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‘Exponential growth’ sounds impressive, but it is really the bare minimum sufficient for sustainability. That is, only exponential growth can offset entropy.
keywords: life, Physics, General Systems Theory, processes

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The following is the ‘silhouette’ of a solution to a certain mathematics problem. Your task is to identify the problem. (We will reference this problem by the code 235711.)
Axiom 1. Each of A and B is a closed set.
Axiom 2. A and B intersect.
Axiom 3. the interiors of A and B do not intersect.
Axiom 4. A union B is the universal set.
Axiom 5. M is a subset of A union B.
We show that:
1. t is an element of M.
2. t is not an element of the interior of A
3. t is not an element of the interior of B
We conclude that t is an element of A intersection B, and this solves the problem.
keywords: challenge

The cycle of day and night: Your tax dollars at work

It’s no news that in elementary school the truth is often pureed to the point of being baloney. Since public school is the lowest common denominator of the educational system, we will focus on what happens there.

In any given regime, the easiest entry for errors and confusion is by way of subtext. A cardinal example of false subtext is what fifth graders are told about Earth’s rotation.

Consider the following question on a science quiz for them:
“Which of these cycles is a direct result of Earth’s rotation?”, with the correct answer intended to be “Day and night”.

However, the fact is: For Earth to experience the cycle of day and night, it is neither necessary nor sufficient for Earth to rotate.

Now, it is certainly true that the particular cycle of day and night that Earth has is do to the particular rotation regime that it has, but the implication, or at least the subtext, of the question is the two-part assertion that:
1) In the absence of rotation, there would be no cycle of day and night.
2) In the presence of rotation, there will be a cycle of day and night.

However, BOTH of these assertions are FALSE.
1) If there is no rotation, then there WILL BE a cycle of day and night – a single full day (of lightness and darkness) being a year in length.
2) It is possible for there to be rotation, but for the rotation to be such that it cancels the relative effect due to the revolution about the Sun, with the result that there is NO CYCLE of day and night.

The question ‘Could you pass a fifth-grade science test?’ is sometimes posed in discussion forums, with many adults admitting that they doubt that they could. Sadly, a better question would be, “Does fifth-grade science pass muster?”

keywords: education, instruction, training, rigor, logic, corner-cutting, shortcuts, sloppiness, planet, Astronomy, Celestial Mechanics