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By Stephen Portz
"The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but, 'that's funny"…
- Isaac Asimov
The case has already been made for changing the way we educate if we are to remain competitive in a brutally aggressive world economy. The only way that we will be able to survive is to develop creativity and quadrant D thinking – this is where new technologies and the developmental exploitation of those technologies reside… but, how is this done?
Where does creativity originate anyway? If it is true that humans are a combination of genetics and learned response, then where do original thoughts come from? Is the thought somehow held dormant in a gene, only to be released at a predetermined developmental time frame? Or, are our thoughts simply a product of our experiences, kind of like a computer - info in, info out? If that is the case, then how is it possible for us to think a purely original thought? For if we have previous knowledge of thing, the thought is not original; and if we are being creative and coming up with original thoughts, then by definition, we have not had experience in the area and have never considered them before. In which case, we would have to dismiss the learned response theory as the source of original thoughts.
The powerful aspect of this condition is that if we have an original thought, an idea that we had never considered before, there is a possibility that no one else has thought of it either, and there is hope that the idea may be exploited in the market.
Parallel Processing
An interesting side note to being the first person to come up with an idea is that many times in the history of civilization, inventions were occurring in different places simultaneously, with no knowledge of each other. It seems that when an invention's time has arrived, it will be developed; If not by a person here, then by another person on the other side of the world. It is almost as if the idea is being broadcast to the whole world and anyone who is tuned in to the correct frequency can discover it. I believe the story of the development of television bears this out:
Who Invented Television?
Probably no other invention in history has been as hotly disputed as the prestigious claim to the invention of 'Tele-vision or 'long-distance sight' by wireless." Since Marconi's invention of wireless telegraphy in 1897, the imagination of many inventors have been sparked with the notion of sending images as well as sound, wirelessly.
The first documented notion of sending components of pictures over a series of multiple circuits is credited to George Carey. Another inventor, W. E. Sawyer, suggested the possibility of sending an image over a single wire by rapidly scanning parts of the picture in succession.
On December 2, 1922, in Sorbonne, France, Edwin Belin, an Englishman, who held the patent for the transmission of photographs by wire as well as fiber optics and radar, demonstrated a mechanical scanning device that was an early precursor to modern television. Belin's machine took flashes of light and directed them at a selenium element connected to an electronic device that produced sound waves. These sound waves could be received in another location and remodulated into flashes of light on a mirror.
On December 2, 1922, in Sorbonne, France, Edwin Belin, an Englishman, who held the patent for the transmission of photographs by wire as well as fiber optics and radar, demonstrated a mechanical scanning device that was an early precursor to modern television. Belin's machine took flashes of light and directed them at a selenium element connected to an electronic device that produced sound waves. These sound waves could be received in another location and remodulated into flashes of light on a mirror.
Another player of the times was John Logie Baird, a Scottish engineer and entrepreneur who achieved his first transmissions of simple face shapes in 1924 using mechanical television. On March 25, 1925, Baird held his first public demonstration of 'television' at the London department store - Selfridges, on Oxford Street in London. In this demonstration, he had not yet obtained adequate half-tones in the moving pictures, and only silhouettes were visible.' - MZTVThe credit as to who was the inventor of modern television really comes down to two different people in two different places both working on the same problem at about the same time: Vladimir Kosma Zworykin, a Russian-born American inventor working for Westinghouse, and Philo Taylor Farnsworth, a privately backed farm boy from the state of Utah.
Up until this point, the concept behind television was established, but it wasn't until electronic scanning of imagery (the breaking up of images into tiny points of light for transmission over radio waves), was invented, that modern television received its start. But here is where the controversy really heats up.
Up until this point, the concept behind television was established, but it wasn't until electronic scanning of imagery (the breaking up of images into tiny points of light for transmission over radio waves), was invented, that modern television received its start. But here is where the controversy really heats up.
"Zworykin had a patent, but Farnsworth had a picture…"the priority patent in the technology. The president of RCA sought to control television the same way that they controlled radio and vowed that, "RCA earns royalties, it does not pay them," and a 50 million dollar legal battle subsequently ensued.
Zworykin is often credited in history books as being the father of modern television. This was because the patent for the heart of the TV, the electron scanning tube, was first applied for by Zworykin in 1923, under the name of an iconoscope. The iconoscope was an electronic image scanner - essentially a primitive television camera. Farnsworth was the first of the two inventors to successfully demonstrate the transmission of television signals, which he did on September 7, 1927, using a scanning tube of his own design. Farnsworth received a patent for his electron scanning tube in 1930. Zworykin was not able to duplicate Farnsworth's achievements until 1934 and his patent for a scanning tube was not issued until 1938. The truth of the matter is this, that while Zworykin applied for the patent for his iconoscope in 1923, the invention was not functional until some years later and all earlier efforts were of such poor quality that Westinghouse officials ordered him to work on something "more useful." It is also interesting to note that Zworykin visited Farnsworth in his lab during this time to check on his work.
In the late thirties, when RCA and Zworykin, who was now working for RCA, tried to claim rights to the essence of television, it became evident that Farnsworth held
Zworykin is often credited in history books as being the father of modern television. This was because the patent for the heart of the TV, the electron scanning tube, was first applied for by Zworykin in 1923, under the name of an iconoscope. The iconoscope was an electronic image scanner - essentially a primitive television camera. Farnsworth was the first of the two inventors to successfully demonstrate the transmission of television signals, which he did on September 7, 1927, using a scanning tube of his own design. Farnsworth received a patent for his electron scanning tube in 1930. Zworykin was not able to duplicate Farnsworth's achievements until 1934 and his patent for a scanning tube was not issued until 1938. The truth of the matter is this, that while Zworykin applied for the patent for his iconoscope in 1923, the invention was not functional until some years later and all earlier efforts were of such poor quality that Westinghouse officials ordered him to work on something "more useful." It is also interesting to note that Zworykin visited Farnsworth in his lab during this time to check on his work.
In the late thirties, when RCA and Zworykin, who was now working for RCA, tried to claim rights to the essence of television, it became evident that Farnsworth held
In the height of the legal battle for patent priority, Farnsworth's high school science teacher was subpoenaed and traveled to Washington to testify that as a 14 year old, Farnsworth had shared his ideas of his television scanning tube with his teacher. With patent priority status ruled in favor of Farnsworth, RCA for the first time in its history, began paying royalties for television in 1939. Philo Farnsworth was recently named one of TIME Magazine's 100 Greatest Scientists and Thinkers of the 20th Century.
Source: http://www.physlink.com/Education/AskExperts/ae408.cfm Extracted from the web Sept 19, 2016.
The development of television illustrates the point I am trying to make, when conditions are right, ideas are borne and inventions come into being - often times in many different places simultaneously; not that these ideas can be forced or evoked at will, but if their qualities and nature are better understood, there may be a way to better recognize them and seize on the opportunity that they present. Albert Einstein, arguably the greatest mind our civilization has known, intimated at where creativity and inspiration came from for him:
"The intellect has little to do on the road to discovery. There comes a leap of consciousness, call it intuition or what you will, the solution comes to you and you don't know how or why."
"There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. All great discoveries have involved just such a leap. The important thing is to not stop questioning."
There also appears to be a consistent pattern or habit that inventors exhibit that causes their mind to relax and allows inspiration to come to them after they have begun to consider a problem. Einstein received the necessary inspiration to develop his ideas on particle theory while watching a game of billiards. On another occasion, he developed his theory of relativity after having a dream about riding on a beam of light. Farnsworth's inspiration for an electron beam scanning tube for television came to him on his family farm in Idaho while considering a freshly plowed field. He was only a young teenager at the time. Archimedes supposedly solved the classic materials volume to density relationship while taking a bath.
What do each of these and many other inventor inspiration stories have in common? It appears that the inventor starts by considering the problem, but instead of wrestling with the problem and exhausting the mind in hopes of forcing the ideas to come, it would appear that the best inventors consider a problem but then they go off and do other things. In this way, the inventor allows their mind to relax, appreciate, wonder and wander in discovery; To find examples, parallels, and patterns; To allow thoughts to flow freely, naturally, and uncoerced, often times in activities that are far removed from the problem in question.
"Every now and then go away, even briefly, have a little relaxation, for when you come back to your work your judgment will be surer."
I have previously mentioned the attitude of my father-in-law with regard to thinking and learning. As a holder of some 30 U.S. patents, many of them classified, and having worked
intimately with many Department of Defense programs, has given him some interesting insights into inventive inspiration. He speaks often of right and left brain functioning – the left hemisphere being used for languages and logic and the right hemisphere being used for feelings, form, and intuition.
intimately with many Department of Defense programs, has given him some interesting insights into inventive inspiration. He speaks often of right and left brain functioning – the left hemisphere being used for languages and logic and the right hemisphere being used for feelings, form, and intuition.
The right side of the brain is the side that you need to tap into to get to inspiration and to go places where no one has gone before. The problem is that the right side of the brain does not speak English, or any other known language for that matter, so it communicates through a feeling structure. It is where we get impressions, hunches, and all original thought. It is also where we come to begin to understand the metaphysical world – or the world that we can not now understand, see, or measure. Dad maintains that he gets much of his insight in dream states where subconscious thoughts dominate. Having degrees in physics and math, dad has strong logic and reasoning quotients but he describes the process of being inspired during sleep in an almost irrational way:
"The right side whispers impressions of an idea to me; the left side of my brain jumps in and starts arguing how impractical the idea is; when the argument gets really heated, that is when I wake up and write everything down. This usually occurs between three and four in the morning."
Dad often uses nature as a rich source of his inspiration. "If there is a problem to solve the first thing that you should do is consider if nature has already solved it."
He relates and account of traveling with his grandfather to the Hopi village of Hotevilla, while just a child of ten and witnessing the sacred Hopi Snake Dance. In the dance, Hopi priests dance with rattlesnakes in their mouths in an effort to petition the gods for rain. As one of the dancers passed near to him, so near in fact, that he was frightened by the snake's appearance as he had never before seen one that close, he noticed some unusual marks below each eye on the snake's head. The marks, as he would come to learn, as the wondering child matured into the adult scientist, were the "pits" of a viper snake.
"If there is a problem to solve the first thing that you should do is consider if nature has already solved it."
"You see it is very interesting, when a rattlesnake hunts at night, it can't see much better than you or I so it has perfected the ability of heat detection by using its pits. The pits are actually heat sensors that have the ability to detect heat in certain frequencies. The way the snake operates to home in on a prey is to wave its head back and forth to discern the three dimensional thermal image. It has to be able to tell the difference between a rat paralyzed with fear and a rock that is still warm from the heat of the day. To further discriminate, the snake may shake its rattles, this serves to scare the rat even more which greatly elevates the creature's heart rate and heats him up for the snake to distinguish which object to strike." This very same thermal recognition effect was used forty years ago as dad worked on the development team that created the redeye missile for the Air Force.
Dr. Yoshiro Nakamats, Japan's most prolific inventor with over 3000 patents to his credit, talks about inspiration in another way. He calls it his five tier pagoda of invention theory: The first tier of the pagoda is the spiritual side, "the spirit must be pure." The second tier deals with the mind and body in the things we eat and drink and the exercise that we get. Dr. Nakamats takes great care in what he consumes, even taking pictures of his meals before eating so that if he feels strong or weak brain functioning he can attribute it to what he ate, and return to, or avoid those foods. In his swimming exercise routine, he always brings something to write on, as some of his best inspiration comes during these times. Nakamats associates swimming and the breath control needed to swim, with increased brain strength and his inventive prowess. To regularly deprive the brain of oxygen by holding one's breath causes the body to compensate by creating an overdeveloped carotid artery, thus supercharging the brain with an abundance of oxygen at times when you are not performing these "breath exercises."
The third tier of the pagoda is knowledge, both scientific and non-scientific. Before inventive thoughts can take place, a foundation of understanding about the world and its workings needs to be laid. Tier four is the experience level. With our knowledge base, we go off into the world and try different things and these trials give us experience and are good, if we learn from them. "If there are two paths, one easy and one hard, we must always choose the hard path, because it strengthens our life and gives us good experience."
The fifth tier of the pagoda is the act of turning your thoughts into inventions. When recounting the experience of how he came up with the idea for the floppy disc for IBM -Nakamats describes listening to classical music (Beethoven's Fifth symphony), and as he did so, he saw a butterfly in his mind. As he watched the butterfly his attention was drawn to its wings, and as he looked at its wings, the wings materialized into a floppy disc.
Cut From a Different Cloth
If these concepts are beginning to sound a little strange to you and if at any moment you expect to hear Rod Stirling's voice and doodoo, doodoo music, then you probably are having the common reaction to a discussion of this sort. The fact is, that few people are inventors of any consequence, but those that are, definitely walk to the beat of a different drummer. For those of us trying to be inventive, perhaps that is our first clue as to what it takes.
Great inventors and innovators have a passion for changing the status quo, they are not content to keep things as they are but are constantly looking to find a better way.
Thomas Edison described his passion in this way:
"…often I am correctly described as more of a sponge than an inventor…
I am always extremely interested in the novel ideas of others… I never pick up an item without thinking of how I might improve it."
Einstein put it this way when referring to his problem solving abilities:
"I have no particular talent. I am merely inquisitive."
And…with regard to the importance of developing creativity:
"Imagination is more important than knowledge."
"When I examine myself and my methods of thought I have come to the conclusion that the gift of fantasy has meant more to me than my talent for absorbing positive knowledge."
Into the Mind of an Inventor
Anyone who has raised a preschooler knows how very imaginative and inquisitive these wonderful little minds are. They are very creative and want to know how everything works. Even kindergarten students are special in this way and come to school filled with wonder and desire to know why things are. Their teachers work with them to answer their many questions, particularly about this new place – school, and teach them the structure needed to function in a school setting. From that point on into the primary grades and beyond, it is pretty much down to business. There is not time for personal inquisitiveness and after awhile, it begins to be extinguished.
Thomas Edison started school in much the same way, but perhaps was even more inquisitive than the normal youngster. At some point in time, his teacher got so frustrated
with his constant questioning that she labeled the boy "addled," which at the time meant that he would be unable to learn as normal students do. His mother, a teacher herself, was so furious, that she removed him from public school and taught him at home; So Thomas Edison is actually one of the first home school success stories since the inception of institutionalized public schools. Needless to say, his experiences with formal education left Edison with a not too favorable impression of that type of learning. When orienting a college graduate to his new position in one of his labs the grad mistakenly asked Edison what the rules were for working for him. Edison retorted, "Rules! There are no rules here; we are trying to accomplish something!"
Einstein had a similar disdain for formal education, but probably not for the reasons that most people infer – especially when they perpetuate notions that he flunked 9th grade algebra or couldn't talk until he was four or read until age seven.
"Although some Einstein biographers have disputed the widely held belief that Einstein
was a poor student, the papers at Princeton lay this to rest once and for all. According to Dr. Stachel,
those who saw Einstein's academic records may have been misled by a reversal in the grading system
of his school in Aargau, Switzerland. Those records show that, for two successive terms, when Einstein
was 16, his mark in arithmetic and algebra was 1 on a scale of 6, in which 1 was the highest grade.
For the next term his mark was 6, which would have been the lowest grade, except that the grading
scale had been reversed by school officials."
Sullivan, Walter. The New York Times – Late City Final Edition, February 14, 1984
In an unpublished biography written by his sister Maja, she confides that Albert was an unusual child from the start, spending great quantities of time in difficult and tedious tasks such as building card houses. Contrary to popular reports, his sister notes that while his development was seemingly slower, he began speaking by the age of two and half years, not four, as many have said. As a testament that her recounts were not just out of sentimental fondness to her brother and to refute earlier "facts," she also notes that when her brother was born, "his mother was shocked at the sight of the back of his head, which was extremely large and angular."
Hayden, Thomas. The Inner Einstein US News and World Report. December 9, 2002. http://www.freerepublic.com/focus/news/800220/posts extracted from the web Sept. 19, 2016.
Perhaps there is some truth to Einstein's "late" development and the stories that have been perpetuated. He himself, admits the reason behind all of his breakthrough work in physics, when the world had already been perfectly described by other great scientists was because, "…my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had grown up" (Hayden, 2016).
Sounds a little child-like in his attitude and appreciation of the wonders of nature doesn't it? Maybe even a little like those preschoolers that we were talking about earlier. At any rate, it is impossible to know exactly what he meant, as Einstein's genius for interacting with reporters and the people who loved to flock to him went far beyond the physics: "A horde of reporters boarded our ship near Long Island," he complains. "[They] asked me extremely stupid questions which I answered with cheap retorts, which they accepted with enthusiasm."
There are other experiences in his life that hint into his unique approach to intellectual growth, as evidenced in the following quote, "the only thing that interferes with my learning is my education." This attitude could have been confirmed by one of his first job placements after college as a patent clerk. More prestigious academic positions were denied him because of poor recommendations from his college professors, this because of his disdain for authority and his casual attendance at their required lectures. There are no reports that Einstein suffered any from the slight though, in fact, he wrote some of his best papers while serving as a patent clerk
If we take any lessons from Edison and Einstein, it would appear that a possible pattern for fostering inventive thinking is to have a curious and child-like wonder about the world around us, and continually think upon how things might be improved.
How We UnTeach Creativity and Problem Solving
In teaching an architecture unit to middle school students, I discovered that they have a difficult time drawing houses the way houses actually look. When drawing houses, these students typically will not draw what they see when they look at their home instead, they will often draw a symbol of a house:
This was frustrating enough that I went to discuss the matter with our art teacher. As the teacher of a very successful art program, I had witnessed how she had the ability to take just about any student and give them technical and artistic methods to make them a passable artist – some with amazing success. So I asked her, "How do you get your students to draw what they see?" And I described the problem that I was having. She laughed and explained what was happening, as apparently this topic has also come up in art circles before: "When children first go to kindergarten, the teacher frequently asks them to draw a picture of their home and family. This activity can tell the teacher a great deal about the child's development and their family and it puts the child at ease as a great icebreaker. The problem is that many children have a hard time with stick figures, much less drawing a house, so the teacher draws the house icon on the board for them to copy. Apparently the imprinting sticks because for many years thereafter, when you ask someone to draw a house this is what you get."
Many other topics of study have the tendency to also get "standardized," in our instruction. There is after all, only one way to look at a problem, there is only one correct
answer, if there wasn't, the tests would take too long to grade. A powerful example of how formal education may have the tendency to squelch creativity and problem solving ability was evidenced in a study by the Carnegie Foundation.
The study of the early 90's sought to understand how certain populations dealt with emerging technologies and so they centered their research on the then popular videocassette recorder. The Foundation asked groups of people to set up a VCR properly so that it would show the correct time and be able to record a program when they were out of the house. The participants were each provided with an operator's instruction manual and all associated equipment and cabling. The study revealed some surprising things about the performance of different age groups and their corresponding educational attainment.
Probably of no surprise, children age 8-12 were the best at setting up the machines. The worst population at performing the task was not only the college educated, but those holding postgraduate degrees. An argument could be made here that the population is older and less familiar with the technology, but wouldn't it stand to reason that they should be the group most able to read the manual, extract the needed information and apply it? Of particular note was the finding that the second best performing subgroup was the young adult population, but not the mainstream as one might expect – it was those individuals that had actually dropped out of high school. This study is very telling about the relationship between the amount of formal education a person has and their corresponding problem solving ability.
Science Research?
"In some ways science is all about prediction, because if a scientific theory is right, it predicts accurately the behavior of some process in nature. The irony is that so much of what happens in the day to day events that lead to a scientific discovery is anything but predictable. The process by which discoveries are made is almost always turbulent with chance or accident, and only very rarely is a discovery the result of careful, rational planning."
-James Burke Author of the Connections Series and the Pinball Effect.
A perfect example of pushing students into a conformance model and suppressing creativity and inquisitiveness has to deal with the science fairs projects of today. Go to many elementary or middle school science fair and witness all the cookie cutter projects so neatly stamped out it is almost as if they were all scripted. It is because many of them are. Books are actually being written to give the students ideas for science projects and how to set them up and present them.
"[The working scientist]…is that he is not following any prescribed course of action, but feels complete freedom to use any method or device…before him that seems likely to yield the correct answer…in short, science is what scientists do, and there are as many scientific methods as there are individual scientists."
Dr. Terry Halwes
Bridman, Percy W. "On Scientific Method". http://dharma-haven.org/science/dispelling-myth-magical-science.htm. Extracted from the web Sept 19, 2016.
I will never forget how excited my third grade son was with his first opportunity to do science fair. It was because there were so many things that he desired to know about; he loved the natural world and wanted to know what made it work. When I asked him what he wanted to study, he said lightening. I told him I thought that that was a great idea. He came back from school the next day a little less excited so I asked him about his science fair project. He said, "my teacher said that for my science fair project to be a science fair project I have to make my idea into a question." So I said to him, "that sounds fine, what question would you like to ask?" He thinks a bit and replied, "What causes lightening?"
I told him that I thought that that would be a really good question for science fair, and off he runs again, so excited. The next day, he comes home and he is really low. When I asked him what is wrong, he said, "My teacher told me that I can't do a science fair project on lightening because I can't do experiments with lightening." My son ended up doing experiments with toothpaste on an egg to see which one cleaned the best; but it sure was a step down from working with lightening, and he never did regain his excitement about science.
I share this story because it is illustrative of some of the conditions in our educational system today; students are often directed away from the things that they are interested in or shoved through a process that takes the creativity, thinking and learning out of it to conform to a convenient structure for the teacher. Science is supposed to be the discovery of why. The question why, may not have a known answer, and it surely does not have to have a hypothesis before it is allowed to be asked. In fact, if you already have a pretty good idea about the answer, enough to form a hypothesis, then doesn't it seems a little silly to take the time to ask the question and do all the experimenting in the first place?
I know, I know, it doesn't matter if the hypothesis isn't proven correct, it is the experimental process that is the important thing. That is always given as the science fair party line, but who gets excited studying something where they already have a good idea what the answer is; or by having their "educated guess" proven wrong, and, when is the last time you saw a project with an unproven hypothesis statement win anything at a science fair? Isn't it human nature that if you think a certain way that it only follows that you would want to be correct in your assumptions, and wouldn't you only be looking for data that proves your point? How do we get away with calling that science? Science is supposed to be unbiased; it is supposed to be the discovery of truth, not just looking for the data that proves a point while neglecting the data that doesn't.
A very famous anthropological study has been called into question over the last twenty years for some of these very arguments of research bias. In the late 1920's Margaret Mead studied the Samoan peoples of the Pacific. She came back and published her findings in a book which she titled, "Coming of Age in Samoa." In this very popular and highly acclaimed book, Mead suggested that Samoan youth undergo less stressful teenage years because of a culture which encouraged sexual promiscuity. Mead's study challenged the notion of absolutes of right and wrong in favor of cultural relativism. That is, that people don't have an innate disposition for good or bad because such things were determined by the norms of their culture. Other anthropologists have since questioned the findings of her study but only after half a century of acceptance and influence in the social sciences community:
"…Nolan said the "Coming of Age in Samoa" became so popular because at the time "there was a strong movement towards sexual freedom in this country and people wanted to believe what she had to say."
"…third, she arrived in Samoa with a false preconception from Edward Handy,
director of the Bishop Museum, that she would find premarital promiscuity as the
cultural pattern in Samoa. Fourth, she idolized Franz Boas and wanted to reach a
conclusion that he would find acceptable."
Nolan, Patrick.(2000) Personal interview. 26 Jan. 2000. Retrieved from the web Sept. 19, 2016, from http://margaretmead2008.tripod.com/mvf.htm
Just as in Mead's scientific study, problems with research bias and the "scientific method" could be resolved by instead of hypothesizing a possible answer which supposedly represents the "scientific method," and going about trying to find data to support the claim, to simply ask, "why a condition exists or why something works?" and, "under what conditions something exists, works or works better, and why?" In this way, all the data could be considered, not just the parts of it that prove a point. A further example of the flaw in the "scientific method," is the promulgation of studies to prove something is good for you, or bad for you. These "studies" are almost always funded by organizations that stand to benefit from the research findings; essentially making a desired hypothesis and then going out to find data that only supports that assertion, while ignoring all others. Sounds kind of familiar, huh? Just like Science Fair.
My father-in-law's attitude in this respect is, "follow the data, theory be damned." Meaning essentially, don't construct a theory and then go around looking for data to support the theory - which is what most people do; rather than do that, we should take in all the data and look for patterns to construct ideas. Anomalies in data are not to be discarded, for they represent amazing opportunities for discovery as a person delves into why they exist and under what conditions they do exist.
America holds a heritage rich in innovation. It began with our pioneer forefathers making a living on difficult frontiers; It was continued in our agricultural era when many people lived on a farm and had to know how to fix what ever didn't work; It carried over as people migrated to cities and suburbia where many had a shop in their backyard, or a garage to tinker in; And it continues today, when breakthrough innovation may hold the key to great wealth in our free market system.
This chapter describes the essence of innovative thought and creativity. Patterns of thought in the lives of great inventors were identified and discussed for their value in nurturing in the lives of our own students. The nature of creativity is elaborated and ideas for encouraging it and just as importantly, not discouraging it, are discussed. As it is pointed out, there is an unfortunate relationship between formal instruction and the creative problem solving process because standardizing thought can have the negative impact of stifling creativity and problem solving prowess. The way we structure educational delivery must consider these relationships if creativity and innovation is to be effectively nurtured in the classroom.


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It's been a week of viral distractions, animal mishaps and snowy views. It's nice to finally have time to sit with a cup of jasmine green and edit a bit of my week to share with you. Hope you enjoy!
Brilliant blue winter sky at the Smithsonian.
Delicate paw prints in the first snow of the winter.
Poor, lovely little sakura you've blossomed too soon. I think we both hope spring comes early this year.
What is this stuff and why is it so cold? You could read the thoughts on Foufee's precious little face. She jumped into Esmé's arms after this and refused to get down. Maybe we need to get her some boots?
Spectacular sunset lit the sky on fire, threatening to melt the snow. It was an empty threat but a lovely show.
A gift of Kumamon from Japan. Aren't they adorable little bears?
Just can't get enough citrus this winter. Mandarin oranges and tangerines are the best!
Esmé brightened the week with her neon style. She's so confident in her individuality and her fashion sense. I was never this cool at 14.
Nora's adorable snow kitty. Don't you want to pet her?
Speaking of petting... Rukia and Foufee snuggled together are irresistible. Had to hug them.
I hope you all stay warm and cozy this weekend. Snuggling is the perfect winter activity, isn't it?
You can learn more about 30 in 30 and meet others who are creating a little magic every day on Chris Galvin's blog.
Please check them out, they are all wonderful.

subset: commoncrawl


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2. To guard their own instincts;
3. To hold men to a high standard
of social purity and to help
them attain it.
Nor does this teaching necessitate morbid consideration of the subject. It will, in fact, in many cases clear away the morbid curiosity and surreptitious seeking after information in which untaught girls indulge. Skillfully and delicately taught this knowledge as an important and serious part of woman's work, girls will be sweeter and more womanly for the knowledge of their responsibility to society and to their unborn offspring.
Schools that attempt such a course for girls are finding their chief difficulty in discovering people properly endowed by nature and properly trained to teach it. To give such work into any but the wisest hands invites disaster. To make it a study of the physical basis of sexual life is disaster in itself. Service, through making one's self a pure member of society, and through helping others to keep the same standard—this must be the keynote of the teaching, an education toward social efficiency and social uplift.
The adolescent girl, already the product of a general training which has aimed at all-round development of body, mind, and spirit, is now ready for the specializing which shall place her in tune with the world of industry and help her to make for herself a permanent and useful place in society. Henceforward the girl's training must face her double possibilities. She must not be allowed to have an eye single to making an industrial place for herself; nor can those who educate her fail to see the double work she must do.
Any consideration of the subject of girls' work outside the home or work in the home for financial return must begin with a general survey of the field of industry, discovering what women have done and are doing, together with the effects of gainful occupation upon the character and efficiency of women.
The United States Census reports for 1910 give the following figures:
Number of Females Ten Years and Over Year Engaged in Gainful Occupations 1880 2,647,157 1890 4,005,532 1900 5,319,397 1910 8,075,772
It is thus seen that gainful occupations for women have increased greatly in the thirty years covered by the report. At present 21.2 per cent of all females, or 23.4 of all over ten years of age, are engaged in work for wages. Further tabulation brings out the fact that, whereas the age period from twenty-one to forty-four shows the largest percentage of men employed in gainful work, women show the largest proportion of their numbers so employed during the age period from sixteen to twenty. Evidently the girls are at work. The figures follow:


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Francis MacDonald
Hamilton Mausoleum Suite CD (Signed)
Release Date: 26/01/2018
Discs: 1
Recorded with the support of Creative Scotland, 'Hamilton Mausoleum Suite' is an album of original chamber music (string quartet & harp) composed, arranged and produced by Scottish, BAFTA-nominated composer/songwriter and Teenage Fanclub drummer Francis Macdonald. Released 26th January 2018 via TR7/Shoeshine Records, the album features soloists from the Scottish Festival Orchestra and will be available on CD, download, stream and limited edition heavyweight vinyl.
The 'Hamilton Mausoleum Suite' music was inspired by – and the album was recorded in – the historic Hamilton Mausoleum that stands on the edge of Strathclyde Park in Lanarkshire, a few miles from the city of Glasgow. The Mausoleum has one of the longest echoes of any man-made building in the world and was constructed in the 1850s for Alexander The 10th Duke of Hamilton. For a time, the duke's remains were interred in an Egyptian sarcophagus on a plinth within the building. The mausoleum, 37 metres tall, now stands empty.
Francis went to secondary school nearby and remembers a family visit to the building when he was a young boy. On trips south from Glasgow via the M74 the Mausoleum is a familiar landmark. A couple of year ago he got the idea to record in the building, celebrating its unique reverberant qualities. Museum officer Linda Barrett was encouraging so Francis set to work composing and planning. The album was recorded in one day.
Francis is currently the drummer with Teenage Fanclub and has recently toured across the world to promote the band's most recent album 'Here'. A member of BMX Bandits for many years, in 1996, he set up Glasgow indie label Shoeshine Records and country/folk label Spit & Polish in 2000.
An accomplished composer and songwriter, his songs and music have appeared in various films and TV projects including having his vocals sampled for Looper's 'Mondo '77'' track which featured on the soundtrack to Hollywood blockbuster film 'Vanilla Sky' (2001) which starred Tom Cruise. In 2013, he was nominated for a BAFTA Scotland New Talent Award for his soundtrack to short film 'The Lost Purse'.
His debut neo-classical album 'Music for String Quartet, Piano and Celeste', released in 2015, was described as "Sublime" by Classic FM and "Nice" by Jarvis Cocker on BBC 6Music. The following year, he contributed an arrangement to the No 1 Classical album 'The Lost Songs of St Kilda' which was performed by the Scottish Festival Orchestra. This led to Francis approaching their fixer, cellist John Davidson, to put together an ensemble for the mausoleum project.
Along with the 'Hamilton Mausoleum Suite' project, Francis recently collaborated with London-based artist Harry Pye for a collection of 'art pop' songs and spoken word pieces for the album 'Bonjour' ("Odd but good") 4 stars, Mojo magazine.
He has worked with a range of artists in a rich and varied career including Alex Chilton, Dan Penn, The Pastels, Kevin Ayers, Kate Rusby, Edwyn Collins, Ian McCulloch, BMX Bandits, Belle & Sebastian, Camera Obscura, Cairn String Quartet and Max Richter.
The musicians that appear on 'Hamilton Mausoleum Suite' are:
Violin I - Justine Watts
Violin II - Stewart Webster
Viola - Emma Peebles
Cello - John Davidson
Harp - Sharron Griffiths
1. Sarcophagus (Quartet & Harp)
2. Whispering Walls (Quartet & Harp)
3. 11th November, 2016 (String Quartet)
4. Folia (Solo Harp)
5. Half Past Midnight (Quartet & Harp)
6. Cantata For No Voices (Harp, Cello & Viola)
7. The 10th Duke (String Quartet)
8. Beam (Quartet & Harp)
9. One Foot Then Another (String Quartet)
10. Stone Lions Lullaby (Harp & Violin)
11. The Mausoleum (String Quartet)


text:
Credit enhancement: a boost to private capital in infrastructure?
A strange irony persists in today's infrastructure investment market: private capital waiting to be deployed into the sector is at an all-time high, yet investors seem reluctant to commit. Even in developed countries, few investors are willing to partake in transactions with merchant or construction risks without taking a higher risk premium.
This can make the financing of infrastructure projects more costly—a challenge particularly acute in emerging markets where further investment risks abound.


text:
Tom Brady stepped to the podium at Gillette Stadium on Sunday as a bright January sun shined down on 25,000 fans who had come to see off the Patriots. The team was about to depart for Indianapolis, where it will take on the Giants in Super Bowl XLVI, and the three-time Super Bowl champion quarterback waited a beat for the fans' cheers to subside.
"Thank you all for coming out here today," Brady intoned, "but don't get too hopeful for next Sunday. I doubt we'll be able to stay in the game against the Giants, much less beat them.
"This is going to be one of the all-time memorable butt-whuppings in Super Bowl history. Something like them 77, us negative-11. We're going to get thumped, crushed, dish-ragged and demolished. I'm honestly considering retiring Wednesday, just to save face, and letting Brian Hoyer take this one.
"But, hey! Thanks for coming."
Brady didn't really say any of that, of course, but apparently the New York tabloids think that's what he should have said.
"TOM'S TAUNT: Brady tells pep rally: Come back for bigger party after Supe." — New York Post
"PART OF JIVE: Hey Giants, Brady already talking about victory bash." — New York Daily News
Good grief. It appears Brady's comments at the pep rally — which by definition is meant to "rally" fans with a little bit of "pep" — were a little too cocky for New Yorkers.
Here's what Brady actually said:
"We have the greatest fans in America. You guys have proved that year in and year out with your support. I wish I could take all you guys to Indy with us. We're going down there, and we're going down there for one reason. We're going to give it our best and hopefully we have a lot more people at our party next weekend."
OMG! GTHO! WTH? Tom wants to win the Super Bowl and have a party!!??!!??!! Stop the presses! (Has anybody actually ever yelled that?)
As far as bold predictions go, it wasn't exactly Moses Malone declaring "Fo, fo, fo."
If recent Super Bowl history between these teams is an indication, the Pats are in a good spot. Prior to Super Bowl XLII, then-Giants wide receiver Plaxico Burress made a much bolder guarantee, predicting the Giants would beat the Patriots 23-17.
As everyone knows, David Tyree made a lucky catch, Asante Samuel failed to do what he was paid to do, and the Giants ended the Patriots' undefeated season.
Check out the tabloids' reaction to Brady's comments on the back covers below.
See, Brady wants to have a party, whereas the Giants just "want to make New York proud." That would probably involve winning the Super Bowl, wouldn't it?
Post cover via nypost.com
Daily News cover via nydailynews.com
"It's been a strength of their team for as long as I can remember. … It seems like they always have guys that can rush the quarterback. Justin Tuck is as good as they come. Osi [Umenyiora], week in and week out, he's a player that can ruin a game for an offense. You look at the group they have now, and they have a ton of depth at the defensive line position. There were times this year where they weren't all out there as a group but… they're out there now, and they're playing extremely hard."
— Brady talking about the Giants' defensive line in a quote that curiously did not receive as much attention in the New York tabloids as his "party" comment. Hmmm…
This spike is brought to you by the letter "G."
Whatever event was going on here, this guy loved it.
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An initial meeting of the RSE Digital Scotland Working Group (DSWG) was held on the 13th November 2009. In addition to a good attendance at the meeting, several other key individuals who had other commitments that day indicated that they would be prepared to contribute towards the development of a Digital Scotland report / advice paper.
It was the view of the working group that there is an opportunity for Scotland to develop a more radical and visionary approach to the use of digital technology than was perhaps possible for the UK as a whole.
It was agreed that it would be worthwhile for the RSE to develop an Advice Paper with a view to advancing digital development in Scotland. It is envisaged that this work will take place over several months with members of the working group engaging in interviews with key groups between meetings.
The overall aim of the DSWG will to be to develop a vision of the society that Scotland can become by embracing the opportunities offered by digital technology. This vision should be about individuals, society, the environment and the economy.
Digital technology should be seen as a vehicle that can and should produce societal benefits and consideration should be given on the broadest frame to what can be achieved.
Saturday, 14 November 2009
Digital Scotland
Posted by Michael Fourman at 01:00
Subscribe to: Post Comments (Atom)


text:
|Eric Blossom
|[Discuss-gnuradio] PowerMate and Contour ShuttlePRO
|Sun, 15 May 2005 21:48:31 -0700
Thanks to Matt's desire to have a knob to twist, gr-wxgui now has support for the Griffin PowerMate USB knob, as well as the Contour Shuttle/Jog controllers (ShuttlePRO, ShuttleXpress) It's up to you to figure out what you want to have them control, but there's code that will send you events on button press/release, dial motion, and shuttle ring position. The code's in gr-wxgui/src/python/powermate.py This uses the Linux /dev/input/event* interface. Support under other operating systems is left as an exercise for the student. Patches welcome! Have fun! Eric
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STARmeterSEE RANK
Down 15,847 this week
Verner Clarges (1846–1911)
Verner Clarges, born in Bath, Somerset in 1846, began on stage in England then America from the 1870's. fine British bald gentleman who starred and supported in many American drama films under the direction of D.W. Griffith at the Biograph Film Company from 1909, the first was 'Was Justice Served? starring James Kirkwood and Gladys Egan, he died ... See full bio »
Born:in Bath, Somerset, England, UK
Died:(age 65) in New York City, New York, USA


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LBC Invited A Tory MP And A Former Kremlin Advisor To Debate Ukraine. The Result Was Explosive
Mar 04, 2014, 02:12 PM
Iain Dale invited Conservative MP Brooks Newmark and former Kremlin Advisor Alexander Nekrassov to debate what should happen in the Ukraine. The result was explosive and phenomenal to listen to.


text:
In a brand new Jumanji adventure, four high school kids discover an old video game console and are drawn into the game's jungle setting, literally becoming the adult avatars they chose. What they discover is that you don't just play Jumanji – you must survive it. To beat the game and return to the real world, they'll have to go on the most dangerous adventure of their lives, discover what Alan Parrish left 20 years ago, and change the way they think about themselves – or they'll be stuck in the game forever, to be played by others without break.Release Date: 20 December 2017
Runtime: 119 min
- Alex Wolff
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- Morgan Turner
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- Ser'Darius Blain
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Director: Jake Kasdan


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Woman Indicted in Ocala For Theft Of Nearly $1 Million Dollars Of Treasury Department Funds
Ocala, FL - United States Attorney Robert E. O'Neill announces the return by a grand jury of an indictment charging Centerria Shantia Farmer with theft of funds belonging to the U.S. Department of the Treasury. If convicted, Farmer faces a maximum penalty of 10 years in federal prison. The indictment also notifies Farmer that the United States is seeking a money judgment in the amount of $902,639.78, which represents the proceeds of the theft of government property.
An indictment is merely a formal charge that a defendant has committed a violation of the federal criminal laws, and every defendant is presumed innocent unless, and until, proven guilty.
This case was investigated by the Internal Revenue Service Criminal Investigation and the United States Secret Service. It will be prosecuted by Assistant United States Attorney Diidri W. Robinson.


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text:
The following series of posts comprises our introduction to complex analysis as taught by Professor Rowan Killip at the University of California, Los Angeles, during the Fall quarter of 2009. Where necessary, course notes have been supplemented with details written by the authors of this website using assistance from Complex Analysis by Elias Stein and Rami Shakarchi. The basic properties of complex numbers will be assumed allowing us to begin with the definition of a holomorphic (or complex-differentiable) function, the central notion in our study of complex analysis.
The basic properties of complex numbers will be assumed, allowing us to begin with the definition of a holomorphic (or complex-differentiable) function, the central notion in our study of complex analysis.
Definition 1.1 Suppose is an open set and . We say is holomorphic (or complex-differentiable) at if there exists We say is holomorphic on if it has this property for all .
We can rewrite this formula in terms of the real and imaginary parts of to surmise the relationship between complex differentiability and real analytic differentiability. Let with and , and write where . Then,
We first notice that this is stronger than the differentiability of the real map in . In the real, multivariable case, the derivative of this map is a linear operator, namely, the Jacobian, ; in our equation above, the matrix on the right hand side is . Clearly, it is endowed with a distinct structure summarized in the following proposition.
Proposition 1.2: The Cauchy-Riemann equations The function is holomorphic at , , with derivative if and only if the functions , where , are differentiable at and
both hold.
Remark There exists a well-known isomorphism between and given by in which it is clear that multiplication by a complex number corresponds to a dilation and rotation via the matrix . Then the above formula indicates that, infinitesimally, a holomorphic map acts like a dilation and a rotation. In particular, if is a holomorphic map such that , then preserves the angle of curves passing through . Such a map is called a conformal (angle-preserving) map. We will discuss conformal maps in further detail later in these notes.
Definition 1.3 A parametric curve is called rectifiable if
Theorem 1.4 If such that is continuous, is open and is rectifiable, then
- denoted by exists.
- If then .
- Given a continuous bijection we have , noting that reversing the direction of the curve changes the sign on the right hand side of the formula above.
Proof: These are immediate consequences of the theory of Riemann integration in one variable and will not be reproduced here.
Theorem 1.5 Goursat's theorem Suppose is a holomorphic function from the open set to the complex numbers and is a solid, closed triangle inside . Then .
Proof: We begin by giving Cauchy's proof of Goursat's theorem, an immediate result of Green's theorem when is necessarily continuously differentiable. Suppose , then by Green's theorem, we have that
An application of the Cauchy Riemann equations demonstrates that both integrals in the sum are equal to zero, hence as desired.
The classical argument by Goursat uses a stopping-time technique that is both elegant and powerful, albeit not as simple as Cauchy's proof. On the other hand, it does not require that and is a more general result. (We will eventually learn, however, that a holomorphic function is, in fact, analytic.) To start, we note that it suffices to show that . Next, we subdivide our original triangle into four smaller triangles by bisecting each leg of the triangle and connecting the midpoints with straight lines. This yields four triangles similar to each other and our original triangle . Denote these triangles and in any order. The line integrals over these triangles cancel out over their shared legs, hence . We can then divide each new triangle into four smaller triangles by the process above and claim that To prove our claim, suppose on the contrary, that it does not hold. Then, ; moreover, . Since the are closed and bounded in , they are compact, hence . By hypothesis, is holomorphic at , so that . Then, for some ,
where we denote the perimeter of , (i.e. by and where the integral on the right hand side vanishes as both terms have primitives, or complex-antiderivatives, in . In particular, we have for sufficiently large. This yields the desired contradiction and proves our claim.
Finally, let be the collection of equivalent triangles formed after subdividing our original triangle times. Clearly, they obey the inequality for all . It follows that
as desired.
Remark It is essential that the triangle be contained in . Consider the function integrated along the perimeter of a triangle containing the origin. Then is holomorphic in , and . This theorem can be extended with ease to a path of any other polygon or rectifiable closed curve with one caveat: we must be able to differentiate between the inside and outside of such a curve. More precisely, the curve must be two sided. We are then free to approximate such a curve by a polygon which we can subsequently approximate with triangles.
Goursat's theorem leads us to one of the most powerful results in complex analysis, the Cauchy integral formula. This result allows us to equate holomorphic functions on sets with integrals over the boundary of these sets. With this isomorphism, one can conclude certain regularity results, in particular, the notion that holomorphic functions are analytic. We begin by considering holomorphic functions defined on sets bounded by the simplest of closed curves: circles.
Theorem 1.5 The Cauchy integral formula Fix and suppose is holomorphic in the set , then,
where .
Proof: Choose and consider the line integral of over the smaller circle . Since this function is continuous in open neighborhoods of this new circle and our original circle (that is, the annulus centered at , containing both circles), we can approximate the integral of this function over both circles arbitrarily closely by integrals over regular -gons, with sufficiently large. Since is open, there exists a simple closed path that connects these -gons. By Goursat's theorem, the integral of over the closed paths connecting these -gons must be zero. In particular, applying Goursat's theorem and letting implies
Next, consider and let be a path over the smaller circle. Integrating over this path, we have
This last statement is simply the average of over our smaller circle. Since is continuous throughout , it follows that as . Since was arbitrary, this concludes the proof of our theorem.
Further insight may be gleaned from another proof of the Cauchy integral formula. One attempts to exploit the regularity of the holomorphic function by writing it as an integral of its own difference quotient. In particular, one considers the integral
As above, the integrand is holomorphic away from , (that is, in an annulus centered at ). As above, one equates this integral with one about a small circle around the point . Letting the radius of this small circle tend to zero implies that the above integral is equal to zero. Finally, one computers the Cauchy integral formula directly. This method of proof alludes to a recurrent theme in complex analysis; namely the use of regularity and integral forms to conclude various results.
It may be helpful to note that we've used Goursat's theorem to scale and translate contours in the complex plane without affecting the value of an integral along such a contour. We can derive more general results of this type. In fact, we will see that the statement above, with a similar proof, holds for general Jordan curves.
We now arrive at another fundamental result in the theory of complex variables: that holomorphic functions are analytic. This is a consequence of the Cauchy integral theorem.
Corollary 1.6 Holomorphic functions are analytic. That is, if is holomorphic on , we can express as a power series at each point . Moreover, given and , the radius of convergence of this power series at is at least .
Proof: Fix and . By the Cauchy integral theorem, we have . Let us rewrite the the integrand as follows:
where ; this implies that, for each , and when , the sum above converges uniformly. Hence we can move it outside of the integral and arrive at
as desired. Finally, an application of Hadamard's formula demonstrates that the radius of the disc of convergence is at least .
Remark Differentiation of the series immediately implies that
from which one can infer the Cauchy estimates:
Corollary 1.7 Morera's theorem If is continuous on an open set and for each where is a solid triangle in . Then is analytic in .
Proof: Continuity and the fact that allow us to reconstruct the proof of Goursat's theorem and arrive at its conclusion without requiring, a priori, that be holomorphic. In particular, the Cauchy integral theorem and analyticity follow immediately from the theorems above .
Corollary 1.8 Suppose is a sequence of holomorphic functions that converges uniformly to on compact subsets of . Then, is holomorphic as well. In addition as well.
Proof: Suppose is compact with a solid triangle contained in E. Then, since the are holomorphic, we have
Since uniformly, is continuous and we have
which immediately implies . Since this holds for all compact subsets of , by the preceding theorem it follows that is then analytic on . To prove the final assertion we apply the Cauchy estimates. Suppose again that is a compact subset of . Then, there exists an such that for each , there exists a closed disc . It follows that is a compact subset of as well. By the Cauchy estimates we have
This assertion holds for all , so our conclusion follows as
This result is in stark contrast to situation in the case of real variables. In general, if uniformly with continuously differentiable, it is in general not true that need be differentiable. That the Cauchy integral theorem allows one to represent holomorphic functions as integrals, confers upon holomorphic functions a powerful regularity that leads to many other results. More generally, the use of integral forms plays an important role in analysis because of their regularity. Consider for example the use of the Picard existence theorem for ordinary differential equations. If , then we can conclude the existence of a solution to this differential equation by applying Picard's iteration and existence to . We can apply the results above to yield further important results.
Corollary 1.9 Liouville's theorem Suppose is an entire holomorphic function, that is, a function holomorphic on all of , and
for some and . Then is a polynomial with degree not exceeding .
Proof: Since is entire, it can be written as a power series about the origin that converges everywhere on , and it suffices to show that . Let , by the Cauchy estimates we have
For large enough , the bound above implies
The assertion follows as .
The analytic nature of holomorphic functions leads to one of the most profound results in the basic theory of complex analysis: the notion of analytic continuity. This theorem states that if two functions, holomorphic on an open and connected set , agree on an open subset, or even on a convergent sequence of points inside , the two functions must be identical. This tells us that holomorphic functions are in some way fixed by their behavior on an arbitrarily small convergent sequence of points.
Theorem 1.10 Analytic continuity Suppose is a holomorphic function with open and connected and is a sequence of points with a limit point such that vanishes on . Then .
Proof: We prove the theorem by contradiction. If , there exists in a disc of radius about . Then
by continuity and by taking along the sequence . Hence in a small disc of radius about .
Next let . This set must be relatively closed in , since, if it were not, we could find such that . But this is absurd since vanishes in a neighborhood of by the above proof, hence , and is relatively closed. Now, is both open and (relatively) closed, therefore, since it is also connected and non-empty, by a standard result from point set topology, we find that , and that on all of , as we wished to prove.
Remark must be in . If not, we have as a counterexample to the previous theorem. In particular, is holomorphic on vanishes at with but is not identically zero.
A common application of this theorem is as follows. Suppose are holomorphic and agree on a set with an accumulation point. Then on at least one connected component. Note, however, that we must ensure that the hypotheses of this theorem are met; not only do we find a contradiction when but also when our set in question is not connected in the desired sense. For example, suppose that on the principal branch and denotes the complex logarithm of with some other branch cut that starts along the negative real axis near the origin, rises into the second quadrant, curves back down through the third quadrant and deletes the negative imaginary axis below for some . Define in addition as the unique continuous function such that when and via the implicit function theorem. Then is holomorphic. Now, and agree on the right half plane but do not agree everywhere; our difficulty in applying the previous theorem lies in the fact that the region on which they are both holomorphic is disconnected.
The previous theorem allows us, in a very general manner, to infer a great deal about a holomorphic function on an open set by studying its zeros. Such insight leads us to consider the zeros and singularities of functions holomorphic on some , where is a discrete set of singularities in . In fact, investigation of the singularities and zeros of holomorphic functions yields considerable insight into their nature; in particular one concludes the residue theorem, the open mapping principle, and the maximum principle, among others. Our study of the singularities of meromorphic functions motivates the construction and use of the extended complex plane and its geometric interpretation as the Riemann sphere. We proceed by further defining precisely zeros and singularities of meromorphic functions and provide a classification of singularities. Then we continue by providing an interpretation of the extended complex plane and conclude with the Laurent expansion of a meromorphic function.
Definition 1.11 For any function , a singularity of is defined as a complex number such that is defined in a deleted neighborhood of , for an appropriate . For example, suppose on the punctured complex plane (that is, the complex plane deleted at the origin). The origin is then a singularity of the function . By setting , we can extend to the origin. Our resulting function is entire as well as continuous; we call such singularities removable singularities. Alternatively, we can consider the function . This function cannot be extended holomorphically at the origin since as and we say that has a pole at in this case. Lastly, the function on the punctured plane exhibits behavior unlike either of the previous examples. As goes to along the positive real line, approaches infinity. On the other hand, when goes to along the imaginary axis, is bounded, however oscillates rapidly; in this final case, the origin is called an essential singularity. These three cases exhaust all possibilities.
Definition 1.12 A complex number is a zero of the function if . Analytic continuity demonstrates that if is the set of zeros for a function holomorphic on the elements of must be isolated. In this case, we call a discrete set.
Theorem 1.13 Suppose is holomorphic in the open, connected set and has as a zero and does not vanish identically in . Then there exists a neighborhood of , a non-vanishing holomorphic function and a unique, non-zero, positive integer such that
for all .
Proof The proof is immediate. Since is not identically zero in , it follows from the power series expansion , of , that there exists an and satisfying the conclusions of the theorem. Alternatively, if we suppose that has a pole at of order , applying this theorem to the function proves that we can write with and as above.
We can infer more about functions exhibiting singularities; first we note that we can decompose such functions into a holomorphic and principal part. In fact, these functions are holomorphic inside an annulus about their singularities. An application of Cauchy's integral formula proves that there exists a generalization of this decomposition, the Laurent expansion. With this framework, properties of analytic functions, both entire functions and those with singularities can be more easily studied. First, two simple theorems demonstrates that functions with removable singularities admit a fairly straight-forward description as a result of Riemann's removable singularity theorem. Our prior example of a function with an essential singularity exhibited erratic behavior near it; we find that this is true in general, as the Casorati-Weierstrass theorem demonstrates.
Theorem 1.14 Suppose is an open neighborhood of , without loss of generality, and suppose is holomorphic on obeying
on with and . Then, there exists a holomorphic function and coefficients such that
The sum above is called the principal part of . When , this result is called the Riemann removable singularity theorem.
Proof: First consider the case . We find that is bounded on . Consider the function . As a result of our boundedness hypothesis, and exist, and it follows immediately that is holomorphic on . In addition, vanishes to at least second order at zero. An application of the previous theorem implies is holomorphic on all of , from which our assertion follows. Clearly, the singularity at the origin must be removable. Now, if , note that ; an application of our prior result to implies
for some function holomorphic on . Expanding in its power series about and dividing by on both sides concludes the proof of our theorem.
One should note that this result is essentially equivalent to the conclusion of the theorem proceeding it. In particular, if is a meromorphic function with a pole at of order , then, can be decomposed into the sum of its principal part and a holomorphic function. Equivalently, .
Theorem 1.15 Casorati-Weierstrass Suppose is holomorphic in with an essential singularity at . Then is dense in .
Proof: Rather, suppose is not dense in . Then there exists and such that . Therefore, if we let
we find that on . By the Riemann removable singularity theorem, must be holomorphic on ; that is, must be holomorphic at or exhibit a pole at , both of which contradict the nature of the singularity at . Hence, must be dense in .
Theorem 1.14 allows one to decompose a function exhibiting a pole singularity into an analytic and principal part. This is true in general, as the Laurent expansion allows one to expand any complex function into a convergent analytic and principal part, the latter with a possibly infinite number of terms. First, we require a lemma. It suffices during the following discussion to consider without loss of generality, functions analytic on an annulus about the origin.
Lemma 1.16 Let with be an annulus and suppose is analytic. Furthermore, suppose such that . Then,
Proof: The lemma is an immediate result of the Cauchy integral formula and was used in its derivation.
Proposition 1.17 Laurent expansion Any complex function that is analytic on an annulus admits as a decomposition
with and analytic, where and are open discs of radius and , centered at the origin. If vanishes at the origin, then the expansion is unique. In the latter case, is called the principal part of the Laurent expansion of .
Proof: We first address the notion of uniqueness. If has two different Laurent expansions, their difference is the Laurent expansion for the zero function, hence it suffices to prove uniqueness for the expansion of the zero function. Suppose . This function is analytic on all of and is clearly bounded, hence, by Liouville's theorem, is constant. This implies that and are both identically zero, thus guaranteeing that the Laurent expansion of the zero function is unique.
As we discussed earlier, the exploitation of integral forms plays a significant role in analysis. Our construction mimics the derivation of the power series expansion for analytic functions. In particular, we exploit the regularity conferred to by its analyticity and write as the primitive of a function much like its own derivative, in other words, an integral form. Provided the necessary assumptions are met, one can then study by manipulating its integral form.
Fix such that and let be defined by
This function is analytic on and has a removable singularity at by the Riemann removable singularity theorem. From this and our prior lemma we find that
In other words, we have
Because lies outside the small circle the function is on open neighborhoods containing this circle. Therefore, we have
On the other hand, the function is not analytic on open neighborhoods containing the large circle hence,
from which it follows that
This is our desired Laurent expansion. We find that
where and,
where . These functions are both analytic, hence we can write them as power series. Therefore,
Finally, if we denote , we conclude
In order to continue with a thorough treatment of complex functions and their singularities, we introduce the extended complex plane, denoted henceforth by and defined by appending the point at infinity to . More precisely, for large values of , we consider the function and identify the behavior of at infinity by the corresponding behavior of at the origin. For example, if is holomorphic for large , then is holomorphic in a deleted neighborhood of the origin. Similarly, the function has a pole at infinity if has a pole at the origin; other behavior of at infinity is defined synonymously.
The extended complex plane admits a powerful geometric description which we consider next.
Definition 1.18 The extended complex plane the Riemann sphere and stereographic projections
Let and identify the -plane with . Furthermore, let be the unit -sphere centered at the origin. Denote by its top most point , that is, . Then, for any point , we can draw a straight line connecting and intersecting the -plane at a point , which we write, in the notation of complex analysis as . Alternatively, given any point on the -plane, say, , there exists a unique point along the vector . Intuitively, we can see that such a correspondence must be bijective. In particular, it is clear that there is a bijective correspondence between and . Now suppose , that is, let the point go to infinity on the -plane. The point then moves arbitrarily close to , and we find that there exists a correspondence between the point at infinity in and the north pole of the unit sphere, . Hence we can identify with the -sphere, otherwise known as the Riemann sphere. The addition of the point at infinity to is called the one-point compactification of since it takes to the compact set by adding one point. In particular, the stereographic projection is given by the map
with inverse
A few fairly simple algebraic (or geometric) manipulations demonstrates that these maps are conformal, assuring us of the validity of our prior discussion. With this construction in mind, we turn to the study of meromorphic functions in our subsequent notes.


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Rainbow Stamp Exchange Collection
This Blog displays stamps and other philatelic Items, that are available with me for exchange. Those who are interested in swapping may select their favourite items of their subject and write to me. It will be a great pleasure to exchange .
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Indian MS ...
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Meter Cancellation
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This comes from Peter Elphick's book "Far Eastern File: The Intelligence War in the Far East 1930-45", which I am currently reading.
It is so beautifully British.
1. In Hong Kong early in 1941 the British started setting up food and ammo dumps, including in caves in the mountains. The stores were transported to the caves by mules under the command of Lt. Bill Wiseman, RASC. Wiseman recorded that "It was no easy task. On top of the fact that the Indian muleteers spoke no English and I spoke no Urdu, I had a wooden leg."
2. During the fighting in Hong Kong after Japan attacked, Lt Wiseman, who had lost his leg in a civilian accident, was wounded in his good leg and ended up in hospital in the same ward as another British officer, Charles Boxer, who had had cordial relations with the Japanese General Ito before the war. Ito and other Japanese officers visited Boxer in hospital and gave him several bottles of whisky. Wiseman woke up to see them hissing and bowing around Boxer's bed. After spending some time at Boxer's bed, General Ito bustled over to Wiseman's bed to hiss and bow exceedingly low to Wiseman.
After the Japanese had left, Wiseman asked Boxer "What was that all about?"
Boxer replied "I told the General you lost your leg at Dunkirk, when you stopped a German tank by thrusting it through the tracks. It mightily impressed him."


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Howe left lasting legacy in San Jose
'Mr. Hockey' turned 1991 unveiling of Sharks sweaters into an eventby Nicholas J. Cotsonika @cotsonika / NHL.com Columnist
SAN JOSE -- Gordie Howe was one of the first people to wear a San Jose Sharks sweater.
It was one day in an epic life, but it's important to remember now. Howe died Friday at age 88 during the Stanley Cup Final between the Sharks and Pittsburgh Penguins.
That the NHL is where it is today, with its marquee event in northern California and western Pennsylvania, with 30 teams across North America and the Board of Governors considering expansion, owes a lot to "Mr. Hockey."
Howe's fame transcended the sport. During his 25 seasons with the Detroit Red Wings, he set himself apart to such a degree that he became a Ruthian figure, well known in popular culture throughout North America and in other parts of the world.
When he joined the Houston Aeros of the World Hockey Association to play with his sons Mark and Marty, Howe brought attention to hockey in a new place. He later played for the New England Whalers of the WHA, who became the Hartford Whalers when the NHL merged with the WHA and added four of its teams. He continued to make an active effort to grow the game for the rest of his life.
Howe was the idol of Wayne Gretzky, "The Great One," who became the face of the game and helped spread hockey to the Sunbelt after the Edmonton Oilers traded him to the Los Angeles Kings in 1988. The NHL continued to expand to new markets.
Video: Sharks F Thornton, GM Wilson remember Gordie Howe
Which brings us to San Jose and February 1991.
The city had been granted an expansion franchise, and the Sharks already had announced their name after holding a name-the-team sweepstakes that drew suggestions from every Canadian province, every American state and some European countries. The Sharks had not unveiled their logo and sweater, however, and they wanted to do something special.
"The Bay Area had established teams in all the other major sports: the Giants, the A's, the Raiders, the 49ers, the Warriors," said Matt Levine, who was the Sharks vice president of business and marketing operations at the time and now runs his own sports consulting company. "We wanted to as quickly as possible get out of being viewed as, 'Oh, they're an expansion team. Give them a few years. They might start attracting our attention.' "
So they called Colleen Howe, "Mrs. Hockey," Gordie Howe's wife and business manager.
"If anybody could transcend the just-another-uniform introduction and make it into something extraordinary, it would be Gordie Howe," Levine said. "We embraced this as a metaphor for how we wanted to be viewed. We thought it would appeal to the local Bay Area and grab people's attention in a way that would give us credibility that we might not normally have going the traditional route."
The Howes accepted the invitation but did not accept an appearance fee, only expenses. The Sharks invited everyone who had suggested the name "Sharks" to a rink in a shopping mall in Cupertino, Calif., and about 300 of them showed up to sit on portable stands set up on the ice. A lot of media showed up too.
After a choreographed skating routine that showed off sample Sharks merchandise, out skated Howe and owner George Gund III wearing the new teal Sharks sweaters, featuring the logo of a shark biting a hockey stick. Howe did interviews. He signed autographs. Here was this new hockey team, and here was Mr. Hockey himself wearing its colors.
Howe returned to San Jose in January 1997, when the Sharks hosted their first big event: the NHL All-Star Game. He played the same role of ambassador.
"He always had that presence," said Dan Rusanowsky, the Sharks radio play-by-play voice from the beginning. "I was so amazed to see kids that weren't even born when he retired look at him with such abject veneration. They knew he was important."
Rusanowsky remembered an interaction with Howe that happened so many times in so many places. A kid approached the legend.
"Mr. Howe," the kid asked. "Can I have your autograph?"
"Well," Howe said, holding a Sharpie, "I've got to see if this pen works."
Howe opened the pen and flicked it playfully on the kid's hand, leaving a mark, lightening the mood.
"Yeah, it works."
Howe signed the autograph.
"It's that sort of little kind of charming moment that happened every day he was here, every minute he was here," Rusanowsky said. "And people in San Jose will always respect and remember that."


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Aqua-Chem pool chemicals are available for purchase from many online retailers of pool chemicals, including Aquachem.com, Sears, Pool Chemical Center, Kmart and Amazon, as of 2015. The Aqua-Chem website is the main resource for its products.
Each site offers specific information on buying Aqua-Chem pool chemicals, but some are more up-to-date than others. For example, the Aqua-Chem website provides information on different pool chemicals and how to find them on the product catalogue. The website has a store locator and shopping list icon to guide buyers. There are steps showing the type of products to buy for chlorination, balancing, algae removal and water testing.
Most sites provide product features and prices for different Aqua-Chem pool chemicals. Sears has different products and their prices, ratings, discounts and information about new arrivals. On the other hand, Pool Chemical Center provides information about Aqua-Chem products and how to make safe and secure purchases from the website.
Kmart lists an assortment of chemical product catalogs where customers can choose from powdered tablet and liquid chemicals. There are rating stars for different products and how customers can access stores. On the other hand, Amazon gives product types, sizes, prices and shipping information. There are feature keywords and customer review stars for the products.


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Android-running tablets preparing to join the market that Apple created, and now dominates, with its iPad are looking "ready for prime time," DisplaySearch senior analyst Richard Shim wrote in a Feb. 4 research note.
The note followed a Google "Honeycomb" event Feb. 2 during which attendees were able to use Google's tablet-optimized Android 3.0, known as Honeycomb, on the Motorola Xoom tablet. The experience of using Android on a large screen, said Shim, enables a "greater graphical usage experience and more opportunity for media-based multitasking."
With a number of iPad competitors now set to launch from the industry's biggest players - among them Research In Motion, Motorola and PC-market-leader Hewlett-Packard - the remaining question, said Shim, is how the tablets should be sold.
"This will be an essential element in the ultimate success of Android tablets," wrote Shim.
Further reading
Underlining the point, Shim offers the example of netbooks, which in the end the carriers weren't great at selling, and which saw high rates of return. Part of the problem was technical support, with customers unsure of whether to contact the carrier, the device maker or even the operating system company.
"If [the answer is] the carrier, there are questions around how well equipped they are to solve the problem," wrote Shim. "Carrier tech support is essentially trained to tell the user to turn off the device and turn it back on as a fix." There's also the issue of users buying WiFi-only versions, to pass on the expense of a carrier contract.
Or, is a tablet more a PC than a smartphone? (The original Dell Streak, with its too-big-to-be-a-phone, too-small-to-be a tablet 5-inch display, was a perfect example of a device that was tugged in both directions but a perfect fit for neither.) If so, says Shim, consider the big PC brands, such as Dell, HP and Acer, that have "tried to create and sell smartphones [but] already failed." The retail channels where PCs are sold, he explains, are a poor fit for smartphones, as they generally don't receive any ongoing revenue from smartphones' voice and data plans.
Google, with its Nexus One, tried still a new tack, selling the device directly, instead of through its carrier partner, T-Mobile - which, notoriously, was a disaster.
That tablets aren't a neat fit for any specific channel makes the decision of how best to sell them problematic.
"We have already started to see some of this tablet channel confusion with the Samsung Galaxy Tab," said Shim. "The company said it had shipped around 2 million tablets since the product's introduction in November, but actual sell-through seems to be less brisk."
The one company that all of this apparently isn't an issue for, is Apple, states the note. Copying the success of the iPad, it turns out, will take more than just cool hardware and tablet-optimized software.
"Apple's iPad is selling well in retail - its own retail - but no one else is replicating the Apple store experience," wrote Shim. "If others are to come close to Apple's success, they will have to create a compelling sales channel."


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SSDN (South Side Day Nursery) SSDN (South Side Day Nursery)
Here's a sample of our volunteer opportunities:VIEW AS
Mission Statement
SSDN's mission is to provide affordable, comprehensive and innovative early childhood education and family support services within a nurturing and educational environment.
Located in South St. Louis City, SSDN (formerly South Side Day Nursery) was founded in 1886 by 15 Unitarian women to provide young children a safe, nurturing and educational environment while their parents were at work. For more than 120 years, SSDN has continued its mission, serving hundreds of families every year. Today we deliver high-quality childcare and preschool education that prepares children for success in school, enabling their parents and guardians to work, receive job training, or attend school.
This information
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Do you work for this organization?
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Monday, July 1, 2013
Easy Strolling in Pop of Colors
21 comments:
cute checkered shirtReplyDelete
Lovely pictures and lovely outfit! Feels like summer ;-)ReplyDelete
@Michele, Isa...thank you so much. Yes, it's summer! I prefer early spring tough:)ReplyDelete
Beautiful photos! Love your plaid shirt :)ReplyDelete
Hi sweetie!ReplyDelete
Such cool & fun photos! :)
I kindly invite you to join a giveaway held on my blog! Three easy steps & you might find yourself on the winners list! :)
Your chance to win in an International Giveaway!
Beautiful photos! I looove nature!ReplyDelete
I invite you to ENTER MY PERSUNMALL GIVEAWAY TO WIN A PIECE OF CLOTHING OR $100 GIFT CARD (following only three easy steps)
Good luck,
Evi xoxo
The Notebook of a Fashion Lover
cute blog!let's follow each other on gfc&bloglovin?ReplyDelete
flw me and tell where u've followed me!
Also I kindly invite u to join Persun giveaway! And win summer clothes or 100$ gift card! Just 3 simple rules! Here is the link http://mooreann.blogspot.com/2013/07/give-them-away.html
All the best
Hermoso paseo y preciosas fotos!!Me encantan esos murales coloridos!ReplyDelete
Amazing :)ReplyDelete
Check out this new giveaway, summer clothes and $100 gift card!
Your Princess is in Another Castle
xx Sofie
I like your shirt and the background of your photos!ReplyDelete
I invite you at my giveaway if you're interested!
--> Win $100 shopping spree-International Giveaway <--
very nice post dearReplyDelete
love;y pics
Very cute photos and I love your shirt!!ReplyDelete
Blog | Cocochic △
Bloglovin | http://www.bloglovin.com/blog/1823055/
@ Cee: Thank you Cee, yes it's comfy as well :)ReplyDelete
@Maddie, Evi, Stepahanie; Thank you :)ReplyDelete
@Silvina, Thank you Silvina. It was nice relax walk indeed, and me too, i like the happy colors of Mural.
@Stella: Thank you Stella, glad you like it.
@Brooklyn Grace: Thank you dear, kisses to you too:)
Lovely photos :) Looks like you had such a great walk.ReplyDelete
Ruth x
Amazing post :)ReplyDelete
Check out this new giveaway, summer clothes and $100 gift card!
Wanna follow each other on GFC and FB?
Your Princess is in Another Castle
xx Sofie
Fab pictures! Love the shirt!ReplyDelete
♥ ♥ ♥ ♥ ♥ ♥
Hi Chacha!! We are a spanish couple that love travelling and photography. That is why we decide to create a project in which show our two hobbies.ReplyDelete
Visit our website! http://kissmein.wordpress.com/
Thanks! and we hope that you like it :)
Cute photos!ReplyDelete
Great photos!ReplyDelete
@Ruth, Sofie, Marta, Sandra, Isa, The Garage Starlets: Thank you! Have a lovely day you all:)ReplyDelete


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April 5th 2017 Meeting
Spring is finally here! Hope you are enjoying the sunshine while it lasts.
This month we have Brian Carline coming to talk to us about Days of Dolly Blue and Izal?? i remember both of these so that shows my age !!!
Don't forget that we need some nominees for our committee. we have four people standing down so we need you to think about whether you can become a committee member.
Don't forget to bring your mugs and as usual we welcome donations of cakes and biscuits!!
See you on Wednesday and please try and get there before 7pm so that we can start on time.


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iWebFilter is a simple web browser that enables to block specific web contents.
It runs as a Kiosk mode which is a mode mainly suited for information stands. Such stands are typically found in libraries, airports, bank offices, or shopping malls.
It supports only basic functions (standard navigation buttons) and print option if AirPrint™ enabled on device.
There are 2 possible ways to use it:
- Kiosk mode: simple browser with a fixed predefined homepage that you have to configure in the application setting. Users have access to any links found in the pages they browse.
- Kiosk mode + filtering: as you can block access to specific urls via a black list to be uploaded in application directory via iTunes, this advanced mode lets the users browse only for the necessary information.
For non-business usage, iWebFilter provides a solution for parents to control unwanted content and provide a safe Internet for the family.


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After he received record 7 heart transplant in March 20 2017 David Rockefeller finally dies.
David Rockefeller along with the Rotchilds family are at the top of the Illuminati Bankers Pyramid.
David Rockefeller was n1 Illuminati family in USA and he controlled USA UN and the world.
Billionaire banker David Rockefeller dies aged 101.
He was thinking was God but was it. God is not dead David Rockerfeller is.
David Rockefeller along with other Illuminati elite banksters were working 24/7 for globalism and creating the New World Order. Their plan is losing with UK going out of EU, with election of Trump as US President. With growing of Russia with Putin. A lot of countries in the world are WAKING UP and try to protect their countries because NWO plan is to eliminate all countries and nationalism.
Former Chase Manhattan Chief Executive David Rockefeller has died at the age of 101.
Rockefeller died in his sleep at home in Pocantico Hills, New York, on Monday morning as a result of congestive heart failure, according to a family spokesperson Fraser P. Seitel.
The businessman, who had an estimated fortune of $3 billion, retired as head of Chase Manhattan in 1981 after a 35-year career.
View image on Twitter
Steve Kopack
Rockefeller foundation statement says David Rockefeller's cause of death at age 101 is congestive heart failure.
10:59 AM - 20 Mar 2017
4242 Retweets
In the statement from the The Rockefeller Foundation confirming his death, Rockefeller was described as "one of the most influential figures in the history of American philanthropy and finance, considered by many to be 'America's last great international business statesman'."
Rockefeller, also known as 'the banker's banker', according to the statement, is said to have donated almost $2 billion over his lifetime to various institutions including Rockefeller University, Harvard University and art museum.
READ MORE: Rockefeller Family charity pulls funds from Exxon Mobil over longtime climate change cover-up
David was the youngest of six children born to John D. Rockefeller Jr. and the grandson of Standard Oil co-founder John D. Rockefeller.
Rockefeller graduated from Harvard in 1936 and received a doctorate in economics from the University of Chicago in 1940. Appointed president of Chase Manhattan in 1961, he became chairman and CEO eight years later.
Rockefeller often spoke about the importance of American capitalism, which he said "brought more benefits to more people than any other system in any part of the world at any time in history."
"The problem is to see that the system is run as efficiently and as honestly as it can be," he added.
Rockefeller was married to Margaret McGrath from 1940 until her death in 1996 and the couple had six children.