Curvy Mathematics

 Are you afraid of mathematics? Do you doubt your intelligence because you can't make a simple subtraction without a calculator? Have you ever wondered why so many people around the world manipulate numbers in order to make money?
 
 Originating back in 1996...
 The story starts back in 1996 when I was looking at the world through the eyes of a teenager at school, trying to acquire knowledge, trying to memorize and hoping that the world can  change and humanity can easily make huge steps forward! Unfortunately, that wasn't exactly the case...Luckily, there were a few people who shared my hopes for a better world! Indeed, a scientific magazine called "Quantum" was published, approachable not only by scientists, but accessible to everyday people. Providing a mixture of spectacular articles from the American and Russian editions of the magazine, it was truly amazing! But very expensive for my teenage wallet... and unfortunately, a little too advanced for my level of mathematics and physics. I was always intrigued by SETI and non-linear (curvy) geometries but I could barely pass my mathematics exams at school. This terrible situation persisted even after acquiring my undergraduate degree in chemistry. I still faced great obstacles concerning my understanding of mathematics.
 
 Heads up and march on!
 In 2010 I contacted the publications of "Quantum" magazine in order to purchase a subscription. I discovered that the distribution of this wonderful magazine had ceased a couple years prior. Needless to say, I was extremely disappointed! Such a useful, educational magazine and there was no audience in Greece to cover its expenses so that more people could have access to such unique knowledge! What a disaster! I explained to the person in charge that it was of vital importance and of sentimental value, for me to acquire a copy of all the issues published. She totally understood and not only did she find all of the copies issued in Greece but she also provided them at a discounted price! Now I am proud to say that I have all issues of "Quantum" ever released in Greece! And above all, I am able to understand the mathematical background of most of the articles(at least of those which I am interested in).
 
 Heads down and advance!
 There is a gap between purchasing all of the issues and managing to comprehend what is written in them. The igniting spark was inside the very first article which was describing dynamic programming, a procedure re-invented a few decades ago but it existed back in ancient Egypt. Not under the same name but under the combination of multiplication and common logic. "How can this be possible?!?!? Ancient Egyptians could comprehend such a complex procedure and I find it difficult to comprehend limits and optimization???" I am too selfish to accept such a fact in a creative way to make a further effort to accept the fact that I am either imbecile or... I have to change my point of view. Things became much easier when I looked at my difficulty from a different angle. And I overcame it!
 
 Valid facts and theoretical understanding generate solutions to harsh problems.
 This is a statement to memorise thermodynamics rules. It is beyond doubt, a valid statement in everyday life too. I am convinced that most people are afraid of mathematics because they have poor guidance. Being a mathematician does not mean that you are able to teach mathematics. Using math makes our everyday difficulties easier to cope with. Mathematics lower, shrink and reduce a problem into a game with numbers, with universal rules. It is much easier to play a game with a fixed set of rules instead of trying to find your way out of a problem using your experience and potential probabilities. Set the rules and play according to them. Get your answers based on your questions. It is the only fair, just, democratic, equal for all and universal game.
 
 The show must go on...
 I am not a certified mathematician but I can show you the way through the labyrinth of mathematics. If I am not able to help you, then I will show you the one who can. "Quantum" was an outstanding magazine but now, obsolete. Not in terms of its content, rather its physical shape and appearance. Paper is costly and severely impacts our environment. An e-magazine eliminates these costs. Additionally, the material should be slightly different, accessible, so that more people will be inspired to dive deeper into mathematics after reading it. Biographies of scientists of the past as well as of contemporary ones shall wave as idols for people to learn from their lives. Applications of mathematics shall exhibit the magnificence of mathematics, even with topics like wagering or investing so that people will learn how to earn money or protect themselves from losses. Quizzes, puzzles, riddles and other games or contests shall retain the interest of readers unabated. And above all, students of all ages will have the chance to be assisted properly so that they will not be dismayed by the difficulties of mathematics.
 
 I wish you an amazing journey into the greatest of all human discoveries!
 Join me, and dive into the non-linear (curvy) world we live in!

Tribute to Karl Schmedders

 Chocolate, cheese, neutrality and financial institutions is what Switzerland is known for to most people. Located in the middle of the European continent, the country provides 1/3 of housing to the CERN Collider and 3/3 of housing to the University of Zurich, which had been the alma mater of Albert Einstein and Karl Young. These days, another "Karl" is teaching at the Department of Business Administration. Karl Schmedders gladly shares his passion for probability theory and he is definitely going to inspire you to dig deeper into this section of mathematics whether you are fond of mathematics or not.

 Mathematics captured his attention during school years and a lifetime relationship has been developed since then. Being afraid to dive into pure mathematics, he has thankfully turned himself to the applied side of mathematics by studying business engineering at the University of Karlsruhe. It was during his studies that he discovered his true love, operations research and he has been occupying himself with it ever since.

 Insisting and persisting has always been his best shot against difficulties. On the one hand, there was his unfinished task of writing his PhD thesis, on the other hand, there was the lack of social life. On the verge of abandoning his duty, he continued with his work, even if this was "an incredibly lonely, frustrating and often "depressing experience". Although publishing some work alone would produce greater acknowledgement from his colleagues, he clearly states that assistance is helpful, even if this would cause to be looked down upon by his colleagues.

 Even though he is not fond of networking in order to promote one's work, he accepts the valid fact that it is inevitable. Marketing and promoting oneself, both unfortunately exist in the world of natural science too. There are many scientists researching the unknown, an activity which can easily be overlooked. This could dishearten the scientist and would definitely result in a drawback for humanity.

 Regarding compensation and recognition, academic (aka useless) research is not a good option if one is pursuing wealth and fame whereas applied scientific research provides higher odds to acquire the above. Still there are scientists who dare to follow the path of knowledge in order to comprehend the way our world is turning even if the compensation for their time spent studying is not proper.

 He believes that daily lives take so much time and energy out of peoples' lives that they have neither the time nor the energy to learn new things "just for fun" after having entered their adulthood. Our chance to turn people's attention to mathematics is to "convince" somehow the children to become engineers or scientists. Humanity has always needed them.

 If only he could turn back time, he would not have chosen the same path of studies. It is way "too applied" for his standards, he would prefer something more abstract with a background enriched with mathematics and statistics. Young students would probably find it beneficial to study mathematics, statistics and computer science since it is very interesting to explore our universe by processing our given data. This could result in financial benefits too apart from already being extremely intriguing.

Tribute to Gregory Chaitin

 The Greek alphabet can be found all over the mathematical universe, circle's π, Fibonacci's Φ, etc. Among them resides a not very common one too, the "big O" or as it is called, Omega number (Ω). Turing's halting problem and Gödel's incompleteness theorem are just two igniting inspirations for the discovery of Omega number by a modern iconoclast, Gregory Chaitin.

 During his childhood, his mind was excited by general relativity and quantum mechanics, so his path was foreshadowed/predetermined. Then Gödel's beliefs had a severe impact on him resulting in abandoning his spyglass watching the skies for the peculiar and obscure path leading to the abyss of theoretical mathematics. It is a periculous path contrary to what most people may think about it but the discovery of fundamental facts is an extremely attractive idea. Despite the danger that lurks in these distant regions of the human mind, where the borders of sanity can sometimes easily be crossed, very few brave mathematicians and scientists dare to walk over there and get lavishly repaid! "Sometimes, in mathematics one thinks like God".

 He was no exception in facing difficulties obstructing his way. The toughest part is to realize that one is standing in front of a treasure, not to discover the treasure. Since his twenties, he had already developed the proper toolkit to mathematically study life and evolution but it took him almost a lifetime to completely conceive the potential of his development. Just like everyone, young minds can easily get distracted and attention gets diverted to different objectives. Thankfully, mathematics is indifferent to age.

 It seems that being a good rhetor can be beneficial in all occupations, in all eras throughout human history. Although the ideal scientist should behave as a hero or as an immortal, mortal needs tend to alter human characters even if they are trained to be scientists. "Fields of science are power structures and do not welcome new ideas especially from outsiders." Like the guilds a few centuries ago, nowadays a scientist has to get adopted by a modern scientific team, if one would like some recognition for one's scientific work. In the past, there was only a bunch of scientists and good science was a relatively easy thing to do.

 Mr Chaitin is clear that things have changed - big time: "Science is a big business with a giant administrative bureaucracy" he states. Scientists get paid which means that they have to be productive. "That explains why there have been no fundamental advances in physics since the 1920s. The shut up and calculate dogma has killed physics".

 The current tendency in modern societies is to spend money that one does not possess to buy things which one does not need. Very few are left wondering very basic questions like "Why are we here?", or very few seem to be interested in trying to find an answer to the primordial questions that almost all humans have when they gaze at the night sky during their childhood.

 He considers himself as a very fortunate person as he had the chance to work on many fundamental, philosophical questions which many mathematicians have no interest in anymore. If he could have chosen a different road in life, then becoming a mountain climber or a martian colonist would probably be some of his options. Definitely, he honours the creativity of the human mind, he admires people who use their mental resources in order to advance the understanding of how our universe works instead of spending their time and resources in doing politics and contracting or improving scientific, public relations.

 Just like his hero, Leibniz who created new mathematical fields in order to give an answer to questions which have remained unanswered for countless centuries. Most of Leibniz's precious ideas were discovered after his death among his writings.

 Unfortunately, many scientific advances have been attributed to the wrong people. Dead cannot speak and the truth is extremely difficult to be unveiled. Additionally, too much attention on one's work draws the admiration of non-specialists as well as the envy and hate of one's colleagues. In the end though, science should be above all these mortal and pathetic matters. "Real science is a lonely, solitary pursuit between you and God".

Tribute to Andrew Siemion

 A few decades ago, the human kind managed to launch their first manned rocket in orbit. A few decades later, the human kind realised that other beings may exist out there, maybe we are not alone. Some people believe we have been created as the only intelligent life form across the universe while some others tend to find this opinion quite arrogant. My belief is that questions concerning valid facts can only be answered experimentally; it is not a matter of belief but a matter of what really happens. This is what Andrew Siemion does via the SETI programme.

 Motivated by a deep sense of awe and wonder about how the universe we live at works, he is now processing signals and all kinds of information that our telescopes and antennae provide in pursuit of conscious life. Many of us have been wondering whether there is life on another planet or whether there is intelligent life when gazing at the bright, celestial bodies. Thankfully, some people managed to work on seeking answers to such questions.

 It is not an easy task. Obstacles have been surpassed, difficulties still exist, adversities will never cease appearing. One factor cannot be yet evaded or overpassed and that is the human factor. One has to understand that we are all only humans and we tend to think like that, unpredictably. This can result in a major problem when a task is not properly accomplished or at least not in the way it was initially supposed to be accomplished. On the other hand, a different opinion may result in a solution against a problem which seemed to have no solution. "Coming to understand that even the profoundest missions are ultimately carried out by human beings and face universal human challenges".

 Astronomy and marketing cannot coexist. Time, apart from having become relative, is precious and in astronomy "it is important to spend time doing careful and rigorous science rather than promotion". Natural science should be like this in all subjects, not only astronomy, but it seems that the flow of money alters humans and human scientists tend sometimes to try to promote their work in order not to lose funding or gain some for their research. Personally, I would like to see researchers not having to worry about survival as their social work is extremely valuable but not always appreciated on time.

 People's attitude towards science is usually indifferent. This happens probably due to the fact that we faced difficulties in mathematics during school years. Even Einstein's statement regarding the relation between imagination and knowledge has not been enough to inspire most of us to admire a scientific breakthrough, not until this finds an application to everyday life and can become commercial. An interesting point of view is that although there are museums all over the globe trying to promote natural science, still many people do not have the opportunity to visit them.

 Natural beauty is here, is there, is everywhere around us and natural scientists put all their effort to comprehend the way nature works and creates such spectacular wonders. Unfortunately, there are people struggling to survive and not only can they not have access to such places but they are not at all interested in science as they have a more important issue to worry about, to live another day. Maybe natural science could achieve greater accomplishments if social inequalities did not exist or were reduced.

 Astrophysics or astronomy (never before have I wondered about their difference but judging from the words'  etymology and scientific history, astronomy has too much of geometry and mathematics generally whereas astrophysics studies interactions between celestial bodies) seem to be able to capture and stimulate human mind and imagination. On some occasions the heart is devoted to these subjects of science. The best way to approach these subjects is an endless study of physics and mathematics. Even if the results seem pointless, most probably they are of vital importance but we have to discover their avail. Never give up on studying physics and mathematics: "I would always like to have taken more!"

Tribute to Jeff Chasnov

 Hidden treasures can be found all across our planet. Real educators live their lives all around the world too but they are rarer than treasures. One of them lives in Hong Kong. He can initiate you into mathematics just by watching one of his online courses.

 Jeff Chasnov is neither from Hong Kong nor he studied to be a mathematician. He started his career as a physics student. It seems that his research area in fluid turbulence had a turbulent effect on his life and career too. Jumping from physics, he ended up in a Math department (thankfully, for the rest of us). It is obvious that interaction between natural sciences occurs as it happens between molecules.

 Just like everyone, he faced difficulties during his scientific career, although he might have been more familiar with chaotic life events due to his research in the fluid turbulence field. A low quota in his initial choice of scientific departments forced him to stay outside and almost abandon all efforts. Despite the fact that a mountain of difficulties and disappointment obstructed his initial path, he persisted on pursuing his goal to study thoroughly natural science and "managed to find a supervisor at NASA" who took him as student. An obstacle can be overpassed or bypassed, the idea is not to forget the target and not to abandon efforts; persist and there are chances to succeed, withdraw from trying and there are no chances at all to succeed.

 Either if money is the scientist's motive, although "most of us scientists did not go into our careers looking to make a lot of money", or if the mainspring is fame as "certainly, we would like our work to be known", the art of marketing of one's work may be of great importance.

 Unfortunately, scientists have been relegated to common professionals and since they already come in vast numbers, their work must be categorised and maybe differentiated from one another. Since the procedure is not done by a strict and unconscientious computer but human thoughts and emotions intervene in judging, then it is inevitable that good marketing of a scientist's job and good public relations can cause a severe impact in one's career, good or bad. Nevertheless, both marketing and public relations are considered to be sciences anymore and they are taught at universities evenly like natural sciences.

 Some people have an innate tendency towards mathematics and science. These people would be attracted to natural science sooner or later. The rest would keep a passive stance towards mathematical thought. For those interested, there are plenty of videos online which "can serve to inspire more young people to go into math and science". Many of these videos are extremely interesting but people seem to ignore their existence. It is of vital importance to make people turn their attention there and discover the greatness of mathematics.

 Has he regretted any of his decisions concerning his studies? "I am sure my study path would be somewhat different concerning what I know now". Decisions usually oblige people not to choose what they want but what they are going to leave behind. The initial decision is the little start, the big bang of all the consequent events. And luck, just like turbulence, "has a lot to do with the trajectory of one's life". Still, we have not managed to fully comprehend luck and turbulence although we try. Some of us feel unlucky while some others feel as they have been favoured by luck. "And I feel like I have been lucky". Perhaps it is just a matter of one's point of view.

Tribute to P.W. Atkins

 It is doubtful that there are chemists in the western world who have never heard of the name P.W. Atkins. He is famous mostly as the author of a spectacular volume of university books about chemistry. In my opinion, he should be honoured for 'The Periodic Kingdom' as it is an outstanding book capable of attracting newbies into the art of manipulating matter: chemistry.

 He chose chemistry back at the age of 15 for various reasons, the most important of which was "the urge to share my joy of understanding from science". For many of us, the joy of understanding an obscure concept or meaning, the pleasure of comprehending a difficult problem or overpassing a mental obstacle is probably the greatest feeling. All students face difficulties, they get disappointed but those who insist, they manage to feel this overwhelming joy of understanding, the quintessence of learning. Science has plenty of such opportunities.

 Difficulties arose during his scientific career too. His real problem was time devotion. Research is extremely demanding, "to do research requires total, obsessional commitment". But "to write books on a large scale requires the same". So how can one organise one's time? Human beings require some "dead" time to sleep, eat, drink, enjoy... No human mind can always be stretched and under tension, eventually it will crack like a bow. The decision, though, to abandon original research because "I was neglecting the young minds of my research group" reflects the altruism which, thankfully, exists in some scientists. There are many university professors and researchers who become pure and strict professionals, they just care about their work and neglect the painful job and stressful role of young assistants and students who sacrifice a lot of their time in order to demonstrate devotion and goodwill to their scientific supervisors.

 It seems that science has not avoided the shroud of marketing. Fame, acknowledgement, money, vanity, still exist among human scientists too. So, this means that apart from being a good scientist, does one have to be a good marketeer too? Unfortunately, science has a gap that allows marketing and public relations to play an important role in one's career. Even today, physicists use the phrase "we believe that...", as in religion or other scientific fields other than natural science which are not based on mathematics. We should not "believe", we should accept facts as valid only when they are proven experimentally and they are consequently backed by mathematics.

 Regarding ordinary people's attitude towards science, we all know that it is of vital importance to alter it. Science needs to become more attractive, more intriguing. Once upon a time, "I would have said 'television'", since television could be described as the fourth authority to create and alter consciences, "but these days people are spending more time away from broadcast TV and more on the Internet, where central authority has no influence. Perhaps some really good scientific version of 'Downton Abbey' would inspire interest". Many people avoid scientific thinking, mostly due to their bad experience with mathematics during school years. If mathematics could become more approachable with a less repulsive appearance, then more people would be attracted to science and spend at least a few Saturday nights occupying their minds with scientific matters. Definitely, mathematics are already simple, pure, universal and democratic as there are no discriminations but a lot of effort is demanded in order to think simply and discover their divine beauty.

 When asked if he would choose the same field of study, if he had the chance to turn back time, the answer is clear: "Yes, it is the central science and enables you to embrace all others". It seems that this answer depends on the point of view of each scientist and the educational system in their country. In any case, a scientist ought to do everything about science at one's maximum effort and capability. Choose properly, present properly and write about it properly.

 It is difficult for the human mind to classify and understand all the different types of complexity that occur in large systems. Two types of such complexity, however, offer some prospect for understanding through developments in applied mathematics and computer analysis. These two types of complexity are usually thought of as opposites and go under the names "chaos" and "order". Yet, there are indications that certain kinds of chaos and order are consequences of the same type of mathematical structure, known as nonlinear equations. Perhaps this is a modern version of the ancient philosophical view of the Greek philosopher Anaxagoras, who believed that opposites emerge from a formless Absolute, and eventually return to it.

 The point being made is that pure mathematics, by definition, need not extend in the real world. Some pure mathematicians will go so far as to prefer it not be applied, as application of the art in some way soils its beauty.

 Some years ago, a prominent American engineer bought an expensive player-piano. It became clear after a week or two that this purchase did not correspond to any particular interest in the music played by the piano but rather to an overwhelming interest in the piano mechanism. For this gentleman, the player-piano was not a means of producing music, but a means of giving some inventor the chance of showing how skillful he was at overcoming certain difficulties in the production of music. This is an estimable attitude in a second year high-school student. How estimable it is in one of those on whom the whole cultural future of the country depends, I leave to the reader.

 The Greeks regarded the act of discovering fire with very split emotions. On the one hand, fire was for them as for us a great benefit to all humanity. On the other hand, the carrying down of fire from heaven to earth was a defiance of the Gods of Olympus, and could not but be punished by them as a piece of insolence towards their prerogatives. Thus we see the great figure of Prometheus, the fire-bearer, the prototype of the scientist; a hero but a hero damned, chained on the Caucasus with vultures gnawing at his liver. We read the ringing lines of Aeschylus in which the bound god calls on the whole world under the sun to bear witness to what torments he suffers at the hands of the gods.

 If a man with this tragic sense approaches, not fire, but another manifestation of original power, like the splitting of the atom, he will do so with fear and trembling. He will not leap in where angels fear to tread, unless he is prepared to accept the punishment of the fallen angels. Neither will he calmly transfer to the machine made in his own image the responsibility for his choice of good and evil, without continuing to accept a full responsibility for that choice.

 Yet for all but a very few, the path to these lies through the performance of perfunctory tasks which in nine cases out of ten have no compelling reason to be performed. Heaven save us from the first novels which are written because a young man desires the prestige of being a novelist rather than because he has something to say. Heaven save us likewise from the mathematical papers which are correct and elegant but without body or spirit. Heaven save us above all from the snobbery which not only admits the possibility of this thin and perfunctory work, but which cries out in a spirit of shrinking arrogance against the competition of vigor and ideas, wherever these may be found!

Tribute to G. Karakatsanis

 Our monetary system creates money via debt. In the midst of the recent financial crisis which started back in 2008, the idea that the current model is no longer viable gains more supporters every single day. The perpetual financial development required to repay debt is not always possible. Debt is steadily being accumulated and its repayment becomes impossible.

 The counter-proposal is that money should be minted by a public, central authority which would decide on the necessary quantity of money for the economic state to function properly. Additionally, money would be injected into this state on public expenses, free of any charge or debt. This way the state would become more independent and the dead-end where the current economic state is led to, would be avoided.

 Supporters of the current monetary system claim that the quantitative control of money from a central authority has failed in almost all cases throughout human history. Since the Roman times, emperors who were in desperate need of extra money in order to further support their armies, were just minting more money to pay their soldiers' wages.

 Money is just a means to exchange materials and store wealth. Whenever the amount of circulating money increases without its matching in gold or any other valuable material being increased simultaneously, then this causes circulating money to lose its value. Whenever new money is minted without any matching to gold or any other valuable resource, then money owners are being robbed as their money loses its value. Such a financial instability caused by many Roman emperors resulted in the collapse of the entire empire.

 On the other other hand, nowadays, a decision to mint new money is taken every time a bank approves of a loan. The bank judges whether the new money will contribute to creating enough wealth so that the initial loan can be repaid. Obviously, the bank's evaluation is vital as in case of a mistaken evaluation, wealth will not be enough for the initial loan to be repaid and the bank will suffer some loss.

 Theoretically, the modern monetary system is far better than the Roman one. There is no general rule or law to "enforce" the minting of new money but this decision is utterly dependent upon the given circumstances. The one who takes the decision ought to do one's best, differently the consequences may be disastrous. Still, there are some vulnerabilities inside this system. The decision to grant a loan is based on the bank's "bona fide"(good faith) that the borrower will repay the debt. If this faith fades away, then the entire system collapses. This is what happened back in 1929 when at least a decade plus a world war were required for the monetary system to recover.

 There are many people who claim that such a crisis is necessary to occur occasionally. Such situations assist in distinguishing weak monetary units from the powerful ones. The weak ones will disappear and new ones will arise. Banks with bad judgement will sustain heavy loss or they will go bankrupt. Following the financial crisis of 1929, more than 4000 banks closed in the USA during the next decade.

 The depression of 1929 is slightly different from the one of 2008. Banks are not local and in vast numbers anymore. Contrary, they are significantly fewer and consist of big organizations. Bankruptcy of any of them can cause the entire monetary system across the globe to shatter. This is what happened with the collapse of Lehman Brothers in 2008. No other bank or financial institution has been left bankrupt since then. Their survival is considered of vital importance and all governments "inject" money to them derived from taxation.

 Such a privileged manipulation of the banks and financial institutions cancels the biggest advantage of the current monetary system. Banks do not put any effort at all to evaluate loan applications properly. Huge flows of money are created on enormous mountains of debt. Obviously, such a debt cannot be repaid and the borrower has no consequences to fear as the taxpayers will cover the bank's loss as a result of improper loan evaluation and judgement. Legislation carries the banks' incapability to properly evaluate a loan application to the taxpayers, so they will suffer the loss.

 As we grow up, we learn to speak our mother language. We learn it by heart and we use it to communicate orally, until we go to school when we learn to write and everything is destroyed. New knowledge has penetrated. New kids on the block. We have to re-organise all we know and all we learn. Somehow it works. Many of us face some difficulties but in the end we manage to learn to properly speak and write our mother languages.

 A great, arising difficulty is the fact that our language has rules. Unfortunately, inequality governs the world we live in and as it happens with state laws, language rules have exceptions too. These exceptions show the difficulty a human mind finds to revolt against habit. We tend to like a habit as we suppose we become better when repeating and someone will admire us and applaud for us. Repetition is an advantage for learning but when it becomes a habit, then the line is crossed, it has already become a disadvantage.

 In the past, someone chose to defy a rule, either because he/she could not follow it or because he/she did not want to comply with it and his/her charismatic personality assisted in transferring the "mutation" to future generations, making it a habit. The language of chemistry, which I am familiar with, still uses names for substances which have remained the same since the age of alchemists.

 Several people are alleged to have a tendency in learning foreign languages. I suppose one should definitely learn the rules and the exceptions in order to comprehend and fluently speak any human language. There are some languages though that have no exceptions at all. Programming languages.

 The idea is simple. Each programming language has a list of pre-set words, a library of defined commands in other words, each of them executing a very specific task without any deviations. A combination of these commands may create an object, just like words create a sentence. The difference is that words may have more than one meaning which depend on the mood of the speaker or the author whereas commands have a strict and clear meaning allowing no doubt about it. Thus, sentences may be interpreted in more than one ways while objects cannot be misunderstood.

 Yet, people tend to face computer programming with some fear. Good command of a human language allows us to impress the others, to manipulate the language and show a virtual supremacy over the rest. Good command of a computer language just makes us faster in commanding a cold machine which will never applaud for us nor will it gaze at us in awe, admiring our knowledge and experience. And this flattens our vanity.

 Personally, I find it incredible that programming is actually a sequence of commands to add the number of times an electrical circuit is carrying electricity. It sounds so simple and it really is. Just imagine that computing is based on mathematics. Here comes the pain of mathematics again.

 Mathematics consists of a language too. A sequence of symbols which helps humanity to degrade a problem into adding units, find a solution according to mathematical rules without exceptions and re-apply the solution in our reality. The entire difficulty lies in translating to/from mathematics. To be honest, mathematics will help in commanding a programming language and each programming language will definitely assist in comprehending the simplicity of mathematics.

 The idea of minimizing risk is called insurance. Entrepreneurs are supposed to take risks. At least this is what they declare to the rest of the world. Shipping companies insure their cargo, financial corporations insure their loss probability, common people go with the flow and insure whatever they can, either because they are obliged by legislation or because they feel that insurance will repay them at all costs. In my opinion, insurance will only deceive common people's minds by allowing them to believe that in case of an unfortunate event, the insurance company will take care of everything. Practically, it will cause more trouble in the case that the unfortunate event finally occurs.

 Insurance companies make money. Neither they generate nor they mint money, they just wager (invest is their favourite term) with their clients' money. In exchange to the clients' goodwill to trust their money in the insurance broker's hands, they repay their clients with some interest. Interest can be high or low, acceptable or unacceptable but this is utterly subjective. Personally, if I could find repayment with an interest greater than the one banks offer, I would choose it. Obviously, I am talking about pension or savings contracts. The insurance company collects, keeps and wagers the customers' money for twenty to thirty years and returns an equal amount of money plus the agreed interest minus the agreed (and random, not always agreed) "costs".

 Just like a bank and a casino, an insurance company can be considered as "The House" too. And The House always wins. They receive money from car insurance, health insurance, fire, death, etc. Do they return all of this money back to the clients? Absolutely not. But this is the way this system has always been functioning. In other words, we pay for services that we do not always use. Legally, it is acceptable. Ethically, I cannot say. It depends on one's background and culture.

 The savings or pension programme works like this: the client deposits every year an increasing amount of money. After the agreed number of years passes, the insurance company returns an amount of money greater than the sum of all yearly installments the client has deposited.

 1st year: Client deposits C

 2nd year: Client deposits C + C×i = C×(1 + i)

 3rd year: Client deposits C×(1 + i) + C×(1 + i)×i = C×(1 + i)×(1 + i)

 4th year: Client deposits C×(1 + i)×(1 + i)×(1 + i)

 Obviously, this is C×(1 + i)^3

 5th year: Client deposits C×(1 + i)^4

 .......

 20th year: Client deposits C×(1 + i)^19

 i stands for inflation and usually varies between 1% and 5%. It is supposed to cover the expenses of the insurance company due to yearly inflation of money. In other words, if the client signs a contract for twenty years, the insurance company supposes that after twenty years the first installment of C will have a very low value. So, the client pays for that every year. But this is fair enough, the company will return every single cent of it.

 Now, the insurance company sums all the yearly installments. It is boring enough(and time consuming) to make all calculations for the sum but since it is a sum of the first twenty terms of a geometric sequence, then the result is C×(1/i)×(1 + i)^19.

 Well, I have made a typographical error above. Most insurance companies prefer to start the inflation from the 1st year, which means that the 20th installment is C×(1 + i)^20 and thus the above sum of all twenty installments is C×(1/i)×(1 + i)^20. In both cases the sum is considered to be a lovely amount of money for every average human being. The client will take it back in either of the cases, it is just that the second case is more expensive. Additionally, the client will receive an interest around 40%.

 Usually, this amount is tax free too. Theoretically. Practically, the government does not apply any direct tax on the final yield but very tiny ones, paid per installment which are not refundable and varying between 0.05% and 2% of the installment. Unfortunately, these "costs" occur randomly and at will by all governments across the globe. It seems that all governments have at least this in common.

State your relationship with mathematics and present yourself.

Currency was once a great human invention. However, through human history it turned out to become a life hunt. What was once holy water, now tastes like bitter wine. Here you can work and acquire influence to spend on community's decisions. FIAT currency does not belong here.

Wagering... Probability theory was not developed for the sacred purposes of immunology or biology but for the sake of gambling. It is difficult to make the difference without putting an asset at stake. At least take logical risks instead of pure gambling. "If you do not take risks, you will always work for someone who does."