Still a Mystery?

The Bermuda Triangle

Who controls the Bermuda Triangle? Is it phenomena, devils, or aliens? Is it just good old Mother Nature playing clever tricks? Whoever or whatever it may be, dozens of missing boats, planes, and bodies have vanished with no survivors—except for one man who defied his fate.

It might appear that the Bermuda Triangle has long been forgotten. The truth is that science research and experiments, professional studies of wreckages along with expedition crews, have continued their ongoing activities seeking extensively to find the truth of what lies at the base of this invisible all consuming vortex. Recent information, based on a video produced by the History Channel, unveils many different approaches of what makes this very large triangular area a baffling mystery. The debates, the disappearances, the data, even a victim survivor, will reveal information that cannot be denied for discounting alien activity.

In 1964, a Paranormal Researcher name Vincent Gaddis coined the phrase, The Bermuda Triangle, when he wrote an article for Argosy Magazine. During the span of 35 years up to the present date, 700 boats, 120 planes, and countless bodies have vanished without a trace after entering the Bermuda Triangle, also known as The Devils Triangle. A triangular area spanning from 500,000 to 1.5 million square miles from the points of Miami, to Puerto Rico, to Bermuda, has been the culprit of the claim.

According to documentation, all of these mystery disappearances occurred during fair weather. The take-off of aircraft’s would be ordinary, their communications and equipment were sufficiently functioning.  It is also recorded; those who called for mayday reported the same activity and surroundings before they vanished. Pilots would report that their compasses malfunctioned or stopped working, or reported that all instruments began to malfunction as they became surrounded by thick fog with no way out, losing their course of direction. As for the disappearance of ships and boats, no distress calls were ever recorded and nothing to indicate that they were in trouble and needed assistance. They merely disappeared without a trace.

An astounding fact is that the first report of a curious citing was recorded in the year of 1492 when Christopher Columbus claimed that his compass began to malfunction. He also recorded seeing strange lights in the sky. In 1918, the USSA Cyclops, a 542 ft. long ship carrying 300 sailors set off in fair weather from Brazil to Baltimore, passing partly through the Triangle. They were seen just hours before they disappeared by a British Patrol who reported all was well. They never arrived to their destination and disappeared without a trace, not even a distress signal. On a routine flight in 1949, Naval Flight 19, consisting of 5 planes and a training crew of 14 members, disappeared 1 hour after take-off.  The weather was perfect. All of the pilots began to report that their compasses were malfunctioning. All 5 planes disappeared and lost communications after flying way off of their course. A 13 crew member Sea Plane was sent out immediately for a rescue. It too, disappeared never to be heard from again. Another pilot on a flight from St. Thomas to Miami radioed that he was in trouble and a thick fog had surrounded him. However, Miami reported that the weather was fair. He said he was disoriented and he was losing engine power and that his plane was going down. Nothing more was heard from him until 11 hours later, 600 miles away from Miami near the Caribbean. He radioed to Caicos towers saying he was 10 minutes away from their runway and asked permission to land. Caicos Towers confirmed his flight number and identity and gave him the go-ahead, but he never landed. He disappeared permanently without a trace. During Charles Lindenburg’s transatlantic flight, he recorded having compass malfunction and lost direction for a long time. But he never recorded a strange fog and recovered without any further problems.

There is a restricted area around Andros Island where most of these disappearances has occurred. A USA Naval facility called AUTEC, or Atlantic Underwater Test and Evaluation Center, is located on this Island where there have been many UFO sightings as well USO (Under Sea Sightings) have been reported. Those living around the Andros Island area in the Bahamas have reported UFO sightings. People of the Bermuda Banks would claim to see glowing objects beneath the water’s surface. In fact, Gian Ouasar, is a leading expert and extensive researcher of the Bermuda Triangle mystery is convinced these disappearances are UFO related. He has studied the list of every aircraft and ship that has disappeared. He stated that not one ELT box was ever activated before any of the hundreds of disappearances. ELT boxes transmit signals of an impact if an aircraft should crash. Due to this fact, it would indicate that they disappeared in mid air. There was one distress call that could confirm the existence of UFO activity. In 1980, Jose Torris was flying his plane through Puerto Rico. He made a distress call: “this is flight 38, mayday mayday! We have a very weird object in front of us that has made us lose our course—mayday mayday!” The tower picked up his signal and also saw another signal just as he reported. Jose then he disappeared and soon the strange signal followed. He was not heard from him again. His ELT box was never activated.

Hundreds of boats, aircraft, and people have disappeared. The FAA National Transport Safety Board does not exist for any investigations into the Bermuda disappearances. Therefore these disappearances go unexplored. They are not considered for extensive ongoing investigations into the disappearances of boats and aircraft, thus leaving these mystery disappearances at a stalemate. Even the military coast guard calls the idea of these disappearances a myth. Greg Little, a professional underwater explorer the mission upon himself and organized a small expedition crew to search for wreckage that may give them a clue as to what happened just before their disappearance out of radars tracking. For the past 7 years they have searched for missing planes within the coastal area of Bermuda. A few wreckage’s of very small planes have been found by the search crew, located about 30 feet or so from the shores with no trace of human carnage, and no proof can be found to confirm these wreckage’s are those who were reported missing during flight within the Bermuda Triangle area. When they check for N-Numbers (numbers to show registration and owner) on the wreckage, none can be found. N-Numbers are as unique as fingerprints and could easily identify the missing persons and the aircraft. Several of the planes are assumed to be drug planes that were ditched after their drug run.

There has been only one man to escape from and survive the clutches of the devil. In 1970, Bruce Gernon was flying his small plane when he began to experience a fog surrounding him. His instruments began to spin and malfunction. All of a sudden he had found himself out of the fog and suddenly at his destination. What should have taken 1 hour from take off to landing, ended up to be a 30 minute flight. He said all he could think of was an electric fog because he said everything felt magnetic. He believed he had time-traveled because there was no way he could make that flight in 30 minutes. From that point onward he devoted his life to solving this mystery. Dave Pares, a physiologist, used NASA reports on solar energy based on the year 2000. He surmises that when abnormal winds collide with normal thunder storm activity it can create a strong electrode-magnetic force. This field has been known to knock out satellites and power grids. It also may create a fog in the area in which the two powers meet. However, every time there had been a disappearance the weather was clear and fair. This could also confirm a UFO activity. UFO’s would not want to fly into turbulent weather when it could endanger their ship and cause them to be exposed. Dave Pares flew a small plane into this much awaited storm system to test his theory and to prove that these were the elements and conditions that caused the disappearances of many aircraft’s. His instruments began to malfunction but there no thick fog developed and there was not enough electrode-magnetic force to cause his small plane to crash, time travel, or to disappear; thus, disproving his theory.

Hans Graber a Scientist and the world’s leading expert on wave dynamics, also the head of the Marine and Science Department at the Universe of Miami Florida, developed a theory about something called Rogue Waves, similar to a tsunami wave and may be responsible for the disappearance of the ships. From a 1300 gallon wave tank he simulated what he believes these supposed Rogue Waves can do to a ship in a matter of seconds. They are a product of small super position waves all flowing along in the ocean. When they meet at a certain time, all at once they rage upward hitting the ship with the speed of a freight train, swallowing up the boat in a matter of seconds. They are approximated to be as high as 90 feet, lasting a matter of less than a minute and as fast as they rise they fall, leaving the surface of the ocean calm. They say this type of wave can swallow an entire ship leaving no trace. However, this is only a theory without a trace of proof that these waves do exist. No one has ever seen one. And this would not explain the disappearances of aircraft’s. But it would confirm USO activity—Unidentified Sea Objects.

Dave Pares, an expert Physicist on research, Hans Graber, the worlds leading expert on wave dynamics, and Greg Little, expert expedition researcher. The results has equaled no matching N-Numbers, no ELT readings, no planes, boats or bodies, no electrode-magnetic fog, and no Rouge Waves. So what are the equations and the answers? The belief of Gian Ouasar, the world’s leading expert on the Bermuda Triangle, makes it evident that UFO’s are equation. Jose Torris and his mayday call, the weird object flying in front of him blocking his way, is the equation and the answer. Are UFO’s responsible for the disappearance of hundreds of boats, planes and people? I believe the facts and documents speak clearly.



My understandings of sociology and the social world has changed throughout the term in that, I was not aware of all that is entailed by the word, sociology. I found that sociology means understanding and researching all phases of life. I didn’t realize that there were categories to describe groups of people. I am now aware of the many categories of groups of people. These groups have labels so we can identify them and the basic function of each group.  I had no idea that in-groups and out-groups are descriptions of a power group, and a stigmatized or less powerful group. In high school we used to call the in-groups “popular” and the out-groups “nerds”.  Reference groups help us to understand or make sense of our position in society relative to other groups, such as in high school (159).

When I first began this class I thought I was quite up on social views and the topics going on in this world. As this course unfolded, I have become more aware of social society and the issues that are faced daily by certain groups; in work places, in school, within industry, and in any phase of social interactions. I see all of what I have learned as a network, or flowchart of life. Even though there are many suggested answers to the problems faced by many groups or individuals, there is hardly ever a workable answer. It seems that there are two categories of people in all categories of social society:  those who dominate, and those who constantly strive to cope with the social pressures of the domineering groups, by banding together with peers of their likeness. And though there are people and groups who change circumstances to some point, it seems the upstream currant takes most of the other unwanted debris, downstream.

As I began to read our text by Dalton Conley, You May Ask Yourself, I began to see that I truly didn’t realize the complexity of the issues that face many people in daily life. Everyone has personal struggles and is victims of circumstances in many cases, far beyond what the media superficially tells us. The very things that I thought I had knowledge about, were only surface. The struggles of people in everyday life are much more detailed than I understood.

Somehow I feel more aware and more matured in my views and understanding for all classes of people, all groups of people, and all situations of people in society today. I used to think that the media greatly influenced the way I think. But now I believe that common knowledge and first hand information has not so much influenced me, as it has informed me.

After I read, Dude You’re a Fag, by C.L. Pascoe, it gave me a deeper look into gender struggles, transgender struggles, male and female struggles, and the superficial way people view masculinity, and the way this word does not only apply to men. I’ve learned that the term masculinity holds a different meaning to different people, and no one seems to agree which is right or wrong answer. Masculinity is an opinion, as is femininity, and it seems that no one agrees which is right or wrong answer. But those who are affected and daily living the life of either of these two extremes, can say which is right and which is wrong.

I was most disturbed by learning about gender discrimination. It just saddened me to know that individuals who are gay can’t even be who they are in their schools. And if one who is gay, becomes popular by standards, and if one is a masculine female, she can be accepted, but the famine guys face torment and harassment and even physical abuse. Today where this style of living is accepted mostly, there should be no persecution from the students or the teachers.

I found it a bit difficult to see the different struggles in life for those who are less fortunate. But the film that I reviewed Mardi Gras, was an eye opener to me. I’ve learned what goes on behind the scenes of something seeming so innocent, like Mardi Gras beads. Where on one hand the people who love to buy them and use them for twisted sort of reasons, the people who make the beads, hate them and think Americans are crazy to be so obsessed by them. I’ve learned that the same one particular thing can have extremely different meanings to two different people, or even to a group of people. There are people who have to fight daily for what they believe is right. And there are people who fight daily to destroy the dreams of others. I was able to see how capitalism differs in other countries. Capitalism in our country can make people prosperous and benefit the workers. But in china, capitalism is oppressive to the workers of the companies. I gained a new appreciation for the freedoms in our country for laws that protect the working man and woman. We have; wage labor, salary, even civil service salary. These are all sources of payments given to the workers in different form (pg 376). But in China, there was only one way of being paid and that was by the number pieces of work that they accomplish in the course of a day.

I think I was enlightened most of all by Dalton Conley’s book, Honky. I think his book is a set of rules that we can all follow as an example of how to live our lives among those we have no tolerance for. Dalton didn’t have the option to tolerate or not. He was stuck in the middle of where he was placed without a choice. Our natural instinct is to fight to get out of or away from what we will not tolerate. We don’t bother to learn the “language” or try to fit in by displaying what we know or don’t know.

I was able to get an insight of what it would be like to live in a society where I would be the minority. And he gave an insight of how someone would cope with these circumstances, even at a very young age. He showed that many times one has to compromise in order to get along with a group or certain class of people, when faced with a circumstance beyond one’s own control. Dalton also showed in his book that no matter if you are white or black; there is no guarantee that you will find favor in the eyes of certain authorities. There are privileges in being a certain race, depending where you are, and what type of category it falls under. In fact, different classes of people have different privileges. The upper class people have great privileges for the reason that they do have money, and businesses want their investments, so they cater to them. People who are of lower class, who want to be popular or rich, want to interact with them hoping they will bring them into their group to reap the benefits. Dalton Conley talked about how he was able to work within, and be accepted by, the different races and classes of his friends by speaking their language or slangs. He would talk lower class slang with his project friends, and has a higher vocabulary for his upper class village friends. And in all cases he was accepted for the most part. But he also found himself separating himself from the old ways of childhood as he matured and began to realize that poor was not acceptable over upper class, and he became discontent to be so. This caused him to resent his position in life as lower class and actually began to steal to get the small luxuries that he was not afforded by his parents. I think it works this way in life. When the lower class or poor class of people begins to feel the pressure of lack, they will sometimes steal to obtain what they lack. It’s a vicious cycle. At one point, his very best friend, Jerome (because of his popularity), had raised him to a higher level of acceptance, even to be tolerated by his “enemies”. But Dalton disregarded the value of the friendship at one point when he had an opportunity to receive a bit of glory at the expense of a tragic event that had taken place in his best friend’s life. He did this by being able to tell the story of knowing first had about his friend being shot. His peers ogled at his privilege of being the first to know. And he then said, he felt only small pangs of guilt from time to time as he continued to tell the story day after day, but not enough to be convicted. I feel this holds true in society today. People will betray their friends for just a small bit of glory.

But still, the media plays a big role in my life and my family’s life because we depend on the media to provide the information that we need for our daily lives, from news to local market and retail sales. World news is a big part of our daily lives considering how much goes on with our government and the wars which we are involved in other countries.

People are portrayed by those who they daily make contact with in their communities, by whom they know, and by what they do. I feel it’s a good thing to have groups categorized by names. This gives others a place, person or thing, to identify with to meet their needs. This is called Social Capital. This function of extending through facilitating by networking is needed because there are so many different categories of people, and it is also a form of organization and can give answers to what is a rather complex society in general.

The challenges I face is the declining population and stagnation in the area in which I live. Since the large Corporations have moved out of the area, retail and medical fields are the two areas of profession for the job force. Many people have moved south to find employment and to make a living. This is one thing I am considering to do after I finish college and receive my degree.

Euclid in the Rainforest

What is your idea of a trip to paradise? Would it be a place full of beautiful flowers, colorful hillsides and plentiful market places surrounded by exotic foods, drinks, and people? Or would it be spending time with like peers who talk endlessly about—even dreaming about—angles, propositions, theorems, observing nothing but geometrical designs all around, including within a water fountain? Joseph Mazur managed to blend both scenarios together in a fun adventure.

Joseph Mazur was very passionate about teaching Mathematics, proving theories, searching for evidences and explaining his discoveries. I found many of his adventures humorous, and yet amazing as he worked and wove geometry into his entire journey. He ventured out to explore the symbiotic connection between the physical and the mathematical worlds.  He basically wanted answers to human reasoning and to define logic and proof. He did so by bringing the elements of Euclid with him along with many other mathematicians’ solutions and thermos. I had fun trying to dig into a deeper meaning or view on certain topics and examples that he revealed in his book.

He explained the three proof of logic which are classical logic (“classical elementary logic” or “classical first-order logic”), plausible reasoning (which is concerned with probability and nature), and logic of infinity (often enough and how many numbers) that we use to determine whether something is true ( pg. xiii-xiv-xv), and he did so extensively.

In this book, Joseph Mazur proved that all triangles are isolates “let ABC be any triangle”, i.e, and abstracts of Thales isolate triangles (267-268). He unraveled syllogisms with cute allegories, like kittens with green eyes (pg 269-273) and the strange law called The Law of Large Numbers that tells us that if we flip a coin long enough, half the time it will come up heads and half the time it will come up tails (pg 220). But this method certainly worked based on probability.

Out of the idea of Pythagoras that “number” was the source of all things, he discovered that the diagonal of a square of side one is irrational and then again when it met the strange paradoxes of the infinite. He declared that disciplined plausible reasoning makes science possible. It is the logic of every day reality. He says that the logic of infinity enables us to make many huge leaps in science and technology. But when it comes to the pursuit of truth, the logic of infinity isn’t the whole story of science (pg 182-183). All of these truths tell me that all three proofs that Joseph Mazur has been trying to convey is summed up by saying, basic logic is proof that we can use and see, ties to plausible reasoning by connecting to science to prove logic, and numbers are infinite based on the fact that numbers translate into letters and at any point, can be used to in proofs of premises, axioms and destructive reasoning. But I found other aspects of this book to be more interesting philosophically, and I maybe ponder few questionable statements that he makes.

His adventure into the rainforest began after reading a book that his brother had given to him on his seventeenth birthday. One of the two books given to him was a 472 page book about algebra. He had hoped this book would be as spellbinding as the one he read before it; however, he got stuck on the second page of the book over a sentence that read, “Clearly, any result which can be proved or deduced from the postulates defining an integral domain will be true in any particular integral domain.” He got stuck on the word cleary.  So in 1960 he set out for the Venezuelan rainforest. His surroundings ignited his drive to continually ponder and solve the claims of many mathematicians’ theorems, also making references to such great philosophers such as: Thales and abstract geometry; Georg Cantor, rational points, real numbers, and irrational points; Plato and plausible cause, conclusions, inference, reasoning, and playfair’s postulate; Hume and belief, infinity, and ink spots; Cavalieri and his invention of calculus (pg cii); Zeno and the law of motion (pg xii, 135), and the works there of, and too many others to list.

As he journeyed onward he travels with an Englishman named Roger who is just as neurotic, if you will, about mathematics. Together they make their way to the Orinoco River and along the way meet a young soldier named Jesus. As they go they discuss the proof of the Pythagorean Theorem and other results of Euclidean geometry. Pythagorean Theorem states that: “The area of the square, built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides”. They hitched a ride with a Venezuelan army convoy traveling five hundred miles into the jungle along dirt roads to Cabruta on the Orinoco River. The truck that they were riding in hit a washed-out part of the road in the mountain and they found themselves teetering on the edge of a cliff. They leave the truck for the night not knowing how they will pull it back up from the gully onto the road. In the morning Joseph used a method of the Pythagorean Theorem in an attempt to pull a truck out of a gully and succeeded (pg. 8).

On one occasion when his travel companions Roger Hooper saw that a bare-breasted young woman in the diorama foreground of dragon trees, guanaco (a South American mammal closely related to the llama), and naked children mimicking spider monkeys. He asked Joseph if she was real and if he should question what his eyes told him (pg. 39). Joseph states that this is a natural question for a mathematician in a forest because we can get so involved in seeing ideas through our minds eye, we overlook the natural world (pg 39). But I find the statement of Rogers a bit strange. Why did he only question about the bare-breasted woman. The children were naked and acting like the spider moneys! He might have questioned the entire show? And I also find Joseph’s answer a bit strange as well. What does being a mathematician in a forest have to do with perceiving what is in front of you in the natural when the natural is what you are perceiving even as a mathematician? I would say that Roger was responding, and possibly wanting to not acknowledge, that he might be seeing something more in his world other than geometry, theorems, proofs and problem solving; so much so, unto the point where Roger talked about the brotherhood of the followers of Pythagoras, saying they were bound to secrecy of the master’s teachings and anything else taught or discovered by the brotherhood (pg 33).  Pythagoras was the first pure mathematician. Pythagoras founded a philosophical and religious school in Croton (now Crotone, on the east of the heel of southern Italy) that had many followers. Pythagoras was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. The beliefs that Pythagoras held were:

(1)that at its deepest level, reality is mathematical in nature
(2) that philosophy can be used for spiritual purification
(3) that the soul can rise to union with the divine
(4) that certain symbols have a mystical significance
(5) that all brothers of the order should observe strict loyalty and secrecy.

Maybe Roger after all, truly could not comprehend what he was seeing, or maybe closed his mind off to the possibly in order not to defile his brotherhood-state-of-mind. Pure thinking says that mathematics is discovered, not invented. Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. It is distinguished by its rigor, abstraction, and beauty. She may have been a beauty, but definitely not mathematical.

Joseph Mazur talks about math and logic; “belief altering memory” and “memory can drive belief”, belief strong enough to change memory, powerful enough to influence future successes. He then talks about Leonard Shelby a protagonist in the film Memento, who quotes, Memory can change the shape of a room, or change the color of a car. Again, Joseph Mazur uses an odd reference to support how dependable memory is. In this film, a man named Leonard Shelby suffers a head injury from a scuffle with his wife’s killers and has lost the ability to make new memories. To compensate, Leonard is constantly taking Polaroid pictures of people he meets and places he goes and writing messages on the pictures.  Important facts such as information about the crime he has tattooed all over his body.  At one point he stops at a local bar where he meets Natalie. She introduces herself and minutes later Leonard cannot remember who she is. Leonard then proceeds to tell a story that is repeated throughout the movie. Joseph states that memories can be distorted they are just interpretations, not a record; and they are irrelevant if you have the facts. I find this a contrary statement considering he used this film as a reference. Then, Joseph questioned himself at one point, if an incident that he saw when he was a child could have actually been in fact true. A man named Mr. Unis, performed an extraordinary stunt on a street near where he lived. The man could stand on one finger. Joseph later began to think that what he saw defied physics and was in fact untrue. Later he encountered the same man at a circus. He saw that he in fact could balance on one finger just as his memory served; however, he doubted what he was seeing because logic defied the act. He proceeded to say as a child, he could more easily belief the one finger balance but as he grew to understand physics, his naivety was replaced with difficulty in believing in magic, spirits and humans standing on one finger.  He refers to David Hume succinctly saying “Belief is something felt by the mind, which distinguishes the idea of the judgment from the fictions of the imagination” (pg 39-40). To me, this statement from Hume says that what you see is true because we perceive with the mind what is in fact true, unless we hallucinate. It seems that fictions and imaginations would not be perceived by the eye at all, only within the mind of the head, in which it would be obvious. The only way I can feel about this statement is I do believe what I see, if it holds truth without doubt.

In a philosophical monument Joseph Mazur talked about facilitative communication (FC). This method had been challenged by The American Psychological Association, saying that this method violated the civil rights of a person with autism or severe mental retardation. He points out that we shouldn’t be persuaded one way or another by one message, that there are other tests. He says this because of an example of an autism girl who had claimed that her father sexually abused her when she was two years old and thus sent him to prison for 7 years, through a communication facilitator. His point was that two different people can see the same thing differently, one being double-blind and possibly being influenced subconsciously suggesting that one person is imposing her own thoughts onto the others communication. However this method of communication was challenged later on in the years and Joseph finds a way by deductive reasoning to prove, or possibly put into theorem, that this method in fact may not be true. He talks about how humans don’t always focus on their tasks and that the FC is human and maybe her mind wasn’t at the task at hand but in another place, or maybe she doesn’t work often enough to be of value. He then segues into talking about the Galton Board created by Sir Francis Galton in the 19th century. Both of these stories end up hypothetical with some credibility to each, but both end up inconclusive (pg 239- 243).  I find this to be very strange for Joseph to refer to Sir Francis Galton, considering that this man is hardly known for his great works in geometry, or mathematical theorems, but rather his scientific works. However, I believe he used it solely as maybe an attempt to prove his own validation at any avenue possible. In this case it’s symmetrically. Symmetrically meaning, having similarity in size, shape, and relative position of corresponding parts, in which I believe Joseph draws a parallel to his way of showing that the percentage of chances for being right when using a FC, and the solution being probable that it is not right or true.

In Chapter 6, he talks about counting to infinity. I find it very interesting that he begins to talk about the primitive way of counting by fingers and stick-like symbols. He says that the only record of ancient finger counting in existence is the codex de computo vel loquela digitorum,”On Calculatin and Speaking with Fingers,” written by Venerable Bede, an 18th century Benedictine monk. On page 94-95, he claims there is strong evidence that suggests all number systems evolved from counting fingers, toes and other body parts. The Yupno an Aboriginal tribe remotely living in the highlands of New Guinea, use an elaborate system of finger counting, ending where the answer is simply associated with the last body part in count. He even talked about a boy named Evan, a young boy, who caught on quickly to the concept of odd numbers, and problem solving.  Joseph wasn’t sure he knew how to teach young children mathematics, but properly presented by using something the mind of a child could understand, a bull’s eye target, the fundamental truths of mathematics were easy to understand.  However, he mentions that this young boy also counted on his fingers (pg 97-97). To me, he is pointing out that all begins at a basic point which is solid and provable. We can count on all ten fingers and prove our answers to be true every time. Two fingers and two fingers equal four fingers and so on unto infinity. I believe that Joseph Mazur wanted to establish basic truths in all three of his categories in this book. I believe he used these examples to show that these finger counting techniques were provable axioms, which is an elementary basis for a formal logic system. I would also have to call this a mathematical thread, referring back to the Egyptians, having come full circle to modern-day counting from the time of the Ishango Bone.

I also found this book a bit hard to put into perspective as his adventures were many. In several parts of this book it seems as if Joseph Mazur attempts of proof would alternate between believing that the hypothesis was true and believing it to be false. I’m not quite sure if the book is meant to be written this way in order to make us find something hidden that we are to guess at and try to solve, or if it is meant for us to stretch our own thoughts looking for other possibilities and solutions, or to make us realize that he is purposely trying to trip us up to turn our attention to his point.

In the chapter 12, Does Math Really Reflect the Real World? Joseph Mazur uses endless examples of “chips”, gambling rooms, and “Good and Plenty” candy, in the chapters through Chapter 14, as he shows the laws of probability, and the curve theorem, using these methods as a metaphor. In these chapters, his class performs a lengthy task to show how to learn something from organizing random samples.

Joseph Mazur devotes several pages to non-Euclidean geometry. I happened to think that this book is called, Euclid in the Rainforest. However, not everything is Euclidean in the Rainforest. I suppose what was Euclidean in the Rainforest was Joseph Mazur’s efforts to prove at hand his three proofs of logic. He states on page 85 that Euclid’s fifth postulate best models the geometry of our world, we inevitably must test space by experimental observation. But we have a problem to show that space is Euclidean. I do logically agree by fact that space is not related to the fifth postulate which says: 5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate. Because this fifth postulate has never been proven as a theorem, we can safely say that space has no lines, therefore space truly is non-Euclidean.

I would say for the most part, if you are aware that this book is all about geometry and the Elements of Euclid, and philosophy, it is clearly written enough to understand where Joseph Mazur is coming from. But it is a bit glib and he does ramble sometimes to make his point, but his points are wells made. However he is a good story-teller. He does document sources at the end of the book.

I read a few criticisms on this book. I searched online to find reviews of this book. I did read one negative criticism out of twenty-one people. It reads: “The book does not deliver to the promise in its title. It is yet another “discover fun in mathematics” book, mixed with a poorly written travel account”.  Some of this I do agree, but I think this person was looking for another type of literary reading, or knew way too much mathematics to be satisfied with this basic reading. Plus, this book was not meant solely to talk about complex geometry and formulas. Someone else pointed out spelling errors in mathematician’s names. And another person liked it, but questioned a few of Josephs statements like his formula about factors, divisions and the eight possibilities: “To find the factors of 8,388,607 one needs to divide only by the eight possibilities, 3, 7, 13, 17, 23, 43 and 47 because one of the factors must end in either a 3 or a 7.

I wasn’t looking for spelling errors as I read this book. All I know is the basics as we have studied in these past modules for our assignments so I cannot decipher on a higher level of mathematical knowledge, to any length of debate. I do admit some of it was over my head. I do not know enough about geometry, further than basics to agree or disagree. I loved his adventures and the descriptions of the towns, cities and places where he traveled. I wonder, if in fact, he did visit all of the places he claimed to have visited. I’m not sure there is a way of knowing, but it was a very interesting journey.

Prophetic Words of Martin Luther King Jr.

In my study of Martin Luther King Jr.s letter from Birmingham jail written on the 16th of April 1963, I was struck by a statement he made, and it has come to pass and has turned prophetic. He said this: “But the judgment of God is upon the church as never before. If today’s church does not recapture the sacrificial spirit of the early church, it will lose it authenticity, forfeit the loyalty of millions, and be dismissed as an irrelevant social club with no meaning for the twentieth century.” This was predicted fifty years ago by him. Wow. He was brilliant and led by God.


Check it out.
“Since the creation of the world God’s invisible qualities-his eternal power and divine nature-have been clearly seen, being understood from what has been made, so that men are without excuse. For although they knew God they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened. Although they claimed to be wise, they became fools and exchanged the glory of the immortal God for images made to look like mortal man and birds and animals and reptiles. Therefore God gave them over in their sinful desires of their hearts to sexual impurity for the degrading of their bodies with one another. They exchanged the truth of God for a lie, and worshiped and served created things rather than the Creator–who is forever praised. Amen. Because of this, God gave them over to shameful lusts. Even their women exchanged natural relations for unnatural ones. In the same way the men also abandoned natural relations with women and were inflamed with lust for one another. Men committed indecent acts with other men and received in themselves the due penalty for their perversion. Furthermore, since they did not think it worthwhile to retain the knowledge of God, he gave them over to a depraved mind to do what ought not to be done. They have become filled with every kind of wickedness, evil, greed, and depravity. They are full of envy, murder, strife, deceit and malice. They are gossips, slanderers, God-haters, insolent, arrogant and boastful; they invent ways of doing evil; they disobey their parents;they are senseless, faithless, heartless, ruthless. Although they know God’s righteous decree that those who do such things deserve death, they not only continue to do there’s very things, but also approve of those who practice them.”
The book of Romans chapter 1, verses 20-31. Check it out.
So, as you see, God gave people over to “evil” ways because they turned their backs on God. God let satan have his way in these people, and obviously the curse carried out through generations. Look at the list of “evil” and you will see, it’s not only perversion of sex, it is also murder, strife, God-haters, greed, heartlessness and so on. To point the finger at being gay, it also includes other “evil” practices. My point is this: Is it a matter of gay marriage? Is it a matter of gossip? Is it a matter of slanderers? Is it a matter of arrogance, ruthlessness? What is the matter? If the President stepped up and said, “I decided to approve arrogance, or gossip, or deceit, or envy.” People would think he was insane. But to say he approves of gay marriage, people are outraged. Quite funny.
According to the Bible, the book of Revelations chapter 20 verse 15. “If anyone’s name was not found written in the book of life, he was thrown into the lake of fire. And chapter 21 verse 22. Nothing impure will ever enter it (heaven), nor will anyone who does what is shameful or deceitful, but only those whose names are written in the Lamb’s (Jesus)  book of life.”
Adultery is sin, murder is sin, and all of the other stuff listed. Homosexuality is just one more category of sin. I, myself, lived in sin until I found out the truth about Jesus. Just because I was not gay, does not mean I wasn’t a sinning with sex and lying, and causing strife and so on. Was my sin just as equal to lusting after the same sex? Absolutely. Do I hate gossipers? I hate gossip because it destroys the lives of people. Do I hate adultery? Yes because it destroys lives. Do I hate murder? Yes because it causes pain, heartache, depression. Do I hate those who do it? Absolutely NOT. They are the vessels, though, willing. In the past I have been guilty of many sins. But there is a lasting way out.
I don’t know enough about “gay” to make a statement other than it is not accepted by God. Just as murder is not, hate it not, prejudice is not, lying is not, etc.  Jesus said that satan is the father of lies, he fathers them. If a person lies, they are a part of satans world. You can go on and on. So is the matter of gay the issue? No. Evil and sin is the issue and it has many categories. One needs to choose what they want at their death. Do they want to live in eternal darkness or hell? Or eternal heaven and life everlasting?

Sad truths

I have an enemy that is unknown to me. However, what I do know about my enemy, is that he or she is a very destructive person. Gossip is a poison dart and can cause the character of a person to become damaged permanently, because gossip spreads like wild fire. No matter how well-liked a person is, just one element of doubt, planted into the mind of any person can make them build up a wall against you, or make them always doubt that you can be word worthy. Enemies are rude when they make degrading comments to your face or behind your back. Murmuring insults as you walk past them is hurtful. Backbiting is something that you can never have a chance to defend because you are always absent from the discussion when it happens. Enemies set you up to look bad. They try to make you fail. They go out of their way to prove that you are every bit as pathetic as they make you out to be. They go to whatever extent they need, to convince someone that you are a bad person. They have a raging jealousy that can never be tamed. My enemy is in places that I have worked, or lived, or frequented. I don’t know anything about the personal life of my enemy because although he or she may be there, I am not aware of who my enemy is around me. Therefore, I know nothing about his or her likes or dislikes, who else they hate, what their favorite movie is, favorite food, favorite color, or any other trait they may have as a human being. This person will always be my enemy and it will always make me sad.

When you finally meet the person who you feel completes you, it’s a better idea to ask for the recipe.

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