Ratio And Proportion Quotes

[The golden proportion] is a scale of proportions which makes the bad difficult [to produce] and the good easy.

The Golden Number is a mathematical definition of a proportional function which all of nature obeys, whether it be a mollusk shell, the leaves of plants, the proportions of the animal body, the human skeleton, or the ages of growth in man.

Socialism increases in direct ratio and proportion with the surrender of personal responsibility to neighbor.

At the end of the day, there are very few people around you who truly want to see you peaceful, happy and content. Most of your friends only want to see you happy, peaceful and content, in ratio to their own happiness, peace and contentment. It's like, "Yeah, I want all your dreams to come true and I want to see you smile, but only for as much as I smile and only in proportion to how many of my own dreams come true." That's what people today call, "friendship" and "care". It's not really friendship and it's not really care. Then there's like one or two people who would celebrate your own happiness and success even if it's out of proportion to their own. And that's a real blessing right there, that's a real friendship.

Thus nature provides a system for proportioning the growth of plants that satisfies the three canons of architecture. All modules are isotropic and they are related to the whole structure of the plant through self-similar spirals proportioned by the golden mean.

The world was horrible. But life continued. What is more, life’s usual proportions stayed the same. The ratio of good and evil, grief and happiness, remained unchanged.

Very harmful effects can follow accepting the philosophy which denies personal guilt or sin and thereby makes everyone nice. By denying sin, the nice people make a cure impossible. Sin is most serious, and the tragedy is deepened by the denial that we are sinners…The really unforgiveable sin is the denial of sin, because, by its nature, there is now nothing to be forgiven. By refusing to admit to personal guilt, the nice people are made into scandalmongers, gossips, talebearers, and supercritics, for they must project their real if unrecognized guilt to others. This, again, gives them a new illusion of goodness: the increase of faultfinding is in direct ratio and proportion to the denial of sin.

Rationality or consciousness is itself a ratio or proportion among the sensuous components of experience, and is not something added to such sense experience. Subrational beings have no means of achieving such a ratio or proportion in their sense lives but are wired for fixed wave lengths, as it were, having infallibility in their own area of experience. Consciousness, complex and subtle, can be impaired or ended by a mere stepping-up or dimming-down of any one sense intensity, which is the procedure in hypnosis. And the intensification of one sense by a new medium can hypnotize an entire community.

The Ark of the Covenant is a Golden Rectangle because its rectangular shape is in the proportions of the Golden Ratio.

In the pentagram, the Pythagoreans found all proportions well-known in antiquity: arithmetic, geometric, harmonic, and also the well-known golden proportion, or the golden ratio. ... Probably owing to the perfect form and the wealth of mathematical forms, the pentagram was chosen by the Pythagoreans as their secret symbol and a symbol of health. - Alexander Voloshinov [As quoted in Stakhov]

De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, 'My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?

The description of this proportion as Golden or Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That’s an incredible role for one number to play, but then again this one number has played an incredible role in human history and the universe at large.

The stars of the Milky Way galaxy trace a big, flat circle. With a diameter-to-thickness ratio of one hundred to one, our galaxy is flatter than the flattest flapjacks ever made. In fact, its proportions are better represented by a crepé or a tortilla.

Central to all these interlinked themes was that curious irrational, phi, the Golden Section. Schwaller de Lubicz believed that if ancient Egypt possessed knowledge of ultimate causes, that knowledge would be written into their temples not in explicit texts but in harmony, proportion, myth and symbol.

It would be hard to know what gigantic proportion of human life is spent in this same ratio of years under water on legs to one premature, exhausted moment on wings.

The pyramid that can be constructed on the diameters of earth and moon bears the precise proportions of the Great Pyramid

The golden ratio is a reminder of the relatedness of the created world to the perfection of its source and of its potential future evolution.

The impulse to all movement and all form is given by [the golden ratio], since it is the proportion that summarizes in itself the additive and the geometric, or logarithmic, series.

It is absurd that energy can be measured in calories, in ergs, in electron volts, in foot pounds, in B.T.U.s, in horsepower hours, in kilowatt hours–all measuring exactly the same thing. It is like having money in dollars, pounds, and so on; but unlike the economic situation where the ratio can change, these dopey things are in absolutely guaranteed proportion. If

The Golden Proportion, sometimes called the Divine Proportion, has come down to us from the beginning of creation. The harmony of this ancient proportion, built into the very structure of creation, can be unlocked with the 'key' ... 528, opening to us its marvelous beauty. Plato called it the most binding of all mathematical relations, and the key to the physics of the cosmos.

We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle

in the case of the given numbers 1, 2, 3, everybody can see that the fourth proportional is 6, and all the more clearly because we infer in one single intuition the fourth number from the ratio we see the first number bears to the second.

Accordingly, Pacioli's book also starts with a discussion of proportions in the human body, "since in the human body every sort of proportion and proportionality can be found, produced at the beck of the all-Highest through the inner mysteries of nature.

The Great Pyramid was a fractal resonator for the entire Earth. It is designed according to the proportions of the cosmic temple, the natural pattern that blends the two fundamental principles of creation. The pyramid has golden ratio, pi, the base of natural logarithms, the precise length of the year and the dimensions of the Earth built into its geometry. It demonstrates.... As John Michell has pointed out in his wonderful little book, City of Revelation, 'Above all, the Great Pyramid is a monument to the art of 'squaring the circle''.

A 2013 study by the National Center on Education and the Economy found that “the mathematics that most enables students to be successful in college courses is not high school mathematics, but middle school mathematics, especially arithmetic, ratio, proportion, expressions and simple equations.

Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind. Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ... To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples.

Terms BEN MARCUS, THE 1. False map, scroll, caul, or parchment. It is comprised of the first skin. In ancient times, it hung from a pole, where wind and birds inscribed its surface. Every year, it was lowered and the engravings and dents that the wind had introduced were studied. It can be large, although often it is tiny and illegible. Members wring it dry. It is a fitful chart in darkness. When properly decoded (an act in which the rule of opposite perception applies), it indicates only that we should destroy it and look elsewhere for instruction. In four, a chaplain donned the Ben Marcus and drowned in Green River. 2. The garment that is too heavy to allow movement. These cloths are designed as prison structures for bodies, dogs, persons, members. 3. Figure from which the antiperson is derived; or, simply, the antiperson. It must refer uselessly and endlessly and always to weather, food, birds, or cloth, and is produced of an even ratio of skin and hair, with declension of the latter in proportion to expansion of the former. It has been represented in other figures such as Malcolm and Laramie, although aspects of it have been co-opted for uses in John. Other members claim to inhabit its form and are refused entry to the house. The victuals of the antiperson derive from itself, explaining why it is often represented as a partial or incomplete body or system--meaning it is often missing things: a knee, the mouth, shoes, a heart

Petrie found nothing that disproved the pyramidologist's assumption that the Great Pyramid had been built according to a master plan. Indeed, he describes the Pyramid's architecture as being filled with extraordinary mathematical harmonies and concordances: those same strange symmetries that had so haunted the pyramidologist. Petrie not only noted, for example, that the proportions of the reconstructed pyramid approximated to pi - which others have since elaborated to include those twin delights of Renaissance and pyramidological mathematicians, the Golden Section and the Fibonacci Series ...

Note II.—From all that has been said above it is clear, that we, in many cases, perceive and form our general notions:—(1.) From particular things represented to our intellect fragmentarily, confusedly, and without order through our senses (II. xxix. Coroll.); I have settled to call such perceptions by the name of knowledge from the mere suggestions of experience.4 (2.) From symbols, e.g., from the fact of having read or heard certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (II. xviii. note). I shall call both these ways of regarding things knowledge of the first kind, opinion, or imagination. (3.) From the fact that we have notions common to all men, and adequate ideas of the properties of things (II. xxxviii. Coroll., xxxix. and Coroll. and xl.); this I call reason and knowledge of the second kind. Besides these two kinds of knowledge, there is, as I will hereafter show, a third kind of knowledge, which we will call intuition. This kind of knowledge proceeds from an adequate idea of the absolute essence of certain attributes of God to the adequate knowledge of the essence of things. I will illustrate all three kinds of knowledge by a single example. Three numbers are given for finding a fourth, which shall be to the third as the second is to the first. Tradesmen without hesitation multiply the second by the third, and divide the product by the first; either because they have not forgotten the rule which they received from a master without any proof, or because they have often made trial of it with simple numbers, or by virtue of the proof of the nineteenth proposition of the seventh book of Euclid, namely, in virtue of the general property of proportionals. But with very simple numbers there is no need of this. For instance, one, two, three, being given, everyone can see that the fourth proportional is six; and this is much clearer, because we infer the fourth number from an intuitive grasping of the ratio, which the first bears to the second.

The conclusion that the Egyptians of the Old Kingdom were acquainted with both the Fibonacci series and the Golden Section, says Stecchini, is so startling in relation to current assumptions about the level of Egyptian mathematics that it could hardly have been accepted on the basis of Herodotus' statement alone, or on the fact that the phi [golden] proportion happens to be incorporated in the Great Pyramid. But the many measurements made by Professor Jean Philippe Lauer, says Stecchini, definitely prove the occurrence of the Golden Section throughout the architecture of the Old Kingdom.... Schwaller de Lubicz also found graphic evidence that the pharonic Egyptians had worked out a direct relation between pi and phi in that pi = phi^2 x 6/5.

Shepherds say too that it makes a difference to the production of females and the production of males not only if mating occurs during north winds or south winds, but |767a10| also if while copulating the animals look south or north. So small a thing, they say, will sometimes shift the balance, becoming a cause of cold or heat, and these a cause in generation. In general, then, female and male are set apart from each other in relation to production of males and production of females due to the causes just mentioned. Nonetheless, |767a15| there must also be a proportion in their relation to each other. For all things that come to be either in accord with craft or nature exist in virtue of a certain ratio (logos).750 Now the hot, if it is too mastering, dries

The stars of the Milky Way galaxy trace a big, flat circle. With a diameter-to-thickness ratio of one thousand to one, our galaxy is flatter than the flattest flapjacks ever made. In fact, its proportions are better represented by a crépe or a tortilla. No, the Milky Way’s disk is not a sphere, but it probably began as one. We can understand the flatness by assuming the galaxy was once a big, spherical, slowly rotating ball of collapsing gas. During the collapse, the ball spun faster and faster, just as spinning figure skaters do when they draw their arms inward to increase their rotation rate. The galaxy naturally flattened pole-to-pole while the increasing centrifugal forces in the middle prevented collapse at midplane. Yes, if the Pillsbury Doughboy were a figure skater, then fast spins would be a high-risk activity. Any stars that happened to be formed within the Milky Way cloud before the collapse maintained large, plunging orbits. The remaining gas, which easily sticks to itself, like a mid-air collision of two hot marshmallows, got pinned at the mid-plane and is responsible for all subsequent generations of stars, including the Sun. The current Milky Way, which is neither collapsing nor expanding, is a gravitationally mature system where one can think of the orbiting stars above and below the disk as the skeletal remains of the original spherical gas cloud. This general flattening of objects that rotate is why Earth’s pole-to-pole diameter is smaller than its diameter at the equator. Not by much: three-tenths of one percent—about twenty-six miles. But Earth is small, mostly solid, and doesn’t rotate all that fast. At twenty-four hours per day, Earth carries anything on its equator at a mere 1,000 miles per hour. Consider the jumbo, fast-rotating, gaseous planet Saturn. Completing a day in just ten and a half hours, its equator revolves at 22,000 miles per hour and its pole-to-pole dimension is a full ten percent flatter than its middle, a difference noticeable even through a small amateur telescope. Flattened spheres are more generally called oblate spheroids, while spheres that are elongated pole-to-pole are called prolate. In everyday life, hamburgers and hot dogs make excellent (although somewhat extreme) examples of each shape. I don’t know about you, but the planet Saturn pops into my mind with every bite of a hamburger I take.

Speaking generally, sociability stands in inverse ratio with age. A little child raises a piteous cry of fright if it is left alone for only a few minutes; and later on, to be shut up by itself is a great punishment. Young people soon get on very friendly terms with one another; it is only the few among them of any nobility of mind who are glad now and then to be alone;—but to spend the whole day thus would be disagreeable. A grown-up man can easily do it; it is little trouble to him to be much alone, and it becomes less and less trouble as he advances in years. An old man who has outlived all his friends, and is either indifferent or dead to the pleasures of life, is in his proper element in solitude; and in individual cases the special tendency to retirement and seclusion will always be in direct proportion to intellectual capacity. For

You too can make the golden cut, relating the two poles of your being in perfect golden proportion, thus enabling the lower to resonate in tune with the higher, and the inner with the outer. In doing so, you will bring yourself to a point of total integration of all the separate parts of your being, and at the same time, you will bring yourself into resonance with the entire universe.... Nonetheless the universe is divided on exactly these principles as proven by literally thousands of points of circumstantial evidence, including the size, orbital distances, orbital frequencies and other characteristics of planets in our solar system, many characteristics of the sub-atomic dimension such as the fine structure constant, the forms of many plants and the golden mean proportions of the human body, to mention just a few well known examples. However the circumstantial evidence is not that on which we rely, for we have the proof in front of us in the pure mathematical principles of the golden mean.

Men are animals. On matters of eros, we accept this as a kind of psychological axiom. Men are tamed by society, kept, for the most part, between boundaries, yet the subduing isn’t so complete as to hide their natural state, which announces itself in endless ways—through pornography, through promiscuity, through the infinity of gazes directed at infinite passing bodies of desire—and which is affirmed by countless lessons of popular science: that men’s minds are easily commandeered by the lower, less advanced neural regions of the brain; that men are programmed by evolutionary forces to be pitched inescapably into lust by the sight of certain physical qualities or proportions, like the .7 waist-to-hip ratio in women that seems to inflame heterosexual males all over the globe, from America to Guinea-Bissau; that men are mandated, again by the dictates of evolution, to increase the odds that their genes will survive in perpetuity and hence that they are compelled to spread their seed, to crave as many .7’s as possible. But

Statisticians say that stocks with healthy dividends slightly outperform the market averages, especially on a risk-adjusted basis. On average, high-yielding stocks have lower price/earnings ratios and skew toward relatively stable industries. Stripping out these factors, generous dividends alone don’t seem to help performance. So, if you need or like income, I’d say go for it. Invest in a company that pays high dividends. Just be sure that you are favoring stocks with low P/Es in stable industries. For good measure, look for earnings in excess of dividends, ample free cash flow, and stable proportions of debt and equity. Also look for companies in which the number of shares outstanding isn’t rising rapidly. To put a finer point on income stocks to skip, reverse those criteria. I wouldn’t buy a stock for its dividend if the payout wasn’t well covered by earnings and free cash flow. Real estate investment trusts, master limited partnerships, and royalty trusts often trade on their yield rather than their asset value. In some of those cases, analysts disagree about the economic meaning of depreciation and depletion—in particular, whether those items are akin to earnings or not. Without looking at the specific situation, I couldn’t judge whether the per share asset base was shrinking over time or whether generally accepted accounting principles accounting was too conservative. If I see a high-yielder with swiftly rising share counts and debt levels, I assume the worst.

Absolute continuity of motion is not comprehensible to the human mind. Laws of motion of any kind become comprehensible to man only when he examines arbitrarily selected elements of that motion; but at the same time, a large proportion of human error comes from the arbitrary division of continuous motion into discontinuous elements. There is a well known, so-called sophism of the ancients consisting in this, that Achilles could never catch up with a tortoise he was following, in spite of the fact that he traveled ten times as fast as the tortoise. By the time Achilles has covered the distance that separated him from the tortoise, the tortoise has covered one tenth of that distance ahead of him: when Achilles has covered that tenth, the tortoise has covered another one hundredth, and so on forever. This problem seemed to the ancients insoluble. The absurd answer (that Achilles could never overtake the tortoise) resulted from this: that motion was arbitrarily divided into discontinuous elements, whereas the motion both of Achilles and of the tortoise was continuous. By adopting smaller and smaller elements of motion we only approach a solution of the problem, but never reach it. Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem. A modern branch of mathematics having achieved the art of dealing with the infinitely small can now yield solutions in other more complex problems of motion which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when it deals with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous. To understand the laws of this continuous movement is the aim of history. But to arrive at these laws, resulting from the sum of all those human wills, man's mind postulates arbitrary and disconnected units. The first method of history is to take an arbitrarily selected series of continuous events and examine it apart from others, though there is and can be no beginning to any event, for one event always flows uninterruptedly from another. The second method is to consider the actions of some one man—a king or a commander—as equivalent to the sum of many individual wills; whereas the sum of individual wills is never expressed by the activity of a single historic personage. Historical science in its endeavor to draw nearer to truth continually takes smaller and smaller units for examination. But however small the units it takes, we feel that to take any unit disconnected from others, or to assume a beginning of any phenomenon, or to say that the will of many men is expressed by the actions of any one historic personage, is in itself false. It needs no critical exertion to reduce utterly to dust any deductions drawn from history. It is merely necessary to select some larger or smaller unit as the subject of observation—as criticism has every right to do, seeing that whatever unit history observes must always be arbitrarily selected. Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.

only increased the debt, as governments rightly have borrowed. By March 2012 there were some $43 trillion of government bonds in issue,8 compared with only $11 trillion at the end of 2001. That is only a fraction of Western governments’ true liabilities, once you factor in pensions and health care. The numbers for many cities are even worse: San Bernardino in California and Detroit in Michigan both filed for bankruptcy because of these off-balance sheet obligations. And who will pay for all this? In “old Europe,” for instance, the working-age population peaked in 2012 at 308 million—and is set to decline to 265 million by 2060. These will have to support ever more old people: The old-age dependency ratio (the number of over-sixty-fives as a proportion of the number of

In Depth Types of Effect Size Indicators Researchers use several different statistics to indicate effect size depending on the nature of their data. Roughly speaking, these effect size statistics fall into three broad categories. Some effect size indices, sometimes called dbased effect sizes, are based on the size of the difference between the means of two groups, such as the difference between the average scores of men and women on some measure or the differences in the average scores that participants obtained in two experimental conditions. The larger the difference between the means, relative to the total variability of the data, the stronger the effect and the larger the effect size statistic. The r-based effect size indices are based on the size of the correlation between two variables. The larger the correlation, the more strongly two variables are related and the more of the total variance in one variable is systematic variance related to the other variable. A third category of effect sizes index involves the odds-ratio, which tells us the ratio of the odds of an event occurring in one group to the odds of the event occurring in another group. If the event is equally likely in both groups, the odds ratio is 1.0. An odds ratio greater than 1.0 shows that the odds of the event is greater in one group than in another, and the larger the odds ratio, the stronger the effect. The odds ratio is used when the variable being measured has only two levels. For example, imagine doing research in which first-year students in college are either assigned to attend a special course on how to study or not assigned to attend the study skills course, and we wish to know whether the course reduces the likelihood that students will drop out of college. We could use the odds ratio to see how much of an effect the course had on the odds of students dropping out. You do not need to understand the statistical differences among these effect size indices, but you will find it useful in reading journal articles to know what some of the most commonly used effect sizes are called. These are all ways of expressing how strongly variables are related to one another—that is, the effect size. Symbol Name d Cohen’s d g Hedge’s g h 2 eta squared v 2 omega squared r or r 2 correlation effect size OR odds ratio The strength of the relationships between variables varies a great deal across studies. In some studies, as little as 1% of the total variance may be systematic variance, whereas in other contexts, the proportion of the total variance that is systematic variance may be quite large,

The Germans, out of a population of under 70 millions, mobilized during the war for military service 13¼ million persons. Of these, according to the latest German official figures for all fronts including the Russian, over 7 millions suffered death, wounds or captivity, of whom nearly 2 millions perished.15 France, with a population of 38 millions, mobilized a little over 8 million persons. This however includes a substantial proportion of African troops outside the French population basis. Of these approximately 5 millions became casualties, of whom 1½ millions lost their lives. The British Empire, out of a white population of 60 millions, mobilized nearly 9½ million persons and sustained over 3 million casualties including nearly a million deaths. The British totals are not directly comparable with those of France and Germany. The proportion of coloured troops is greater. The numbers who fell in theatres other than the western, and those employed on naval service, are both much larger. The French and German figures are however capable of very close comparison. Both the French and German armies fought with their whole strength from the beginning to the end of the war. Each nation made the utmost possible demand upon its population. In these circumstances it is not surprising that the official French and German figures tally with considerable exactness. The Germans mobilized 19 per cent. of their entire population, and the French, with their important African additions, 21 per cent. Making allowance for the African factor, it would appear that in the life-and-death struggle both countries put an equal strain upon their manhood. If this basis is sound—and it certainly appears reasonable—the proportion of French and German casualties to persons mobilized displays an even more remarkable concordance. The proportion of German casualties to total mobilized is 10 out of every 19, and that of the French 10 out of every 16. The ratios of deaths to woundings in Germany and France are almost exactly equal, viz. 2 to 5. Finally these figures yield a division of German losses between the western and all other fronts of approximately 3 to 1 both in deaths and casualties. All

Contrary to the widespread conventional belief -that the Great Pyramid can be scaled down, the Divine Proportions contributing in the Great Pyramid's geometry cannot be embedded linearly into its structure, hence, the pyramid's size does indeed matter. Therefore, the ratio between its height and its base perimeter is irrelevant in the context of its scalability.

When the study was completed and the data analyzed, Rich reported that the group of incest survivors had abnormalities in their CD45 RA-to-RO ratio, compared with their nontraumatized peers. CD45 cells are the “memory cells” of the immune system. Some of them, called RA cells, have been activated by past exposure to toxins; they quickly respond to environmental threats they have encountered before. The RO cells, in contrast, are kept in reserve for new challenges; they are turned on to deal with threats the body has not met previously. The RA-to-RO ratio is the balance between cells that recognize known toxins and cells that wait for new information to activate. In patients with histories of incest, the proportion of RA cells that are ready to pounce is larger than normal. This makes the immune system oversensitive to threat, so that it is prone to mount a defense when none is needed, even when this means attacking the body’s own cells.

Nor are the elite modern institutions selecting for personality qualities of independent and inner motivations and evaluations that are an intrinsic part of the Endogenous personality – quite the opposite, in fact; since there are multiple preferences and quotas in place which net exclude Europeandescended men (that group with by far the highest proportion of Endogenous personalities – i.e. having the ultra-high intelligence and creative personality type). This can be seen in explicit group preference policies and campaigns enforced by government (and the mass media), and informal (covert) preferences – leading to ratios and compositions at elite institution (especially obvious in STEM subjects: i.e. Science, Technology, Engineering, Medicine) that demonstrate grossly lower proportions of European-descended men than would result from selecting for the Endogenous personality type.

The OECD study also found that women’s words translated into action. As female political representation increased in Greece, Portugal and Switzerland, these countries experienced an increase in educational investment. Conversely, as the proportion of female legislators in Ireland, Italy and Norway decreased in the late 1990s, those countries experienced ‘a comparable drop in educational expenditures as a percentage of GDP’. As little as a single percentage point rise in female legislators was found to increase the ratio of educational expenditure. Similarly, a 2004 Indian study of local councils in West Bengal and Rajasthan found that reserving one-third of the seats for women increased investment in infrastructure related to women’s needs.5 A 2007 paper looking at female representation in India between 1967 and 2001 also found that a 10% increase in female political representation resulted in a 6% increase in ‘the probability that an individual attains primary education in an urban area’.

That a mother should wish to see her daughters happily married, is natural and proper; that a young lady should be pleased with polite attentions is likewise natural and innocent; but this undue anxiety, this foolish excitement about showing off the attentions of somebody, no matter whom, is attended with consequences seriously injurious. It promotes envy and rivalship; it leads our young girls to spend their time between the public streets, the ball room, and the toilet; and, worst of all, it leads them to contract engagements, without any knowledge of their own hearts, merely for the sake of being married as soon as their companions. When married, they find themselves ignorant of the important duties of domestic life; and its quiet pleasures soon grow tiresome to minds worn out by frivolous excitements. If they remain unmarried, their disappointment and discontent are, of course, in proportion to their exaggerated idea of the eclat attendant upon having a lover. The evil increases in a startling ratio; for these girls, so injudiciously educated, will, nine times out of ten, make injudicious mothers, aunts, and friends;

In a way, the Phi Triangle of the Golden Mean could be compared to the path of light sent forth from the great All-Seeing Eye of God in the beginning, and which paved the way for the creation of the Universe.

The Pythagoreans... were fascinated by certain specific ratios, ...The Greeks knew these as the 'golden' proportion and the 'perfect' proportion respectively. They may well have been learned from the Babylonians by Pythagoras himself after having been taken prisoner in Egypt. Ratios lay at the heart of the Pythagorean theory of music.

The golden section was discovered by the Egyptians, and has been used in art and architecture, most commonly, during the classical ages of Egypt and Greece.

Schwaller de Lubicz identifies the Golden Mean as "the fundamental scission," or division of one into two, that creates three things - the original whole and two parts, one in golden proportion to the whole and the other in golden proportion to that.

The Golden Mean was considered a fundamental constant by the Egyptians and the fundamental division of the whole into two parts.

As I explain at some length in 'The Crystal Sun' this particular angle, which we can call the 'golden angle,' is the precise value of the acute angle of of a right-angled 'golden triangle' that embodies the golden mean proportion .... The Danish art historian Else Kielland established with conclusive and absolutely overwhelming evidence and analysis that this angle was the basis for all Egyptian art and architecture. She did this in her monumental work 'Geometry in Egyptian Art' ..... The King's Chamber inside the Great Pyramid embodies no fewer than eight occurrences of the golden angle, and the coffer in the chamber embodies yet more.

One would expect to find a comparatively high proportion of carbon 13 [the carbon from corn] in the flesh of people whose staple food of choice is corn - Mexicans, most famously. Americans eat much more wheat than corn - 114 pounds of wheat flour per person per year, compared to 11 pounds of corn flour. The Europeans who colonized America regarded themselves as wheat people, in contrast to the native corn people they encountered; wheat in the West has always been considered the most refined, or civilized, grain. If asked to choose, most of us would probably still consider ourselves wheat people, though by now the whole idea of identifying with a plant at all strikes us as a little old-fashioned. Beef people sounds more like it, though nowadays chicken people, which sounds not nearly so good, is probably closer to the truth of the matter. But carbon 13 doesn't lie, and researchers who compared the carbon isotopes in the flesh or hair of Americans to those in the same tissues of Mexicans report that it is now we in the North who are the true people of corn. 'When you look at the isotope ratios,' Todd Dawson, a Berkeley biologist who's done this sort of research, told me, 'we North Americans look like corn chips with legs.' Compared to us, Mexicans today consume a far more varied carbon diet: the animals they eat still eat grass (until recently, Mexicans regarded feeding corn to livestock as a sacrilege); much of their protein comes from legumes; and they still sweeten their beverages with cane sugar. So that's us: processed corn, walking.

Value of a Trade Mark is directly proportional to your Aggression and Risk Ratio.

Time and space are inversely proportional. Dimensions are created as nested cycles of time. These specific ratios are carried like echoes where the harmonious frequencies have more duration and the discordant ones decay quickly. When we arrive at the Plank scale I do not think we will find triangles because nature is lazy, what we will probably find is a fractal or multi-fractal feature of nested relationships.

The 5/6 ratio stems from the calendrical proportions of ancient Egypt which we witness on the circular zodiac of Dendera; it's calculated by dividing the 30 days of the month (i.e. five periods of six decans each) over the total number of decans in a year (i.e. 36). The result corresponds with the decanal-system daily contribution to the month and is in accordance with my interpretation of the zodiac for including one additional period (of six decans) that is not part of the month and rather of a geometrical significance to reference the eastern portals.

We know, indeed, that the producers, although they constitute hardly one-third of the inhabitants of civilized countries, even now produce such quantities of goods that a certain degree of comfort could be brought to every hearth. We know further that if all those who squander today the fruits of others' toil were forced to employ their leisure in useful work, our wealth would increase in proportion to the number of producers, and more. Finally, we know that contrary to the theory enunciated by Malthus - that oracle of middle-class economics - the productive powers of the human race increase at a much more rapid ratio than its powers of reproduction. The more thickly men are crowded on the soil, the more rapid is the growth of their wealth-creating power.

Wittkower's response - which resonated for decades - to the manifest lack of robustness of modern civilization was to reassert the absolute difference between the past and the present: premodern societies were oriented, and they knew hierarchy. Wittkower argued, on the basis of the texts by Alberti and Palladio, that the architecture of the Italian Renaissance materialized a mathematical program: a system of ratios that pictured the invisible structure of the cosmos. Architecture placed the human body within this system. It is hard to see the difference between this and Sedlmayr's view except that the one believes that man's image was best framed by forms based on the divinely measured proportions of the human body, and the other believes that man's image was best framed by an image of divinity itself. Wittkower recovers a religious conception of architecture but detached from Christianity: the Renaissance church as a Hindu temple, as it were.

Pythagoras concluded that ratios govern not only music but also all other types of beauty. To the Pythagoreans, ratios and proportions controlled musical beauty, physical beauty, and mathematical beauty. Understanding nature was as simple as understanding the mathematics of proportions.

But the knowledge that Filippo sought to uncover was unique. In calculating the proportions of columns and pediments he determined the measurements specific to the three architectural orders (Doric, Ionic, and Corinthian) that had been invented by the Greeks and then imitated and refined by the Romans. These orders were governed by precise mathematical ratios, a series of proportional rules that regulated aesthetic effect. The height of a Corinthian entablature, for example, is a quarter of the height of the columns on which it stands, while the height of each column is ten times its diameter, and so forth. Numerous examples of these three orders existed in Rome in the early 1400s. The columns in the Baths of Diocletian are Doric, for instance, while those at the Temple of Fortuna Virilis feature the Ionic, and the portico of the Pantheon the Corinthian. The Colosseum makes use of all three: Doric on the lowest level, Ionic on the second, and Corinthian at the top.

The God of Plato’s Timaeus is the Demiurge, the Architect of the Universe—in a profound sense, the Master Builder. Plato tells us He constructs the physical world from the five Platonic solids by incorporating the four physical elements—earth, air, fire, and water—in proportions to ratios such as 1:2:4:8 and 1:3:9:27. What holds Plato’s world together is literally “geometrical proportion.”43 Thanks in large part to the school of Chartres, by 1150 the image of God as Geometer was appearing everywhere, in medieval manuscripts and in statuary. And the most important geometric form of all was the cube, the only figure with a 1:1:1:1 ratio, which every student of Plato or Pythagoras knew was the symbol of divine unity or Oneness.

Small nonlinearities were easy to disregard. People who conduct experiments learn quickly that they live in an imperfect world. In the centuries since Galileo and Newton, the search for regularity in experiment has been fundamental. Any experimentalist looks for quantities that remain the same, or quantities that are zero. But that means disregarding bits of messiness that interfere with a neat picture. If a chemist finds two substances in a constant proportion of 2.001 one day, and 2.003 the next day, and 1.998 the day after, he would be a fool not to look for a theory that would explain a perfect two-to–one ratio.

NATIONAL SYMBOLS National Flag Our National Flag is a tricolour with deep saffron at the top, white in the middle and dark green at the bottom in equal proportion. The ratio of the width of the flag to its length is 2:3. In the centre of the white band is a navy blue wheel known as Ashok Chakra. It has 24 spokes. Each colour of the flag has its own significance : Saffron — signifies courage and sacrifice White — signifies truth and peace Green — signifies faith and prosperity The wheel is a symbol of progress round the clock.   National Emblem Our National Emblem is a Lion Capital, adopted from the Ashoka’s Pillar at Sarnath.

See Leon Podles, The Church Impotent: The Feminization of Christianity (Dallas: Spence, 1999), who notes that in 1952 the adult attenders on Sunday morning in typical Protestant churches were 53 percent female and 47 percent male, which was almost exactly the same as the proportion of women and men in the adult population in the U.S. But by 1986 (after several decades of feminist influence in liberal denominations) the ratios were closer to 60 percent female and 40 percent male, with many congregations reporting a ratio of 65 percent to 35 percent (11-12). Podles focuses primarily on Roman Catholic and liberal Protestant churches in his study, and he concludes that, if present trends continue, the “Protestant clergy will be characteristically a female occupation, like nursing, within a generation” (xiii). See also, Why Men Hate Going to Church, by David Murrow (Nashville: Thomas Nelson, 2005). Murrow describes in detail the increasing “feminization” of many churches, a trend that is driving men away.

This relationship, often called the Golden mean, has been discovered and rediscovered at various times in history as a unique proportion believed to have both aesthetic and mystic significance. That the Egyptians knew of it and used it seems certain.

The golden era of the golden number was the Italian renaissance. The expression divine proportion was coined by the great mathematician Luca Pacioli in his book 'De divina proportione', written in 1509.

When the Ant-People rebuilt the actual Moon we see, they made it of similar proportions to the first natural Moon that had been destroyed, but they devised it to be four hundred times smaller than the Sun and set it four hundred times closer, so that it would fit perfectly its diameter during eclipses. This coded message for any intelligence was to remember the Ant-People as the first civilization on Earth. It explains why this perfect ratio is nowhere else to be found in our solar system, nor in any other.

With all of the data and analytical tools at our disposal, you would not expect this, but a substantial proportion of business and investment decisions are still based on the average. I see investors and analysts contending that a stock is cheap because it trades at a PE that is lower than the sector average or that a company has too much debt because its debt ratio is higher than the average for the market. The average is not only a poor central measure on which to focus in distributions that are not symmetric, but it strikes me as a waste to not use the rest of the data.

The first is the belief that the universe is essentially harmonious, and that the source of that concord lies in mathematical proportions which can be directly related to musical harmonies. Pythagoras, in an oft-repeated legend, was said to have meditated on the sound of smiths beating hammers upon anvils, and to have argued that a hammer half as heavy produced a note an octave above its full-sized fellow.3 More important were the experiments with a single string, or monochord, attributed to him by his successors. If a stretched string is divided exactly into two it produces a sound an octave higher than the fundamental pitch (the ratio 2:1), the intervals of the fourth and fifth can similarly be expressed as the ratios 4:3 and 3:2 respectively, and all other intervals can be described in mathematical terms.4 These numerical proportions were then extended to describe the relationships of the planetary spheres, both in their relative distance one from another, and in the speed of their movement. The ideas were given influential (if obscure) expression in Plato’s Timaeus, and endlessly elaborated in succeeding centuries up to the Renaissance. One of the final manifestations of this understanding is provided in the illustration of cosmic harmony from Robert Fludd’s Utriusque cosmi … historia 1

Plato considered the golden section proportion the most binding of all mathematical relations, making it the key to the physics of the cosmos.

Flower of life: A figure composed of evenly-spaced, overlapping circles creating a flower-like pattern. Images of the Platonic solids and other sacred geometrical figures can be discerned within its pattern. FIGURE 3.14 FLOWER OF LIFE The Platonic solids: Five three-dimensional solid shapes, each containing all congruent angles and sides. If circumscribed with a sphere, all vertices would touch the edge of that sphere. Linked by Plato to the four primary elements and heaven. FIGURE 3.15 PENTACHORON The applications of these shapes to music are important to sound healing theory. The ancients have always professed a belief in the “music of the spheres,” a vibrational ordering to the universe. Pythagorus is famous for interconnecting geometry and math to music. He determined that stopping a string halfway along its length created an octave; a ratio of three to two resulted in a fifth; and a ratio of four to three produced a fourth. These ratios were seen as forming harmonics that could restore a disharmonic body—or heal. Hans Jenny furthered this work through the study of cymatics, discussed later in this chapter, and the contemporary sound healer and author Jonathan Goldman considers the proportions of the body to relate to the golden mean, with ratios in relation to the major sixth (3:5) and the minor sixth (5:8).100 Geometry also seems to serve as an “interdimensional glue,” according to a relatively new theory called causal dynamical triangulation (CDT), which portrays the walls of time—and of the different dimensions—as triangulated. According to CDT, time-space is divided into tiny triangulated pieces, with the building block being a pentachoron. A pentachoron is made of five tetrahedral cells and a triangle combined with a tetrahedron. Each simple, triangulated piece is geometrically flat, but they are “glued together” to create curved time-spaces. This theory allows the transfer of energy from one dimension to another, but unlike many other time-space theories, this one makes certain that a cause precedes an event and also showcases the geometric nature of reality.101 The creation of geometry figures at macro- and microlevels can perhaps be explained by the notion called spin, first introduced in Chapter 1. Everything spins, the term spin describing the rotation of an object or particle around its own axis. Orbital spin references the spinning of an object around another object, such as the moon around the earth. Both types of spin are measured by angular momentum, a combination of mass, the distance from the center of travel, and speed. Spinning particles create forms where they “touch” in space.