Computational Complexity and the Origin of Universals :: Mathematics Mathematical Philosophy Papers

Computational Complexity and the Origin of Universals ABSTRACT: This paper establishes close relationships between fundamental problems in the philosophical and mathematical theories of mind. It reviews the mathematical concepts of intelligence, including pattern recognition algorithms, neural networks and rule systems. Mathematical difficulties manifest as combinatorial complexity of algorithms are related to the roles of a priori knowledge and adaptive learning, the same issues that have shaped the two-thousand year old debate on the origins of the universal concepts of mind. Combining philosophical and mathematical analyses enables tracing current mathematical difficulties to the contradiction between Aristotelian logic and Aristotelian theory of mind (Forms). Aristotelian logic is shown to be the culprit for the current mathematical difficulties. I will also discuss connections to GÃ ¶del’s theorems. The conclusion is that fuzzy logic is a fundamental requirement for combining adaptivity and apriority. Relating the mathemati cal and philosophical helps clarifying both and helps analyzing future research directions of the mathematics of intelligence. I. Introduction: Mathematics and Philosophy The two-thousand year old debate on the origins of universal concepts of mind was about the roles of adaptivity or learning from experience vs. the a priori knowledge (the inborn or God-given). It is closely related to the epistemological problem of the origins of knowledge. The problem of combining adaptivity and a-priority is fundamental to computational intelligence as well as to understanding human intelligence. There is an interrelationship among concepts of mind in mathematics, psychology, and philosophy, which is much closer than currently thought among scientists and philosophers of today. From the contemporary point of view, the questions about mind posed by ancient philosophers are astonishingly scientific. A central question to the work of Plato, Aristotle, Avicenna, Maimonides, Aquinas, Occam, and Kant was the question of the origins of universal concepts. Are we born with a priori knowledge of concepts or do we acquire this knowledge adaptively by learning from experienc e? This question was central to the work of ancient philosophers, medieval theologists, and it was equally important to theories of Freud, Jung, and Skinner. The different answers they gave to this question are very similar to the answers given by McCulloch, Minsky, Chomsky and Grossberg. When 2300 years ago Plato faced a need to explain our ability to conceptualize, he concluded that concepts are of a priori origin. The philosophy based on the transcendental, a priori reality of concepts was named realism. During the following 2000 years the concept of a-priority was tremendously strengthened by the development of monotheistic religion in Europe, to the extent that it interfered with empirical studies.

Today’s Education System

An Essay on the Present Education SystemWe live otherwise in the twenty-first century. This century is extremely connected with engineering promotion, high mobility, globalisation, and coevals Z. Generation Z or iGeneration is a name used for the cohort of people born from the early 2000s to the present twenty-four hours. This coevals has some different features with its predating coevals, leting us to implement different attack in instruction.Our Education System: TodayI will get down with the job of our current instruction system. The biggest job is, it did non actuate childs. Millions of childs do non cognize any purposing of traveling to school, except duty. When we went to school we were indoctrinated by scenario: work hard, rewarded did good, acquire a college, and eventually you will hold a occupation. But in the hereafter, it is non guarantee any longer, non if the path to it marginalises what you think of import about yourself. Furthermore, confronting the unpredictable econ omic fortunes. This current system was designed and conceived for a different age: Victorians, between 18th and nineteenth century. It was arranged in the rational civilization of the enlightenment and in the economic fortunes of the industrial revolution. The rational theoretical account of the head stated that the existent intelligence consist of capacity of deductive logical thinking and cognition of the classics, what we come to believe as academic ability. It divides people to academic and non academic, smart people and non-smart people. In effects, many superb people think that they are non. In this system, these childs are medicated. They are forced to bury any distraction such as games, iphones, telecasting, and concentrate to the deadening material at school. Students start losing their involvement, barely believing heterosexual, and losing their attending wholly. In category, they are given the theory and required to memorise it, without cognizing the relevant of that context in existent universe. That is why pupils still disengaged. It becomes more terrible with quantitative standardized proving. They merely know they oblige to analyze and go through the criterion. Education is modeled based on the involvement of industrialisation and in the image of it. Schools are organised on mill lines and pupils are its manufactured merchandises. The Victorians produce instruction which remake us photocopy of each other. How make you be submissive, how do you sit patiently be disengaged for approximately two hours and take it. The humanistic disciplines are the victims of this outlook. The humanistic disciplines, particularly address the thought of aesthetic experience, when senses are runing at their extremum. When we collaring about the exhilaration of these things with our experiencing, when we are to the full alive. While anesthetic is experience which shut your senses off and dampen yourself to what is go oning. We are acquiring our kids educated by anesthetizing them. The deductions are easy to be described. These childs merely give replies based on what their instructor said. They are afraid to see things from different positions, lose their critical accomplishment, and really bad foretelling what will do them happy.The New Model of SchoolPlaning new theoretical account of instruction demands coaction of pupils, instructors, schools, and authorities. Lets start with basic inquiry, what sort of end product that we truly want from instruction system? I ever imagine if schools can be topographic point where pupils can come excitingly, full of autonomous cogniti on, so much more passion and information about they want to make. It is the existent acquisition procedure, they learn something when they have ground to larn it. First, we should waking them up to what is inside of themselves! If we are interested in the theoretical account of acquisition, we should non get down from production line outlook. We have to alter our way from conformity-standardised testing and course of study to divergent thought. Divergent thought is an indispensable capacity for creativity-the procedure of holding original thoughts that have value. It is ability to see tonss of possible replies to a inquiry, tonss of ways to construe a inquiry, and to believe laterally, non merely in additive or convergent ways. We might non judge this topic is superior and this is non. We teach them how to believe their ego involvement, appreciate it, and facilitate that. It besides important to alter the civilization of our establishments that dainty academic pupils as the potencies merchandise and non-academic pupils as the remainders. Second, we have to cut the disengaged concatenation between school and the world. We must revised our end: mark oriented become geographic expedition oriented. Students are non teached how to reply inquiries on the test, but how one job in the existent word can be connected and answered by theory they learned in the category. They must non coerce to bury their favorite games or telecasting channels, but we lead unite them with instruction. The point is, we do non restrict their imaginativeness. They may come with alone inquiries or even unanswerable, but it is the manner they can get down believing critically.Students will understand how their school linked to their life, and they used to see things from scientific discipline position. Third, concentrating on the reading comprehension and critical accomplishment. Actually, it based on Indonesia status. Trends in International Mathematics and Science ( TIMSS ) and Progress in International Reading Literacy Study ( PIRLS ) appraisal revealed that the reading ability of Indonesian kids is low. Whereas, reading ability is the fundamental of scientific discipline acquisition. Why it can go on? One of the ground is, we do non hold reading comprehension course of study, we merely have linguistic communication course of study. I besides have merely learned that reading to understanding is by doing note beside the of import paragraph and rewrite it on our ain words through essay, non the multiple pick. The multiple choice-we used to utilize, is non stimulate pupils to love literacy and read, doing the open-minded is non formed. Finally, they do non cognize how to work out a problem-things they will confront in world. As I said earlier, this instruction reform besides need teacher coaction. We know, sometimes teacher treats their pupils as how they were treated by their instructor. It is wholly different. Today coevals is immune from such stiff school and strict regulations are non effectual any longer. Teachers have to cognize how to do them travel to school voluntarily and to the full motivated. The schoolroom has to be designed to supply adequate infinite for bettering pupils imaginativeness and geographic expedition. However, instructors are the executor of course of study in the category. Go through state with the best instruction system, Finland, instructors there are good educated and trained. Better instruction system need better human resource to present it. Finally, what I hope to be in the new theoretical account of school and high school for twenty-first century are the pupils that full of larning enthusiasm and the instructors that focuses on geographic expedition instead than how to fix pupils go throughing the test. I want reading-writing civilization and wonder colored the school. I do non desire modern establishment dumped critical thought merely because there is non any statement facilitator. Education is non knowledge transportation that remake pupils as a design of their instructor. Students must hold ability to transform the cognition, so the concluding end of instruction to set out coevalss who can reply the epoch menace can be achieved. As the Malcolm Forbes quotes â€Å" Education ‘s intent to replace an empty head with an unfastened one †

Staying Focus Essay

   Staying focus To know the real man behind the name Cleveland, starts with my dynamic support team, my family. I was fortunate to have a strong foundation in the beginning, that is still on going today. That being said, it has kept me grounded and able to give me the unique abilities that I have in me today. The ability to turn my negatives into positives. Dwelling on issues and difficult situations that occur in my life, is not something I waste my time doing. Searching for solutions, while always finding the positives is what I’m about. Being interested in tasks in my life keeps me constantly planning and preparing for the next phase. Which is teaching Junior Reserve Officers Training Corps in one of Texas’s finest High School. I have given over twenty years of my life to the United States Army, with no regrets. I never lost that passion for our United States Armed Forces. So my interest now, that it is time for another chapter in my life, which is to teach our next generation the tools in life in setting goals and knowing how to achieve them to become successful in this world. I look forward to sharing (teaching) with them what that experience has taught me. I will conquer that by informing them how it has empowered me to never give up on dreams. Also letting them know how it has taught discipline, integrity, values, respect, honor and leadership. Among other things such as great sacrifices, for example ; one of my greatness sacrifices that I have made ( with no regrets) for it has and still is my family. It was not easy being absent from my love ones for long periods at a time. Praying and hoping that it would not be the last time that I saw them again, but that was a sacrifice I was willing to make to ensure a better life for my family and the world. I am very passionate about my family. They are the back bone, as I stated before my strong foundation that represents me. My family keeps me motivated and focus. My wife is constantly reminding and assuring me that nothing is impossible for me to achieve. My gifts, as my lovely wife would explain is that I have â€Å"the gift of Gab†. I have always been fortunate in being introduce to individuals of high statue, which was caused by someone I made a good impression on. I have been able to touch others lives in a special way that was positive just by conversation. I am a true believer that a great personality goes a long way in this world. My talents goes a long way, from the basketball courts, football fields and now the golf course. The one talent that I am happiest about is I love helping people achieve things in life that they could never imagine doing. Over the years while being a recruiter for the United States Army I met lots of people with no dreams or aspiration to succeed, but after spending a couple of hours with me they changed their views. When ever I approached people my goal was to always put a

Simplest Formula From Percent Composition

Simplest Formula From Percent Composition This is a worked example chemistry problem to calculate the simplest formula from the percent composition. Simplest Formula from Percent Composition Problem Vitamin C contains three elements: carbon, hydrogen, and oxygen. Analysis of pure vitamin C indicates that the elements are present in the following mass percentages: C 40.9H 4.58O 54.5 Use the data to determine the simplest formula for vitamin C. Solution We want to find the number of moles of each element in order to determine the ratios of the elements and the formula. To make the calculation easy (i.e., let the percentages convert directly to grams), lets assume we have 100 g of vitamin C. If you are given mass percentages, always work with a hypothetical 100-gram sample. In a 100 gram sample, there are 40.9 g C, 4.58 g H, and 54.5 g O. Now, look up the atomic masses for the elements from the Periodic Table. The atomic masses are found to be: H is 1.01C is 12.01O is 16.00 The atomic masses provide a moles-per-gram conversion factor. Using the conversion factor, we can calculate the moles of each element: moles C 40.9 g C x 1 mol C / 12.01 g C 3.41 mol Cmoles H 4.58 g H x 1 mol H / 1.01 g H 4.53 mol Hmoles O 54.5 g O x 1 mol O / 16.00 g O 3.41 mol O The numbers of moles of each element are in the same ratio as the number of atoms C, H, and O in vitamin C. To find the simplest whole number ratio, divide each number by the smallest number of moles: C: 3.41 / 3.41 1.00H: 4.53 / 3.41 1.33O: 3.41 / 3.41 1.00 The ratios indicate that for every one carbon atom there is one oxygen atom. Also, there are 1.33 4/3 hydrogen atoms. (Note: converting the decimal to a fraction is a matter of practice! You know the elements must be present in whole number ratios, so look for common fractions and become familiar with the decimal equivalents for fractions so you can recognize them.) Another way to express the atom ratio is to write it as 1 C : 4/3 H : 1 O. Multiply by three to obtain the smallest whole-number ratio, which is 3 C: 4 H : 3 O. Thus, the simplest formula of vitamin C is C3H4O3. Answer C3H4O3 Second Example This is another  worked example chemistry problem to calculate the simplest formula from the percent composition. Problem The mineral cassiterite is a compound of tin and oxygen. Chemical analysis of cassiterite shows that the mass percentages of tin and oxygen are 78.8 and 21.2, respectively. Determine the formula of this compound. Solution We want to find the number of moles of each element in order to determine the ratios of the elements and the formula. To make the calculation easy (i.e., let the percentages convert directly to grams), lets assume we have 100 g of cassiterite. In a 100 gram sample, there are 78.8 g Sn and 21.2 g O. Now, look up the atomic masses for the elements from the  Periodic Table. The atomic masses are found to be: Sn is 118.7O is 16.00 The atomic masses provide  a moles-per-gram conversion factor. Using the conversion factor, we can calculate the moles of each element: moles Sn 78.8 g Sn x 1 mol Sn / 118.7 g Sn 0.664 mol Snmoles O 21.2 g O x 1 mol O / 16.00 g O 1.33 mol O The numbers of moles of each element are in the same ratio as the number of atoms Sn and O in cassiterite. To find the simplest whole number ratio, divide each number by the smallest number of moles: Sn: 0.664 / 0.664 1.00O: 1.33 / 0.664 2.00 The ratios indicate that there is one  tin atom for every two  oxygen atoms. Thus, the  simplest formula  of cassiterite is SnO2. Answer SnO2

An Came First

An Came First An Came First An Came First By Maeve Maddox A reader writes: I propose that an was invented to prevent us from having to interrupt the flow of speech. And it still fills that purpose before unaccented first syllables starting with h. This comment suggests that the indefinite article form an developed from the form a as a means of facilitating pronunciation. Unlike Esperanto, English is not an invented language, but the product of more than a thousand years of development. An was not invented to facilitate the flow of language. Neither did it begin its life as â€Å"an indefinite article.† It started out as a numeric adjective. The English indefinite article a/an derives from the Old English word for one: ane. The word was written ane, anne, aenne and aene in its various declensions. As it evolved into our modern indefinite article, sometimes it signified the number one and sometimes the article a. For example, in an OE version of the New Testament parable of the workmen who are all paid the same for different amounts of work, the owner of the vineyard pays them â€Å"anne pening,† that is, â€Å"one penny.† In the account of the voyages of Ohthere and Wulfstan, Ohthere refers to Skiringssal as â€Å"an port,† that is, â€Å"a port.† Even in modern usage, the article a/an can be used in the sense of â€Å"one,† as in, â€Å"I’ll have a hamburger, a cherry Coke, and two orders of fries.† Like the reader whose comment prompted this post, some modern speakers feel that that an â€Å"still fills [a] purpose before unaccented first syllables starting with h.† According to a note in the OED, â€Å"many (perhaps most) writers down to the 19th century retained an before sounded h and some even before eu, u, as â€Å"an historian,† â€Å"an euphonic vowel,† and â€Å"an united appeal.† Most modern usage guides, however, recommend a. That’s not to say that you can’t say â€Å"an historic† if you want to. Related posts: A Useful Reminder About An A Historic vs. An Historic Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Grammar category, check our popular posts, or choose a related post below:50 Rhetorical Devices for Rational WritingConfused Words #3: Lose, Loose, Loss25 Idioms with Clean

The 50 Most Commonly Used Words in the English Language

The 50 Most Commonly Used Words in the English Language If youre an English learner, knowing which words are most commonly used in the language can help you to improve your vocabulary skills and gain confidence in  casual conversations.   Dont  count on these words to help you become fluent in English, but do use them as a resource to help you build your skills as you grow more  comfortable with the English language. Top Vocabulary Words All Everyone in a group.All the children did their homework. And A conjunction that joins parts of speech together in a sentence.She jumped, jogged, and danced in gym class.   Boy A male child.The little boy asked his mother if she would buy him candy. Book A long text of words that people read.The college student had to read a 500-page book for English class. Call To yell out or speak loudly; to contact someone by phone.  The girl called out to her brother so he would wait for her. Car A four-wheeled vehicle that transports people from one place to another.He drove the car from school to work. Chair A piece of furniture that can hold one person.My mother is the only one allowed to sit in the big chair in the living room.   Children Young people who have not yet reached adulthood.The children didnt listen to what their parents told them. City A place where many people live.New York is the biggest city in the United States. Dog   An animal that many people have as a household pet.My dog likes to play with bones. Door A passageway from which you can enter or exit a room or a building.  The students rushed through the classroom door just before the bell rang.   Enemy   The opposite of a friend. A competitor or rival.  The hero of the story killed his enemy with a sword. End To finish something or come to a conclusion.The end of the book was a happy one. Enough To have more than one needs of something.  Most Americans have enough food to eat, but thats not true in other countries.   Eat To consume food.  The children liked to eat apples and bananas after school.   Friend The opposite of an enemy. Someone on your side and with whom you enjoy spending time.The girl played with her friend in the yard until her mother told her to come inside. Father A male parent.The father picked up his child when she started crying. Go To travel to and from a location.  We go to school every day. Good To behave well or in a kind manner.My mother said that if Im good and dont hit my brother, she will take me to the movies. Girl A female child.  The girl dropped her schoolbooks on the ground.   Food An edible substance that people, animals, and plants eat to live.Starving people do not have enough food to eat and may die. Hear To listen to something.  I could hear my brother and sister arguing from the other room. House A place where people, often families, live.My friend lives in the biggest house on the street. Inside The internal part of something or to be located within something.  The inside of the house was warm and cozy.   Laugh To express that you find something amusing.  The children laughed after the clown made a joke. Listen To hear something.  We listen to music because we like to dance.   Man An adult male.The man was much taller than his son.   Name The title of a place, book, person, etc.  I never liked my name growing up.   Never Not ever.I am never getting back together with my boyfriend. Next The thing that happens after something else in a sequence; to be situated by something else.  Lets go to the next question. New Something just created or unused or unopened.My mother bought me a new doll for Christmas. It was still in the package. Noise Loud sounds, especially made by music or a group of people.  There was so much noise at the party, the neighbors called the police.   Often To happen frequently.  My teacher gets mad because I often forget my homework.   Pair Two things that go together.  I like the new pair of shoes my sister bought me for my birthday. Pick To choose or select.  I picked the cupcake with vanilla frosting.   Play To have fun with someone or engage in an activity or sport.  I like to play football with my brother.   Room A part of a home, building, office or another structure.  The room at the end of the hall is the coldest in the building.   See To watch or observe something.  I see clouds in the sky, which must mean it will rain soon. Sell To offer a service or a good for a price.I am going to sell my surfboard for $50 because its time for a new one.   Sit To rest on a floor, chair, or another surface.  The teacher told the children to sit on the carpet.   Speak To say something.I speak too loudly sometimes.   Smile To grin or show pleasure.I smile when my brother tells jokes. Sister The opposite of brother. The female child in relation to other children of the same parents.My parents took my sister and me to the circus. Think To contemplate something or have an idea or belief.  I think all pets should have a home.   Then Something that comes after an event in a sequence.  I opened the refrigerator. Then, I ate some food.   Walk To travel on foot.  I walk home from school every day. Water A substance plants, people, animals, and the earth need to survive.If animals dont have enough water to drink, they will die.   Work To make a living, engage in an activity for pay, or to reach a goal.  I work as a teacher because I like children.   Write To put something on paper with a pen or pencil. To use a computer to type text.I have to write three essays in English class this semester.   Woman A female adult.That woman was our new school principal.   Yes To answer affirmatively or respond to ones name being called.  Yes, Im here, the student said when the teacher called her name.

Thomas Paine's 'Common Sense' Essay Example | Topics and Well Written Essays - 500 words

Thomas Paine's 'Common Sense' - Essay Example From this situation, the best scenario is that these people create the laws by which they will live under themselves. This does not explicitly refer to the American colonists, but it does imply their current state at that time. Paine then turns his attack directly towards the British government by arguing that the system contradicts itself and places too much power on the monarchy. Furthermore, the monarchy itself is corrupt because the very idea of a monarch was formed out of a false argument. The people can choose who they want to be king in the first place, yet they have no choice about the king’s descendants. This presents an opportunity for greed and corruption as no one will dare to stop the monarch from continuing this practice. Paine argues that America should have the freedom to choose its leaders so that the leadership of the country will not remain within one extended family. Furthermore, Paine dispels the myth that America could not survive without the help of Britain by arguing that America has progressed to a point where it can flourish on its own two feet. Loyalists would claim that America has only progressed to what it was then because of the help of the king, and also the protection that has been provided to fend off outside enemies. Paine comments that Britain has only been doing this in order to look after its own interests. He even gives an example of British troops attacking some American colonies, although the British would protest this view and say that they have only been looking after America the whole time. Paine remarks that America has no benefit to remain linked with Britain because America can engage in more profitable trade with the rest of Europe. The British argument would be that the colonies can remain strong by trading with Britain because trade will benefit everyone. However, Paine says that trade will only benefit Britain beca use the British only see the colonies as a means