Theories of Time

Past, present, and future. Which is real and which is not? Philosophers have had various theories, and a century ago, philosopher JME McTaggart classified two common theories as the A series and the B series. He hoped to prove that time is unreal by arguing that time satisfies both the A series and the B series, and that those two theories contradict each other. Thus, time has no reality.

Here are all the possible theories. I have added the growing block universe, a halfway theory between presentism and eternalism, and also four other theories which I have named, and which seem to have no advocates.

TheoryPast?Present? Future?
Unreality
X
A series, presentismX
Growing block universeXX
X
XX
XX
B series, eternalism, block universeXXX
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Genesis 1 Structure

With the new editor’s support for tables, I decided to take on the structure of the first creation story in the Bible. Each number is for the day when something is created.

EnvironmentsInhabitants
Celestial1. Day, night4. Sun, Moon, stars
Far Terrestrial2. Sea, sky5. Flying animals, aquatic animals
Near Terrestrial3. Land, (plants)6. Land animals, humanity

On the day after these labors, God rested, taking the first day off in the history of the Universe. This is rather obviously a charter myth for the seventh-day Sabbath.

Back to the previous six days, God creates each of these three kinds of environments, and then returns to create their inhabitants. It is very orderly and systematic, and very unlike the second creation story, with its very improvised look. It even fits the factorization of 6 into a product of 2 and 3 — environments vs. inhabitants and three kinds of environments.

This structure explains the oddity of flying animals before land animals, and the story also has the oddity of placing plants in environments rather than in inhabitants.

The Fermi Paradox: Are We The First?

This is a possible consequence of the “too rare” solution, that we may be the first ones to emerge in our galaxy, or even all of the Universe that we can observe. However, this solution only requires rarity before our emergence, and not after.

But considering when we emerged, it is hard to point to what might make our emergence rare before when we emerged and common afterward. An obvious possible limiting factor is metallicity, the abundance of elements heavier than hydrogen and helium, what astrophysicists call metals. Old and exploding stars have gradually been enriching the interstellar medium with metals, giving later-forming stars more and more of metals. However, Earth-sized exoplanets have been detected orbiting stars with a wide range of metallicities, sometimes much less than the Sun’s (An abundance of small exoplanets around stars with a wide range of metallicities | Nature). This makes it unlikely that the Solar System was the first planetary system with habitable planets.

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Fuzzy logic

Fuzzy logic is the addition of other sorts of values to true and false, like adding a “maybe true or false” value, and using a continuum of values between true and false. Traditional mathematical logic, with only true and false, is sometimes called crisp logic by comparison. It is also known as Boolean algebra, from 19th cy. mathematician George Boole, who found analogies between logic and arithmetic.

Fuzzy logic has turned out to be very useful for device control, because it is a good way of handling real-world conditions. For instance, when does gray stop being black and start being white? For crisp logic, one can say black – medium gray is dark and medium gray to white is light. That is not very informative, so we subdivide these ranges: black to dark gray is dark-dark, dark gray to medium gray is dark-light, medium gray to light gray is light-dark, and light gray to white is light-light. One can continue with these subdivisions, reinventing binary representations of numbers. But once one does that, one can use the numbers directly. Black is 100% dark and 0% light, dark gray 75% dark 25% light, medium gray 50% dark 50% light, light gray 25% dark 75% light, and white 0% dark 100% light. Once one has such numbers, one can then use them in fuzzy analogs of crisp-logic operations like “not”, “and” and “or”.

Below the fold, I will construct some a simple system of fuzzy logic using “maybe true or false”.

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Genesis 1 – Indo-European?

This may seem very odd, but I have developed a hypothesis for that, by assembling various bits and pieces of history and mythology.

The story starts with the speakers of Proto-Indo-European dialects some 6000 years ago in the grassland between eastern Ukraine and Kazakhstan. They had a creation story that goes something like this:

Once upon a time, there were two twin brothers, *Mannus, and *Yemos, Man and Twin. Man sacrificed Twin, dismembered him, and constructed the familiar universe from his body parts.

They also had a story about how a god of storms and war fought and killed a reptilian water monster.

They spread out from their homeland, and though they eventually got assimilated in the Fertile Crescent, these stories were picked up by local people and conflated into a Chaoskampf, “chaos struggle”. The older gods are threatened by a chaos monster, and they send out a younger god to fight it. He defeats it, he creates the familiar universe from its parts, and he becomes the ruler of the gods.

This story is picked up by some Israelites, and they trim it down by God cutting up primordial material. “In the beginning, God separated the heaven and the earth”. The story was then revised into its present form, and it was turned into a charter myth for the seventh-day Sabbath.

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“…branding on my forehead: SLAVE”

I’ve finished reading the book Bruce Levine’s book “The Fall of the House of Dixie: The Civil War and the Social Revolution That Transformed the South”. It’s excellent. I find it especially curious how the plantation-slaveowner elite reacted to the war. It was a war waged on their behalf, a war waged so that they could continue owning slaves. But after the first few months to a year, they could not be bothered to do much to support the war effort, something that some Confederates themselves found rather odd.

They exempted their sons from the military draft with the “Twenty Negro Law”, they were not willing to grow much grain or sell it at low prices, and they were not very willing to hire out their slaves for tasks like building fortifications. The poorer Confederate citizens ended up grumbling that they were fighting for people who were clearly not doing as much as they could. “A rich man’s war and a poor man’s fight.” That sentiment was especially strong in parts of the South with relatively few slaves. Western Virginians succeeded in seceding from their state, but eastern Tennesseeans’ attempt to do so was crushed by the Confederate Army.

Consider the case of South Carolina plantation owner, politician, and slavery defender James Henry Hammond. He argued that the slaves were very suited for doing the work that they were made to do, that they were better off enslaved than free, and that higher civilization rests on the labors of an underclass of people that never get much for their labor — the “mudsill theory” of society. But when a Confederate army officer stopped by to requisition some grain, he tore up the requisition order, tossed it out a window, and wrote about it that it compensated him too little, and that it was like

branding on my forehead

SLAVE

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WFF ‘N Proof, a mathematical-logic game

“WFF ‘N Proof, the Game of Modern Logic”, is a game that I had had in my childhood, though I now only have its rulebook. A WFF (“woof”) is a well-formed formula, one that is syntactically correct, and in the game, one creates proofs with inference rules. The game has dice with operation and variable names on them, and one tries to find WFF’s and proofs that fit what is on the dice. The game also includes an hourglass for timed play.

It was created by Layman Allen in 1962, and he has also created On-Sets, on set theory, and Equations, on arithmetic, both played much like WFF ‘N Proof.

I wish that I could recommend WFF ‘N Proof, but it has several deficiencies.

  • It uses a prefix representation for its binary operators, (and) p q, with no attempt to relate it to the more usual infix form, p (and) q.
  • It does not use the logical constants (true) and (false), and it does not have truth tables, tables of output values for input values (arguments).
  • It does not name the operator properties that it has proofs of, like (and) and (or) being commutative and associative.

After the fold, I will describe the formalism in WFF ‘N Proof in more detail.

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