Pro basketball coach Gregg Popovich made very critical comments about Donald Trump and his presidential victory to ESPN reporters, and I am repeating the story here because I think his emotions echo those of many Americans.
Gregg Popovich: 'Still sick to my stomach' after Trump's election win
Michael C. WrightESPN Staff Writer
SAN ANTONIO -- Spurs coach Gregg Popovich spoke Friday about his frustration with Tuesday's election of Donald Trump as the 45th president of the United States.
"I'm still sick to my stomach, and not basically because the Republicans won or anything, but the disgusting tenor, tone and all the comments that have been xenophobic, homophobic, racist, misogynistic," he said before the Spurs' home game against the Detroit Pistons. "And I live in that country where half the people ignored all that to elect someone. That's the scariest part of [the] whole thing to me.
"It's got nothing to do with the environment, Obamacare and all the other stuff. We live in a country that ignored all those values that we would hold our kids accountable for."
Popovich spoke with reporters for nearly six minutes about the election. He said he understands why some, including political leaders, are calling for Americans to support the president-elect. But Popovich said Trump's words cannot be simply overlooked and forgotten.
"Everybody wants him to be successful. It's our country; we don't want it to go down the drain," Popovich said. "Any reasonable person would come to that conclusion, but it does not take away the fact that he used that fear-mongering and all the comments from day one. The race-baiting with trying to make Barack Obama, our first black president, illegitimate. It leaves me to wonder where I've been living and with whom I'm living."
Popovich also expressed empathy for minority groups that might be adversely affected by Trump's remarks during his campaign.
"What gets lost in the process are African-Americans, Hispanics, women and the gay population, not to mention the eighth-grade developmental stage exhibited by him when he made fun of the handicapped person," he said. "I mean, come on. That's what an eighth-grade bully does, and he was elected president of the United States. We would have scolded our kids. We would have had discussions and talked until we were blue in the face trying to get them to understand these things. And he is in charge of our country. That's disgusting."
Popovich emphasized that his problem with Trump isn't merely a matter of political affiliation.
"Values to me are more important than anybody's skill in business or anything else because it tells who we are, how we want to live and what kind of people we are," he said. "That's why I have great respect for people like Lindsey Graham, John McCain, John Kasich, who I disagree with on a lot of political things. But they had enough fiber and respect for humanity and tolerance for all groups to say what they said about [Trump]."
When a reporter interrupted to start a new line of questioning, Popovich cut him off.
"I'm not done," he said. "One could go on and on. We didn't make this stuff up. He's angry at the media because they reported what he said and how he acted. It's ironic to me. It just makes no sense. So that's my real fear. And that's what gives me so much pause and makes me feel so badly, that the country is willing to be that intolerant and not understand the empathy that's necessary to understand other groups' situations.
"I'm a rich, white guy. And I'm sick to my stomach thinking about it. I couldn't imagine being a Muslim right now or a woman or an African-American, a Hispanic, a handicapped person, and how disenfranchised they might feel. And for anyone in those groups that voted for him, it's just beyond my comprehension how they ignored all that."
As his remarks ended, Popovich said he was concerned that the U.S. is on the same path as the Roman Empire.
"My final conclusion is, my big fear is, we are Rome," he said.
Popovich is just one of many coaches and athletes who have shared their opinions on the election following Trump's victory Tuesday.
As anti-Trump protests spread nationwide after the election, Clippers coach Doc Rivers said Wednesday night that "there was nothing wrong" with people protesting Trump's election victory but that they should be open to giving him the opportunity to prove himself.
"The election didn't go the way I wanted it to go," Rivers said. "I personally know Donald Trump. I've golfed with him, and I know him. I don't think there's anyone who runs for president that wants to do bad. I really don't. So, you know, he won. My take on it: Let's give him a chance and see what he can do. That's the only way anyway now. So, let's go with that."
Pistons coach Stan Van Gundy said he noticed his players were uncharacteristically quiet because they were thinking about the election, and Van Gundy told the Detroit Free Press that Trump was "openly and brazenly racist and misogynistic."
"I have problems with thinking that this is where we are as a country. It's tough on [the team]," he said. "What we have done to minorities ... in this election is despicable. I'm having a hard time dealing with it."
What the Flag Means - a Tribute to American Heroes - A Song after 9-11
This is the most well-received song I've ever written and published. You can find the lyrics on various patriotic websites, and the lyrics about Captain Patrick Brown were published in a book written by a woman who works for the New York Times, but I've always had an uneasy feeling about it.
I originally wrote the song after the 9-11 terrorist attack, as a tribute to American heroes, and it was my way of trying to help people get over the sadness of the event, but the song had a side-effect that I had never intended. I became fearful that the song would inspire young men and women to join the armed forces and possibly cause them future harm. During the time it was published on Youtube, I received an email from one man who thanked me for writing it, and he told me that he had used it to try to instill a sense if patriotism in his own son, and this set off a warning alarm in my mind.
I've never considered myself patriotic as an American. I consider myself a citizen of the universe before anything else. I wrote the song as a tribute to those who have sacrificed themselves for the welfare of our country, often with their lives, but I never intended to inspire others to risk their lives, and after the Second Iraq War began, I took the song down.
The main reason I am publishing it again is to bring attention to the heroism of all our American heroes, but especially to Captain Patrick "Paddy" Brown of the NYFD, whose life should have been celebrated in a major movie by now (I do believe that a small-budget film was made about his life).
When Patrick came back from the Vietnam War as a decorated marine sergeant, he felt very disillusioned as did many other returning veterans, but his life turned around for the better when he joined the New York Fire Department, and after several daring rescues, he became a well-known hero in the city, His was the life that great movies are made of. After Patrick died while leading his men up the burning north tower on 9-11, his life became immortalized, and he was the reason I wrote this song. See this link for a short biograpy: http://paddybrown.org/Paddy_Brown_s_Biography.html.
I only wish that my vocals could have been better.
I included Olympic star Michael Johnson in the video because, at the moment he stood with his hand over his heart during the gold medal award performance of the National Anthem, he appeared to be brought to tears by a powerful "invisible force" generated by the heroic actions of patriots of the past, or so it seemed to me at the time. Perhaps he realized at that moment, "what the flag means" to patriotic Americans and lovers of democracy and freedom all over the world.
Long live the memory of Captain Patrick Brown and all other American heroes who have given their lives for the welfare of us all.
"I know God very well, from his pointy little tail to the horns upon his head!"
(This poem is dedicated to the memory of Lou Reed)
People who say "God" too much
Sound remarkably like used car salesmen
Trying to unload the worst lemon on the lot-
Slapstick evangelists bumping their heads
Into every known law of science and simple logic-
The Pat Robertson Psychic Network;
The Jerry Falwell School of Bigotry;
Shills for ideas that even their inventors would dump
Into the rubbish pit of abandoned monuments to the dense
Demolished by the wrecking ball of common sense.
People who say "God" too much
Are quick to start an argument, eager to start a war.
It begins with debates over trivial differences
Between their own superstitions and others'
And grows into threats of death and damnation.
The father of their opponents' misguided lies
Is always that arch-fiend Satan,
The horned rabble-rouser who leads
His endless legions of assaulting facts
And forever pokes his contentious pitchfork
Into the bilious delusions of gas-bag preachers
Who have blotted the last hopeful ray of doubt from their minds,
Cast down from the heavenly light of endless possibilities
To roam the shadow-world where fear has eclipsed reason,
The dark corner the dictator of truth paints himself into
With the leaking shrouds and inkblots of decaying dogmas.
People who say "God" too much
Have a god that looks remarkably like themselves-
The same race and social status,
The same comical facial expressions of self-righteousness.
The egoist makes god in his own image.
Tell him that he worships his own delusions
And that when he "talks to god"
It is his malformed left brain
Talking to his chemically imbalanced right,
And he will often tremble and relegate you
To the next available hot-plate in hell.
The only place where people say "God" too much
More than born-again prison inmates do
Is in psychiatric wards where raving prophets
Often use the word to address themselves.
The more often a person says "God"
The closer he gets to the ultimate godhead
Of the tyrant, the terrorist, and the psychopath.
And when one of our fearless leaders claims
To be on a mission from god, be sure
That we're heading for hell in a hallelujah hand-basket.
The acme of science is the death of religion.
If you see Jesus or Moses or Buddha kill him;
It's only your image in a vanity-glass.
To hear the sound of one hand clapping
Slap yourself in the face.
And when you tire of zealots and salesmen,
Follow some drunken pilgrim who takes the hardest roads
To the highest places and ponders trails of stars.
Befriend the seekers of wonder, the artists of the self,
And every doubting Thomas
Who has ever probed the wounds of a suffering savior
To see if the truth shines beneath the scabs.
"Straw Man" by Lou Reed
The humility of Jesus, as described in the Bible
Jesus' disciples were discussing among themselves about who was the greatest. "At that time the disciples came to Jesus, saying, "Who then is greatest in the kingdom of heaven?" {2} Then Jesus called a little child to Him, set him in the midst of them, {3} and said, "Assuredly, I say to you, unless you are converted and become as little children, you will by no means enter the kingdom of heaven. {4} "Therefore whoever humbles himself as this little child is the greatest in the kingdom of heaven. {5} "Whoever receives one little child like this in My name receives Me" (Matthew 18:1-5 NKJV).
"... Whoever wishes to become great among you must be your servant, and whoever wishes to be first among you must be slave of all." (Mark 10:43-44)
"When you are invited by someone to a wedding banquet, do not sit down at the place of honor, in case someone more distinguished than you has been invited by your host; and the host who invited both of you may come and say to you, 'Give this person your place,' and then in disgrace you would start to take the lowest place. But when you are invited, go and sit down at the lowest place, so that when your host comes, he may say to you, 'Friend, move up higher'; then you will be honored in the presence of all who sit at the table with you. For all who exalt themselves will be humbled, and those who humble themselves will be exalted." (Luke 14:8-11)
"Two men went up to the temple to pray, one a Pharisee and the other a tax collector. The Pharisee, standing by himself, was praying thus, 'God, I thank you that I am not like other people: thieves, rogues, adulterers, or even like this tax collector. I fast twice a week; I give a tenth of all my income.' But the tax collector, standing far off, would not even look up to heaven, but was beating his breast and saying, 'God, be merciful to me, a sinner!' I tell you, this man went down to his home justified rather than the other, for all who exalt themselves will be humbled, but all who humble themselves will be exalted." (Luke 18:10-14)
The Apostle Paul taught the principle of humility through Jesus' example, saying, "Let this mind be in you which was also in Christ Jesus, who, being in the form of God, did not consider it robbery to be equal with God, but made Himself of no reputation, taking the form of a servant, and coming in the likeness of men. And being found in appearance as a man, He humbled Himself and became obedient to the point of death, even the death of the cross" (Philippians 2:5 - 8).
The Apostle Paul explains: "For you know the grace of our Lord Jesus Christ, that though He was rich, yet for your sakes He became poor, that you through His poverty might become rich" (2 Corinthians 8:9).
Again, the Apostle Peter continued his exhortation on humility to the church, saying, "for God resists the proud but gives grace to the humble. Therefore humble yourselves under the mighty hand of God, that he may exalt you in due time" (1 Peter 5:5b & 6).
"So when He had washed their feet, taken His garments, and sat down again, He said to them, "Do you know what I have done to you? {13} "You call me Teacher and Lord, and you say well, for so I am. {14} "If I then, your Lord and Teacher, have washed your feet, you also ought to wash one another's feet. {15} "For I have given you an example, that you should do as I have done to you. {16} "Most assuredly, I say to you, a servant is not greater than his master; nor is he who is sent greater than he who sent him. {17} "If you know these things, blessed are you if you do them" (John 13:12-17 NKJV).
Love Knows No Distance - a Poem by Mark Heffron (with sunset video)
Sunset over Lake Winnebago at the High Cliff State Park Harbor
Love Knows No Distance
The mother has buried her only child And grieves in his bedroom the long winter nights, Caressing his clothing and empty shoes. She feels his impression in the wale of the bedding And sails the small lifeboat to a starry shore. She follows his footprints where love knows no distance, As the child has followed the trail of her tears, And fashions a shelter where her heart has broken To cradle his memory till love's resurrection.
The drunken man weaves through the streets of the harbor. He so loves the world that their eyes look away. So he talks to the ghosts who still answer his voice With the laughter of children who play through the night. At each echoing step their voices grow louder Till a small hand beckons from the moon-speckled bay And takes him to rest where love knows no distance.
The pilgrim wanders from church to church Seeking the beloved who blesses his dreams. He sees her face in each morning's horizon. In each chapel he finds her a steeple away. He traces her form in the ocean of stars That flicker like distant harbor lights Calling the wayfaring stranger home. When his eyes grow dark on a mid-winter's night There a light still glistens like a frozen tear Wept at the altar of the loving Redemptress In the bright homecoming where love knows no distance.
In the coves where shadows kiss and whisper Sweet parables of the lovers' moon, The tide that weds their ecstasy Soon ebbs to leave the barren sands. Born from love and sentenced to death, Their ardor spills across seawalls of time. The sweet elixir that shines in their blood Overflows the grail of their suffering. When the heart's battered sails meet the reefs of death The invisible tide that guided their love Will seal their marriage in a timeless harbor Where moon meets water and love knows no distance.
Whose face awaits you in the silent hour? Who else could rise but the ones you loved? The heart writes its story in every cell. In the script's final scene, the passion play's ending, Shine the faces of the immortal beloved- So close they were always a heart-beat away, At the end of longing, the great embrace, Where love knows no distance.
Bad karma hits the fan for the Republican Party with the rise of Donald Trump
Trumpenstein takes down Wisconsin's wimpy governor Scott Walker early in the Republican Primary
"What goes around, comes around" the old saying goes, and the Republican party is getting its comeuppance in spades this year with the emergence of Donald Trump as its leading candidate.
This is the same party who has always put the welcome mat out in subtle ways to white American voters who blame black people and other minorities for all the ills of society. For these people, it is black people who are committing all of the crimes, Hispanics who are taking jobs away from legitimate citizens and receiving unearned subsidies from the government, and other minorities who are also responsible for the decline of the American civilization. These voters view the world with a simplistic and xenophobic tunnel-vision. They remember the "good old days" of white Christian neighborhoods with little crime and good jobs, while having little understanding of the socioeconomic causes of the changes that have occurred since then. I have known many such people in my life, and they are generally not bad people. Most are hard workers and good family people with high moral values who dislike the direction that America is taking, and many of them vote for candidates whom they believe will control the increasing wave of various minorities who are entering the U.S.
Jesse Helms attack ad on "racial quotas"
Once upon a time these people generally voted for Democrats like George Wallace, politicians from southern states who still promoted segregation of the races in an attempt to "protect the white man". As the southern "Dixiecrats" disappeared from the public platform, the Republican party took up their torch, and through subtle ways such as opposing Affirmative Action and using black people in campaign attack ads to suggest that their opponents were "coddling" such people, the GOP became the party of choice for the "disenfranchised white person". Well-known campaign attack ads used by the Republican Party, including the 1988 Willie Horton attack ad which George Bush used against Michael Dukakis, became the sources of much "race-baiting" which used to attract disgruntled racist white voters.
The infamous Willie Horton attack ad of 1988
Conservative media sources have been responsible for many subtle and not-so-subtle racist comments and election attack ads in recent times, from the "nappy headed hoes" comment made about black female basketball players by radio personality Don Imus to various comments made on the Fox News network with racial overtones. Both a Fox News station and conservative talk show host Geraldo Rivera even mistakenly announced that President Obama was dead after Osama bin Laden was killed.
Don Imus' notorious comments about "Nappy Headed Hoes" and "Jiggaboos" (I used to listen to Imus on the radio on my job years ago and was always amazed by the comments made by his sidekick who would read the latest news with his own personal racist slant
Classic 'Freudian slip" or wishful thinking?: Fox News station and Geraldo Rivera announce that President Obama is dead
Most racist political attack ads look like this
After the Willie Horton ad came out, the Republican party was outed by many in the media for their race-baiting, and since then these kinds of ads have become more infrequent as their intent has become so obvious to voters. The new trend in political attack ads, at least in elections where judges are involved, seems to have headed towards "guilt by association" by portraying your opponent as a person who is soft on crimes by child-molesters. In the present Supreme Court race in Wisconsin, the following attack ad against JoAnne Kloppenburg by Scott Walker appointee Rebecca Bradley appeared recently.
Kudos to Fox6 News in Milwaukee for their political Reality Check series
As is the norm, mud was eventually slung back at Rebecca Bradley when it was discovered that she wrote articles when she attended Marquette University in which she called gay people "queers" and "degenerates" and said voters who elected Bill Clinton were "either totally stupid or entirely evil." Wisconsin Governor Scott "Wimpy" Walker declined to condemn them, too busy trying to devise schemes to borrow more money to add to Wisconsin's record debt problems caused by his incompetence (see Wisconson's current debt-clock here), but Bradley apologized, saying she was "deeply sorry" and "horribly embarrassed" by the disclosure of the anti-gay opinion pieces.
As Bradley has disavowed the opinions and apologized for them, she should be forgiven, but also advised that she needs to wash her hair more often now that she is appearing in public forums.
How to stop attack ads in elections:
According to pollsters, attack ads work, suggesting that voters generally believe them, even if they
are false, and tend to vote against the subject of the attack ad. If you are tired of seeing this garbage on your television, I suggest that people start voting the opposite way. During the election season, take note of the candidates with the worst attack ads, assume that they must have serious character flaws, and then vote against them. If enough people did this, attack ads would end, and politicians would stick to issues in their ads instead. Even Gov. Scott Walker, whose abysmal approval rating has dropped to 40% (one of the lowest in the country) since being squashed like a bug by Donald Trump on national TV, is being used in attack ads by by Milwaukee County Executive Chris Abele in his reelection bid (no, it's no longer the Willie Hortons of the world, but child molesters and inept politicians being used in the guilt by association political name-game).
Democrat Chris Larson is tied to unpopular Scott Walker in Chris Abele attack ad
Chris Larson points out the falsehoods in Chris Abele's attack ad
By the way, it is Chris Abele who is currently holding Scott Walker's old job as County Executive, where Walker first rose to prominence and became the darling of many conservatives until he started increasing the state's debt by leaps and bounds, leaving a total mess for his successor. But back to Trumpenstein, the man who squashed Walker's career.
Did Fox News create the Donald Trump phenomenon, to their own detriment?
Donald Trump has the Republican Party by the balls:
Enter Donald Trump, the new darling of the "disgruntled white guy". He is now leading all Republican candidates in delegates for the nomination for President, and Fox News and the Republican National Committee hate him. From my viewpoint, it's another good example of a karmic "getting what you wish for". In their racist baiting of voters, the Republicans have created their own Frankenstein monster who has now come back to haunt, torment, and perhaps destroy them.
Racist episodes have already reared their ugly heads at recent Donald Trump rallies, including the well-known sucker punch thrown by a white man at a black protester in Fayetteville, North Carolina.
Black protester is punched by a white man at a Donald Trump Rally
The big problem for the RNC and Republican strategists is that Donald is holding a very dangerous "trump card" when it comes to the election: namely the possibility that he could run as a third party candidate and destroy any chance the Republicans have of winning the 2016 presidential election, and perhaps also destroy any chance that they have of holding onto a senate majority. Should the RNC try to sabotage Trump's chances of winning the Republican nomination for president, the results could be disastrous. Even though Trump had earlier promised not to run as a third party candidate, he has recently been making comments that this promise was made with the assumption that he would be treated fairly by the RNC during the presidential campaign. This is obviously an overt threat that he might change his mind and run as a third party candidate should the Republican establishment continue to try to sabotage his candidacy, and this presents the RNC with an ultimate nightmare scenario where Trump's loyal followers might feel even more disenfranchised than ever and decide to bolt and turn on the Republican Party in a mass revolt.
Trumpenstein and one of his creators, Doctor Quackenstein
After many years of race baiting, the RNC and Fox News have created "Trumpenstein", a dangerous monster created in their own self-image who, due to his popularity among their fans, will probably haunt them for many years to come, and perhaps even become an autocratic Ras-Putin who will hypnotically dominate their existence until a future political revolution of common sense takes place.
Birds of a feather?
Speaking of Putin, he and Trump seemed to have been engaged in a mutual admiration relationship until Trump's recent humorous attack ad on Hillary Clinton, and there are similarities between the two men.
Before this ad came out (Putin did not like it very much), Trump and Putin seemed to be pals
With all their faults, both Trump and Putin appear very patriotic in their own ways. Putin is popular with Russian nationalists, even though he has turned their economy into a disaster during his autocratic reign (111 people control 19% of the personal wealth in Russia and the rest of the population averages $10,000 of personal wealth, a wealth inequality that is the worst in the world, even worse than that of the U.S.). Otherwise, Putin consistently puts Russia first, and his political moves, especially on Russia's borders, are made to reinforce his county's security.
Trump promises to do the same by greatly increasing the military strength of the U.S. He has pledged an "America-first" economic policy that will punish companies which move jobs out of the country, and he has also promised to be tough with China and other countries so that the U.S. gets better deals in trade negotiations, These promises sit well with many middle-class voters who have seen their wages erode over the years. Republicans fear that Trump will not be a "free trader" and will return America to the days when we put tariffs on many countries' goods (protectionism) to create better-paying American jobs. It remains to be seen if Trump will actually do this, but many working-class people are probably hoping so.
The Trumpenstein Monster created by the RNC and Fox News
Personally, I think that Trump will probably abandon some of the ideas which are meant to appease conservative voters, such as the "Mexican wall", if and when he wins the Republican nomination. He'll probably do more to strengthen security at the border, but walls don't stop people when they can just dig tunnels under them. From his previous comments, Trump appears to be what I call a "Republicrat", someone whose political views do not conform to either party's rules. His wealth gives him the freedom to ignore lobbyists and political donors and do what he wants to do.
The "Great Negotiator" and/or the "Great Divider":
On his "Celebrity Apprentice" reality television program, Trump was an expert at pitting people against each other in his boardroom when he was about to fire one of them. He would goad them into "defending themselves" if they were criticized by a competitor and did not fight back. People he considered too soft to defend themselves or unwilling to stoop to the level of their attacker would be fired by Trump right away (probably seeing that their refusal to mud-sling would hurt his show's ratings).
Donald Trump goads Kenya Moore and Viveca Fox into an embarrassing cat-fight with yes-man Geraldo Rivera assisting him
It's no stretch of the imagination to believe that Trump might resort to this same "divide and conquer", or "divide and get favorable ratings" strategy of he should become president. If elected, he will probably give new meaning to the term "bully pulpit", using press conferences to disparage "idiots" who hinder him and praise "good guys" who agree with him. Here is a headline I can foresee during a future Trump Administration: April 1st, 2017: President Trump requests legislation allowing him to "fire" congressmen whom he considers incompetent or "losers" In some ways, Trump might be the perfect president for the next four years, when the national debt passes the $20 trillion level. After all, he is an expert in corporate bankruptcy and barely avoided personal bankruptcy through skillful negotiating and cost-cutting. Anyone who has ever had debt problems, such as credit card debt, knows that there is a tipping-point that is reached when your interest payments become so large that you will never be able pay off the debt. I don't know if we've reached that point yet as a country, but American politicians have definitely created the "perfect storm" for an economic disaster, with the Democrats continually spending money they don't have on social programs, and the Republicans refusing to increase revenue through higher taxes on those who can afford to pay them. Perhaps Trump can successfully preside over the Bankruptcy of the United States of America.
If nothing else, the current presidential election cycle has provided more controversy, entertainment value, and fodder for late night comedians than any in recent memory.
Donald Trump comments about a protester: "I'd like to punch him in the face!"
Fractal Magic - an essay about fractal equations, their present applications and future implications
The Beauty of Fractals
Fractal Art has become very popular on the Internet, with a host of new fractal-making software programs, many of them freeware, including Ultra Fractal, Mandelbox and Mandelbulb, Fractal Explorer, and others. A recent search on the online art website Deviantart.com yielded almost 800,000 results for fractal art and animations.
Fractal geometry is being used in many different novel ways. In cinema, the founder of Pixar Animation Studios began experimenting with fractals to make his computer graphics appear more realistic, and this technique gave rise to many of the software packages now being used in the computer graphics industry to create more realistic special effects, such as the Genesis planet in Star Trek II and the damaged Death Star in Return of the Jedi.
Fractal geometry is being used for a new kind of image compression, converting images consisting of random information into fractal code, saving only a small,representative amount of information which is used later to re-created the original image. Because the fractal image is now computer code instead of pixels, the file size is reduced drastically and the image can be scaled to any size without losing its sharpness.
In biology, fractals are being used to accurately model the human lung, heart-beats and blood vessels, the brain, and many other physiological processes. Researchers are using fractal geometry to build models which they hope will identify microscopic patterns of diseases.
Fractal lungs
In the financial markets, after the financial crisis of 2007, many theorists started turning to the work of Benoit Mandelbrot, whose fractal approach to price variations revealed that the crash was not as unlikely as conventional forecasts had predicted. Mandelbrot dismissed the theory of efficient markets as too generalized and simplistic, and commented that the real world is not tidy or infinitely stable, that turbulence is a natural and unavoidable force. In 2004, Mandelbrot had discussed these views in his book "The (Mis)behavior of Markets: a Fractal View of Risk, Ruin, and Reward", co-written by Richard Hudson.
Fractal patterns in the markets (fractals are contained in the rectangular areas)
In the realm of climate science, scientists have recently demonstrated that the distribution of large branches to smaller branches in a single tree exactly replicates the distribution of large trees to small trees in an entire forest. Current research is underway to use this information to measure how much carbon dioxide a single forest is capable of processing. Then scientists will be able to apply their findings to every forest on earth, calculating how much carbon dioxide the entire earth can safely absorb.
Fractals can be found in the branching of tracheal tubes, the leaves in trees, the veins in the human hand, water swirling out of a tap, cumulus clouds, an oxygen molecule or DNA molecule, and the patterns of the stock market. In astronomy, most astronomers believe that the universe is smooth at very large scales, but some dissident scientists are starting to argue that the structure of the universe is fractal at all scales. With the proliferation of space probes into our solar system, it has been found that the outer boundary of our Oort cloud of icy planetesimals exists about half-way to Alpha Centauri, the nearest star to us. and it has been postulated by some astronomers that the edge of our Oort cloud at the outer limits of our solar system might interact with a similar Oort cloud surrounding Alpha Centauri, and that this interaction might be the cause of many new comets entering our solar system. If this relationship between the two stars is true, then our two planets might be part of a celestial fractal branch of a great cosmic tree. Astronomers have already found strings or filaments of gravitationally bound galaxies that appear to be separated by voids of space. Recently, these "voids" have even been found to contain shorter strings of faint galaxies, called "tendrils", by a team of astronomers at the University of Western Australia, who have stated: "The universe is full of vast collections of galaxies that are arranged into an intricate web of clusters and nodes connected by long strings. This remarkably organized structure could be called the 'cosmic web'." It would not be surprising to eventually find the hallmarks of fractal geometry in celestial structures: repeating patterns or self-similarity at every scale, and expanding or evolving symmetry as the space of our universe inflated after the big bang. There might also be an expanding self-similarity from the motions of particles at the very small quantum level, such as the orbits of electrons around nuclei, up to the larger levels of planetary systems and revolving galaxies, and beyond, all the way up to the higher dimensional "multiverse" which is conjectured to exist by modern Superstring theorists.
A simulation of the "cosmic web"
In 2004, wide-field telescope observations (made with the Blanco Telescope in Chile) of a region of space that contains galaxies from a period when the universe was only a fifth of its present age, have revealed an enormous string of galaxies about 300 million light years long. This structure defies current models of how the universe evolved, which can't explain how a string this big could have formed so early, and shows that our current theories of how Dark Matter operates are lacking.
A cluster of galaxies: twisted, helical pairs like DNA/RNA strings
Video of the ancient galaxy string
With the discovery of galactic strings, another question which might be asked is this: Is there a self-similarity between the smallest level of our universe, where the tiny "strings" of String theory, which theoretically make up the quantum world, exist, and the galactic strings we observe in the vastness of space? If the current universe expanded from a tiny "zero point energy" (vacuum energy or Dark Energy) at the moment of the big bang, was there already a pattern in this small field that foreshadowed the structures of quantum and galactic strings in its own inner energy structure, similar or analogous to a DNA string? Just as galactic strings have been found to resemble DNA strings in their helical structure, quantum strings, which have never been found experimentally because they are so small, might be helical strings too. Perhaps this helix was present in the "cosmic egg" of vacuum energy at the "big bang" birth of our universe (see my essay on the theory of how black holes create new universes for more of my theory on this subject).
In a different essay, I will propose an idea for what the "fourth dimension" of hyperspace (or the "bulk" which contains various three-dimensional universes or "branes" such as ours in string theory) actually is and how it functions. This theory also relates to a fractal concept, in which the fourth dimension is similar to the trunk of a great tree, which connects all of the 3-D universes within the 4-dimensional hyperspace, through which the mysterious force of gravity ascends and descends through worlds of different densities (different fractal levels in universes created by continual iterations of black holes creating offspring "baby" universes). In my theory, the fourth dimension is basically a dimension of consciousness which connects the various levels of the "Great Mind" of the Cosmos. I know this sounds very metaphysical, but I believe I have some scientific evidence for such a theory; it is different from other modern theories about the "personified" or conscious universe, as far as I can ascertain. Perhaps the hypothetical graviton is the unifying unit or stringy tendril of conscious love, and orbiting celestial bodies are wedded in blissful gravitational love affairs. That would be elegant.
The equation below the fractal was used to create it
The two most important features of fractal geometry are self-similarity on different levels and non-integer dimensions. If you magnify or zoom in on a fractal image, you will see the same shape at every magnification; this is the self-similarity feature of fractals. If you zoom in on the classic Mandelbrot fractal below, you will see the same shape appearing over and over.
Deep Mandelbrot zoom video
The second feature of fractals, the non-integer dimensions, is a little harder to understand. Classical geometry deals with objects of integer dimensions: zero dimensional points, one dimensional lines and curves, two dimensional plane figures such as squares and circles, and three dimensional solids such as cubes and spheres. But many natural phenomena are better described mathematically using a dimension between two whole numbers. While a straight line has a dimension of one, a fractal curve will have a dimension between one and two, depending on how much space it takes up as it twists and curves. The more the flat fractal fills a plane, the closer it approaches two dimensions. Likewise, a hilly fractal scenario will reach a dimension somewhere between two and three. So a fractal landscape made up of a large hill covered with tiny mounds would be close to the second dimension, while a rough surface composed of many medium-sized hills would be close to the third dimension. The video below does a good job of explaining how fractal dimensions are calculated.
Calculating fractal dimensions
Two of the most popular types of fractals are complex number fractals and iterated function system fractals.
In the first type, complex numbers are used to produce the fractals. A complex number consists of a real number, which is a value that represents a quantity along a continuous line, added to an imaginary number. A complex number is commonly called a "point" on a complex plane. If the complex number is Z= (a + b*i), the coordinates of the point are a (horizontal - real axis) and b (vertical - imaginary axis). The i is the unit of imaginary numbers,, the square root of a negative one, which is an imaginary number, because any number squared is a positive number, and there is no such thing in the "real" mathematical world as the square root of a negative number.
Why imaginary number are real and their usage
The two leading researchers in the field of complex number fractals are Benoit Mandelbrot and Gaston Julia. and both have fractal "sets" named after them.
The Mandelbrot set is the set of points on a complex plain. To build such a set, you have to use an algorithm based upon the recursive formula: , separating the points in the complex plain into two categories, points inside the Mandelbrot set, and points outside the Mandelbrot set. The image below shows a portion of the complex plane, where the points of the Mandelbrot set have been colored black.
It is also possible to assign a color to the points outside the Mandelbrot set. Their colors depend on how many iterations have been required to determine that they are outside the Mandelbrot set. Below is a colored version of the Mandelbrot set.
The Mandelbrot set is determined by iterating or repeating the equation over and over again, plugging the new values back into the equation . You start with an initial value for Z and C (C is a complex number and its value will determine the Mandelbrot set), and after plugging these numbers into the equation, you get a new value for Z. Then you plug that value for Z into the equation and get a new value for Z. This process is repeated over and over again; that is why it is called an iterative equation.
Computers are used to filter through a large sampling of the infinite number of points on the complex plane, and to determine which of these points fit the Mandelbrot set criteria for C. The computer performs this task by running iterations of the equation until it can verify that for a given value of C, Z never gets larger than 2. If the computer is assured of that fact, then it determines that C is in the Mandelbrot set and it plots that value of C on the complex plane by placing a dot of an arbitrary color (which can be set by the user) on the computer monitor. The only other possibility is that for the value of C, Z eventually does exceed 2, and the computer does not plot it.
By plotting the millions of C values that are a part of the Mandelbrot set, the computer creates the unique and distinctive Mandelbrot geometry. This process can be described as the "migration" of the initial point C across the plane. Different colors can be chosen for the points in the complex plain which are not a part of the Mandelbrot set, based upon how many iterations of the equation it takes before it is shown that the value of C is outside the set (or how quickly the value of Z heads toward infinity), and this is what gives many versions of the Mandelbrot set image their multi-colored features and interesting effects.
Julia sets are related to the Mandelbrot set in that they are created by iterations of the Mandelbrot equation with one exception: the value of C is constant throughout the process, while the value of Z varies. The value of C determines the shape of the Julia set and each point of the complex plane is related to a particular Julia set. After a point C is chosen on the complex plane, the equation is iterated with the value of the initial point Z to see how far it will migrate from its origin. If it remains close to its origin, it is a part of the Julia set; otherwise its value will go toward infinity and a color is assigned to Z depending upon how quickly the point escapes from its origin. To produce an image of the whole Julia set associated with the value of C, the process must be repeated for all the points Z in the complex plane whose coordinates are included within a distinct range of numbers.
A Julia set fractal image
Iterated Function System (IFS) fractals are created through simple plane transformations, including scaling, dislocation, and plane axis rotation. Well-known fractals related to this process include the Sierpinski Triangle (see the video for calculating fractal dimensions to see how this fractal is created) and the Koch Snowflake,
First four steps of the Koch Snowflake construction
Many other examples of IFS fractals can be found on the web, such as fern leaves and spirals.
An IFS fern leaf fractal
Fractal design is still in its infancy, but already many interesting fractal images and animations have been created which bear an eerie resemblance to known designs in our universe. Recently, a fractal animation by an artist who calls himself FractKali was banned on many Internet websites (perhaps one of the reasons is that he gave it the title: "Fractal Orgy") because it appears to contain sexual content, even though it was created with a fractal computer program using a mathematical formula (a raw fractal).
"Fractal Orgy" by FractKali
As the development of fractal design and scientific applications of fractal geometry progress, one can only wonder how accurately artists and scientists will mimic designs and processes of the physical universe in the future. Could advanced fractal geometry and mathematical equations be at the heart of all creation? Many scientists already believe that all processes in the universe can ultimately be reduced to mathematical constructs, that free will is an illusion, and that our world, including life itself, is completely deterministic. I personally find this idea repugnant. I believe that our brains are microcosms (emphasis on micro) of the Great Cosmos, and that our mathematics, no matter how far it advances, can only hope to approximate the Cosmos' functions because of our brains' limitations (a part can never contain a whole unless it is the same thing; it can only mimic). I will be writing a different essay on this subject soon, which will also explore the concept of randomness and whether true randomness actually exists in our universe.
Fractal art: "Spirally Born" by Fractali: Iteration of complex sin function and Julia Set circle inversion, colored by exponential smoothing technique
Nova's special on Benoit Mandelbrot and Fractal Geometry
