lorem ipsum

(suggested new terminology)
def: a hopscotch number is an integer w > 1 such that if p is a prime dividing w and n is the largest positive integer such that p^n divides w, then n = 1 or n is a prime less than p.
Theorem: Every square-free number is a hopscotch number.
Proof: Obvious.
def: a bulging number is an integer w greater than 1 that is not a hopscotch number.
Theorem: Every power of 2 greater than 2 is a bulging number.
Proof: Obvious.
keywords: Mathematics, Number Theory, divisibility

RECIPROCITY

The degree to which you attend to corner conditions times the degree to which you succumb to decorations is constant. The fact that decorations so often pose a danger, and that care consists of attending to corner conditions, is the basis of Benjamin Franklin’s saying, “Want of care does more damage than want of knowledge.” (-and is the basis of A. E. Housman’s observation: “As long as the sun and moon endure / Luck’s a chance, but trouble’s sure.”) Doing right ultimately consists of attending to corner conditions. Hence a good rule of life is: “Keep calm and proofread.”
cf:
“It is not your business to succeed, but to do right; when you have done so, the rest lies with God.”
— C. S. Lewis
keywords: reason, cause, religion, spirituality, choice, decision

OBSERVATION

School defaults to being merely the antechamber to the hall of learning. (This is why so many perceptive people regard the system of public education as being ‘broken’.) The antechamber to the hall of learning consists of descriptions and injunctions given in ordinary (as opposed to technical) language, and defaults to exotic phenomena described in ordinary language. (There is nothing more exotic than something, such as unicorns, that is nonexistent, and much of what is proffered in the antechamber (e.g., black holes) is nonexistent.) In regard to the distinction between background and foreground, background consists of the content of the hall of learning. Foreground consists of the sensory data in the antechamber (which can be identified with the shadows on the wall of Plato’s cave). The false sense of arrival that an antechamber can give has long been exploited, such as the antechamber of a pharaoh’s burial site to mislead tomb-plunderers. The antechamber of the hall of learning is constantly expanding, via importation from the hall of learning. For example, not long ago only specialists knew what DNA was. Nowadays, it is on the lips of everyone. Legislation applies only to phenomena within the antechamber of learning (especially what is to be regarded as historical fact), but since there is some random overlap between the antechamber of learning and the hall of learning, from time to time legislation has been passed, or at least proposed, that later looks ridiculous, such as the idea of fixing the value of pi by statute.
The old saying: “Every man goes through three stages in his life: First, he believes in Santa Claus. Second, he does not believe in Santa Claus. Third, he IS Santa Claus.” can be rendered in technical language as follows: “Every man goes through three stages in his life: First, he believes he is in the hall of learning, when in actuality he is merely in the antechamber of the hall of learning. Second, he realizes that he is merely in the antechamber of the hall of learning. Third, he arrives (possibly, by being carried, kicking and screaming,) in the hall of learning.”
cf:
“No man who worships education has got the best out of education. Without a gentle contempt for education no man’s education is complete.”
— G.K. Chesterton
keywords: training, instruction, illusion, portal, fantasy, censorship

lorem ipsum

“We are not merely imperfect creatures who must be improved; we are rebels who must lay down our arms.”
— C. S. Lewis
keywords: religion, orientation, priority, priorities, decision, surrender, subordination, obedience