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Word Gems 

exploring self-realization, sacred personhood, and full humanity


Editor’s collection of notes:




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please click on each link-icon



Fraction: Numerator, Denominator

Numbers: Cardinal, Ordinal, Nominal

Number vs. Numeral

Order of Operations: PEMDAS

Property, Associative: Addition, Multiplication

Property, Commutative: Addition, Multiplication

Property, Distributive: Multiplication over Addition, Subtraction

Property, Equality: Addition, Subtraction, Multiplication, Division

Property, Equality: Reflexive

Property, Equality: Substitution

Property, Equality: Symmetry

Property, Equality: Transitive

Property, Identity: Addition, Subtraction, Multiplication, Division



Algebra: definition













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‘his whole affection given to purer speculations, not to vulgar needs of life; to studies of beauty and grandeur’

“La Mort dArchimède,” Death Of Archimedes,
painted in oil, 1815, by Thomas Degeorge 


lost in thought, the greatest mind of the ancient world, put to the sword by a brash soldier with a bruised ego

Plutarch, writing c.100 AD, writes of the death of the Greek scientist and mathematician, Archimedes, during the Roman siege of Syracuse, Sicily, 212 BC.

The Roman general, like the Allies hoping to capture German rocket scientists, had given strict orders that the famed inventor of war machines not be harmed. However, an insolent soldier, commanding Archimedes to follow, became enraged when the 75 year-old genius, lost in thought over a math problem, refused to leave his work; and so the legionnaire killed him on the spot.

Archimedes Thoughtful
by Domenico Fetti, 1620


in pursuit of the beautiful

Plutarch comments that Archimedes, despite successfully engineering various advanced weaponry, had come to a point in his life of “repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit.” Instead, he had now given himself to the pursuit of knowledge for its own sake, a quest for the “beauty” found in nature, a desire to witness a “grandeur” expressed in science and mathematics.

All thinking, all high-minded people, of every culture and age of history, yearn with Archimedes for a better world, one without war machines, violence, and oppression. And we would seek for the beautiful, for truth, for the mind of God. In the “real world,” in Summerland, this is exactly how maturing persons conduct themselves; those who do not have some “unfinished homework to complete” in the Dark Realms before they can join civilized society.

The quest for the beautiful is no optional side-route. Without this focus, as discussed elsewhere, we will not survive “the terror of living forever.” Our world, more and more, is marching toward greater expressions of incivility, oppression, and totalitarianism. Nothing has changed since the days of Archimedes, there’s been no real progress of the ego-led human spirit since that time.

We can’t change the world with its endless pendulum swing of evil’s “rise and fall,” but we don’t need to be part of it; we have to live in it for now, but our spirits can enjoy a detachment. We can seek for, and make note of, beauty, as we find it, in our studies and observations of the natural world; as did Archimedes.