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"Allt är matematik"

brytburken — Mon, 30 Nov 2009 10:28:00 +0000

Allt är matematik. Allt är nummer, och nummer är inte något abstrakt. Enligt Pythagoras är tingen en manifestation av den numeriska strukturen inneboende i dem. Han talar om ett “levande universums andning”. Det finns en systematisk ordning som våra två ögon inte kan se, men som vi möjligen kan känna. Enligt honom och hans efterföljare är universums ordning matematisk och musikalisk, avståndet i naturen mellan de jordiska och himmelska sfärerna är ordnade likt perfekta ackordföljder. När skapelsens kroppar rör sig i samklang hörs en musik i naturen som vi uppfattar som tystnad.

(Harmoni är dock inte enbart tystnad, men även balanserat ljud, på så sätt som minimal techno väger upp oväsen från gatan, och lämnar sinnet klarare och mer rörligt.)

Nietzsche hade svårt för matematiken, och odugligförklarade den då naturen uppenbarligen inte följer någon slags decimal exakthet. För övrigt älskar naturen att gömma sig för oss, som Herakleitos sade (?) i ett av sina fragment.

Pythagoras hämtade mycket inspiration från sina resor i Indien, Persien, Babylonien, osv, vilket får en att revidera bilden av Grekland som den västerländska civilisationens vagga. Visserligen sammanställde de gamla grekerna grunden för vår vetenskap, men mycket hämtades uppenbarligen från andra högstående kulturer.

René Descartes: Milline on selle põhjus nördimus puhul

studiacartesianaestonica — Sat, 28 Nov 2009 13:15:15 +0000

Art. 127

Naer, mis mõnikord kaasneb nördimusega, on tavaliselt kunstlik ja tehtud. Ent kui see on loomulik, näib see tulevat rõõmust, mis tuleb sellest, et nähakse end suutvat kahjust, mis pahandab, puutumatuks jääda ja koos sellega, et tuntakse üllatust olevat uudsusest või kahju ootmatust osakssaamisest. Edasi viisist kuidas rõõm, vihkamine ja imestamine seda tagavad. Ometigi tahan ma uskuda, et see võib olla tekitatud ka ilma mingi rõõmuta, ainuüksi vaenulikkuse liikumisest, mis saadab põrna vere südame suunas, kus see on hõrendatud ja lükatud kopsudesse, mida veri paisutab kergesti kui kohtab peaaegu tühjust. Ja üldiselt kõik see, mis võib paisutada äkitselt kopse sellisel moel põhjustab naeru väliseid märke, välja arvatud siis, kui kurbus muudab selle ägamisteks ja karjatusteks, mis saadavad pisaraid. Mille kohta Vives[1] enesekohaselt kirjutas, et kui ta oli olnud pikka aega söömata, siis esimesed söögipalad, mis ta suhu asetas panid teda naerma, mis võis tulla sellest, et tema kopsud, olles toidu puudumise tõttu verest tühjad, olid paisusid kiiresti esimesest mahlast, mis läks maost südame suunas ja ainuüksi söömise ettekujutamine võis seda tekitada, isegi enne kui lihatükikesed, mida söödi makku jõudsid.

[1] Descartes osutabveerul: J. L. Vives, 3. de Anima. Cap. De. Risu. 1538

He Knows All the Angles

makya20 — Tue, 24 Nov 2009 09:35:43 +0000

To: Pythagoras@greece.com

From: plato@greece.com

Subject: New theorem

Dear Pythagoras,

The council has examined your new theorems. Firstly, let me reiterate that your past contributions to the world of philosophy and mathematics are greatly appreciated. Perhaps you ought to focus on your continued teaching of these past ideas, rather than obsessing with creating new theorems.

Specifically, you’re contribution – “when it comes to triangles of the right variety, b squared plus a squared is equal to c squared.” Surely you don’t think we would not notice this as a simple reorganization of your prior theorem. Ditto for “of the right triangle sort, it is always true that c squared be equal to the sums of a squared and b squared.” You had a great run, buddy, don’t push it.

เก่งเลขให้ถึงแก่น ด้วยทฤษฎีบทคณิตศาสตร์

สำนักพิมพ์ ส.ส.ท. — Mon, 16 Nov 2009 03:54:10 +0000

ทฤษฎีบท คือข้อความ (หรือสมการ) ที่พิสูจน์แล้ว ไม่ว่าใครก็ยอมรับว่าเป็นจริงและสามารถใช้ในการอ้างอิงเพื่อพิสูจน์ข้อความอื่นได้ หนังสือเล่มนี้ได้รวบรวมทฤษฎีบททางคณิตศาสตร์ที่สำคัญ ๆ และเป็นประโยชน์มากกว่า 30 ทฤษฎีบทโดยแต่ละทฤษฎีบทที่กล่าวถึงนอกจากจะมีการพิสูจน์ให้เห็นจริงแล้วยัง มีเรื่องราวความเป็นมาของตัวทฤษฎีบทและบรรดานักคณิตศาสตร์ที่ค้นพบและอยู่เบื้องหลังทฤษฎีบทเหล่านั้น ซึ่งจะทำให้ผู้อ่านได้เข้าใจถึงที่มาที่ไปและรู้สึกสนุกไปกับการเรียนรู้ ทั้งยังจะเป็นประโยชน์สำหรับการเรียนคณิตศาสตร์ในระดับสูง…มาร่วมแกะรอย และพิสูจน์ให้ถึงแก่นแท้เพื่อความเข้าใจอย่างถึงกึ๋นไปกับทฤษฎีบทคณิตศาสตร์ ที่น่าหลงใหลเหล่านี้กัน!!

ผู้แต่ง : Akimichi Sekine
แปลโดย : ดร.อรรณพ เรืองวิเศษ
เรียบเรียงโดย : ดร.บัณฑิต โรจน์อารยานนท์
จำนวนหน้า : 264 หน้า
ISBN : 9789744433848

—————————————-

สอบถามรายละเอียดเพิ่มเติมได้ที่ book4u@tpa.or.th

Liefde voor getallen

davincie — Wed, 11 Nov 2009 16:52:19 +0000

Laatst kwam ik tijdens een schoolreünie in gesprek met een oude vriend die al geruime tijd bezig is zijn eigen weg te vinden. Een boeiend gesprek volgde. Hij vertelde dat zijn leven de afgelopen jaren vol pieken en dalen was geweest.

‘Maar weet je wat het voordeel is,’ zei hij, ‘door al die ervaringen heb ik geleerd om te gaan met teleurstellingen en weet ik pieken op waarde te schatten. Ik ben baas over mijn eigen tijd en bepaal zelf wat ik doe. En weet je Vince, dat maakt mij gelukkig. Waarom zie ik maar zo weinig mensen die dat doen?’

Iedereen volgt in zijn leven zijn eigen weg. Daarop kom je uitdagingen tegen. Zolang je die niet doorziet, kom je ze vroeg of laat weer tegen. Heel frustrerend, je hebt het gevoel dat je vastloopt. Dit gevoel moet op een of andere manier worden gecompenseerd, bijvoorbeeld door overmatig werken, kopen of porno kijken. In de Volkskrant stond een T-shirt van Gummbah waarop dit treffend stond verwoord: ‘To wash your soul with porn, is to clean your glasses with shit’.

Ik ben ook lang op zoek geweest naar het hoe en waarom van het leven. Totdat ik een aantal jaren geleden stuitte op numerologie. Volgens Pythagoras vormen getallen de bouwstenen van ons universum. Alles en iedereen om ons heen kan namelijk worden uitgedrukt in getallen. Elk getal bezit unieke krachten en valkuilen. De getallen uit je naam en geboortedatum geven inzicht in bijvoorbeeld je eigen ontwikkeling en uitdagingen. Door me hierin te verdiepen, heb ik duidelijkheid en vertrouwen gekregen in mijn levensweg, heb ik een partner ontmoet die werkelijk bij me past….en de seks? Beter dan ik me ooit had kunnen voorstellen.

Saint Pythagoras

S.C. Denney — Wed, 11 Nov 2009 16:34:18 +0000

Theology and the belief in eternal and exact truth is founded in the Pythagorean theory on mathematics and metaphysics. Exact reasoning and ideals belong not to the sensible world, but to the ethereal. Nothing on earth is exactly this or that. Everything is, as Plato (a Pythagorean) said, an illusion — a shadow of the truth. This line of reasoning has been continued ever since, from Plato and the ancient philosophers to the Enlightenment thinkers to postmodern giants like Derrida. The theological endorsement of contemplating the ideal, through mathematics or philosophy, dignified the academic life and ensured that thoughts about the way things ought to be would be entertained by earth’s greatest minds.

Inovasi Animasi Matematika Kreatif Power Point: Pythagoras (Phytagoras)

apiqquantum — Wed, 04 Nov 2009 15:22:55 +0000

APIQe kembali meluncurkan inovasi terbaru berupa cara kreatif berpetualang dengan segitiga siku-siku

The Symbolic Aphorisms of Pythagoras

Christoph de la Cruz — Tue, 03 Nov 2009 04:01:00 +0000

I. Declining from the public ways, walk in unfrequented paths. By this it is to be understood that those who desire wisdom must seek it in solitude. The initiatic journey is one of isolation and exploration along paths taken by very few.

II. Govern your tongue before all other things, following the gods. Here Pythagoras warns us that words have a tendency to misrepresent our true Self. If a thought or argument cannot be articulated clearly and properly without sentimental bias or emotional clouding, it is best to remain in silence.

III. The wind blowing, adore the sound. We are reminded to take a moment to appreciate the “voice” of the elements. All things in Nature manifest through harmony, rhythm, and order and through attuning ourselves to Nature’s expressions we are confronted with the very principles of Divine law.

IV. Assist a man in raising a burden; but do not assist him in laying it down. This aphorism instructs the initiate to help those who despite their failings are industrious in attempting to better themselves or their situation, but to never assist those who seek to evade and hide from their problems. In other words, aid the diligent and not the indolent.

V. Speak not about Pythagoric concerns without light. A simple warning to not attempt to interpret the mysteries of God and embark on the initiatic path without first seeking spiritual and intellectual illumination. Furthermore, all of the initiate’s Great Work must operate in spiritual and moral alignment with the Divine.

VI. Having departed from your house, turn not back; for the furies will be your attendants. Pythagoras here warns us that once the initiatic path is taken, it must be completed to fruition. Turning back from the path of spiritual enlightenment and returning to our former ways of bestial vice and ignorance will cause one to suffer exceedingly; as stated by Iamblichus, ” it is far better to know nothing about Divinity than to learn a little and stop without learning all.” There is no place for dabblers on the initiatic path.

VII. Nourish a cock, but sacrifice it not; for it is sacred to the sun and moon. Here the cock is to be understood as a symbol of our body as well as our worldly ambitions. At face value this aphorism warns us against sacrificing living things to the gods. Life is the sacred product of the union of the masculine(Sun) and the feminine (Moon) principles of Divinity and should not be destroyed by man. As such it is also a plea against suicide. It is also an instruction for the initiate to continue to nourish his physical body and worldly ambitions and actions and not to “sacrifice” these along his journey. Giving up or sacrificing the cock is symbolic of foregoing our desire to wake in the morning, our desire to live. Even when we have reached the point to where the Universe has unveiled its mysteries and all that is physical seems trivial we should continually strive to understand the mystery of life.

VIII. Receive not a swallow into your house. This aphorism instructs the initiate to not allow drifting thoughts to flutter into his mind, nor shiftless people enter his life. The symbolism of the swallow can be interpreted as either a good or bad omen, but at all levels relates to rather material and shallow sentiments.

IX. Offer not your right hand easily to anyone. Pythagoras warns us to keep our own counsel and not offer wisdom (our right hand) to those incapable of appreciating it. Be prudent with whom you share the wisdom of the mysteries with, for, let us not forget that there are those who will indeed bite the hand that feeds them.

X. When rising from the bedclothes, roll them together, and obliterate the impression of the body. This aphorism is directed to those who have awoken from the sleep of ignorance. It instructs the awoken individual to eliminate from their recollection all memory of their former spiritual darkness. Iamblichus writes that “a wise man in passing leaves no form behind him which others less intelligent, seeing, shall use as a mold for the casting of idols.”

** The bold italic phrases are attributed to Pythagoras while my commentary following the 10 aphorisms is based on Iamblichus’ interpretation.

Plutarch’s Lives: Numa Pompilius – The Lawgiver of Rome

Ben Jackson — Wed, 28 Oct 2009 03:02:15 +0000

Many people know that Romulus and Remus, those wolf-suckled brothers, founded Rome, but what happened between them and the Roman Empire of aqueducts, Caesars, and gladiators? By Plutarch’s account, it was Numa Pompilius who used religion and clever social engineering to lay the foundations of what became the eternal city of Rome.

At the time the Romulus died (or was taken up into the heavens by a whirlwind, according to some accounts), Rome was divided between the group that settled the area with Romulus and the Sabine tribe, which said it was a colony of Sparta. Neither group wanted to be subservient to the other, so after a long discussion, the two decided that each would pick a member of the other tribe to be king. The Romans chose a Sabine, and the Sabines gave their choice to the Romans, because they wanted to have a Sabine king. The man chosen was Numa Pompilius.

Now, in the choice of Numa, we see again the idea of leadership versus command. He was chosen, Plutarch tells us, because he “disposed to virtue, which he had yet more subdued by discipline, a severe life, and the study of philosophy; means which had not only succeeded in expelling the baser passions, but also the violent and rapacious temper which barbarians are apt to think highly of; true bravery, in his judgment, was regarded as consisting in the subjugation of our passions by reason.”

Because of these traits, both groups trusted him to make the right decisions for the future of the state and so picked him to lead, rather than submitting to his command out of fear of some sanction.

On being persuaded to take office, which took some doing on the part of the Romans, Numa began to create a unified state out of Rome by remaking it in accordance with his thoughts about how an individual should lead life. In his speech to the ambassadors who came to offer him the kingship, he says these traits will like not make him a good king.

“The very points of my character that are most commended mark me as unfit to reign, — love of retirement and of studies inconsistent with business, a passion that has become inveterate in me for peace, for unwarlike occupations, and for the society of men whose meetings are but those of worship and kindly intercourse, whose lives in general are spent upon their farms and their pastures. I should by be, methinks, a laughingstock, while I should go about to inculcate the worship of the gods and give lessons in the love of justice and abhorrence of violence and war to a city whose needs are rather for a captain than for a king.”

Still, he took the job of king, and then proceeded to lay the foundations for a much greater city by giving the kinds of lessons he described. Of course, looking at it from modern eyes, it is easy to see Numa as a clever politician as well.

His first step as a king was to make a sacrifice to the gods and wait for an auspicious sign so he could ascend the throne with divine approval. Once he had that, he formally took on the job and first disbanded Romulus’s official guard, saying that he would trust the people that put their trust in him.

To Numa we owe the creation of the vestal virgins. He also created many other religious offices, including the pontifex maximus. He reorganized the Roman calendar, making December the last month, and he decreed that when the city had public processions and sacred prayers, the citizens should stop working and give their full attention to religion “free from all noises and cries that accompany manual labour, and clear for the sacred solemnity.”

“At times, also, he filled their imagination with religious terrors, professing that strange apparitions has been seen, and dreadful voices heard; thus subduing and humbling their minds by a sense of supernatural fears.”

Along with the religious efforts, Numa practiced some social engineering as well to get all the people of Rome to see themselves as Romans. As noted above, when Numa was chosen to be kind, the city residents divided themselves along tribal lines. Numa reorganized people by their trades into companies and guilds and assigned to each of them courts, councils, and religious observances. “In this manner, all factious distinctions began, for the first time, to pass out of use, no person any longer being either though of or spoken of under the notion of a Sabine or a Roman, a Romulian or a Tatian; and the new division became a source of general harmony and intermixture.”

The results of Numa’s work were that the gates of the temple of Janus, which were only open during a time of war, remained closed for 43 years, and the people of Rome and all of Italy enjoyed peace and prosperity, according to Plutarch. “Festival days and sports, and the secure and peaceful interchange of friendly visits and hospitalities prevailed all through the whole of Italy.”

Plutarch writes, “perhaps, too, there is no need of compulsion or menaces to affect the multitude, for the mere sight itself of a shining and conspicuous example of virtue in the life of their prince will bring them spontaneously to virtue, and to a conformity with that blameless and blessed life of good-will and mutual concord, supported by temperance and justice….”

By Plutarch’s account, Numa lived a life of piety and temperance. He also may have been a friend or student of Pythagoras, the philosopher and scientist who gave us the theorem about the right triangle. (As an aside, we normally think of the ancients as ignorant folk who thought the sun revolved around the earth. Plutarch tells us that the fire in the temple of Delphi was lit with a device made from mirrors that concentrated the rays of the sun, and that the Pythagoreans through that the earth moved and kept a circular motion around “the seat of fire.” In other words, the Earth revolved around the sun.)

Now, there are a variety of other reasons that this peace and goodwill may have reigned over Italy, if in fact it did, and Plutarch is not reporting a past viewed through rose-colored glasses. Crops may have been abundant, the leaders of the various tribes may have felt secure and found more profit in trade than raiding, and Plutarch does point out that as the Roman Empire grew, the gates of war were nearly constantly open. Numa does not seem to have been very interested in the growth of the Empire.

Still, I think it is important to consider the power of context. In the modern book, The Tipping Point, author Malcolm Gladwell talks about how the context in which people live can determine their behavior. As examples, he talks about Bernard Goetz, the man who shot three teens on a New York subway and the changes in the crime rate in New York City in the 1980s and 1990s. He also talks about how phenomena like suicide rates can be powerfully affect by context.

Other recent research shows that social networks can affect powerfully obesity rates and whether or not smokers quit smoking.

What this seems to point to, is that Numa may have been using these social tools to affect not only Rome, but also the city’s neighbors. The example that he set, by truly possessing the qualities he sought to inculcate in the populace, and the religious rites and ceremonies he created may have formed a very powerful context in a world devoid of mass communications.

Next Time: Comparing the Spartans – Plutarch Has Lycurgus and Numa Go Head to Head

A tiny triangle theorem

oisteing — Sun, 25 Oct 2009 12:08:01 +0000

A very small post about a tiny theorem. I found this in the excellent book Proofs without Words.

http://www.geogebra.org/en/upload/files/Norwegian/oisteing/blog/A_tiny_theorem_of_a_hypotenuse.html

Numerologie nach Pythagoras - 3

Longtide — Sun, 25 Oct 2009 10:32:14 +0000

Bevor ich zu der Deutung der Zahlen komme, möchte ich erwähnen, dass ich nicht überzeugt davon bin, dass ein System wie Dieses hier wirklich Sinn macht. Es ist faszinierend, ja, doch jede Struktur engt ein, und es ist wichtig darauf zu achten, dass man sich nicht darin verliert.
Man kann dieses System nutzen, um sich inspirieren zu lassen, um Einsichten zu bekommen, zur Unterstützung von Selbstfindungsprozessen. Die Wahrheit, so es sie gibt, liegt immer hinter der Struktur verborgen, und das Nutzen von solchen Systemen ist immer nur ein Anfang, ein Werkzeug, das mit der Zeit überflüssig werden kann, denn irgendwann ist es das Herz, das tiefer blickt.

Jede Deutung ist immer nur eine Idee, eine Möglichkeit und kann stets durch Änderung der Perspektive in völlig neuem Licht erscheinen. Jede Zahl ist fluidisch, es gibt keine Starre, jede Wirkung kann sich wandeln, jeder Bezug neu ordnen.

So ändern sich üblicherweise die Schwerpunkte der Zahlen im Laufe eines Lebens.
Es kann sein, dass sich ein Mensch in seinem Bewusstsein ganz auf die Karma Zahl ausrichtet und die restlichen Zahlen kaum wahrnimmt.
Es ist auch möglich, dass jemand aus bestimmten Gründen den Halt verliert und vorübergehend aus dem Potential der Energien der Zahlen herausfällt – dann scheinen sie keinen Sinn mehr zu ergeben, doch es ist schlicht Ausdruck von einem Verlust, von einer Destabilisierung des Menschen.
Ferner ist natürlich immer die Auflösung dieser karmischen Muster möglich – der Mensch kann die Schwingungsmuster durchbrechen und sich daraus erheben, in einem Akt der spirituellen, umfassenden Erkenntnis.

Die Bedeutung der Zahlen

die 1: Stärke, Kraft, Stabilität, Selbstvertrauen

die 2: Sensibilität, Feinfühligkeit, Schwäche, Unsicherheit

die 3: Liebe, “die kleine Liebe”

die 4: Auseinandersetzung, Herausforderung, Problem (-bewältigung), Abwehr, Schutz

die 5: Leichtigkeit, “es fällt mir leicht”, Selbstverständnis, Egoismus

die 6: Liebe, “die große Liebe”

die 7: Spiritualität, “hinter den Vorhang schauen”, Neugierde, Forscherdrang, Selbstfindung, missverstanden sein

die 8: Energie, die Mitte finden, Wechsel von “Hoch” und “Tief”, viel bewegtes Potential (man betrachte die 8 als Energiekreislauf)

die 9: Vollendung, “die vollendete Liebe”

die 11: Meisterzahl, die absolute Kraft

Ich halte die Deutung der Zahlen bewusst kurz, um nur Richtungen aufzuweisen – der Rest findet sich durch eigene Erfahrung.

Wichtig: Das Potential der 1 findet sich in der 2 wieder, das Potential der 1 und der 2 in der 3, usw
Somit ist die 9 die Vollendung, denn sie birgt das Potential aller Zahlen.

Die 11 ist eine Ausnahme, daher Meisterzahl.

Numerologie nach Pythagoras - 2

Longtide — Sat, 24 Oct 2009 14:56:05 +0000

Bedeutung der Position der Zahlen

Der Tag
Die Art, wie der Mensch wirkt.
Das bedeutet sowohl, wie Andere ihn/sie empfinden, als auch die Art und Weise, wie der Mensch mit den weltlichen/materiellen Dingen umzugehen pflegt.
Der Monat
Das Herz, die Gefühlswelt, die emotionale Wahrnehmung
Das Jahr
Der Kopf, der Verstand, das Denken, der Intellekt
Die Karma Zahl: Tag + Monat + Jahr
Die Schwingung, welche der Mensch in diesem Leben tiefer ergründet/erlebt; die Erfahrung des Selbst

Die Verbindungszahlen (umkreist) zwischen diesen Hauptzahlen nun stellen dar, inwiefern diese verschiedenen Bereiche miteinander kommunizieren, inwieweit sie sich gegenseitig unterstützen, wie sie miteinander harmonisieren.
Wie vertragen sich zB Kopf und Herz, wie interagieren sie?
(9 _ 11 _ 2)
Die 11 zeigt die Qualität dieses Weges auf.

Sowohl die beiden Verbindungszahlen, die zum Tag (hier: 1 + 3), als auch Jene, die zur Karma Zahl (5 + 3) hinführen, geben außerdem noch Auskunft über den Weg, auf welchem die unterschiedlichen Aspekte transportiert werden.

Auf welche Art kann das Potential des Herzens ins Außen gebracht werden?
(2 _ 3 _ 1)
Die 3 zeigt die Qualität dieses Weges auf.

Auf welchen Wegen bringt der Verstand den Menschen zur Erfahrung des Selbst?
(9 _ 3 _ 3)
Hier ist es wiederum die 3, die die Qualität dieses Weges vermittelt.
usw

Durch diese Aufstellung kann nun leicht die Verteilung der Energien des Menschen betrachtet werden. Oftmals gibt es klare Schwerpunkte, zB eine Dominanz des Verstandes, eine Tendenz zum Rückzug ins innere Erleben, ein starkes Identifizieren mit der materiellen Welt, usw.

Es gilt stets, die Zahlen in ihrer Gesamtheit zu betrachten – eine einzelne Zahl hat kaum Bedeutung, denn sie wird durch ihre Nachbarn unterstützt und geprägt.

Numerologie nach Pythagoras - 1

Longtide — Sat, 24 Oct 2009 11:52:16 +0000

Hier handelt es sich um eine alte Variante der Numerologie, mit den ursprünglichen Deutungen nach Pythagoras. Die Interpretationen, wie sie in neumodischeren Büchern zu finden sind gefallen mir nicht so gut, diese Version hier erscheint mir klarer, einfacher, tiefer. Soweit ich weiß, wird diese Version nicht mehr gedruckt – ich habe sie in keinem Buch gefunden.
Los geht`s:

Zum Beginn nimmt man sich ein Geburtsdatum, zb:

01.02.3456

Nun wird aus jeder Zahl die Quersumme genommen, dh:

01 = 1

02 = 2

3456 = 3 + 4 + 5 + 6 = 18 = 1 + 8 = 9

Das malt man dann wie folgt auf:

Die Zahl ganz rechts (hier die 3) ist die Quersumme aus Tag, Monat und Jahr
(T + M + J):
1 + 2 + 9 = 12 = 1 + 2 = 3

Die kleinen, umkreisten* Zahlen sind jeweils die Quersummen der beiden Nachbarzahlen.

Also:
1 _ 1 _ 9 , weil 1 + 9 = 10 = 1 + 0 = 1
1 _ 3 _ 2, weil 1 + 2 = 3
2 _ 5 _ 3, weil 2 + 3 = 5, usw

Wichtig: Die 11 ist die einzige zweistellige Zahl, die nicht reduziert wird!

2 _ 11 _ 9, weil 2 + 9 = 11
und nicht: 2 _ 2 _ 9

So entsteht der Aufbau.
Jede Zahl hat ihre Bedeutung, so wie jeder Platz seine Bedeutung hat.

_{*Ich habe diese Zahlen nur zur Kennzeichnung umkreist, zur Verdeutlichung.}

mencari sisi miring

stonelampung — Wed, 21 Oct 2009 04:37:40 +0000

mencari sisi miring bila dua sisi lain diketahui

Spring Cleaning

lisamariedemarte — Tue, 20 Oct 2009 10:28:51 +0000

The change in seasons is an ideal time to take stock of one’s habits (health or otherwise) and implement improvements where necessary.

Recently I had a realisation as I unblocked a sink… What HAD been flushed down that drain??? Evidently it was severely clogged, and my best efforts (vinegar & bicarb of soda and draino) weren’t having a lot of success! So I took apart the components and used a wire to vigourously dislodge the offending build-up. Oh my goodness… those amazing mud-packs used for skin cleansing coupled with avocado and other edenic delights, over time, had created a plug of gunk that was encased in a soapy/rubbery tube (thanks to some little children with a fascination with emptying soap into the drain!). Little wonder that the drain cleaners weren’t having much effect! The rubbery plaque enveloping the mud and created an impenetrable barrier!

Then it hit me… substitute our bodies for the sink and then it is pretty clear why our ‘pipes’ get clogged with mucus, plaque and other nasties that are the harbingers of disease.

So, to cut a long story short… this is about internal housecleaning… upping the intake of whole foods such as fruit and vegetables. For me, it is about embarking upon a 30 day challenge – a cleanse for champions as it were…

Whole food genius, Don Tolman and his son Tyler Tolman have paired up as a dynamic duo, sharing an age-old secret to assist with this exact process:

“What if nature embedded within every plant—every fruit, nut, berry, grain and seed—a unique code? A code that resonates with a specific part of your body—to help maintain harmony and balance, restore health, and banish dis-ease.”

It starts with a colon cleanse (nothing too fancy there, just a LOT of fibre and bentonite clay)… Seems to follow the principle of the blocked drain; a rubbery case will envelope the contents and then lots of water to flush it all through. Many people that do colon cleanses seem to think that this ‘rubber’ was the mucous and gunk trapped inside them. Part might be, but that would be absorbed by the bentonite clay (nothing like some mud or clay to draw out toxins). The rubbery coating just helps facilitate an easier transit through the intestines (otherwise you’d be clogged up with clay that just sits there!). No mystery, just common sense in my opinion.

Next comes ’supplementation’ with pure nutrition – whole foods in a precise ratio to maximise nutrient uptake and energy levels. I’m about to embark upon a regimen of eating “Pulse” (yes, the “Pulse” from the Bible) and by the looks of the flavours and ingredients, I’m going to be very happy and energetic!

I’ll give regular updates to talk about my experience, and more specifically the results! Anyone else keen to join me in the 30 day challenge????

For more information, below is a link to the philosphy, principles and products:



Holy Heretics
theosophywatch — Tue, 20 Oct 2009 08:54:14 +0000
IN ANY age, when doctrine becomes dogma, and when fanaticism compels lip service to exclusive group 


Numerology....A Brief History
modernintuitive — Mon, 19 Oct 2009 05:21:11 +0000
Lets start with Pythagoras: Greek philosopher, mathematician, mystic and scientist.  He is considered the Father of Math.  Remember the Pythagorean theorem from geometry class?  Trying to figure the length of a side of a right triangle?  The Babylonians had their hand in it as well, however our dear friend Pythagoras was credited with it, although not proved until after he passed.  He contributed greatly to, not only modern day mathematics, but astrology, music, philosophy, science and of course….NUMEROLOGY! 
“Know thyself, then thou shalt know the universe and God” was his constitution.  The only requirement to be a student of this great teacher, was a deep and sincere longing to learn and discover the meaning of life and of love through personal independence, and to help free the soul of religious and political confinements.  A great man if you ask me!
Pythagoras developed the concept that every number, no matter how large or how many digits, can always be reduced down to one single digit and each single digit 1-9 has a specific vibrational frequency, or energy, as I often refer to it.  Our favorite Greek philosopher believed that numbers are the measure of form and energy in the world and that the numbers 1 through 9 are symbolic representations of stages in the human life cycle. 
Lets now go forward to the early 1900’s.  Mrs. L. Dow Balliett, who was a very influential speaker in the New Age Thought Movement, took on Pythagoras’ theories and is credited with bringing Numerology to the Western world.  Her teachings were spiritual in nature, and focused on allowing people to realize themselves as divine beings.  Being the enigmatic woman that she was, she became a profound influence over many including a Dr. Julia Seton, who is the mother of Dr. Juno Jordan.  Now, Dr. Julia Seton is responsible for turning the “study of numbers” into what we call it today….NUMEROLOGY!
Now let’s go to Dr. Juno Jordan, daughter of Dr. Julia Seton, and The California Institute of Numerical Research.  Dr. Juno Jordan graduated from the Denver Dental College in 1905…..yes, she was a dentist…..but she took more towards the spiritual side studying the occult and metaphysics and making strides in bringing Numerology to a more respected study in the Western world.  She created the California Institute of Numerical Research, and along with a group of women, researched and studied every aspect of Numerology.  For 25 years, Dr. Juno Jordan and her colleagues got together weekly to test, prove and dis-prove every phase of the science of names and numbers. 
Every respected numerologist today has their studies and work based upon the information these women of the California Institute of Numerical Research have found and proved.  Most notably, Dr. Juno Jordan, who continued on teaching and writing about Numerology until she passed in 1984, just short of her 100th birthday.
These are not only the leaders in the field of Numerology, but they have helped define and shape the beautiful science behind names and numbers.  This amazing concept helps people have a better understanding of who they are and the kind of life they have to live. 
It is a science, it is an art and it is an honor to study, teach and help others with this astounding practice.  If you would like a Numerology chart made for yourself or someone you know, please contact me through my website www.modernintuitive.com.
Namaste



Pythagoras and his theorem
sayingenough — Mon, 12 Oct 2009 09:07:22 +0000
Numbers are all around us. They’re in the food we eat – “4 table spoons of sugar, 250g of butter, etc.” They’re on our television screens – the TV show Numb3rs is about a mathematical genius, Charlie Eppes who helps his brother, FBI Special Agent Don Eppes, solve cases using numbers. They’re in Pop music too, without numbers, we wouldn’t have our top 100 hits charts, and artists wouldn’t be able to get their songs to No.1.
And not to mention telephone numbers. Without numbers, maybe telephones and mobiles phones will use pictures to identify a person? – “Oh sorry, I called you by mistake; I wanted to call your twin, so sorry.” But a part of what makes numbers so very important is our age. Without numbers, we wouldn’t know when we were born, or how old we are.
Now another good thing about numbers (or a bad thing about numbers depending on you) is math. Math, like numbers, is terribly useful and can be used to find the areas of triangles and other important things like that.
If you have studied math before, no doubt you would have heard of the Pythagorean Theorem. Which is the formula for finding the area of a right angled triangle:  a² + b² = c². What that means, is a², or the height of the triangle, multiplied by b², the base of the triangle, equals c², the hypotenuse of the triangle. See the diagram below for a clearer view.

Pythagoras' Theorem
This mathematical formula is a priceless and significant part of math as we know it today. So who could have been so clever to think up this formula? None other than a man called Pythagoras.
Pythagoras and math
Pythagoras (c. 570 BC – c. 495 BC) was a Greek mathematician, musician, philosopher and scientist. He was a significant part of the development of math, yet not much is known about him as none of his writing has survived. Though he didn’t leave behind any great writings, he left behind a way of life. His disciples called themselves the Pythagoreans.
The Pythagoreans were a select and secretive group and were divided into two groups merely on the base of their interest. One of them were called the akousmatikoi (“listeners”), who were focused more on the religious side of Pythagoras’ teachings, and the other were the mathēmatikoi (“learners”) who were focused more on of the scientific and mathematical side of Pythagoras’ teachings.

A bust of Pythagoras himself.
Nonetheless, the Pythagoreans in general adored numbers, and believed them to be the building blocks of life. They believed that each number had their own personality, and that the explanation for something existing could be explained through numbers.
But becoming a disciple of Pythagoras the man supposedly “sent from the gods”, was a very long process. The applicant’s charter, habits, feelings, words, actions and their way of life in general would be examined by Pythagoras himself, and only if they passed successfully would they be accepted into his school.
If they succeeded, they would then have to give all their property to the school, as everything was held in common. Then, for the next three years, they would have no vote in proceedings, and no medical treatment. And after that, they were required by the school to observe silence for five years, with the aim of training them to tame themselves, first to listen and then to attain wisdom.
If after those long eight years or so the pupil was considered unsuitable, he would be expelled and all his property returned. But, despite the risk of being expelled after all the hard work put in, many people from all over the region flocked to Pythagoras’ school, with hopes of learning from the great master himself.

Pythagoras is the bald one in the middle. He is teaching his disciples music.
Pythagoras and music
 
Pythagoras not only discovered his famous theorem, but he also discovered the overtone series, which is what you hear on a modern piano today.
It is said that one day Pythagoras was passing by a blacksmiths workshop and he noticed the various harmonies coming from the blacksmiths shop. Later, he went back to investigate, and found that the different tones that came from the blacksmiths hammer when it hit the metal changed according to the weight of his anvil.
Pythagoras was intrigued. He experimented and found that by plucking a string one foot long it vibrates x times per second, and by plucking another piece of string two feet long, it vibrates 2x per second, but at the same pitch. Thus, plucking both strings simultaneously or one after the other, creates an octave.
After further experimenting, Pythagoras found that by dividing one of the strings into halves, thirds, quarters, or fifths of the original length while keeping the other string the same length and then plucking in a similar fashion created an octave, a perfect fifth, and a major third respectively. To hear the differences click here.
This discovery was very important to Pythagoras, for he realised that these tones played musically and in the right sequence on an instrument could change the behaviour patterns of a person and accelerate the healing process.
Pythagoras’ discovery of music prompted the opening of a Pythagoras Graduate School of Music and Sound Research in Finland, and focuses more on the academic side of music and less on the performance side. Their main research fields are:

Musical acoustics and sound      processing
brain research
music theory
psychology of music
media design

Pythagoras’ significant discovery lent further proof to the belief of the Pythagoreans: that everything, including music, was fundamentally made out of their beloved numbers.



The Golden Verses of Pythagoras
Seti — Wed, 07 Oct 2009 02:28:36 +0000





(Note: This work is attributed to Pythagoras, but is presumed to be attributed to him as was the Pythagorean custom.)
1. First worship the Immortal Gods, as they are established and ordained by the Law.
2. Reverence the Oath, and next the Heroes, full of goodness and light.
3. Honour likewise the Terrestrial Dæmons by rendering them the worship lawfully due to them.


4. Honour likewise thy parents, and those most nearly related to thee.
5. Of all the rest of mankind, make him thy friend who distinguishes himself by his virtue.
6. Always give ear to his mild exhortations, and take example from his virtuous and useful actions.
7. Avoid as much as possible hating thy friend for a slight fault.
8. [And understand that] power is a near neighbour to necessity.
9. Know that all these things are as I have told thee; and accustom thyself to overcome and vanquish these passions:–
10. First gluttony, sloth, sensuality, and anger.
11. Do nothing evil, neither in the presence of others, nor privately;
12. But above all things respect thyself.
13. In the next place, observe justice in thy actions and in thy words.
14. And accustom not thyself to behave thyself in any thing without rule, and without reason.
15. But always make this reflection, that it is ordained by destiny that all men shall die.


16. And that the goods of fortune are uncertain; and that as they may be acquired, so may they likewise be lost.
17. Concerning all the calamities that men suffer by divine fortune,
18. Support with patience thy lot, be it what it may, and never repine at it.
19. But endeavour what thou canst to remedy it.
20. And consider that fate does not send the greatest portion of these misfortunes to good men.
21. There are among men many sorts of reasonings, good and bad;
22. Admire them not too easily, nor reject them.
23. But if falsehoods be advanced, hear them with mildness, and arm thyself with patience.
24. Observe well, on every occasion, what I am going to tell thee:–
25. Let no man either by his words, or by his deeds, ever seduce thee.
26. Nor entice thee to say or to do what is not profitable for thyself.
27. Consult and deliberate before thou act, that thou mayest not commit foolish actions.


28. For it is the part of a miserable man to speak and to act without reflection.
29. But do that which will not afflict thee afterwards, nor oblige thee to repentance.
30. Never do anything which thou dost not understand.
31. But learn all thou ought’st to know, and by that means thou wilt lead a very pleasant life.
32. in no wise neglect the health of thy body;
33. But give it drink and meat in due measure, and also the exercise of which it has need.
34. Now by measure I mean what will not incommode thee.
35. Accustom thyself to a way of living that is neat and decent without luxury.
36. Avoid all things that will occasion envy.
37. And be not prodigal out of season, like one who knows not what is decent and honourable.
38. Neither be covetous nor niggardly; a due measure is excellent in these things.
39. Do only the things that cannot hurt thee, and deliberate before thou dost them.


40. Never suffer sleep to close thy eyelids, after thy going to bed,
41. Till thou hast examined by thy reason all thy actions of the day.
42. Wherein have I done amiss? What have I done? What have I omitted that I ought to have done?
43. If in this examination thou find that thou hast done amiss, reprimand thyself severely for it;
44. And if thou hast done any good, rejoice.
45. Practise thoroughly all these things; meditate on them well; thou oughtest to love them with all thy heart.
46. ‘Tis they that will put thee in the way of divine virtue.
47. I swear it by him who has transmitted into our souls the Sacred Quaternion, the source of nature, whose cause is eternal.
48. But never begin to set thy hand to any work, till thou hast first prayed the gods to accomplish what thou art going to begin.
49. When thou hast made this habit familiar to thee,
50. Thou wilt know the constitution of the Immortal Gods and of men.


51. Even how far the different beings extend, and what contains and binds them together.
52. Thou shalt likewise know that according to Law, the nature of this universe is in all things alike,
53. So that thou shalt not hope what thou ought’st not to hope; and nothing in this world shall be hid from thee.
54. Thou wilt likewise know, that men draw upon themselves their own misfortunes voluntarily, and of their own free choice.
55. Unhappy that they are! They neither see nor understand that their good is near them.
56. Few know how to deliver themselves out of their misfortunes.
57. Such is the fate that blinds mankind, and takes away his senses.
58. Like huge cylinders they roll to and fro, and always oppressed with ills innumerable.
59. For fatal strife, innate, pursues them everywhere, tossing them up and down; nor do they perceive it.
60. Instead of provoking and stirring it up, they ought, by yielding, to avoid it.


61. Oh! Jupiter, our Father! if Thou would’st deliver men from all the evils that oppress them,
62. Show them of what dæmon they make use.
63. But take courage; the race of man is divine.
64. Sacred nature reveals to them the most hidden mysteries.
65. If she impart to thee her secrets, thou wilt easily perform all the things which I have ordained thee.
66. And by the healing of thy soul, thou wilt deliver it from all evils, from all afflictions.
67. But abstain thou from the meats, which we have forbidden in the purifications and in the deliverance of the soul;
68. Make a just distinction of them, and examine all things well.
69. Leaving thyself always to be guided and directed by the understanding that comes from above, and that ought to hold the reins.
70. And when, after having divested thyself of thy mortal body, thou arrivest at the most pure Æther,
71. Thou shalt be a God, immortal, incorruptible, and Death shall have no more dominion over thee.





The illusion of knowing is the major obstacle to discovery
adonis49 — Mon, 05 Oct 2009 08:45:08 +0000
The illusion of knowing is the major obstacle to discovery; (October 4, 2009)
 
            Even a century ago, a scientist published a single manuscript after a life time of research and toiling; transmission of opinions and suggestions were sent via long erudite letters by peers. Translators of these remarkable books didn’t go unnoticed and were rewarded academically. Nowadays, any “respectable” scientist works for several institutions, private and public, and at various nations.  Two centuries ago, scientists did not need to refer to Pythagoras or Archimedes.  Modern scientists have no time to refer to Copernicus, Galileo, Newton, Laplace, Lavoisier, or Kelvin; soon Einstein and Heisenberg will be outmoded.
            The team of the geeks in “Sciences and Future” met in August for brainstorming in “pause mode” to deliberate on the unique question “In the last few decades, what discoveries were true breakthroughs?”  The team reached an understanding on five scientific fields: climatology, neuroscience, astronomy, cellular biology, and Internet. Consequently, I will answer a few of the questions that you might think you know in these fields so that our knowledge is no longer an illusion.
 
The internet shifts from the virtual to the real
            There are three generations of internet or Web. The first generation or Web1.0 was created from 2003 to 2005 and is represented by MySpace, Facebook, and YouTube that gathers people on common interest social aspects or making “friends”.  The second generation or Web 2.0 is represented by Twitter or the microblogging platform for messages restricted to 140 characters. Thus, these micro messages can be regrouped and analyze to constitute a story contributed by many Twitter bloggers.  The third generation of Web 3.0 is ready technologically; this generation is already labeled object oriented intelligence sources.  For example, you record a message on your cell phone and then stick a yellow sticker on a wall or an object. The next visitor will pass his cell phone over the sticker and copy your message of whatever you have seen or appreciated. This generation can zip all kinds of products and gather intelligence and compare with other resources.  Personally, I think that even the Twitter is already a perfect source of information by intelligence agencies; these centers can hire thousands of Twitter users and direct them on specific topic of interests in many countries.
 
Cells can be rejuvenated to its embryo stage
            The lab technician would take samples of your skin. The skin cells can be treated to reach its first born state.  Whatever genetic diseases that cell inherited it will take another 30 years for the disease to emerge.  All the while you are thirty years younger. Better, skin cells can be treated to isolate a specific cell for any body member like liver, heart, brain, or whatever.  The sick tissue in any part of your body can be rejuvenated within a month. This biomedical technique of treating adult cells into embryo state was made possible because many laws prohibited using fetus embryo on the ground that the cell belonged to another person.
 
Is man’s activity altering nature more than geophysics?
            Man feared the return of the ice age; it turned out that the climate is getting hotter and the poles are melting.  The emergence of urban and industrial societies as a geophysical force is altering the environment power for rejuvenation according to human threshold for survival.  Since 1824, Joseph Fourier theorized that gases in the atmosphere have the potential to increase surface temperature. Even in 1896, John Tyndall predicted that the concentration of CO2 will increase temperature to 5 degrees by the end of the 20^th century. Now, this is a fact and each year the casualties in man and nature are increasing by the violence of climatic changes. People are waiting anxiously the international summit on the environment in Copenhagen this December. Awareness of man effective participation in climatic changes was proven when the ozone layer of O3 in the stratosphere was depleting. Seas level is increasing 3 mm a year since 1993.  So far, only Danemark produces the fourth of its power using eoliens or wind turbines.
            Ex-President Bush Junior said in 1992: “The American way of life is not negotiable.” The philosopher Michelle Serres said in 1990: “This world that we treated as an object is returning as a subject; capable of vengeance.”  The humorist Coluche said: “For an ecologist to be elected as President then trees should be allowed to vote.”
 
The brain is in perpetual re-structuring
            There are specialized neurons that can be activated when an action is executed or when an action is also observed (mirror neurons).  These mirror neurons are the biological basis for empathy, imitation, and training; almost every decision is influenced by our emotions.  Neurons have the potential to flow or transfer from one brain to another when recycling cognitive aptitudes such as reading and writing are elevated.  Neurons and connections are modified when training tasks are memorized.
            We have 8 varieties of intelligence; mainly the visual, spatial, naturalist, logic-mathematics, corporal, musical, inter-personal, and intra-personal intelligences. The new battery of experiments for testing cognitive and movements capabilities are designed to account for our eight kinds of intelligences. It is the quantity of synapses (connections) and not the weight of the brain that differentiate among the various intelligences. There are phases in our sleep when brain activities are most intense while muscular activities are extremely inhibited; this phase is called “paradox sleep”.  We produce new neurons at every stage of growth, especially in the hippocampus and the smell brains. Almost 10% of our synapses are established when we are born and they increase with our activities and cognitive demands (efforts, mental and physical, mean increase in fresh synapses and neurons).
 
Hormones or chemical messengers for the brains   
 
            Serotonin is a chemical messenger to the brains; it is implicated in sleep, feeding and sexual habits. A decrease in its production is associated to depressive moods. Anti-depressant drugs increase the concentration of serotonin in the blood.
 
            Dopamine is a chemical hormone that controls movements, moods, addiction, and the circuit of pleasure; its deficiency generates rigidity in the muscles which is the symptoms of Parkinson disease.
 
            Adrenaline is a chemical hormone that is secreted at moments of stress and is attached on large numbers of receptors to re-enforce cardiac functions, accelerate the heart beats, elevate arterial pressure, inhibit digestion and increase the level of glycemy.
 
            Cortisol is secreted in moments of stress to increase the rate of glucose in the blood stream and liberating energy to counter dangers.
 
            Insulin enhances the stock of glucose in the tissues and thus decreases glycemy.
 
            Acetylcholine is a neuro-transmitter that excites the targeted brain when acquiring new training and for enhancing memory; its deficiency is the origin of Alzheimer disease.
 
            Erythropoietin stimulates the synthesis of red blood cells; its deficiency results in anemia.  The word “doping” is related to sport competitors abusing of this hormone.



Magical 7 again
horse11 — Thu, 01 Oct 2009 13:35:38 +0000
28/9寫了篇關於”7″的文章，30/9參加一個talk，來自新加坡的靈療師Ann Tay忽然問我生日有沒有7字？我回答沒有。”This year you will


Ist Gott eine Zahl?
sirhanselot — Wed, 30 Sep 2009 20:49:59 +0000

Eine interessante Doku (wenn auch etwas outdated, vor allem was die Erfoschung des Bewusstseins sowie die Animationen und Effekte angeht) über Griechen, Gott, Mathematik und deren Zusammenhänge mit der Realität, den Gedanken und dem Bewusstsein des Menschen und nicht zuletzt die Frage was Fraktale mit all dem zu tun haben!




Taliban squared + LeT squared > ISI squared
churumuri — Fri, 25 Sep 2009 07:34:24 +0000
E.R. RAMACHANDRAN writes: The telephone rang in the middle of the night. Pythagoras (570-495 BC) woke up with a start but did not know what to do or how to stop the noise.
Euclid was equally puzzled.
Luckily Srinivasa Ramanujan was around. He asked Pythagoras to lift the hand set, say ‘Hello’ and listen to the voice first and then speak, if need be.
“Hello!”
“Hello! Is it janaab Pythagoras?”
“Yes, it is. What do you want?”
“Listen. We need more proof for your theorem of the right-angled triangle. Without that, we cannot teach your theorem in our schools any more.”
“May I know who is speaking, please?”
“Pytho-saab, I am Shah Mehmood Quereshi, foreign minister of Pakistan. Our secondary school board chief and President, Asif Ali Zardari, feel your theorem lacks irrefutable clinching proof. Do you understand? Irrefutable clinching proof. Without that I am afraid we will have to drop your theorem from our schools and madrassas.”
“Pakistan? Zardari? Madrassa? Are these new theorems? My theorem simply states: ‘The sum of the areas of the two squares of a right angled triangle is equal to the square of the hypotenuse’. I have proved it myself and I believe there are around 80 proofs for my theorem now. I don’t understand what your problem is.”
“Pytho-ji. Please understand. We in Pakistan need more proof that would hold good even in court… By the way, has the United Nations approved your theorem?”
“Mr Quereshi, you cannot make a triangle with just two sides. This is elementary geometry. You must have a third side to make it a triangle and call it UNO or something like that.”
“I was using a short form of UNO. Anyway, I will call you again tomorrow. If you want your theorem should be taught in our schools, you will have to provide more conclusive, clinching proof. Otherwise, we will drop your theorem from our curriculum. Do you understand?”
“Yes.”
“Khuda hafiz.”
***
Pythagoras did have Euclid, Garfield and Ramanajan with him for company. But none of them could think of irrefutable clinching evidence which could be used in Quereshi’s courts, schools, madrassas etc. Finally they found someone who felt he could satisfy Quereshi.
Pythagoras was relieved.
Next day when the call came, Pythagoras was ready.
“Do you have conclusive proof now?” asked Mr Q.
“Yes. Note down please. As you know, my theorem is: A squared + B squared = C squared.  I have modified the theorem for you. You can now read the theorem as: Taliban squared + LeT squared = ISI squared. where ISI is equal to members of Inter-Service Intelligence, and Taliban and LeT is equal to the terrorists.  This in a way describes your country too. I hope your President and students will be able to understand the theorem better and follow the proof I have given earlier.”
“Thank you Mr Pythagoras, now it is pretty clear you have been decorated with the nishaan-e-Greece. I get the complete picture.  I can also use it for the 26/11 Bombay seige. We are unable to prosecute some of our people for lack of irrefutable, clinching evidence. By the way, who helped you with the modified theorem? Some South Indian, I suppose?”
“No, no. These Indians are still happy finding water on the moon! It was your countryman General Zia-ul-Haq who helped. He explained the various forces that operate in your country. This helped me to modify my theorem.  If you know how many Talibans and LeT are there with you, you can easily calculate the number of ISI in your government It is just the square root of Taliban squared plus LeT squared. General Zia was confident this will help you a lot. Is this so?”
“Yes, it will.”
“If you know any two, you can calculate the third.”
“Now your theorem makes sense. QED.  We will use the modified theorem. Thanks again, Pythagoras saab“.
“Hang on, there is a corollary to my theorem. I understand the position in Pakistan is always rather acute. If that is so, Taliban squared + LeT squared will always be greater than ISI squared. Got it?”
“Yes. Thank you Mr Pythagoras. Khuda hafiz.”
“Take care, my friend.”



Ethics: Delphi, Solon, and Pythagoras - Discuss!
alexandrabond — Fri, 25 Sep 2009 07:04:10 +0000
This discussion continues from On Ethics, Defense, and Spirituality…
I was asked in a comment what I think of the Delphic Maxims in comparison with Solon’s “Commandments” or the Golden Sayings of Pythagoras.
The Delphic Maxims are wide and varied, but share aspects with Solon’s Commandments and the Golden Sayings of Pythagoras.  Here are some things they share in common…

There are significant differences between the three sources.  Pythagoras lists avoidance of consuming meat among his sayings, yet this is not mentioned by Solon or Delphi.  Whereas Solon has an interesting point about how to make recommendations: “When giving advice, do not recommend what is most pleasing, but what is most useful” and Delphi recommends: “If you are a stranger act like one (Ξepsilon;νος ων ισθι)”.
What these sources have in common provides valuable insight into the most emphasized values in antiquity.

Delphi: “Crown your ancestors”. (Προγονους στεφανου) <—> Solon: “Have regard for your parents.” <—> Pythagoras: “Honour likewise thy parents, and those most nearly related to thee.”

The common theme here is honoring ones parents and ancestry.  By extension, Delphi emphasizes respect for the dead “Do not make fun of the dead (Επι νεκρω μη γελα)” & “Do not wrong the dead (Φθιμενους μη αδικει)” & Respect the elder (Πρεσβυτερον αιδου).  Revere who came before, especially those responsible for your birth (ancestors).

Delphi: “Guard friendship. (Φιλιαν φυλαττε)” & Despise a slanderer (Διαβολην μισει) & Honor good men (Αγαθους τιμα) <—> Solon: “Do not be hasty in making friends, but do not abandon them once made.” & “Do not associate with people who do bad things.” <—> Pythagoras: “Of all the rest of mankind, make him thy friend who distinguishes himself by his virtue.”

The connection is harder to see between Delphi and Pythagoras and Solon, but with the emphasis on living honorably throughout the Maxims and praising those who behave virtuously and despising those who don’t behave well, that implies the three share a common thread.  Solon perscribes “Do good things.” and Pythagoras recommends “Do nothing evil, neither in the presence of others, nor privately” as well as “And if thou hast done any good, rejoice.”  All three sources emphasize association with honorable people, making them your friends, cultivating that friendship, and protecting it.
Aside: on protecting friendship, that requires one to defend friends from enemies. See On Ethics, Defense, and Spirituality.

Delpi: Worship the Gods. (Θεους σεβου) <—> Solon: “Honor the gods.” <—> Pythagoras: “First worship the Immortal Gods, as they are established and ordained by the Law.”

In any relationship, there is give and take.  We give sponde, choe, offerings, and sing the praises of the gods in an attempt to reciprocate the much more valuable gifts They bestow upon us.  That is why we honor the gods first, because our relationship with them is the strongest, and therefore, most important.  Solon, Delphi, and Pythagoras all make this an imperative.
The Hellenic Polytheistic culture emphasizes community.  To build a community, one must associate with friends (carefully chosen) who are worthy of defense and will likewise defend in turn.  Reciprocity is key in friendship, as it is in the guest-host relationship and hospitality (Delphi: “Give back what you have received (Λαβων αποδος)”.  But above all, one must honor the gods, because our connection with Them is the most sacred and timeless of all and demands the most back.  Without Hestia, there is no hearthfire for the oikos or polis at large to gather around.
Asides:

There are also values that are surely outdated and not suited for a modern Hellenic Polytheist, such as Delphi: “Rule your wife (Γυναικος αρχε)”.  As always, I ascribe to the practice of treating reconstruction like rebuilding (and remodeling) a house.  It will probably need new amenities, even if the general style is like that of the house that was.  We have to live in it, after-all.
For a good read on contrasting Athenian with Hebrew codes of ethical conduct, I recommend Richard Carrier’s article The Real Ten Commandments contrasts Solon’s Commandments with Moses’s Ten Commandments is a fascinating article. He wrote it in response to those who claim that the Ten Commandments of Moses were the founding of Western Morality.