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Old April 2nd, 2017, 01:58 PM   #81
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So, to recap :

Every book in this infinitely chaotic Library makes perfect sense in some grammar(s) or code(s) -- and each code can be represented by some one of the hyper-infinity of real numbers.

Moreover, every single real number is a meaningful code that makes sense in one or more of a hyper-hyper-infinity of languages by which the codes can be interpreted !

And this stack of languages and hyper-languages just goes on forever and ever -- world without end !!
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Old April 2nd, 2017, 02:04 PM   #82
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You should seriously consider taking NOTHING into serious consideration. You might feel better that way!
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Old April 2nd, 2017, 02:10 PM   #83
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I did a search for " मनतेज सिंह धवन", and this came up:

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Old April 5th, 2017, 04:57 PM   #84
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Lorentz Frames

Clock Synchronisation

Relativity of Simultaneity

Einstein Synchronisation

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According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. If the two events are causally connected ("event A causes event B"), then the relativity of simultaneity preserves the causal order (i.e. "event A causes event B" in all frames of reference)....

A mathematical form of the relativity of simultaneity ("local time") was introduced by Hendrik Lorentz in 1892, and physically interpreted (to first order in v/c) as the result of a synchronization using light signals by Henri Poincaré in 1900. However, both Lorentz and Poincaré based their conceptions on the aether as a preferred but undetectable frame of reference, and continued to distinguish between "true time" (in the aether) and "apparent" times for moving observers. It was Albert Einstein in 1905 who abandoned the (classical) aether and emphasized the significance of relativity of simultaneity to our understanding of space and time.
It is a subtle question : consider : Ehrenfest's Paradox
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Old April 5th, 2017, 05:13 PM   #85
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Anything is possible. The question is: is it probable?



The Science of Farting

What exactly is a fart? The word "FART" can stand for: Frequency Actuated Rectal Tremor. Farting, also known as flatulence, is the act of passing intestinal gas from the anus. Intestinal gas comes from several sources: air we swallow, gas that seeps into our intestines from our blood, gas produced by chemical reactions in our guts, and gas produced by bacteria living in our guts. Burps are not farts that come out your mouth. They have to do with your stomach.

Who Cut the Cheese? Finding the Farter

Have you heard that saying: "Whoever smelt it, dealt it?" A fart smells the same to the person who delivered it and to the person smelling it. However, the farter probably smells it last because the fart is propelled away from the body in the opposite direction of the farter's nose. Unless the fart happens upwind.

Why Do Farts Smell?

The smell of farts comes from gas and mercaptans (other gases) in the mixture. These compounds contain sulfur. The more sulfur-rich foods you eat, the more sulfides and mercaptans will be made by the bacteria in you guts, and the more your farts will stink. Foods like cauliflower, eggs and meat are really bad for making stinky farts. Beans on the other hand, may make you fart a lot but they aren't usually the smelly kind.

Let it Rip! The Sound Of Farting

The sound of a fart is caused by the vibrations of the anal opening. The sound of your fart depends on the speed of the fart leaving your body and the tightness of the sphincter muscles of your anus.

Famous Fart Food

The most famous farting food is the bean. What is it about these little things that cause such a stink? Beans contain sugars that we can't digest. When these sugars make it to our intestines, the bacteria go berserk, start feasting and make loads of gas. Other foods that are great for making you fart are broccoli, cabbage, raw apples, milk and raisins. So if your best friend has a broccoli and cabbage salad for lunch with an apple for recess and a big glass of milk - Don't sit too close on the bus ride home.

Farting Under Pressure

Think about this: If you could go into space without a suit and you let one rip, your fart would have enough pressure to push you forward.

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Old April 6th, 2017, 04:01 PM   #86
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fart has its origin in the Indo-European root *PERD-, and is cognate with the Latin pedere.

From the same root:

feisty, fizzle, petard, partridge.
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Old April 6th, 2017, 04:44 PM   #87
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One of my favorite tales of self-referential paradox is that of The Crocodile and the Baby

Greek philosephers liked to tell about a crocodile that snatched a baby from its mother. Said the crocodile :
___"Will I eat your baby? Answer correctly, and I'll give your baby back to you unharmed -- for I am a very philosophic crocodile, and I love the truth."
___"Oh! Oh! Your'e going to eat my baby!"
___"Hmmm. What shall I do? If I give you back your baby, you will have spoken falsely. I should have eaten it."
The crocodile has a problem. He has to both eat the baby and give it back at the same time.
___"Okay, so I won't give it back."
___"But you must! If you eat my baby, I spoke correctly, and you have to give it back!!"
The poor crocodile was so upset that it let the baby go. The mother grabbed her child and ran.
___"Darn! If only she'd said I'd give the baby back. I'd have had a juicy meal."


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Let's examine this famous paradox more carefully to make sure you understand how clever the mother is. She said to the crocodile: "You are going to eat my baby." Whatever the crocodile does is sure to contradict his promise. If he gives the baby back, the mother spoke falsely, which entitles him to eat the baby. And if he eats it, the mother spoke truly, which forces him to return the baby unharmed. The crocodile is caught in a logic paradox from which he can't escape without contradicting himself.

Suppose, instead, the mother had said: "You're going to give the baby back." Now the crocodile can return the baby or eat it, in both cases without contradiction. If he gives it back, the mother spoke truly, and the crocodile has kept his word. On the other hand, if he is mean enough, he can eat the baby. This makes the mother's statement false, which frees the crocodile from the obligation to give the baby back.
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Old April 9th, 2017, 04:58 PM   #88
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Chaos Theory for Beginners

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How Chaos Theory was born and why.
It all started to dawn on people when in 1960 a man named Edward Lorentz created a weather-model on his computer at the Massachusetts Institute of Technology. Lorentz' weather model consisted of an extensive array of complex formulas that kicked numbers around like an old pig skin. Clouds rose and winds blew, heat scourged or cold came creeping up the breeches.

Colleagues and students marveled over the machine because it never seemed to repeat a sequence; it was really quite like the real weather. Some even hoped that Lorentz had built the ultimate weather-predictor and if the input parameters were chosen identical to those of the real weather howling outside the Maclaurin Building, it could mimic earth's atmosphere and be turned into a precise prophet.

But then one day Lorentz decided to cheat a little bit. A while earlier he had let the program run on certain parameters to generate a certain weather pattern and he wanted to take a better look at the outcome. But instead of letting the program run from the initial settings and calculate the outcome, Lorentz decided to start half way down the sequence by inputting the values that the computer had come up with during the earlier run.

The computer that Lorentz was working with calculated the various parameters with an accuracy of six decimals. But the printout gave these numbers with a three decimal accuracy. So in stead of inputting certain numbers (like wind, temperature and stuff like that) as accurate as the computer had them, Lorentz settled for approximations; 5.123456 became 5.123 (for instance). And that puny little inaccuracy appeared to amplify and cause the entire system to swing out of whack.

Exactly how important is all this? Well, in the case of weather systems, it's very important. Weather is the total behavior of all the molecules that make up earth's atmosphere. And in the previous chapters we've established that a tiny particle can not be accurately pin-pointed, due to the Uncertainty Principle! And this is the sole reason why weather forecasts begin to be bogus around a day or two into the future. We can't get an accurate fix on the present situation, just a mere approximation, and so our ideas about the weather are doomed to fall into misalignment in a matter of hours, and completely into the nebulas of fantasy within days. Nature will not let herself be predicted.
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Old April 9th, 2017, 05:01 PM   #89
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Nature and Nature's laws lay hid in night:
God said, "Let Newton be!" and all was light.


It did not last; the devil cried, "HO,
LET CHAOS BE!!" and so restored the status quo.


I think everyone who does not understand the chaotic nature of weather, and its inherent unpredictability, should be drummed out of the 21st century.

"Ignorance, from being an amiable individual defect, has become a monstrous and deadly social crime."

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Up to the Quantum Mechanical Revolution people believed that things were directly caused by other things, that what went up had to come down, and that if only we could catch and tag every particle in the universe we could predict events from then on. Entire governments and systems of belief were (and, sadly, are still) founded on these beliefs....
Humans are so easily hypnotized!! The Newtonian paradigm was so impressive that no one dreamed of questioning it -- yet there there were obvious reasons for doing so staring them in the face !!

For instance, the intractability of the "Three Body Problem"!!

For centuries, people tried to solve the problem of predicting the orbits of three astronomical bodies, and could never make the predictions accurate -- yet there was no problem in predicting the orbits of two bodies on Newtonian principles!!

It should have been obvious that the difficulty was the inaccuracies in precisely defining the initial conditions, yet history shows that, for centuries, innumerable very intelligent people were just not able to crawl that far out of the box of predictable Newtonian mechanics, because they were so over-awed by its astounding successes !!

Likewise, vast amounts of effort for many years were wasted in pursuing the Holy Grail of refining weather analysis to make weather predictable far into the future.

At last, with chaos theory, they finally twigged to the notion that it was necessarily impossible ever, by any means whatsoever, to make the weather really predictable !!

One of the greatest mathematical achievements of the 20th century was the clear realization that means of proving things to be impossible are, fundamentally, even more important than proving them to be possible!

Unhappily, most humans have still not caught up to this fundamental insight.
But then, nothing new in that, is there ? · ·
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Old April 9th, 2017, 05:21 PM   #90
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Garbage without discussion

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Old April 11th, 2017, 05:11 PM   #91
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John Searle's Chinese Room

When I was a teenager, I was mightily impressed by the fact that a Turing Machine could do anything the most sophisticated computer could do, given enough time.

I was sure that a Turing Machine, a simple mechanical device, in principle no different from a lever or a thermostat, was not conscious in any human sense. So since then I have been amazed that so many computer geeks have become so roboticized that they cannot see any difference between human consciousness and computer processing.

John Searle's "Chinese Room" is just another example of this basic problem, and to my mind not so good an example as the old-fashioned Turing Machine.

I am sure that a Turing Machine, as it is normally defined, is unconscious, even if it may be intelligent. Consciousness and intelligence are not synonymous.
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Old April 11th, 2017, 05:19 PM   #92
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Garbage without discussion
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Old April 11th, 2017, 05:28 PM   #93
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I can imagine with complete equanimity that a machine (based on other principles than a Turing Machine) could have a consciousness analogous to human consciousness (or even superior to human consciousness); I can imagine a machine having reactions analogous to human emotions. What seems quite unreasonable is to imagine that the machine could have mind, spirituality or emotions identical to those of humans. The properties of silicon and metals just differ too much from the properties of long-chain organic molecules and their chemical reactions.

Furthermore, I maintain that the evolutionary histories of the two entities will also forever distinguish them. You cannot divorce humans from the long evolutionary and cultural history that produced them -- and which surrounds them and governs almost everything they do.

Computers have a completely different history and environment.

Humans, both separately and in societies, possess properties which could not arise without the evolutionary processes that produced them.

Humans are chimpanzees that have learned how to lie and who can lob nuclear bombs around the world.

What people can't seem to grasp is that the human mind and consciousness (such as they are) do not come from within us, but reside in the material and social environment which has evolved over thousands of years. It is because we have been raised in that complex environment, and been socially conditioned by it, that we have any consciousness at all. The human mind is almost entirely a reflection from outside.

Humans have evolved very little. It is their environment which has evolved. It contains all the information, which, reflected into the chimpanzoid brains of zombie humans, causes them to imagine the delusion that they are conscious and intelligent !!

Naturally, the human brain has changed, in response to its physical and social environment, but compared to the sophistication of the human cultural environment, the brain has changed very little.

It is our environment that is intelligent, not ourselves. Without that environment, we would be little more conscious and intelligent than our ape relatives.
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Old April 13th, 2017, 04:26 PM   #94
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One interesting aspect of the "holotropic" view of the universe is that, while the two-dimensional representation of the universe contains as much information as the three-dimensional representation, the continuity of the two spaces differs wildly, and irreconcilably. This can be given a concrete instantiation by considering the following partial representation of a Sierpinski curve :



If you continue the paradigm indicated here, over and over, making the closed curve ever more complicated, the final result, after an infinite number of iterations, is a one-dimensional closed curve, which is infinite in length, never intersects itself, passes through every point in the square which bounds it, and yet the square, of course, is finite in area !!

It is easy to see that two points which are close together in the two-dimensional space are not necessarily close to each other on the one-dimensional line.

Here is a view of the curve at a greater degree of elaboration, though of course, not the final view, which can be attained only after an infinite number of iterations.


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Old April 22nd, 2017, 04:27 PM   #95
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Meanwhile, back in the real world....

Buddhist Nothing (Sunyata) is not difficult to understand directly. What does take time and effort is to cultivate that understanding.

The Buddhist dictum that "there is not the slightest difference between Emptiness and the World of Suffering; there is not the slightest difference between the World of Suffering and Emptiness" * usually strikes the unprepared mind as absurdly paradoxical, but is, in fact, quite easy to understand. There is no better exemplification of this doctrine than the famous woodblock print by Hokusai: The Great wave at Kanagawa. This is the reason why the print is so famous in Japan.



The boats are foundering in the Sea of Illusion and Unrest; in the far distance is Mt. Fuji, the symbol of perfect Enlightenment and Peace. However, this is another illusion; standing on Mt. Fuji, you would be enveloped by freezing cold and danger, and the distant ocean would appear calm and peaceful.

The essential reciprocal nature of Enlightenment and Illusion is perfectly expressed by this picture. When I lived in Japan, I met many ordinary, unremarkable Japanese people who understood the meaning of the picture and revered it for the spiritual truth which it expresses.

Understanding the nature of Enlightenment and Suffering is not difficult and well within the mental capacity of ordinary people. Cultivating that understanding, so that it is adequately expressed in one's thought and actions, is a challenge to the abilities of any human being. Deepening one's understanding requires a lifetime of cultivation (or perhaps several lifetimes )

This is exemplified in the legend of Hui Neng, the Sixth Chan patriarch. Hui Neng, so the story goes, achieved Perfect Enlightenment and was recognized by the Fifth Patriarch as his successor. Subsequently, Hui Neng went to an isolated forest and lived in a village of huntsmen for many years. Supposedly, he survived by eating only the vegetables cooked in the stewpots of the hunters. (Perhaps the greatest test for a vegetarian is to live in a village of carnivores)

After many years, he began a life of wandering. One day, he came upon a group of monks arguing beneath a flagpole. Some insisted that the flag was moving; others, that the wind was moving. They asked Hui Neng to give his opinion. He said, "Neither flag, neither wind. Mind is moving." The monks were deeply impressed by the great understanding of Hui Neng, and became his disciples.

I sometimes wish that I lived in those days; perhaps there would be more people who would understand what I am saying.

In the unlikely event that someone on this site has kept his or her mind calm enough to understand what I have written here, you are now Enlightened !! Congratulations !!

Now you just need to deepen and refine your enlightenment---the way Hui Neng did.

* Na samsârasya nirvânât kimcid asti vishesanam.
Na nirvânasya samsârat kimcid asti vishesanam.

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Old April 23rd, 2017, 07:26 PM   #96
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Among all the people of the world, Westerners seem to be the most absorbed in their egos, and among Westerners, Americans seem to be those who are generally most absorbed in seeing life as a series of transactions engaged in for profit. I must admit that I find such an attitude to be very low and debased, and not one worthy to be a part of a true human life. I think it is fit only for the pig-sty.

Such a lot depends on one's point of view. Life is often like one of those ambiguous pictures that looks one way if one's brain processes the image in a certain fashion, and looks like a completely different thing if perceived under a different mode of processing the image.

If one is not overly concerned with one's ego, so many of these moral "problems" just disappear from the picture. I have often done things of benefit for other people, in ways that more self-absorbed people thought were reckless and damaging to myself. I find it amazing how often such actions have worked to my benefit, often in quite surprising ways. I am quite sure that calculations of self-benefit were quite absent from my motivations, nor, in many cases, could they have been foreseen. What I did seemed as natural as breathing --- feeling my way to a little more harmony and beauty in my environment.

I opine that the more that one perceives harmony and beauty and truth, the more does self-gratification vanish from one's relations with the universe --- it becomes trivial and unimportant.

Though I find their views repugnant and harmful, I am also amused at the attitudes of those who 'think' that "the guy who accumulates the most toys, wins." A moment's clear reflection tells you that when you die, that is the end of personal existence. What is the significance of accumulating toys, conquests, and personal gratification? The moment you have breathed your last breath, they are all as if they had never been.

As the Buddhists say, all things are "as illusions in the sky, a fault of vision, as a lamp, a mock show, dew drops, or a bubble, a dream, a lightning flash, or cloud...." All these things have their place in the pageant of existence, but to imagine that there is anything enduring about them is ridiculous.

I do not know what is the ultimate nature of existence, but I sense that there is something wonderful, harmonious and beautiful in the enduring mystery of Truth. I certainly cannot prove this to the satisfaction of a logician; one cannot hold the sun or moon in one's hand; the best one can do is to lift one's hand and point to them shining in the sky.

I received a lasting impression when I visited the city museum of Taibei, Taiwan. There were a number of ancient ceramic plaques with images impressed upon them, scenes of Buddhist mythology and symbolism, expressive of Buddhist doctrine and philosophy. These plaques were very ancient, dating from the Tang Dynasty, more than a thousand years old. Originally, they were plastered on the outer façade of Buddhist temples. What was interesting about them was that they contained human ashes mixed in with the clay out of which they were made. When devout Buddhists died, they had their bodies cremated, and the remaining ashes were incorporated in these plaques, so that even in death they could continue to proclaim the essential, eternal truth of Buddhism: the transience of all things. There is a wonderful, paradoxical, Chinese quality to what they did. Eternal truth proclaimed by the dead ashes of vanished men? What is in fact enduring, and what must pass and fade?

I am sure that you appreciate the pleasingly paradoxical quality of this! They were thus permanently proclaiming the doctrine of impermanence, or, if you please, by their impermanence affirming the Permanent Truth of impermanence.

Also, what they did took more courage than might appear. In traditional China, it was considered vital to bury family members with proper rites and in propitious locations. The future happiness of an entire family was considered to depend on this. The people who mixed their ashes into plaques did something that was roughly equivalent to us throwing the bodies of our dead parents by the side of the road for dogs to eat. They apparently thought proclaiming Truth to be more important than following social convention.

Was what they did altruistic, or not? I think the question blushes to annihilation in a world view in which Truth is real, and ego an illusion.

P.S. --- Some time later, I met a Tibetan lama and mentioned this little story to him. With an enthusiastic surprise and glee which I thought inappropriate for such an esteemed religious figure, he said, "Why, I visited that very museum and saw those same plaques myself!"

He was quite impressed that I, a mere untutored Western savage, had seen them and understood their deep meaning.

With such an impressive imprimateur attesting to the depth of my understanding, what need do I have for Buddhism? I have reached the Other Shore and no longer need the boat that brought me there. I may throw it away, or shove it back across the river for others to use.
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Old April 27th, 2017, 02:24 PM   #97
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Poor Hegel !!

It is pretty easy to poke fun at someone who was ridiculously wrong in almost every idea he had about physical science, and who regarded the Royal Prussian state as the highest and final culmination of political development!!

The Commies dislike him, and Schopenhauer was pretty hard on him, too!!

However, to his credit, he brought at least a rudimentary awareness of dialectics to leaven the crudity of Western ways of thinking. Under the influence of Hegel and his followers and critics, Western thought may, in a thousand years, achieve the subtlety and profundity already enjoyed by Chinese Daoism.

Read what Hegel has to say about, Being, Non-Being, and Becoming.

Logic of Being, Nothing, and Becoming

Pretty cute! And, perhaps, even acute!!

A Hegelian term in which the thin upper crust of those who enjoy philosophical puns take delight is the antanaclasis AUFHEBUNG (etymologically: HEAVING UP : raising from a lower level to a higher level; storing up; carrying away; abolishing; retaining -- cognate with English have; Latin capio, "I seize"; Greek kópe, handle, oar, kápto, I gulp down; Sanskrit kapatî, two handfuls) -- the process of cancelling, preserving and elevating, all-at-once. It is the Hegelian term which is usually translated as "synthesis" or "sublation."

A good example is the way that Newtonian physics is sublated in relativistic physics, which supercedes it, but also preserves it, as a special case in a wider framework, appropriate to low velocities and energies.
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Old May 2nd, 2017, 05:02 PM   #98
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To maintain a state of aporia is not as easy as those who have never tried to do it may think.

To never come to a final conclusion on any matter, to maintain a state of suspended belief about all things is not an approach which is congenial to the human mind, yet it is essential if one is to make any headway in the search for truth. No matter how earnest one is to maintain absolute neutrality about all views, the mind is always prone to topple over into accepting some conclusion as truth.

One way to avoid such a defeat for the mind is always to oppose one view with an opposite or alternate view. So the Sixth Patriarch of the Chan [Zen] school of Buddhism said:

Suppose someone asks you about the meaning of things: If he asks you about "existence," answer with "non-existence." If he asks you about the ordinary person, let your answer be about the Wise Man. If he asks about Wisdom, indicate how the mutual dependence of dualistic relative conceptions gives birth to the balance of the Middle Way. In this way, each of the questions has its reply. If you deal with all other questions according to this procedure, then you will not lose the principle of Wisdom.

The proper function of the mind is to take a firm stand upon an infinite series of collapsing foundations. Clinging to ideas is a disease of the mind.

There is an old Chinese fable about a man who went to visit a hermit who lived far out in the wilderness. The hermit was so holy that the birds and the animals brought him fruits and nuts and roots for him to eat. As the two men were talking, a tiger roared nearby, and the visitor was startled. The hermit remarked, "Ah, I see that there are still things to which your mind clings!"

Later, when the hermit was away, the visitor took out his brush and ink and wrote the Chinese character for "Buddha" on the top of a large, flat rock upon which the hermit habitually sat in meditation. The hermit returned, went to the rock, saw the character, and hesitated to put his rump on the Holy Name. The visitor remarked, "Ah, I see that there are still things to which your mind clings!"

Hearing this, the hermit suddenly achieved full Enlightenment --- and the birds and animals no longer brought him food to eat!

Of course, clunky-minded Westerners will immediately protest, "No one could possibly survive in the world if they really did as you suggest; you have to believe in something!"

Well, no, you don't. Instead of beliefs, you can follow the procedure of science and make provisional hypotheses which you are always ready to test.

Sphaerus, the Stoic, said to Ptolemy Philopator, king of Egypt: "A wise man always knows. He never holds mere opinions and so is never misled." The king had waxen pomegranates made and placed them in a bowl at a banquet. When Sphaerus took one of them, the king pounced and cried, "Aha! You see, you have given your assent to a misleading presentation." "Not at all," said Sphaerus, unperturbed. "I did not assent to the proposition that they were real pomegranates, but to the proposition that there was a reasonable probability that they were real pomegranates."
---Diogenes Laertius
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Old May 3rd, 2017, 04:15 AM   #99
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I wonder what kind of shock pulse results from crushing material fabricated in that shape?!

In aerospace, when you need to create a mechanical shock pulse that not semi-sinusoidal, nor sawtooth, nor have any other
shock pulse shape, actually needing a relatively square pulse, (constant G-level deceleration for X amount of time) you
perform your mechanical drop test with honeycomb shaped material between the bottom of the shock testing machine,
and the impact base.

Honeycomb apparently crushes at a uniform level vs. time, resulting in square wave.

I MISS THOSE DAYS!!! (WINNING the cold war).

Drop test machine (apparently rubber is positioned for semi-sinusoidal pulse):


Typical crushing material:


Nomex:

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Old May 3rd, 2017, 03:51 PM   #100
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There is a delightful little story by Karl Capek entitled, "The Death of Archimedes." It begins :

The story of Archimedes did not happen quite the way that has been written; it is true that he was killed when the Romans conquered Syracuse, but it is not correct that a Roman soldier burst into his house to plunder it and that Archimedes, absorbed in drawing a geometrical figure, growled at him crossly: "Don't spoil my circles!" For one thing, Archimedes was not an absent-minded professor who did not know what was going on around him....for another thing, the Roman soldier was not a drunken plunderer but the educated and ambitious staff centurion Lucius, who knew to whom he had the honor of speaking....

The Roman officer tries to convince Archimedes to put his skills to use in serving the Roman war machine, but Archimedes is uninterested. Finally, the Roman, in growing irritation, blurts out :

"Archimedes, aren't you attracted by the idea of winning world mastery with us? --- Why don't you answer?"
"I beg your pardon," grunted Archimedes, bending over his tablets. "What did you say?"
"That a man like you might win world mastery!"
"Hmm, world mastery," said Archimedes in a bored tone. "You mustn't be offended, but I've something more important here. Something more lasting, you know. Something which will really endure."
"What's that?"
"Mind ! Don't spoil my circles ! It's the method of calculating the area of a segment of a circle."

Later it was reported that the learned Archimedes had lost his life through an accident.

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