Meaning and Intellectual Beauty

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I think that the concept of "Being" is accepted by most people far too uncritically, and requires profound analysis.

When you look at the concept of "Being" closely, it tends to fall apart into a variety of disparate concepts.

In common, everyday language we say, "That is a table"; That is a desert mirage"; That is the definition of a circle"; or, "That's a shame!" We never consider what miracles that simple little "is" performs for our convenience.

Name a visible object which is not made of matter, has no substance or weight, has no specific location in space, and which has a front side but no back. Impossible? A rainbow.

It "is" strange what enormous dissimilarities the little word "is" can obscure. A table, a rainbow, a circle, a mathematical theorem, a desire, an awareness --- all these things seem to exist, yet what do they really have in common? Little, if anything.

One way of dealing with this problem might be to create two different classes of concepts: defined and indicative.

As examples of defined words, we might take "circle", " the square root of minus one", "entropy", etc. Within a particular frame of reference, they have very clear and well-defined meanings.

"Indicative" words are words like "good", "art", "beauty", "God", "mind", and, I would suggest, words like "being" and even "matter".

These words are notoriously difficult to define, and I suggest that their usefulness comes precisely from their lack of clarity, their vagueness, and perhaps even from their logical incoherence.

What I call "indicative" words are like arrows pointing out a direction along which to travel. Their very lack of meaning may make them suitable to be "pointers" in a large variety of frames of reference.

For example, the word "God", even if it is totally meaningless and has no objective referent, has been historically a kind of metaphor or conceptual seed which has suggested concepts of infinity, concepts of causality, etc. which might not have developed without the impetus of this metaphor.

I think we should look more closely at the differences between "defined" and "indicative" concepts, and we should consider the possibility that even meaningless ideas may serve a function in producing meaning. Perhaps the same is also true of meaningless activities.

But we must keep in mind that there are great dangers in confusing the functions of defining and indicating.

There is a story about a student who did not know what the moon is. He went to a teacher and asked, "I've heard people talk about the moon, but I don't know what they mean. What is the moon?"

As an answer, the teacher lifted his hand and pointed to the moon shining in the night-time sky. But the student looked only at the pointing finger and thought that it was the moon! So not only did he mistake the finger for the moon, but he also confused the concepts "dark" and "bright", since he thought that the dark finger was the bright moon!
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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 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 transcience 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? Very few of these plaques remain, a mere handful in a glass case in a museum. At some point in time, not one of them will remain. Yet the strange, paradoxical, eternal truth that all things pass away will remain, ready to pop up out of non-existence whenever there is a mind able to perceive it.

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.
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More on Hardy's Paradox and "weak measurements":

Hardy's Paradox
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Ah, the logarithmic spiral ! the spira mirabilis !

The form of a mollusc which is growing continuously, always at the same rate.

e, the base of the natural logarithms, is defined by a bank account, which like the mollusc, is always growing at the same rate and compounding in ever shorter intervals, until it is compounding at every instant !

One example is an account that starts with $1.00 and pays 100 percent interest per year. If the interest is credited once, at the end of the year, the value is $2.00; but if the interest is compounded and added twice in the year, the $1 is multiplied by 1.5 twice, yielding $2.25. Compounding quarterly yields $2.4414..., and compounding monthly yields $2.613035....
This sequence approaches a limit for more and smaller compounding intervals. Compounding weekly yields $2.692597..., while compounding daily yields $2.714567..., just two cents more. Using n as the number of compounding intervals, with interest of 100%/n in each interval, the limit for large n is the number that came to be known as e. With continuous compounding, the account value will reach $2.7182818....

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Ah, glorious, glorious 2.718281828459045.... !!!
The gateway into an infinite variety of astounding beauties!!!
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Aufgeblassen said:

One problem: 2.7182818.... does not equal 2.18281828459045.... l

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The four dots after the decimal indicates that the numbers go on forever.

"e" is an irrational number, it has no finite numerical representation.

pause

Oops! My bad! I didn't notice that I didn't type the 7 after the decimal point! Good catch, Auffie!
I shall wallow in sackcloth and ashes for not catching your drift.

Ah, well, "even Homer nods."
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Aufgeblassen said:

No duh! But you still did not answer the question. What is the significance of approx. 10 month compounding?

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How is one to answer someone who apparently thinks a year equals ten months?

"Mit der Dummheit kämpfen Götter selbst vergebens"

"Against stupidity the Gods themselves contend in vain"
--- Friedrich von Schiller
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One of the consequences of Heisenberg’s Uncertainty Principle — that you can’t know a quantum state’s energy exactly for a finite duration of time — means that when you’re talking about very short time intervals, there are large uncertainties in the energy of a system. Over short enough timescales, the energies are large enough that particle-antiparticle pairs wink in-and-out of existence all the time!





Take two identical, uncharged, parallel metal plates, and put them close to one another. The vacuum fluctuations in between the plates cause there to be a pressure pushing the plates together. This isn’t the gravitational force or an electromagnetic force, but a force due to empty space itself.



Now, that’s what we know we can get, even from nothing. But there are many things we can’t do, either practically or theoretically: violate charge or energy conservation, decrease the total entropy of the Universe, or figure out where our initially inflating Universe came from. (Yet!) But we definitely can get something for nothing; quantum field theory not only allows it, it demands it.


The only true vacuum that has ever been found is the space between two human ears.

Space boils with energy -- it can be bent, twisted, curved -- it is quite different from "Nothing."

The Cassimir Effect is hard, experimental proof of this. The force between the two plates arises because the longer wave lengths of the virtual particles which fill space cannot "fit" between the two plates -- the distance between the two plates is too short for them. So there are more virtual energies outside the plates than between them, which creates the pressure which drives them together -- and the experimental results agree closely with the theoretical predictions.

Moreover, the elementary particles have magnetic moment -- due to their quantum mechanical spin. It should be 2 exactly -- but external effects due to interactions with the virtual particles and energies of the vacuum change this figure, for the electron's anomalous magnetic moment, to : 2.00231930436153(53).

At last reading, this is the most accurately measured figure in the entire history of physics, and is the most accurate fit between theoretical calculation and experimental measurement that has ever been achieved.

The quantum flux of virtual particles is clear and proven, and the vacuum is NOT "Nothing" !!
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Approximate and true golden spirals. The green spiral is made from quarter-circles
tangent to the interior of each square, while the red spiral is a Golden Spiral,
a special type of logarithmic spiral. Overlapping portions appear yellow.
The length of the side of one square divided by that of the next smaller square
is the golden ratio.

Golden Ratio

The Golden Rectangle and the logarithmic spiral may appear to be different things, but to the mathematical mind they are just two different glimpses of a magnificent Mathematical Object for which crude human speech has no adequate name.
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Some math behind e:




The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler.

e is the unique number with the property that the area of the region bounded by the hyperbola y=1/x, the x-axis, and the vertical lines x=1 and x=e is 1. In other words,



With the possible exception of pi, e is the most important constant in mathematics since it appears in myriad mathematical contexts involving limits and derivatives.

The numerical value of e is

e=2.718281828459045235360287471352662497757...
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I think it is a very unwarranted assumption to imagine that humans have any perception of reality -- possibly some mathematicians do, but even that is debatable.

In my long and varied history of doubting, there is only one proposition which has defeated my ability to doubt: it is the first proposition of Proclus' Elements of Theology :

"Every manifold in some way participates the One."

Without getting into the technical meaning of "participates", the argument can be put into modern terminology by saying that without some form of unity in the manifold, the manifold would not be a manifold, but would disintegrate into a Borel Set -- which John Wheeler picturesquely described as "a bucket of dust." That is, the supposed manifold would disintegrate into unendingly infinitesimal fragments.

It is a very clever reductio ad absurdum, particularly for the time period of Proclus, about 450 A.D. If you can come up with a really good argument demolishing Proclus, I will admit that you are a better sceptic than I, but not before. It may not be the last word in philosophy, but if anything exists, then it is true.

It's about the closest to a firm initial axiom that I have come across.

The Neo-Platonists: great stuff. But you won't get anywhere with them if you don't understand their vocabulary.

All of philosophy lies between the following two limits which the Neo-Platonist, Plotinus, enunciated !!

The One is the formless Form.

Matter resembles the form of formlessness --- if there could be such a thing.
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To think of philosophy in terms of proof is extremely wrong-headed. There is no way to prove anything absolutely.

One cannot prove that the world was not created five minutes ago, complete with all our memories and a highly articulated structure indicative of a long previous existence. Such a possibility may seem ludicrous and highly improbable, but there is no way to be absolutely sure that it is false.

Similarly, it may seem to me that it is a virtual certainty that the sun will rise tomorrow, but I cannot prove that it will do so. It has always risen in the past; but that is merely an inductive argument, and provides no logical certainty that it will do so in future. What I know of physics and astronomy provides a firm foundation for thinking that the sun will rise tomorrow, but it is not absolute proof. My entire life could be a dream or a virtual reality simulation.

Absolute proof might be something attainable by a god, or by a mathematician in some limited area of mathematics, but ordinary mortals such as ourselves must be satisfied by probability, by establishing a plausable story. The more articulated and detailed the story is, the more intricately and subtlly its parts hang together in a coherent whole, the more does it inspire confidence that it may be relied upon as a guide to thought and action.

From this point of view, truth is more a matter of aesthetics than of logic.
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Referring back to this posting:

Here is an easy, yet thought provoking, discussion of infinity :

A Finite History of Infinity

All the possible decimals between zero and one can be represented by arrangements of the books in the Infinite Library of Babel. Each letter in every book can be converted into a number -- indeed, by a code like morse code each letter can be converted into a sequence of dots and dashes, or zeros and ones, so each book would be converted to numbers in binary arithmetic. Then, each real number on the line between zero and one would consist of a finite or infinite sequence of volumes in the Library.

"Real numbers" consist of all the "rational numbers" (finite or repeating decimals, by which all the fractions of whole numbers can be represented) and of all the "irrational numbers" (infinite decimals which do not repeat the same sequence over and over forever).

Cantor's "diagonal method" demonstrates that the real numbers are a hyper-infinity compared to the very lesser infinity of the rational numbers. The real numbers can be equated to the infinity of possible grammars and codes (all the ones in English, and in all the other possible languages and codes which might ever be conceived) by which a single volume in the library can be turned into a sensible message. All the hyper-infinity of grammars and codes are "enfolded" into the library, and each consists of some sequence of volumes (either finite or infinite in number) in some intelligible language.

In the past hundred or so years, two of the towering influences in mathematics were Georg Cantor and Kurt Gödel.

Georg Cantor was the great elucidator of the transfinite numbers, and the discoverer of the "diagonal proof":

Cantor Diagonal Argument

Gödel's extension of Cantor's diagonal method was essential to the construction of his proof in regard to the incompleteness of all systems of formal logic which include arithmetic.

From a different point of view, imagine an infinite sequence of boxes :

█ █ █ █ █ █ █ █ █ █ █ . . . . . . . .

each of which can contain a fraction between zero and one, a fraction consisting, of course, of whole numbers. Each fraction will fill one and only one box (It does not matter if they are reduced to their lowest common denominator or not). There is a one-to-one corresponence between the infinite number of boxes and the infinite number of fractions -- Cantor's diagonal method proves it.

Now imagine each box in the infinite sequence of boxes filled with either a zero or a one.

There is an infinity of possible different sequences of zeroes and ones -- each sequence representing one possible real number on the line between zero and one.

But the sum total of all these sequences is a hyper-infinity compared to the poky, puny infinity of the boxes -- no matter how many boxes you have, or however many ways you arrange the numbers in the boxes, there will be an infinity of real numbers which will never, never have a box to fit into -- Cantor's diagonal method proves it.

As an extension, instead of discrete boxes, imagine a line composed of all the points of the real numbers.

At each point on the line, put either a zero or one. Then that particular line will consist of a hyper-infinite "sequence" of points, each point on that line either occupied (1) or unoccupied (0).

There are an infinite number of possible lines composed in this fashion -- but it is a hyper-hyper-infinity of possible lines!! This is a hyper-infinity compared to the infinity of real numbers -- Cantor's diagonal method proves it !!

One way to imagine it is to consider a graph with x and y axes. For every point on the x-axis there is an infinity of points on the y-axis which may be occupied by a single point representing some real number. So, a specific point on a curve drawn on the graph represents some real number paired with a real-number point on the x-axis.

Then, the total number of possible curves that can be drawn on the graph represent the hyper-hyper-infinity described above.

It should be noted than in mathematics the word "curve" has a broader meaning than it does in ordinary language. The continuous curves are only a small sub-set of the possible curves. Most of the "curves" described above would have gaps in them, indeed even an infinite number of gaps, so that they might even consist of an exceedingly sparse "dust" of points, with large segments of vacancy between them.
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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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Lorentz Frames

Clock Synchronisation

Relativity of Simultaneity

Einstein Synchronisation

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.

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It is a subtle question : consider : Ehrenfest's Paradox
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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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