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Old February 21st, 2017, 04:15 PM   #1
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Meaning and Intellectual Beauty

'
The vast number of "uh's" (that is, the "schwa" sound) in the unaccented syllables of English leads to certain sensitivities to expression which foreign speakers find very difficult to master. Spoken English words are very "fuzzy;" it is very easy to hear them in several different ways and make associations with a variety of other words and meanings. That is why English speakers are more prone to making puns than most continental Europeans. Foreigners often find English speakers vague and imprecise; part of the reason is that we are constantly moving around in a fog of associations in what we say. English also lacks the grammatical structures of declension and conjugation which make most other Indo-European languages more certain and precise in their expression. This is all very good for poetry, but has disadvantages in everyday, practical communication.

As an example, consider this little story: If most native English speakers hear it read aloud in normal, unaccented English, they immediately know what it is and what it is about, for it is a story which they have often heard. I wager that most foreigners, no matter how good their English is, will be at sea as to what is going on! In a couple of days, I will provide a "translation" which indicates how most English speakers hear the story:

Ladle Rat Rotten Hut

The above site also has the story read aloud.

LADLE RAT ROTTEN HUT

Wants pawn term, dare worsted ladle gull hoe lift wetter murder inner ladle cordage, honor itch offer lodge dock florist. Disk ladle gull orphan worry ladle cluck wetter putty ladle rat hut, an fur disk raisin pimple colder Ladle Rat Rotten Hut.

Wan moaning, Rat Rotten Hut's murder colder inset, "Ladle Rat Rotten Hut, heresy ladle basking winsome burden barter an shirker cockles. Tick disk ladle basking tutor cordage offer groin-murder hoe lifts honor udder site offer florist. Shaker lake! Dun stopper laundry wrote! An yonder nor sorghum-stenches, dun stopper torque wet strainers!"

"Hoe-cake, murder," resplendent Ladle Rat Rotten Hut, an tickle ladle basking an stuttered oft. Honor wrote tutor cordage offer groin-murder, Ladle Rat Rotten Hut mitten anomalous woof. "Wail, wail, wail!" set disk wicket woof, "Evanescent Ladle Rat Rotten Hut! Wares are putty ladle gull goring wizard ladle basking?"

"Armor goring tumor groin-murder's," reprisal ladle gull. "Grammar's seeking bet. Armor ticking arson burden barter an shirker cockles."

"O hoe! Heifer blessing woke," setter wicket woof, butter taught tomb shelf, "Oil tickle shirt court tutor cordage offer groin-murder. Oil ketchup wetter letter, an den - O bore!"

Soda wicket woof tucker shirt court, an whinny retched a cordage offer groin-murder, picked inner widow, an sore debtor pore oil worming worse lion inner bet. Inner flesh, disk abdominal woof lipped honor bet an at a rope. Den knee poled honor groin-murder's nut cup an gnat-gun, any curdled dope inner bet.

Inner ladle wile, Ladle Rat Rotten Hut a raft attar cordage, an ranker dough belle. "Comb ink, sweat hard," setter wicket woof, disgracing is verse. Ladle Rat Rotten Hut entity bet rum an stud buyer groin-murder's bet.

"O Grammar!" crater ladle gull, "Wood bag icer gut! A nervous sausage bag ice!"

"Battered lucky chew whiff, doling," whiskered disk ratchet woof, wetter wicket small.

"O Grammar, water bag noise! A nervous sore suture anomalous prognosis!"

"Battered small your whiff," insert a woof, ants mouse worse waddling.

"O Grammar, water bag mousy gut! A nervous sore suture bag mouse!"

Daze worry on-forger-nut gulls lest warts. Oil offer sodden, throne offer carvers an sprinkling otter bet, disk curl and bloat-thursday woof ceased pore Ladle Rat Rotten Hut an garbled erupt.

Mural: Yonder nor sorghum stenches shut ladle gulls stopper torque wet strainers.

.

Last edited by numan; February 22nd, 2017 at 01:10 PM.
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Old February 22nd, 2017, 01:14 PM   #2
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.LITTLE RED RIDING HOOD

Once upon a time, there was a little girl who lived with her mother in a little cottage on the edge of a large, dark forest. This little girl often wore a little cloak, with a pretty little red hood, and for this reason people called her Little Red Riding Hood.
One morning, Red Riding Hood's mother called her and said: "Little Red Riding Hood, Here is a little basket, with some bread-and-butter and sugar cookies.
Take this little basket to the cottage of your grand-mother who lives on the other side of the forest.
Shake a leg! Don't stop along the road; and under no circumstances, don't stop to talk with strangers."
"Okay, mother," responded Little Red Riding Hood, and took the little basket and started off.
On the road to the cottage of her grand-mother, Little Red Riding Hood met an enormous wolf.
"Well, well, well," said this wicked wolf, "If it isn't Little Red Riding Hood! Where's our pretty little girl going with her little basket?"
"I'm going to my grand-mother's," replied the little girl.
"Grand-ma's sick in bed. I'm taking her some bread-and-butter and sugar cookies."
"Oh, ho! Have a pleasant walk," said the wicked wolf, but he thought to himself, "I'll take a short-cut to the cottage of her grand-mother. I'll catch up with her later, and then ---- Oh, boy!"
So the wicked wolf took a short-cut, and when he reached the cottage of the grand-mother, he peeked in the window and saw that the poor old woman was lying in her bed. In a flash, this abominable wolf leaped on her bed and ate her up.
Then he pulled on the grand-mother's night-cap and night-gown, and he curled up in her bed.
In a little while, Little Red Riding Hood arrived at the cottage and rang the door-bell.
"Come in, sweet-heart," said the wicked wolf, disguising his voice.
Little Red Riding Hood entered the bed room and stood by her grand-mother's bed.
"Oh, Grand-ma!" cried the little girl, "What big eyes you've got! I never saw such big eyes!"
"Better to look at you with, darling," whispered this wretched wolf, with a wicked smile.
"Oh, Grand-ma! What a big nose! I never saw such an enormous proboscis!"
"Better to smell you with," answered the wolf, and his mouth was watering.
"Oh, Grand-ma! What a big mouth you've got! I never saw such a big mouth!"
These were the unfortunate girl's last words. All of a sudden, throwing off the covers and springing out of bed, this cruel and blood-thirsty wolf seized Little Red Riding Hood and gobbled her up.
Moral: Under no circumstances should little girls stop to talk with strangers.


.
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Old February 22nd, 2017, 01:19 PM   #3
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Have you gone through some kind of metamorphosis?

just curious

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Old February 22nd, 2017, 01:25 PM   #4
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'
More is involved here than an amusing word game. There is a deep and subtle philosophical point: Where is the dividing line between normal, permissible variation in speech or writing (or for that matter, in any pattern or form) and a regime in which we must say that cryptological analysis is necessary? I hope that the story of "Ladle Rat Rotten Hut" strongly suggests to the reader that, ultimately, no firm-and-fast dividing line is possible. In fact, for a computer, the cryptological analysis in Edgar Allan Poe's story, "The Gold Bug," would be far easier to accomplish than a correct reading of "Ladle Rat Rotten Hut." A relatively simple, mechanical, mathematical algorithm would suffice for Poe's coded message; but it is very difficult to imagine that a computer, ever, could unriddle the story of "Ladle Rat Rotten Hut." The problem is very far beyond the capabilities of any electronic speech-recognition system which presently exists. Certainly any computer which could solve the enigma of "Rat Rotten Hut" would be inconceivably more complex and sophisticated than any we might imagine today.

Westerners seem to have a fundamental limitation in their thought due to their extremely egoistic way of thinking. All too often they fall into the fallacy of thinking,
"I am the master of my fate:
I am the captain of my soul."

And even if they are not quite that insane, they still tend to feel that every phenomenon is isolated, complete, existent in and of itself. Such an attitude is, of course, absurd; but it is a current which runs throught the warped thinking of most Westerners.
Is "Ladle Rat Rotten Hut" gibberish, or is it an easily understandable variant of the story "Little Red Riding Hood?" That depends on the mind which is reading the story. It should be obvious that a volume of the Encyclopaedia Britannica, here in my library, is quite different from the same volume transported to Tang Dynasty China, or teleported to the hyper-dimensional plasma-beings of planet Qwerty.

In 1901 the German writer, Kurd Laßwitz, wrote a short story entitled, "Die Universalbibliotek." Here is a link to an on-line copy:

Die Universalbibliothek von Kurd Laßwitz - Text im Projekt Gutenberg

His story of a Universal Library was improved upon by Jorge Luis Borges in his short story, "The Library of Babel," on-line version at:

http://jubal.westnet.com/hyperdiscor..._of_babel.html

In the Library of Babel, every book is a random jumble of letters, spaces and typographical symbols. Any possible combination of symbols will occur on some line, page or book somewhere in the library. One must travel light-years to discover a single, grammatical sentence of English. Yet not a single sentence in the library is without a clear and distinct meaning. For there are an infinite number of possible languages, and the grammars and manuals of instruction for those languages must all exist in an infinite library, and each sentence in the library will have one or many meanings in certain languages. Even a sentence consisting of "aaaaaaaaaa...." will have a meaning in some cryptological code, and that code will be explained in one or more volumes somewhere in the library.
It is a corollary of the mathematical proofs of Georg Cantor that although the Library consists of an almost infinite number of books distributed in a disorder of infinite extent, this infinity is exceeded by the hyper-infinity of the languages and codes which explicate even a single volume of the Library ---- and this hyper-infinity is "enfolded" in the relatively small infinity of the volumes in the Library!
Into such deep and subtle matters is the story of "Ladle Rat Rotten Hut" a gateway.

Mysterious and yet more mysterious:
The Gateway into the teeming Wonders.

---Dao-De Jing (1)
.
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Old February 22nd, 2017, 02:07 PM   #5
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And thus do we see all things as possibility in an infinite Universe...nothing becomes nonsense when all is truth.

Here we note a reason (the only reason) for the minds of humankind, as it is capable of setting limits on an infinite universe....such power does it hold.
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Old February 23rd, 2017, 03:58 PM   #6
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'
It is very difficult to convey the divine beauty of mathematics to a non-mathematician. Thomas Aquinas, attempting to describe what he conceived as angelic consciousness, noted one aspect: that an angel, seeing a simple geometric figure, such as a triangle, would instantaneously and simultaneously perceive, as an act of intuition and not of discursive reason, all propositions of geometry and, indeed, the whole structure of geometry, as a single divine, Platonic Idea in the mind of God. Now whatever you may conceive to be the ontological status of God and angels, it is a fact that, for a good mathematician, his intuition of geometry is not radically different from that of Aquinas's angel.

A more concrete metaphor may help to convey the mysterious grandeur of mathematics. Imagine that a beautiful and subtle novel has come into your hands, and that you have read it through with great aesthetic pleasure. Now imagine that you change each of the letters in the novel according to some simple rule---say, A to B, B to C, C to D, etc. You find to your amazement that you have not produced gibberish, but a completely new novel, of even better quality than the first! And you find that you can go on in this fashion forever, producing ever more beautiful, subtle and mysterious works of art.

This is a dim image of the wonders of mathematics.
This aspect of mathematics was well-known to the greatest thinkers of ancient Greece, and led them to the conception of Platonic Forms ---- objects of Super-Reality whose dim and mutable shadows are all we know of matter and sensation, and whose awful majesty radiates through the ephemeral illusions of time and space. We may see this awareness in the arrangements of the propositions of Euclid.

Proposition 47 of Book I is a proof of the famous Pythagorean Theorem: "The square on the hypotenuse of a right-triangle is equal in area to the areas of the squares produced on the two legs of the triangle."

Euclid's Elements, Book I, Proposition 47

It is a proof, but it is not the easiest proof; it is relatively complex, a fact which has puzzled many people. The reason is that it is meant to be understood in connection with a very similarly constructed proof concerning all possible triangles and the parallelograms that can be constructed on the sides of any triangle. This proof appears in Pappus, and it shows that the Pythagorean Theorem is merely a special case of a more general proof concerning the Platonic nature of all triangles.

Pappus

We see a similar development of thought in Book III, Proposition 31 of Euclid where it is first proved that an inscribed triangle, constructed upon the diameter of a circle and touching the circumference at the third point of the triangle, is a right-triangle; and as you move this third point around the circumference you generate all possible right-triangles.

Euclid's Elements, Book III, Proposition 31

Next is a generalization from this and deals with triangles constructed on all possible chords of a circle---thereby generating all possible triangles. This demonstrates that circles and triangles are identical ---- there is no difference between them in their Platonic essence. They are both aspects of a single nature.
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Old February 23rd, 2017, 04:23 PM   #7
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sheepshearing
Sheepshearing Festival
Gore Place’s 30th Annual Sheepshearing Festival
SATURDAY, APRIL 29, 2017 from 10:00 am to 5:00 pm.
This will be our 30th year of Sheepshearing! Stay tuned for more details!

$20 adults, Free to children 12 and under and Gore Place Members. Children must be accompanied by an adult.

Our festival features both traditional manual blade sheep shearing and electric sheep shearing. Sheep fleeces are collected to be weighed in the kids’ activity tent and later sold. Our merino sheep and sheared the traditional way and other sheep are brought in for the electric shearing.

Our fiber tent area offers dozens of fiber artists specializing in wool yarn, roving, knitting kits, and finished wool products. Some even bring animals or special demonstrations.

Our crafter area has 76 booths with artisans selling handmade candles, birdhouses, jewelry, metalwork, pottery, and more!
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Old February 24th, 2017, 03:03 PM   #8
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'
Blowhard, this thread is meant for people who have minds and can think.

You should go back to your threads about adult toys and gluttony.
.
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Old February 24th, 2017, 03:15 PM   #9
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Quote:
Originally Posted by numan View Post
'
Blowhard, this thread is meant for people who have minds and can think.

You should go back to your threads about adult toys and gluttony.
.
I didn't post it yet! You must be psychic!

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Old February 24th, 2017, 03:28 PM   #10
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'
God is, after all, ultimate reality. And you can't argue that ultimate
reality doesn't really exist. You can only ask what it's all about.

---Logan Pearsall Smith

Beauty, Harmony, Truth are my shining lodestars, or ---- to give them all a single name, as Plato did ---- the Good.

The Absolute cannot be precisely defined, as Kurt Gödel proved mathematically. But Beauty is a finger pointing to the Absolute, shining at the Infinite Horizon.

Aesthetic relativism, like moral relativism, can carry you only so far. Moreover, one should make a distinction between Art and craft (or, more likely, the lack of craftsmanship). There are many styles of art and many techniques of craftsmanship, but Art and Beauty transcend all of them. There are many systems of mathematics, an infinity and a hyper-infinity of them, but it is a logical and provable necessity that they cannot, in their dizzyingly infinite totality, exhaust Mathematics Itself ---- which overarches them all in a way which is, in strict logic, inexpressible and transcendent.

Creation is the irruption of a transcendent order of Reality into the limited realm of Being which we inhabit.
---- Yours Truly

But why do we live for anything but Beauty; What is there that gives a meaning to the world but Beauty; ---- these splendors that seem to fall upon us from the empyrean, from climes of bliss beyond the constellations?
---- Logan Pearsall Smith

Das schönste, was wir erleben können, ist das Geheimnisvolle. Er ist das Grundgefühl, das an der Wiege von wahrer Kunst und Wissenschaft steht.
---Albert Einstein, Wie ich die Welt sehe
[The most beautiful thing which we are able to experience is Mystery. It is the fundamental emotion which stands at the cradle of true Art and Science]

I think that there are many things in the universe that we cannot perceive or penetrate and that also we experience some of the most beautiful things in life only in a very primitive form. These mysteries I sense deeply.
---Albert Einstein, The Private Albert Einstein

Mathematics, like the Nile, begins in minuteness, but ends in magnificence.
---James Sylvester

Probably the most concrete introduction to the wonders of mathematics is the Mandelbrot Set. This is an object created by a ridiculously simple recursive function that is, quite literally, an infinite object, and one of breathtaking and supernal beauty. As such, it is an excellent metaphor for mathematics itself.

Here is a Deep Mandelbrot Set Animation. It is equivalent to starting from far beyond the observable universe and zooming down to far below the dimensions of an elementary particle --- but it is just a tiny part of the environment of the Mandelbrot Set, and could go on forever.

Now how is this possible? How can such awesome beauty arise from what is, after all, a mere game, a mindless procedure which a machine like a computer can create by an infinitely tedious series of repetitive steps? This is the mystery which we must set out to understand.

As a hint, it can be pointed out that no contradiction is involved here. Mathematics can be a realm of Divine Beauty and Truth, and it can also be totally mindless, repetitive procedure.

The two apparent opposites are enfolded together seamlessly, in a Unity that (almost) defies understanding. It is like a picture which, when you look at it one way, is a jolly, pretty lady, and when you look at it another way, is an ugly old crone. The picture is what it is; only your viewpoint changes.



The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.
---Niels Bohr
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Old February 24th, 2017, 03:32 PM   #11
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Old February 24th, 2017, 03:38 PM   #12
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'
By the way, this picture:



is an excellent illustration of a four-valued logic common in Far Eastern philosophy --- as opposed to the two-valued logic of Western Aristotelian logic (A or not-A).

1) It is A --- a picture of a pretty lady.

2) It is not-A --- it is not a pretty lady, it is an old crone.

3) It is both A and not-A --- both completely a pretty lady and completely an old crone.

4) It is neither A nor not-A --- it is just what it is, colors and lines on a screen.
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Old February 24th, 2017, 03:44 PM   #13
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Quote:
Originally Posted by numan View Post
'
By the way, this picture:



is an excellent illustration of a four-valued logic common in Far Eastern philosophy --- as opposed to the two-valued logic of Western Aristotelian logic (A or not-A).

1) It is A --- a picture of a pretty lady.

2) It is not-A --- it is not a pretty lady, it is an old crone.

3) It is both A and not-A --- both completely a pretty lady and completely an old crone.

4) It is neither A nor not-A --- it is just what it is, colors and lines on a screen.
.
The ONLY time along the space-time continuum when A = -A, is when A=0, at which time you are void of anything.
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Old February 24th, 2017, 03:57 PM   #14
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I (all by myself, I might add) have proven that infinity X 0 = 1.

Here's how:

To the limit, 1/infinity = 0, so therefore in the equation infinity/1 X 1/infinity = 1, because the infinities cancel each other out when one of them is in the numerator, and the other is in the denominator, so you end up with 1/1, or simply 1!!!
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Old February 26th, 2017, 03:29 PM   #15
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Quote:
Originally Posted by Aufgeblassen View Post
To the limit, 1/infinity = 0
Or, 1/0 = infinity. However, division by 0 is undefined. You can only say that , in the expression 1/n, as n goes to infinity, 1/n approaches 0 (1/n ---> 0), not that 1/n equals 0!

Consider Grandi's Series:

1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + ...

Using parentheses,

(1 − 1) + (1 − 1) + (1 − 1) + ... = 0 + 0 + 0 + ... = 0.

Alternately,

1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + ... = 1 + 0 + 0 + 0 + ... = 1.

Or,

S = 1 − 1 + 1 − 1 + ..., so
1 − S = 1 − (1 − 1 + 1 − 1 + ...) = 1 − 1 + 1 − 1 + ... = S
1 - S = S
1 = 2*S, resulting in S = 1/2 !!

This is an example of a divergent series --- which, appropriately analysed, can sum to an infinite different numbers.

This may be perceived intuitively in the example of a Thomson Lamp.

A Thomson Lamp is free of all the constraints of physics, so that it may be a pure mathematical thought experiment.

One turns a Thomson Lamp on-and-off over a period of one minute.

Specifically, one turns it on for a period of 30 seconds, and then turns it off for 15 seconds, turns it on for 7-and-a-half seconds, turns it off for 3-and-three-quarters seconds, and so on --- reducing the time by one-half each time.

The question is: at precisely the one minute mark, when the lamp has been turned on-and-off an infinite number of times,

is the lamp on, or is it off?

The relationship with Grandi's Series should be obvious.
.
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Old February 26th, 2017, 04:46 PM   #16
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The real and ultimate bottom line is there is no reality.

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Old February 26th, 2017, 05:17 PM   #17
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'
I always suspected that you were a solipsist. ---
.
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Old February 26th, 2017, 05:20 PM   #18
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Quote:
Originally Posted by numan View Post
'
I always suspected that you were a solipcist. ---
.
That's odd!

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Old February 28th, 2017, 02:59 PM   #19
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Ah! The wonderous nature of the prime numbers!!
The very mention of them is enough to send me into rhapsodies of praise -- at least, into such rhapsodies of which my nature is capable! · ·

God created the primes -- all the rest is a series of footnotes to the primes
[My apologies to both Leopold Kronecker and to Alfred North Whitehead]
· ·

From the Riemann Zeta-Function, to quantum mechanics, chaotic spectra, entropy and into the utmost reaches of mathematics -- having penetrated into the innermost chambers of the Holy of Holies -- one finds the primes on their divine throne, wreathed with supernal beauty, intricacy and subtlety, far, far beyond the works of Man and Nature, literally infinite in glory, sending shafts of purest radiance out to every region of existence, penetrating the inner core of all things!!

I particularly like exploring the sum of the reciprocals of the prime numbers*.

* Merrifield, C.W., "The Sums of the Series of the Reciprocals of the Prime Numbers," Proceedings of the Royal Society, vol. 33, Nov. 17, 1881, pp. 4-10

The sum of the reciprocals of the natural numbers approaches, as a limit, ln(n) plus the Euler-Mascheroni Constant.

The sum of the reciprocals of the primes approaches, as a limit, ln(ln(p)) plus a constant. This very interesting constant, which is sometimes called Mertens Constant, can be derived from the Euler-Mascheroni Constant minus an infinite series whose terms consist of the sums of the reciprocals of the natural numbers raised to integer powers in a fairly complex, but regular, way. This constant, which as far as I know has no generally recognized name, is approximately 0.3157184520.... It was, as far as I know, first calculated by Merrifield and Glaisher in the 19th century, but due to the calculational limitations of their time, they did not truly recognize its significance. That was done later by Hadamard de la Vallée Poussin and others.

Anyway, the sum of the reciprocals of the prime numbers possesses internal relationships which are truly astonishing, breathtaking and supremely beautiful.
The divine economy is more truly revealed in mathematics than in any other region of human experience.
.
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Old March 1st, 2017, 02:36 PM   #20
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All my life I have heard so much blither about Plato! If only people would actually read Plato, rather than parroting the clichés they have heard about him!

For instance, people seem to be determined to misunderstand the Republic! Plato had his political ideas, but the Republic should be viewed primarily as an extended metaphor, as a disquisition upon the proper ordering of the individual human soul. For cryin' out loud, Plato himself says this as clearly as anyone could:

Quote:
"[Glaucon and the rest] wanted to arrive at the truth, first, about the nature of justice and injustice, and secondly, about their relative advantages. I told them what I really thought: that the enquiry would be of a serious nature, and would require very good eyes. Seeing then, I said, that we are no great wits, I think that we had better adopt a method which I may illustrate thus: suppose that a short-sighted person had been asked by some one to read small letters from a distance; and it occurred to some one else that they might be found in another place, which was larger, and in which the letters were larger --if they were the same text, and he could read the larger letters first, and then proceed to the smaller -- this would have been a rare piece of good fortune!

Very true, said Adeimantus; but how does the illustration apply to our enquiry?

I will tell you, I replied; justice, which is the subject of our enquiry, is, as you know, sometimes spoken of as the virtue of an individual, and sometimes as the virtue of a State.

True, he replied.

And is not a State larger than an individual?

It is.

Then, in the larger, the quantity of justice is likely to be larger and more easily discernible. I propose therefore that we enquire into the nature of justice and injustice, first as they appear in the State, and secondly in the individual, proceeding from the greater to the smaller and comparing them."

--- Book II, 368D
Could anything be clearer than that?! The entire Republic is primarily an investigation of the individual psyche, and is only secondarily about "politics" as we understand them! Yet vast masses of brainwashed "intellectuals" continue to drone out the same tired clichés that Plato was some sort of proto-fascist---as though you could meaningfully compare the politics of someone living in the 4th century BC with those of an inhabitant of the 21st century AD!
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