of light rays near the sun. Massless photons with no field of their own are still affected by a gravity field just because space itself is curved. If something is mass, it can never reach the speed of light, according to relativity.
For our Green Lantern substance, we will not make a sharp distinction between mass and energy. Instead, we will compare fields and particle speeds:
It seems there is an inverse relation between speed and field. A slower speed has a bigger field.
What is a field? Definition
A field is an area where force or some other quality manifests. We will address the aspects of speed, range, intensity, force, and momentum to derive a Green Lantern UFT. Begin with E=MC2 or E equals MC squared, or energy equals mass times the speed of light times the speed of light. This is a kind of statement of the ultimate potential energy in mass. Dividing both sides of the equation by the speed of light, we now have E/C=MC. This is a momentum field of mass times the speed of light. Here we depart from relativity theory because in real-world physics this is supposed to be impossible. So our Green Lantern's mass M is not yet matter in the conventional sense. If it is really moving at the speed of light C then it is a photon. It can be modeled as an electromagnetic force, but it does not have the force fields of matter like gravity, binding, or radiation. It moves in a straight path as energy, whereas all the fields of matter would confine it to a local area. To become fielded as matter, it's straight line path must change.
Enfielding by Euler's
There is a mathematical symbol which is interpreted in physics to mean rotate 90°. It is the letter i which also stands for the square root of negative one, √-1. This is part of Euler's famous equation e to the pi-i plus1 equals zero: eπi+1=0 or eπi =-1. The symbol pi or π is defined as the ratio of the circumference to the diameter of a circle, and Euler's equation can be interpreted as a way to describe cyclical patterns. If a straight path photon of energy begins a 90° or 90-degree rotation from the diameter of the circle to move along the circumference we can say that it has become enfielded into matter.
This is one way to interpret the meaning of i. Another interpretation of Euler's equation is that exi = cos(x) + isin(x). Which again would be the cosine wave in the real world plane and a sine wave in the 90-degree imaginary i-plane. However, when x is pi this cyclical wave motion is also just equal to -1 which could mean the opposite direction that a photon was moving in before it became enfielded and took an orbit at a right angle. So then Euler's equation would be a multiplying factor in the UFT formula.
This explains the how but not the why of enfielding. It would also explain the how of the reverse process of unfielding where a matter particle or wave stops harmonizing in it's self-contained area and resumes a straight path as a photon vibrating with its wave-like properties. Something of the why may be due to the +/ - nature of the direction of the equation which was defined as one. When two Green Lantern particles collide we will take that to be the final multiplication of their masses, and we will only consider the directional value of +/-1. Positive one has been defined as the path of a photon while -1 has been defined as the path of enfielded mass. A few basic possibilities exist:
-1 X -1 = +1 two masses collide and convert to photons,
-1 X 1 = -1 mass absorbs a photon,
1 X 1 = 1 photons collide and merge or remain photons.
Those would be the rules according to basic arithmetic. The other possibilities which would not conform to standard arithmetic are:
1 X 1 = -1 photons collide and emit a mass,
-1 X 1 = +1 mass absorbs a photon and converts to photon,
-1 X -1 = -1 two masses collide and remain mass.
Space-time (st) defined as MC
So our particle of Green Lantern material has now become fielded mass and is no longer moving at the speed of light C. Then what was the meaning of a potential momentum field MC? This is the ultimate momentum from the ultimate energy that any mass can have. For conservation of energy, this is the structure of space-time. In any inertial frame of reference, a particle's total momentum is MC merely due to its existence in space-time. A Cartesian grid would have the X and Y axes represented each by a C vector, meaning the speed of light. Note that area is two dimensions or C squared, as in E=MC2.This can be interpreted as the three-dimensional aspects of the grid, and the two dimensional plane of C squared would be analogous to the curl of the field while one-dimensional vector momentum is analogous to the divergence of the field. MC is the space-time tension that any particle has. Left on its own, that particle can move along the grid as a photon or other energy particle. The next cover gives some idea of how this can be visualized.
All covers Copyright © DC Comics
4. A Universe Compared
Scale of forces
The following table is from a standard textbook cited in the sources:
Gravity thus 1/100
The table uses the Strong nuclear force as a unit of one since it is the strongest. The relative strengths of the other forces in the table are compared to that. One implication from the table is that gravity is also not really an infinite range. We see that gravity is less than the strong force by a factor of 10 to the -40 power. If there is an inverse relation between speed and field, then it may also show up between strength and range. We may thus conclude that the range of a gravity field is greater than a strong field by the factor of 10 to the 40th power. Multiplying these two factors means that we combine the exponents to get the range of a gravity field as: 10^-15m X 10^40 = 10^25 meters.
We can compare this result to the known size of the universe, 8.8 X 10^26 meters. Rounding this up to 10^27m we see that the universe is about 10^2 or 100 times bigger than the extent of a single gravity field. Our galaxy is said to be only 5X10^20m across, which is well contained within any single gravity field. A galaxy may only affect 1/100 of the rest of the universe, with its gravity. This may explain so many astronomical observations which at present do not fit any theories.
Spin cycles for field strength
If we subtract exponents in the above table we see that electromagnetism is 10 to the 28th power stronger than gravity, or 1028. The two forces have different inverse square laws, one based on charge Q and the other based on mass M. Our Green Lantern field should only have a single inverse square law. Besides that law, it also has the new Euler factor eni where the exponent n pi i allows for many cyclical waves or spins represented by the letter n. The value of n may be the only difference in field strengths. For comparison, let us say that n equals 1 for the gravity field G and we don't know the value of n for the electromagnetic field Q. We do know that the ratio or fraction Q/G equals 1028. All other field formulas in the fraction have canceled out leaving only:
eni/ ei = 1028. This simplifies to e(n-1)i= 1028. Solving for n we get:
n = (28ln10)/(i)+1 as how many more cycles or spins the enfielded particle had to make to go from gravity to electromagnetic strength. In this context if we treat the i as just one then the value of n is 21.522 or 21 and a half spins. Similar calculation results for strong and weak forces will appear in a table below.
All covers Copyright © DC Comics
Inertia, where is +/- always
The value of n may also determine where is a +/- polarity in the Green Lantern field, which is always seen in Q but never recognized in gravity’s G. Consider the above cover for Green Lantern issue 123 with its curving lines showing Hal’s flight against gravity. Instead of a sideways S pattern, imagine the two curves extended into complete circles side by side: a OO pattern. This could represent the spinning (st) cycles of two enfielded masses. General relativity would make this out to be the (st) funnel of mass without any spin. By spin I refer to the n value of the Euler field factor. If the spins are in the same direction they have the same sign whether +/+ or -/-. If the spins are in the opposite direction they have different signs whether +/- or -/+, and the circular paths will come around to go through the middle of the OO shape in the same direction. This is opposite signs attracting in (st). If the spins are in the same direction and get out of sync the paths will collide in the middle of the OO, opposing each other in reverse direction. This is repulsion of the same signs whether +/+ or -/-.
What of the neutral charge, which can show up on a neutron that may split into a +/- proton and electron? Where does the spin go for a fielded yet neutral mass? On a two-dimensional figure, the spin may shift off of the diagram into the third dimension, losing its mutual or opposite flow to a 2-d spin path. This then raises the prospect of neutrons and antineutrons in their own +/-/0 plane of action.
The question remains, where is repulsion with the force of gravity? All around us we see everything attracted with gravity as if everything has opposite +/- polarities. Part of the answer may be in an anthropic principle: If the anti-gravity were not already gone we would not be here to notice. There are suggestions that galaxies are separating at an accelerating rate, and this would clearly be due to repulsion of their net gravitational fields. The cosmological constant of general relativity may then be an index of anti-gravity repulsion. On an everyday level, where else could anti-gravity repulsion show up? Modeling gravitational motion occurs in two dimensions, one in the direction of attraction and the other at an inertial right angle. Inertia is plain velocity not acceleration so it is a momentum not a force. The momentum that keeps two masses moving away from each other or towards each other as the case may be. Maybe sometimes inertia is from the force of repulsion. In a broader inertial frame of reference where special relativity would apply, but too local for general relativity, anti-gravity only happens on a gravity scale. In a Green Lantern UFT there is only one kind of repulsion: when n values get out of sync.
Quantum unit basis
One way to get a real value of n is to use quantum theory and Planck's constant h. Combining E=hF and E=MC^2 makes MC^2=hF which gives the frequency F= MC^2/h for a matter wave. If we put in the numbers for the reduced constant h and the Planck mass then we get:
2.18X10^-8 (3X10^8)^2/1.05X10^-34 = 18.6857X10^42 = 1.8X10^43
This is the Planck frequency in Hz for the upper bound of electromagnetic or cosmic rays. Since this is the highest possible frequency, it can represent the strongest force of nuclear binding.
Radioactivity-binding +/-
The next table will show the relative spin-cycle n values for each force and also their characteristic electromagnetic spectrum frequencies:
The characteristic frequencies for electromagnetic and weak force are both in the high gamma range. Since gamma rays are part of radioactivity emissions this is not surprising for the weak force. It is more surprising that it would be the basis of charge Q. Gravity does give a good fit merely by subtracting exponents, though of course gravity waves are not considered electromagnetic waves. This 10^3 frequency could be the actual angular speed of a single-n spin speed.
All covers Copyright © DC Comics
The above cover to Green Lantern issue 47 shows the usual way binding force is thought of. As Hal Jordan is stuck to the magnet by the superior force of Doctor Polaris, so the binding force is assumed to overcome the like-charge repulsion of protons. If there is only a single binding inverse-square force then this is no longer the case. However, if experiment does show that such amounts of energy are involved in the nucleus then it makes sense to keep these relative magnitudes of forces to make the tables for this Green Lantern UFT. The next cover for Green Lantern issue 19 can represent the atomic model with Alan Scott as the nucleus binding force upon his fellow Green Lanterns.
All covers Copyright © DC Comics
Here our comic book speculation is at an end, and we still do not have a mechanism for how the Green Lantern's will power can influence the field.
Sources
Astronomy: The Cosmic Journey By William K. Hartmann and Chris Impey Brooks/Cole, 2002 - Sixth edition - 553 pages https://books.google.com/books/about/Astronomy.html?id=KxSIPwAACAAJ
P.491 table 27-1: The Fundamental Forces of Nature
The Constants of Nature By John D. Barrow Vintage Books, 2002 - 271 pages https://books.google.com/books/about/The_Constants_of_Nature.html?id=MJXuAAAAMAAJ
P.146 Euler and action principles P.233 Einstein and UFT
Green Lantern: A Celebration of 75 Years DC Comics, 412 Pages Print Release Date October 20 2015 https://books.google.com/books/about/Green_Lantern_A_Celebration_of_75_Years.html?id=ENGHCgAAQBAJ&source=kp_book_description
Green Lantern: Cover Gallery Grand Comics Database https://www.comics.org/series/1448/covers/
https://www.comics.org/issue/50454/cover/4/
Magic ring. From Wikipedia, the free encyclopedia This page was last edited on 11 April 2019, https://en.wikipedia.org/wiki/Magic_ring
Tuesday, October 5, 2021
Sunday, September 5, 2021
PUBLICATION ANNOUNCEMENT
The e-book of Imaginary Heroes in the Age of Science
has also been posted on the Internet Archive, available in the Community Texts collection for free download:
https://archive.org/details/im-heroes-1st-ebook-plain-cover_20210302/mode/2up
It's on another member's favorites list already!
Monday, August 30, 2021
Tuesday, September 8, 2020
20-year recap wrapup
Reconstructing Mythic Algebra
By Michael Griffin
Abstract
This is the tenth in a series of papers on an algebra, derived from mythology,
that can model symbolic processes. Previous papers used literary semantics,
mythology, semiotics, philosophy and mathematics. The main features of the
algebra are set-based elements and making association a new operation. While
such a system can be reductive, it need not be. It may reconstruct into a more
useful tool. Various implications for its foundations are considered.
6 Keywords:
algebra, association, mathematical modeling, numbers, reduction
1. Introduction
Mythic algebra began as a system to model
mythology, then expanded into narration, thence to cover a host of mental
processes using the operation of association (2003). Once the system was
completed, new applications were made into semiotics and mathematics (2008).
One may question just how far can a system go that is derived from mythology.
A guiding assumption was that the mental processes that manifested as myths
would also manifest as anything else, if only the underlying system was found.
The guiding principle was to use the features of
basic algebra, looking for group principles and two distinct operations. The
results became the following system represented in a formulaic lineup:
(p,q,x,y,s,t), M, R, M/R, R/M, ↆ, =, #, S, $,+, ౼, *, %
This lineup separates into levels as:
Sets (p,q,x,y,s,t) of elements people p and their actions q, things x and
their actions y, space s and time t.
Functions M, R, M/R, R/M, ↆ,
set states mythic M or real R that can map elements among them by / or just
alter elements or states by ↆ.
Relations =, #, S, $ of equality,
inequality, similarity, or dissimilarity.
Operations +, ౼, *, % of addition, subtraction, association or dissociation.
2. Discretion
Sets have discrete elements. By discrete, we mean
separate, distinct, and also countable if we cared to. The meaning of
countable will be explored in a later section, while here we look at the most
basic definition of elements, their separate, distinct quality. Whether
elements are in the same or different sets, they remain distinct from each
other. A set of (A,A,A) has three A’s just as (A),(A),(A) does or the listing
A,A,A does.
Concrete reality clearly has things we
perceive as distinct from each other: a rock is not a tree even if we have no
names for them. Nature builds itself by using discrete elements, from atoms up
to cells and beyond. Alfred North Whitehead (1967) in 1925 noted this fact of
reality and examples of the advance in human thought once we recognize it:
The influence of atomicity was not limited to chemistry. The living cell is to
biology what the electron and the proton are to physics. Apart from cells and
from aggregates of cells there are no biological phenomena. The cell theory
was introduced into biology contemporaneously with, and independently of,
Dalton’s atomic theory. The two theories are independent exemplifications of
the same idea of ‘atomism.’ (99-100)
Our languages have modeled or mimicked this
reality of discrete elements by using discrete words, regardless of the
particular syntax or semantics. Labeling with words requires otherness,
difference. Before Derrida wrote anything on deconstruction, the Zen
philosopher Alan Watts (1959) observed the troubles that arise when making
discrete distinctions that may be arbitrary:
For the function of these nonsense terms is to draw our attention to the fact
that logic and meaning, with its inherent duality, is a property of thought
and language but not of the actual world. The nonverbal, concrete world
contains no classes and no symbols which signify or mean anything other than
themselves. Consequently it contains no duality. For duality arises only when
we classify, only when we sort our experiences into mental boxes, since a box
is no box without an inside and an outside. (80)
This “inherent duality” goes at least as far back as Plato and Aristotle, whose ideas were expressed as three Laws of Thought: 1. The law of identity [A is A]. 2. The law of contradiction [either A or not- A] . 3. The law of exclusion, or excluded middle [only A or not- A] (Law of thought, 2019).
Not only languages, but thought itself may become biased into useless or
useful dichotomies. As the Taoists noted millennia ago (2007), once you make
a discrete thing or quality you then have to have something else that is not
that thing:
For is and is-not come together,
Hard and easy are complementary;
Long and short are relative;
High and low are comparative;
Pitch and sound make harmony;
Before and after are a sequence. (2)
Cut out windows and doors
In the house as you build;
But the use of the house
Will depend on the space
In the walls that is void.
So advantage is had
From whatever is there;
But usefulness rises
from whatever is not. (11)
(Blakney 60, 70)
Some basic dichotomies exist in mythic algebra, too. There is a
static-dynamic principle to divide elements: static p,x,s or dynamic q,y,t.
There is also a distinction of persons-things or neither, as p,q or x,y or
s,t. This has been critiqued, for what defines a person whereas a sentient
creature like a pet is a thing? If this criterion is a human body, then
sentient minds don’t count. One has to define the elements according to
need.
Then the states of sets divide into the basic dichotomy of mythic M or real
R, with mythic defined as not-real. Generalizing states into F or G still
means that state G is not-F. Any number of distinct states can then be
notated, all defined as not each other: A,B,C,D,E,F,G,H,I,J,K,L,N,O,U,V,W,Z,
etc.
What criteria make them not
equivalent? It depends on the context. For mythic stories, the M-R
distinction was based on an M(s,t) mythic spacetime which was not in our
everyday world. For an F-G distinction it could simply be two separated
sets, though seemingly equivalent elements: F(a,b,c), G(a,b,c). F is this
one, G is that one.
So we now have sets of six basic
elements which can vary in their definitions. The state functions of these
sets can also vary in definition, just as long as they differ from each
other: M-R, F-G, etc. The elements and states are discrete because they
differ in binary polarities. Elements p,x,s are similarly static, yet p,q
are similarly of people but x,s are not. The utility of a people-things
distinction fits realms in which people figure, such as the human mind or
cultures. In realms of physical nature or pure mathematics, this may not
matter.
These four different realms of use will be
examined also in a later section. For now we can conclude that elements and
states of sets are only defined by the quality of being discrete from each
other. Another meaning of discrete is unconnected, which brings us to
consider the next levels of mythic algebra.
3. Plus -- or Not
The basic operation that all mathematics is
founded upon is addition. Once we have discrete units we combine them.
Undoing addition is subtraction, extended addition is turned into the
shortcut of multiplication, or its undoing is division. Mythic algebra does
not consider multiplication-division operations, presuming they are implied
by addition-subtraction. But what else may elements do besides combine by
adding? They may add to stay distinct, such as: A+B = A+B, or they may add
to transform, such as: A+B C, like 1+2=3 as a new number.
These kinds of operations work well with
discrete elements, but elements can also have a continuous connection apart
from this, even if they maintain their discrete character. Such connections
may not fit addition, but rather addition may fit into such broader
connections. This continuous connection or linkage has been modeled as the
* operation of
association. Some sketches can show the inadequacy of addition to fully
convey all possible connections of discrete point-elements:
Points A,B,C,D are linked as A* B, A* C,
A*D and arbitrary
measures of the paths may be taken as the magnitudes of points B,C,D. In the
first example, A+B+C+D = 2+2+2 = 6, and in the second example 3+3+3 = 9 yet
in both examples the paths are the same lengths. Any scale of distance does
not really matter to A* B, etc.
Or consider defining point A by its unequal
links:
On the left, A= 1+1+2+3 =7
On the right, A= 1+1+1 =3
Yet A and B are the same path and actual distance in both cases. Even B in
these examples has magnitude 2 or just 1. Traditional number lines avoid
this confusion of miscounts by keeping connections in a single dimension to
measure, so any differences of scaling can be compared:
A__+__+__B is 3/3 which equals A___+____B or 2/2
But such additive lines are single components of possibly endless continuous
links:
whether on a two-dimensional page or any-dimensional space. As if out of
Flatland (1884), a line connecting two points may only convey part of
their total linkage:
A________B
And if we only define the point's magnitude by measure along that single
dimension, we miss all of the other magnitudes and path-connections notated
by the asterisk symbol
*.
4. Levels
Besides the extra dimensions of connectivity,
levels of organization may upscale or downsize in a fractal-like style of
structure, maintaining mythic algebra at any level just as arithmetic does.
The results of any use of mythic algebra may be subsumed into a new basic
set element, its opposite elements then noted, and the usual mythic algebra
operations and functions performed on these new elements.
By opposite, I mean pairs of static-dynamic
elements. Even the space-time pair (s,t) can be a basic static-dynamic pair,
if we define space as the field that allows differing elements to occur, and
time as the force that allows change to occur, such as motion or mapping or
any action.
This makes a kind of reduction, but not
reductive to the single operation of addition, as arithmetic does, and the
edifice of mathematics built upon that. The properties of one level may not
be predictable from the association links' principles at a different level,
so no perfect reductionism exists. A structure can still be sketched to show
how one group of associations may be arbitrarily defined as the next level's
new basic elements:
Circled collections would be new element-points.
With the newer elements we may have only a
sketch of:
And such a rescaling of perspective itself need not be on a uniform scale
measurable by arithmetic.
However, natural science does model reality using
levels of scaling of uniform numerical measure. We proceed from the units of
ecology – whole organisms, to units of biology – body parts, to units of
chemistry, to underlying physics, to theoretical mathematical models of the
basis of physics. Each level uses numerical addition to construct the next
level, but even here we get new properties unexpected and not predictable
from earlier levels.
Still, these new properties can usually
be modeled with the same arithmetic-based mathematics that also is used for
reduction between levels. The addition operation, using discrete numbers,
does well to model nature. It is simply a starting fact without prior
justification, such as is remarked upon mathematics by Wigner (1960).
If additive numbers are just one aspect of
a larger mythic algebra using
* connections, then
anything modeled by mathematics may have other real links missed by the
traditional mathematics. It remains to prove such links and avoid the
pitfalls of false analogies and wishful, magical thinking. And perhaps
nature is so only because it is limited to arithmetical number-mathematics.
But any emergent properties in nature may indicate the missing
* links of the
association operation.
5. New Math
I have always viewed askance any system of claims to knowledge that can’t be
turned into a visual diagram or also into a structural symbolic system such
as mathematics or logic, even though I consider all such systems merely
provisional, pragmatic knowledge. Nonetheless, any long tome I consider as
talking a subject to death without getting to any deep understanding. This
is undoubtedly a bias of my own brain, and an urge to simplify and unify.
Since words to me are mere labels, I look for symbols that convey real
force, more reality than labels. Our scientific civilization has a few such
systems, mainly of mathematics, and perhaps this has been its appeal to me,
a feeling that it is truer than mere word labels. Yet such truths seem so
limited, that one can believe that a better, truer mathematics is possible.
Perhaps this has been an urge upon me, too.
References
Abbott, Edwin A. Flatland, A Romance of Many Dimensions, 1884 ed.
www.gutenberg.org/ebooks/201
Blakney, R.B. Tao Te Ching. New York: Signet Classics, 2007.
Griffin, Michael. ‘Looking Behind the Symbol: Mythic Algebra, Numbers, and
the Illusion of Linear Sequence.’ Semiotica 171, 2008, 1-13.
www.mythicalgebra.blogspot.com/2015_01_01_archive.html
-- ‘More Features of the Mythic Spacetime Algebra.’
Journal of Literary Semantics 32, 2003, 49-72.
www.mythicalgebra.blogspot.com/2014_11_01_archive.html
Law of thought, From Wikipedia, the free encyclopedia, last edited on 29 August 2019,
https://en.wikipedia.org/wiki/Law_of_thought#The_three_traditional_laws
Watts, Alan W. The Way of Zen. New York: Mentor Books, 1959.
Whitehead, Alfred North.
Science and the Modern World: Lowell Lectures, 1925. New York: The
Free Press, 1967.
Wigner, Eugene. ‘The Unreasonable Effectiveness of Mathematics in the
Natural Sciences.’
Communications in Pure and Applied Mathematics, vol. 13, No. 20
(February 1960).
www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
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