Sunday, January 15, 2017

Donald Trump Against the Decline and Fall

Donald Trump was not my first choice for the Republican nomination. He often makes intemperate statements, and comes across as his own worst enemy during the campaign. He might not be the best person lead the United States down the right road to a secure and prosperous future, but he is at least on the right road. If we're on the wrong road, as represented by Hillary Clinton and the Democratic National Committee, we have no chance whatsoever of reaching any destination except national ruin.

Robinson, Breasted, and Smith's most recent edition of Earlier Ages was written in 1965, more than 50 years before the current issues it describes with uncanny precision. These issues are, quite simply, as Michael Savage describes them: "Borders, language, and culture." Donald Trump has shown clearly that he wants to choose the road that leads us away from the Roman Empire's fatal mistakes while Hillary Clinton wants to repeat them.

Donald TrumpOne of the discussion questions for the chapter on "A Century of Revolution" is, "The racial change which took place in the population was the greatest single cause of the downfall of Rome" (page 366).
Page 355 makes it clear, however, that "racial" does not refer to skin color or ethnicity as it does today, but rather to attitudes, values, and culture. Rome benefited enormously from ethnic diversity while foreign, inferior, and non-Roman attitudes and values were the principal causes of its destruction.


Desirable Immigrants Helped Build Rome and the United States

Hillary Clinton and the Democratic Party support unrestricted immigration while Donald Trump welcomes only immigrants who have job skills along with American values, or who are at least willing to adopt our values. The roles of desirable and undesirable immigrants in Rome are object lessons here.

Greece played a major role in civilizing Rome, just as Rome later civilized most of Western Europe along with Britain. Romans were the classical world's greatest engineers, and they built roads and aqueducts to last forever; Europeans still drive on Roman roads today. The Romans, however, owed most of their natural sciences and fine arts to desirable immigrants from Egypt, the Near East, and especially Greece. These immigrants' role in building Rome was similar to that of equally desirable immigrants in the growth of the United States.

The Greeks were, after all, the people whose stories described assault robots (Talos), industrial robots (Hephaestus' mechanical helpers), and flying machines (Daedalus and Icarus) roughly 2000 years ago. Modern experiments leave it open to question as to whether Archimedes used a heat ray from a parabolic array of mirrors to incinerate Roman warships, and modern solar furnaces use similar arrays of mirrors. Heron of Alexandria proved that steam could perform useful work while Dionysius of Alexandria built the contemporary equivalent of a machine gun. The Greeks were, in summary, the people who taught the Western World how to think.

The Greeks who wrote stories about Hercules could have even been said to have invented hydraulic mining because the hero diverted a river to wash excrement from the Augean Stables. The Romans put into practice the idea that water could remove other soft materials like dirt to reveal desirable ores and metals. This legacy from the Greeks is why the Western World and Westernized World (e.g. Japan) are still the sources of almost all patents and Nobel Prizes while the Third World and especially the Islamic world lag far behind.

Many of Rome's desirable immigrants were admittedly involuntary immigrants (more commonly known as slaves), but their influence on Roman society was nonetheless positive. The presence of a Greek tutor in a Roman household was a status symbol. Wealthy Romans might even purchase a Greek physician, who was then obviously treated as a valuable household retainer rather than as a domestic animal, the usual fate of unskilled slaves on farms or in mines.

The United States benefited similarly from desirable immigrants who included our own ancestors, unless we are Native Americans. The bottom line is, however, that all these immigrants either brought with them values and attitudes similar to ours, or they adopted ours in a process that used to be called "assimilation."


When Diversity Becomes Perversity

Diverse and dysfunctional values and culture, rather than ethnic diversity, ruined Rome roughly 1900 years ago the way they are ruining Europe today, and are likely to ruin the United States.

"Moreover, slaves were constantly gaining their freedom, and they frequently retained slave ideas of conduct even after they were freedmen. This change in the nationality of the citizens, and the subsequent change in ideals, conduct, and government, were perhaps the chief causes of the downfall of Rome."

Donald TrumpThis is happening very openly in Germany, France, Sweden, the United Kingdom, and several other European nations that have not only permitted but welcomed an influx of fundamentalist "Muslims" substantial numbers of whom have nothing whatsoever in common with the advanced societies they now infest. They lack the Euro-American work ethic, Euro-American (originally Greek) inventiveness and creativeness, and indeed anything else of value to an infidel nation. They produce little and invent nothing except for particularly cruel ways to murder those who are unlike themselves.

An alarming share of the young males do believe they have the Allah-given right to kill, rob, rape, and/or enslave those who do not share their depraved ideology, which is why European governments are urging women to dress according to the standards of the 19th rather than the 21st century. After all, a woman who does not wear a sack over her head is "uncovered meat" whom any militant "Muslim" has the right to "take." Barack Obama, Hillary Clinton, and most of the Democratic Party wants to welcome this flood while Donald Trump wants to admit only those who have job skills along with values that are consistent with our society.

Slavery was eradicated from our country more than 150 years ago, but the Democratic Party is nonetheless infusing elements of African-American society with "slave ideas of conduct" in the 21st century. The Democratic National Committee wants to keep Black people in a state of dependence on government programs because, while Black lives might not matter, Black votes do. While it was never proven that Lyndon B. Johnson said that he would have the N-words voting Democratic for the next 200 years, there is audio of Johnson using the N word along with an ethnic slur for Poles. Hillary Clinton's reliance on somebody like Al Sharpton to deliver the Black vote, or a substantial portion thereof, shows clearly how little she thinks of African-Americans.

This is not the only area where Obama, Clinton, and the Democratic National Committee seek to lead us down the same path that led the world's greatest civilization to ruin. The other issue is economic.


Excessive Government Regulation Ruined Rome

Earlier Ages (pages 359 to 360) describes how the Roman government ruined itself economically by spending far more than it could collect in taxes, the same way our government increases its deficit every year. A progressive income tax system, in which Rome looked to its "one percent" for revenue, resulted in a situation in which "there was no incentive to hard work when success in business meant ruinous over-taxation."

Rome's most productive citizens therefore "went John Galt" long before anybody ever heard of John Galt, with the result that Emperor Diocletian tried to force people to continue to practice their occupations. He added wage and price controls that reduced the ordinary Roman to a condition "just where the peasant on the Nile had been for thousands of years." Diocletian's modern incarnation, Hillary Clinton, wants similarly to raise taxes not only on the one percent but also on the middle class, and the middle class can meanwhile attest to how Obama's so-called "Affordable" Care Act has affected its finances and access to health insurance. Hillary also made it clear that she believes that the estates of wealthy people somehow belong to the government even though the government had no hand in creating them.

The United States is at a crossroads where one road leads to a prosperous and secure future while the other leads to the ash heap of history where the Roman Empire already resides. Donald Trump may or may not be the best person to lead us down the former path, but we know for certain that Hillary Clinton will take us down the latter. This leaves voters with only one viable alternative in November.

William A. Levinson is the author of several books on business management including content on organizational psychology, as well as manufacturing productivity and quality.

By William A. Levinson

Source: American Thinker

Sunday, January 8, 2017

Golden Ratio Myth, Fact and Misunderstanding: The missing evidence

There are many misconceptions and misrepresentations about the golden ratio. Some look too fervently for patterns and say it exists where it really doesn't. Some whose goal is to debunk golden ratio myth say it doesn't exist where it really does, missing the obvious and often not stating what proportions appear instead. People on both sides often just repeat what they've heard rather than personally performing the analysis required to support their conclusions. Intelligence and education are not always factors in getting to the truth, as even Ph.D.'s in mathematics sometimes get it wrong. As the author of this site since 1997, I've changed my views and the information on this site as well. Let's look at some of the common points of confusion and debate, covering beauty, the Parthenon, the UN Secretariat Building, the Great Pyramid, Nautilus shell, use by famous artists (Da Vinci, Botticelli, Seurat, etc.) and other topics. I'll provide objective answers, with additional evidence in the supporting articles for each topic. I'll also welcome any evidence to support opposing views.

Golden ratio proportions
Golden ratio proportions of the teeth/lips and nose in relation
to the distance from the pupils to the bottom of the chin

Does the human face reflect golden ratios in its proportions?

Not everyone will agree, but there is much evidence to demonstrate that the answer is "Yes." There's some truth to the adages "beauty is in the eye of the beholder" and "beauty is only skin deep," yet there is no denying that there's almost universal agreement when asked to distinguish between a very attractive face and a very unattractive face. Let's acknowledge that every human face has many unique measurements and proportions. As a result no single measure can be said to apply to every aspect of every face. The real question is whether the golden ratio represents an average or ideal in human facial dimensions. The even more interesting question is whether golden ratios in facial features impact our perceptions of attractiveness and beauty. Debunkers will point out the variations, and perhaps suggest that those who find golden ratios in a beautiful face did so because they were looking for them. Consider the following studies though, which demonstrate that the connection to beauty is based on much more than looking for data to fit the desired result:

  • Dr. Stephen Marquardt, a maxillofacial surgeon and recognized expert on beauty, studied hundreds of faces in his studies on attractiveness to develop his patented "beauty mask." The mask identifies archetypes for the faces perceived as most beautiful. The mask is based on dodecagons, which are based on golden ratios. Below is an example of a face that has been morphed to fit the beauty mask. Make your own assessment and see the YouTube video of the step-by-step transformation.
    beauty mask
  • In 2009, a university study identified ideal facial proportions, as selected by study participants who chose the most attractive face from a series of photos. The researchers were not looking for the golden ratio. To the contrary, they concluded that it didn't exist and announced their own two "new golden ratios" of attractiveness. My subsequent analysis, however, shows that their ideal facial features reveal a dozen golden ratios, in both horizontal and vertical dimensions of key facial markers. See image and details further below in this article.
  • In 2012, a UK cosmetic company ran a competition to find Britain's most perfect face. The winner was selected from 8,000 contestants. Her face shows almost two dozen golden ratios in both the horizontal and vertical dimensions of key facial markers, as shown in an accompanying YouTube video to the article.
                         


Does the design of the Parthenon reflect the golden ratio?

The front facade of the Parthenon
Yes, but only in part, and not in the way you often hear. The front facade of the Parthenon is often shown with a golden rectangle framing it to illustrate its golden ratio proportions. Unfortunately, a precise golden rectangle would need to start at the second of four steps approaching the Parthenon, rather than the base of its columns. The golden rectangle would then end at the peak of the Parthenon, a point which has to be estimated because the structure is in ruins. Even as a golden ratio enthusiast, this is rather arbitrary and unconvincing as evidence. It's close to a golden rectangle, but not close enough to conclude that it was used in its design. That, however, is not the end of the story. The top structure across the columns has dimensions that appear to be very close to the golden ratio. More interesting yet, the fourteen rectangles across the horizontal beam each appear to be divided exactly at their golden ratio point, as closely as can be determined from photos. These golden ratios may or may not have been included intentionally among all the other numbers and ratios represented in the Parthenon. The golden ratio was written of by Euclid almost 100 years before its construction though, so the architects of the Parthenon certainly could have been aware of it. The Parthenon has a complex design that embodies many numbers and mathematical relationships. It's not unreasonable at all that the golden ratio would have been among those represented.


Is the spiral of the Nautilus shell based on the golden ratio?

The spiral of the Nautilus
It can, but not in the way you often hear. The traditional "golden spiral" is constructed from a series of adjacent golden rectangles. This creates a spiral that increases in dimension by the golden ratio with every 90 degree turn of the spiral. The spiral of the Nautilus shell does not match this golden spiral, which is a source of the confusion on this question. There is, however, more than one way to create a spiral with golden ratio proportions. As one example, you can create a spiral that expands by the golden ratio with every 180 degree turn of the spiral. This spiral is a closer match for the spirals of many Nautilus shells, especially in the first several rotations of the spiral. An even closer match yet is found when when measuring to spirals on opposite sides of the center point.


Did Renaissance artists (Botticelli, Da Vinci, Michelango) use the golden ratio in composition of their paintings?

Renaissance artists
Yes. This is often contested by debunkers as being completely unsupported. One frequently referenced article by a Ph.D. in mathematics points out that there is no mention of the golden ratio in two biographies written about da Vinci. Wouldn't it be better to actually measure the paintings than to read a biography?  Another debunker, also with a Ph.D. in mathematics, claims there is "no evidence" that da Vinci used the golden ratio, but in his presentation shows only da Vinci's simple sketches rather than his masterpiece paintings on religious subjects. Unfortunately, most commentary on da Vinci's use of the golden ratio in his paintings is based on The Mona Lisa, which has very few linear composition elements from which to definitively measure a golden ratio. Golden ratios are really quite easy to see if you have the right tools.  Da Vinci's "Last Supper", "The Annunciation" and Salvator Mundi are much better examples and show clear composition lines at golden ratio points. Botticelli's "Birth of Venus" was painted on a canvas which is itself a golden rectangle, and key elements of the painting are at golden ratio points of the painting's height and width. Botticelli also created several renditions of "The Annunciation" which also have clear golden ratios in their composition. Michelangelo's "Creation of Adam" has God finger touching Adam's finger at the precise golden ratio point of the width of the area in which they are framed. That is just one example of how Michelangelo used this Divine proportion in the Sistine Chapel. Raphael's "The School of Athens" features a golden rectangle placed front and center in the foreground of the painting, and the main scene above reveals many golden ratios in its composition. As noted by "Civilisation" author Kenneth Clark, "This union of art and mathematics is far from our own way of thinking, but it was fundamental to the Renaissance."


Are the spirals seen in nature based on the golden ratio?

spirals
Some are, but most are not. The spirals most commonly seen in nature are equi-angular (aka logarithmic) spirals. This simply means that the spiral expands at a constant rate. This occurs because it creates an even flow of energy or distribution of tension. This has nothing at all to do with the golden ratio. Accordingly, all the illustrations of spiral arms of galaxies, curves of ocean waves, spiraling hurricanes, etc. that are incorrectly identified as a "Golden Ratio" or "Golden Spiral" should be relabeled or removed to avoid further confusion in perpetuating this golden ratio myth. There is another type of spiral that is related to the golden ratio, however, that occurs very commonly in nature. The spirals that appear in pine cones, pineapples, seed pods and similar plant structures are usually based on two successive numbers of the Fibonacci sequence. For example, if there are eight spirals in a clockwise direction, you will find thirteen spirals going in the counter-clockwise direction.  Neither of these spirals is necessarily a "golden ratio" spiral on its own, but the ratio of these successive Fibonacci numbers approximates the golden ratio.


Did French painter Georges Seurat use the golden ratio in the composition of his paintings?

painter Georges Seurat
Yes. One art critic claimed that Georges Seurat "attacked every canvas with the golden section." At least one debunker says this is a simply "myth that needs to be dispelled." The truth is somewhere in the middle. My examination of over 100 Seurat paintings reveals that over 30 of them show very clear golden ratio composition lines. This analysis was based solely on the height and width of the canvas, where there is no room for interpretation or error.  Seurat chose to paint about one-quarter of his work on golden rectangle panels. Of his 103 paintings listed at Wikimedia, at least two dozen of them had a height to width ratio to within 0.1? of the golden ratio. Other paintings show golden ratio between elements within the composition. So the correct answer is that Seurat frequently used the golden ratio in his artistic compositions, but probably did not attack every canvas with it.


Is the Great Pyramid of Giza based on a golden ratio?

Great Pyramid of Giza
Possibly, but unknown. This is also subject to debate and interpretation, and there is no certain answer. There is no mention of the golden ratio in the existing historical record of the Egyptians. The outer limestone skin of pyramid is now missing, which makes its exact original dimensions subject to some estimation. The outer skin is still intact at the top though, and thus provides good guidance as to the original form. What we do know is this: The estimated original dimensions of the Great Pyramid per Wikipedia reveal a pyramid with an average base measure of 230.4 meters and height of 146.5 meters. This height is different from a phi-based triangle by only 0.0367 meters, a variance of only 0.025%. There's another school of thought that the Pyramid's proportions are based on the arc of a circle whose circumference is equal to the perimeter of the base of the pyramid. If that's true, then the estimated height is different by only 0.177 meters), a variance of 0.1%. Other geometries are also possible, one based on surface areas and another on gradients using Egyptian units of measure. There is also evidence that the relative sizes and positions of the pyramids at the Giza site embody golden ratio proportions. The truth is that there is much that we do not know about these pyramids or their construction, so the dimensions could be based on any of these methods and geometries. The Great Pyramid was clearly constructed with some specific geometry in mind, and with exacting precision, so we can reasonably assume that its architects did not create a pyramid with these very special and unique geometries by blind chance. A very interesting question still remains: Even if the pyramid wasn't consciously designed with a knowledge of phi, why did they pick a geometry for the Great Pyramid that so closely embodies the golden ratio, the one number that has a ubiquitous presence in geometry, and that is associated with nature and beauty?


Is there a "new golden ratio" that can determine facial Human face - new golden ratio and actual beauty proportions attractiveness with two measurements?

facial Human face - new golden ratio
No. The 2009 study claimed to have debunked the relationship of the golden ratio to beauty and claimed to have discovered two "new golden ratio" measurements that defined attractiveness. The faces identified as the most attractive, however, had over a dozen golden ratios in the dimensions of their key facial features. The researchers apparently didn't realize these golden ratios existed and devised their own alternative measurement points. It should be obvious that human facial beauty cannot be reduced to a single vertical and single horizontal measurement, and it's quite easy to prove this with a few simple examples of unattractive faces that still happen to fit those two measurements.


Is Mecca at the golden ratio point of the Earth?

Is Mecca at the golden ratio point of the Earth?
No, at least not exactly. There are two golden ratio points in latitude between the Earth's poles, one in each hemisphere. Mecca is approximately 12 miles from the golden ratio latitude in the northern hemisphere. The golden ratio of the longitude is not easy to determine as there is no natural reference point like a rotational pole. The claim for Mecca was based on a Mercator projection of the Earth, which spans from dividing point between the US and Russia. Using this as the basis, Mecca is 938 kilometers from the golden ratio point of the longitude. Using other starting points as a basis there are many other golden ratio longitude points on the Earth.


Is the design of the UN's Headquarters building based on the golden ratio?

Yes. This was supposedly "debunked" in an an article by Dr. George Markowsky, a Harvard Ph.D. in Mathematics, who calculated the simple ratio of the building's height to width. He noted that the ratio was 1.76 and not 1.618, came to his conclusion, and missed many historical and mathematical facts. One of the lead architects, Le Corbusier, created a design system based on the golden ratio just years before his involvement with the UN project. A well-known, award-winning Disney education film illustrates that the golden ratio relationship is based on three horizontal golden rectangles stacked vertically, not its height vs. width. Golden ratios appear in the visual dividing points on the face of the building, and these are easily can be measured and calculated. Other very clear golden ratios are present in the dimensions of  the curtain wall, windows and front entrance.


Is the golden ratio unique and special, or a myth to be debunked?

It quite definitely a special number with unique properties and it is found in nature, in some quite unexpected places. Even those whose goal is to debunk golden ratio myth will agree that the golden ratio has properties that make it very unique in mathematics and geometry. This one number has intrigued and inspired countless people throughout mankind's history, and earned a special place in their hearts and minds. It is probably for that very reason that some people have taken it beyond fact to fantasy and mysticism. That, in turn, has led others to summarily dismiss it with just as much zeal. Both extremes in position are flawed and keep us from knowing the truth and applying it.

Is the golden ratio a universal constant of design in nature? No. Must all features of a face be in perfect golden ratio proportion to be beautiful? No. Can it help us to better understand and appreciate beauty in nature, and apply it in our own lives? Yes.

Is the golden ratio required to create great art? No. Can it help to better appreciate some great art and to create with better composition and design? Yes. It's used for that purpose in art, photo cropping and composition, logo design, product design and other areas of design.

Like many things in life, it provides us with insight into the nature of things, the opportunity to better appreciate them, and the ability to use them to advantage. With all the misinformation and misconceptions that exist, it is best to keep an open mind, and not accept claims made without investigating evidence on both sides, experimenting on your own and coming to your own conclusions.

By Gary Meisner

Source: GoldenNumber.net