Shine
Bright
闪耀着光芒
Shǎnyàozhe guāngmáng
明るく輝く
Akaruku kagayaku
ps107
Clare splendere
The broken bowl bell
held food quite well
until it fell.
The squeaking squeal from the wheel
yields wealth in health appeal
from the way the appeal feels.
Mop up the mess.
It's part of the test.
Sweep up the ceramic.
You won't have to panic.
This piece was shaped like a diamond.
My mind looked to the horizon.
A diamond shines bright
with the facets of light’s life
in a mind with insight.
She smiles for miles
with the delight of her sight.
Diamonds start as coal.
Earth is the source for the intense force that cajoles
the carbon in its moles to make tiny holes
extol less space for lex taste holding the philosopher’s stone
as a blown tome now known
as the most remarkable clone.
Opaque matter, darker than night,
becomes transparent, shining sparkles in light.
Hardship hardens your core for sure
to make your heart shine as pure.
Purity is the cure that lures.
Performers stay healthy
so their products are wealthy.
The best work smart with rested heart
for the next test to start.
These followed their food.
These chopped what the beaver chewed.
These grew what they could.
These shot from where they stood.
These worked in mines.
These hunted from blinds.
These worked in fields.
These negotiated deals.
These squealed for appeals.
These worked in a factory.
These made customers happy.
These worked in the field.
'No mind' was their shield.
Mugwort and hemp
healed that which was bent.
The redeemer’s redemption came
by correction in detention for those who lost their way to fame
and became lame with respect for the rules of the game
These formed conception with education
to avoid the deception of perception
by the sensation of the senses.
All these weathered the storm;
while these struggled through thorns.
These strengthened their homes
while these burned diseased bones.
When the mist came with Spring.
these felt they had to travel and sing.
When they strayed from the path
they became children of wrath.
They rode and they fought.
They forgot what they had been taught.
Some went to the sea to travel in ships
to ply their trade without loose lips.
They moved straight on the ocean
when the crab didn't make the motion.
They beheld the wonders of the deep.
Things went so well they felt that they could weep.
Then a storm bossed the wind and the waves of the sea.
They rose so high they tossed the ship like a flea on a sheep.
The ship mounted the heavens then fell back to the depths.
Their hearts melted groan. Some actually wept.
They staggered and fell like the most practiced of drunkards.
They looked to the sky and prayed for their mothers.
The wind carried their prayer to the height of the sky.
They were delivered from the storm as if by their cry.
The storm was stilled to a whispering purr.
The sea felt so soft she seemed like the cure.
They all felt glad because of the calm of the sea.
The harbor they made soothed them like the balm of morality.
Let them give thanks for the love of sweet mercy.
The sailors were saved from wet death with the thirst for eternity.
The Redeemer redeemed lost time as the story.
Joy was embraced as a parcel of glory.
The weather is the greatest of friends
or the worst to offend.
We accomplish all things with the goodness of weather.
Natural disaster destroys anything, but buh-bling or bird feathers.
A silver cord streams
from the container of dreams.
We were made to be loved
with light from above.
A nation without borders isn't secure.
The strength of security gives length to endure.
Citizens carry rights that are earned as learned.
Participation in the media tests substance affirmed.
Legal immigration is a start on the path
to the blessing that heaven grants beyond wrath.
Conservative policy insists on a balance
between foreign and domestic investment in talents.
The ethics of morality in law
has a measure in the observation of what you draw.
Drink truth deep from your heart before sleep.
It will help you keep what you seek
looking sleek.
Shine like a diamond.
You will be alive then.
You won’t feel like a siren
on an island off the horizon.
------------------------
Psalm 107
Part I
Confitemini Domino
Acknowledge Mastery
1 Give thanks to the Lord, for he is good,
and his mercy endures for ever.
2 Let all those whom the Lord has redeemed proclaim
that he redeemed them from the hand of the foe.
3 He gathered them out of the lands;
from the east and from the west,
from the north and from the south.
4 Some wandered in desert wastes;
they found no way to a city where they might dwell.
5 They were hungry and thirsty;
their spirits languished within them.
6 Then they cried to the Lord in their trouble,
and he delivered them from their distress.
7 He put their feet on a straight path
to go to a city where they might dwell.
8 Let them give thanks to the Lord for his mercy
and the wonders he does for his children.
9 For he satisfies the thirsty
and fills the hungry with good things.
10 Some sat in darkness and deep gloom,
bound fast in misery and iron;
11 Because they rebelled against the words of God
and despised the counsel of the Most High.
12 So he humbled their spirits with hard labor;
they stumbled, and there was none to help.
13 Then they cried to the Lord in their trouble,
and he delivered them from their distress.
14 He led them out of darkness and deep gloom
and broke their bonds asunder.
15 Let them give thanks to the Lord for his mercy
and the wonders he does for his children.
16 For he shatters the doors of bronze
and breaks in two the iron bars.
17 Some were fools and took to rebellious ways;
they were afflicted because of their sins.
18 They abhorred all manner of food
and drew near to death's door.
19 Then they cried to the Lord in their trouble,
and he delivered them from their distress.
20 He sent forth his word and healed them
and saved them from the grave.
21 Let them give thanks to the Lord for his mercy
and the wonders he does for his children.
22 Let them offer a sacrifice of thanksgiving
and tell of his acts with shouts of joy.
23 Some went down to the sea in ships
and plied their trade in deep waters;
24 They beheld the works of the Lord
and his wonders in the deep.
25 Then he spoke, and a stormy wind arose,
which tossed high the waves of the sea.
26 They mounted up to the heavens and fell back to the depths;
their hearts melted because of their peril.
27 They reeled and staggered like drunkards
and were at their wits' end.
28 Then they cried to the Lord in their trouble,
and he delivered them from their distress.
29 He stilled the storm to a whisper
and quieted the waves of the sea.
30 Then were they glad because of the calm,
and he brought them to the harbor they were bound for.
31 Let them give thanks to the Lord for his mercy
and the wonders he does for his children.
32 Let them exalt him in the congregation of the people
and praise him in the council of the elders.
-----------------------
David - beloved
Ziba- army
Mephibosheth- mouth of shame
2 Samuel 16:3-4
The king said, 'Where is your master's son?'
Ziba said to the king, 'He remains in Jerusalem. He said, "Today the house of Israel will give me back my grandfather's kingdom."
The king said to Ziba, 'All that belonged to Mephibosheth is now yours.' Ziba said, 'I do obeisance. Let me find favor in your sight, my lord the king.'
-----------------------
A nation without borders isn't secure.
The strength of security gives length to endure.
Conservative policy insists on a balance
between foreign and domestic investment in talents.
=================
Acts 22:27-29
The tribune came and asked Paul, 'Tell me, are you a Roman citizen?' He said, 'Yes.' The tribune answered, 'It cost me a large sum of money to get my citizenship.' Paul said, 'I was born a citizen.' Immediately those who were about to examine him drew back from him. The tribune was also afraid for he realized that Paul was a Roman citizen and he had bound him.
-----------------------
Citizens carry rights that are earned as learned.
Participation in the media tests substance affirmed.
=================
Mark 11:7-10
They brought the colt to Jesus and threw their cloaks on it. He sat on it. Many people spread their cloaks on the road. Others spread leafy branches that they had cut in the fields. Then those who went ahead and those who followed were shouting,
'Hosanna! Blessed is he who comes in the name of the Lord!
Blessed is the coming kingdom of our ancestor David!
Hosanna in the highest heaven!'
-----------------------
Legal immigration is a start on the path
to the blessing that heaven grants beyond wrath.
=================
Posterity
Pierre de Fermat (fair-ma)
b. 10.31.1607 Beaumont-de-Lomagne, France
d. 1.12.1665 Castres, France
Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France. He was also an amateur mathematician.
His exploration of mathematics as a hobby resulted in some major developments for the field of study. He has been given credit for early developments that led to infinitesimal calculus.
He presented the notion of adequality as an approximate equivalence. This broadened the practical application for calculation.
He is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines. Finding the maxima and minuma is used in differential calculus today.
He made notable contributions to analytic geometry, probability and optics.
He is best known for his principle for light propagation and his Last Theorem in number theory.
His largest contributions to mathematics as a field were in analytic geometry and number theory.
His theorem led to the consideration of the development of exponential notation as a key contribution in either application.
------------------------
It is helpful to consider the state of education during the 17th century to understand how significant Fermat's contributions were.
Grammar, logic and rhetoric were essential to a classical education as explained in Plato's dialogues. The three subjects together were denoted by the word trivium during the Middle Ages. The trivium was fundamental to education in Latin, but the tradition of first learning those three subjects was established in ancient Greece.
The quadrivium consisted of arithmetic, geometry, music and astronomy. These followed the preparatory work of the trivium. The quadrivium was considered the foundation for the study of philosophy (sometimes called the "liberal art par excellence") and theology.
The trivium and the quadrivium comprised the seven liberal arts. The liberal arts presented instruction in the skill of thought. It was distinguished from the practical arts (such as medicine and architecture).
The Renaissance brought an increased emphasis on mathematics and science to Europe. There was period of transition from a sectarian feudal and ecclesiastical culture. There was an increase in the emphasis on a non-sectarian society.
Early Renaissance figures added mathematics to their other occupations. Luca Pacioli was a Franciscan friar who founded accounting. Niccolò Fontana Tartaglia was an invalid with a speech impediment who became a notable engineer and bookkeeper.
Gerolamo Cardano was a doctor of medicine who was also the earliest founder of probability and binomial expansion. Robert Recorde was a physician. François Viète was a lawyer.
Descartes was originally trained as a lawyer, but he acquired greater instruction in mathematics when he studied military engineering in the Netherlands.
The modern form of exponential notation was introduced by Rene Descartes in his text titled La Géométrie early in the 17th century.
Descartes is also widely regarded as one of the founders of modern philosophy. He differed from Aristotle and the revived Stoicism of the 16th century on two major points.
He rejected the splitting of corporeal substance into matter and form. Form and matter are intrinsically interconnected in substance. Aristotle had used the distinction between the two to suggest the difference between the idea of the object and the thing itself. Descartes also rejected any appeal to final ends, divine or natural, in explaining natural phenomena.
His dualism embraced the idea that mind and body are distinct but closely joined. While many contemporary readers of Descartes found the distinction between mind and body difficult to grasp, he thought it was entirely straightforward.
He employed the concept of modes as the ways in which substances exist. He explained in Principles of Philosophy that we cannot understand the mode apart from the substance. The perception of a modal form apart from its substance requires an intellectual abstraction.
Two substances are distinct when each of them can exist apart from the other.
Descartes laid the foundation for the continental rationalism that was later advocated by Spinoza and Leibniz. This was later opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley and Hume.
Leibniz, Spinoza and Descartes were well-versed in mathematics as well as philosophy. Descartes and Leibniz contributed greatly to science as well. Spinoza presented an axiomatic argument for constitutional monarchy.
Rene Descartes was born in La Haye en Touraine (now Descartes, Indre-et-Loire), France, on 31 March 1596. His mother, Jeanne Brochard, died soon after giving birth to him. He was not expected to survive. His father, Joachim, was a member of the Parlement of Brittany at Rennes.
René lived with his grandmother and with his great-uncle. Their family was Roman Catholic, but the Poitou region was controlled by the Protestant Huguenots.
The Swiss politician Besançon Hugues had been allied with John Calvin in Geneva. They sought an alliance between the city-state of Geneva and the Swiss Confederation. The label Huguenot was purportedly first applied in France to those conspirators who were involved in the Amboise (am-bwas) plot of 1560 to wrest power from the Catholic House of Guise (gees) in France.
Descartes entered the Jesuit Collège Royal Henry-Le-Grand at La Flèche (flesh) in 1607. It was late because of his fragile health. He was introduced to mathematics and physics. This included Galileo's work.
He studied for two years (1615–16) at the University of Poitiers after graduation in 1614. He earned a Baccalauréat and Licence in canon and civil law in 1616 in accordance with his father's wishes that he should become a lawyer. He moved to Paris from there.
He abandoned the study of letters. He resolved to seek knowledge from himself and the "great book of the world." He spent the rest of his youth traveling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing himself in the situations that fortune offered to reflect upon whatever came his way in order to derive the profit from it.
His ambition was to become a professional military officer. He joined the Protestant Dutch States Army in Breda under the command of Maurice of Nassau as a mercenary in 1618. He undertook the study of military engineering as established by Simon Stevin.
This is the period where he began to gain distinction as a mathematician. The study did not produce mathematicians as such. The field was subordinate to logic or physics at the time. He received much encouragement in Breda to advance his knowledge of mathematics.
He became acquainted with Isaac Beeckman, the principal of a Dordrecht school, in this way. He wrote the Compendium of Music (written 1618, published 1650) for Beeckman. Together they worked on free fall, catenary, conic section and fluid statics. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics.
Descartes was present at the Battle of the White Mountain outside Prague while in the service of the Catholic Duke Maximilian of Bavaria in November 1620. He shut himself in a room with an "oven" (probably a cocklestove) to escape the cold while stationed in Neuburg an der Donau on the night of 10–11 November 1619 (St. Martin's Day).
He had three dreams and believed that a divine spirit revealed to him a new philosophy in the room. He had formulated analytical geometry and the idea of applying the mathematical method to philosophy.
He concluded from these visions that the pursuit of science would prove to be the pursuit of true wisdom and a central part of his life's work. He saw that all truths were linked with one another. The use of logic from the discovery of a fundamental truth would open the way to all science.
He expressed the Latin "Cogito ergo sum" in his native French. It is translated to English as "I think, therefore I am."
He left the army and returned to France in 1620. He was present at the siege of La Rochelle by Cardinal Richelieu in 1627.
He went to listen to a lecture by an alchemist about a new philosophy at the residence of the papal nuncio in the fall of the same year. Cardinal Bérulle urged him to write an exposition of his own new philosophy in some location beyond the reach of the inquisition.
Descartes returned to the Dutch Republic in 1628. He joined the University of Franeker in April 1629. He enrolled at the Leiden University to study mathematics the next year under the name "Poitevan."
He wrote all his major work during his 20-plus years in the Netherlands despite frequent moves. Galileo was condemned by the Italian Inquisition in 1633. Descartes abandoned plans to publish Treatise on the World. He had been working on the publication for the previous four years.
He published parts of this work in three essays in 1637. "Les Météores" (The Meteors), "La Dioptrique" (Dioptrics) and "La Géométrie" (Geometry) took the first important steps in the description of science with math. These essays were preceded by an introduction, his famous Discours de la méthode (Discourse on the Method).
"La Geometrie" laid out the principles and mechanics for the development of analytic geometry. The base definitions and mechanics for his discovery are taught in high school algebra courses in the US. The work included the explanation of exponential notation.
Exponents are shorthand for repeated multiplication of the same thing by itself. The shorthand for multiplying three copies of the number 5 for instance is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 5^3. The notation is read as 5 to the 3d power.
The "exponent" is 3 in this example. It stands for however many times the value is being multiplied. The thing that's being multiplied is 5. It is called the "base".
Analytic geometry would become dependent upon algebraic notation with exponents to formulate the curves that were to be drawn on graphs.
Knowledge of conics had developed the first forms with exponential equations. These forms for open and closed figures were adapted for functions. Functions are graphs of equations that depict growth or diminishment.
The vertices, co-vertices and foci are related by the equation c^ 2 = a^ 2 − b^ 2. When we are given the coordinates of the foci and vertices of an ellipse, we can use the relationship to find the equation of the ellipse in standard form.
An ellipse is a modular form.
Number Theory
Fermat's Last Theorem
No three positive integers a, b and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
The Note in the Margin
It is not possible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers or in general for any number that is a power greater than the second to be the sum of two like powers. Fermat wrote, "I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."
The (Not) Proof
A centuries old math mystery may have been cracked by a Princeton professor. His colleagues estimate that only one-tenth of 1 percent of mathematicians could understand his explanation.
Did Fermat have the solution? His skill in mathematics was largely limited to his letters to friends and associates. He didn't write for the public much. His writing about math lacked exposition in certain important regards. He helped define analytic geometry with a work on the topic published before Descartes.
Fermat wrote his marginal note on exponents around 1630 when he first studied Diophantus's Arithmetica. All his other theorems were stated and restated in challenge problems that he sent to other mathematicians. He knew how to answer the special cases of n = 3 and n = 4 as challenges.The general theorem was never mentioned again by Fermat.
No one came up with an example wherein the sum of two cubes resulted in another cube. The sum of two lines can result in a sum with the same power as a line: 1^1 + 2^1 = 3^1. Any addition problem satisfies the condition. The first power is usually not written.
The sum of two squares isn't as easy, unless you count 0^2 as an option: 0^2 + 2^2 = 2^2. Any number of examples can be produced with this device. There are other solutions:
5^2 = 3^2 + 4^2
or
25^2 = 7^2 + 24^2 = 15^2 + 20^2.
There are cases where the sum of three or more cubes equals another cube, but a cube simply can't be divided in two and retain an equal length to the sides around the two halfs of the divided cube.
The lines for the object have to be equal in length by definition. The length of the divided lines will always be half of the distance for the lines that are not divided.
The consideration of geometric solids helped Fermat to rule out the possibility of higher exponential equations. The act of dividing a cube in half demonstrates that two cubes can't be added together to equal another cube. It can't be done.
While it is conceivable that the volume for two cubes could possibly be added together to equal the volume for another, such an equation hasn't been discovered. While this explanation doesn't fit the general criteria for a theoretical proof, it has yet to be disproved.
The proof has only been proved insofar as it remains in a state that has not been disproved.
Godel would eventually argue that this kind of incompleteness is the case with proofs in general. There is always some element in any argument that can not be completely proven. It justifies the attachment of the word 'theoretical' to the argument that qualifies as logically consistent enough to be called a proof.
There is something in the description of reality that defies completeness. It is as though the incompleteness is a challenge to come as close to completeness as possible without working too hard at it.
Pierre de Fermat
S. 皮埃尔德费马
T. 皮埃爾德費馬
皮 Pi skin 皮 hi pelt Pie ぴえ- ピエ- Pi 피 blood
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ma 마 hemp
-----------------------
The ethics of morality in law
has a measure in the observation of what you draw.
=================
When the sum of cubes equals a cube
Sum of Cubes equal to a Cube
wiki Trivium
wiki Quadrivium
Equations of Ellipses
wiki Pierre de Fermat
wiki History of Exponential Notation
Wolfram Fermat's Last Theorem
wiki F's Last Theorem
History of F's Last Theorem
Wiles Solution to F's Last Theorem
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