Tag: <span>mathematics</span>

04 Oct

The Joy of Learning Mathematics

For many students, maths is a phobia at par with the fear of snakes, lizards, elevators, water, flying, public speaking, and heights. Though the “ailment” is neither genetic, nor infectious, they “inherit” it from their parents; and “catch” it from their friends. What are the reasons behind maths’ dreadful reputation that divides the society into mathematical “haves” and “have-nots”?

“One reason why students fare badly in Maths is that they are learning it mechanically, often not understanding what they are learning and they are unable to apply it to real-life situation,” says Vijay Kulkarni, the leader of the First Annual Status of Education Report (ASER) released recently by the well known Bombay-based non-governmental organization, Pratham.

Explaining the dismal scenario that the report portrays, especially about mathematics – forty two per cent of children between seven to ten years cannot subtract – Kulkarni says that the children are turned off, because the straitjacketed conventional teaching in classrooms has squeezed out the joy of learning, turning the schools into robotic factories.

Outdated teaching methods and an outdated curriculum – far removed from the students’ everyday experiences – contribute nothing to a student’s appreciation of the subject. Intelligence is often measured by the marks he gets in mathematics and his self confidence is eroded when he gets drubbed as dumb for scoring less in it.

Yet, taught the right way, learning mathematics can be easy, fun and can fill one with a sense of awe, with its inherently beautiful harmony and order. Both parents and teachers should convey the message that learning mathematics can be fun. Their expressions of interest, sense of wonder and enjoyment are critical to the child’s interest in the subject.

“Parents are the first mentors for a child. Even before the children can be formally admitted in pre-school kindergartens, they can start playing with numbers,” suggests Dr.MJ Thomas, a child psychologist in the city. Children are playful by nature and have irrepressible curiosity to explore the world through experimenting with the objects around them: see, touch, hear, taste, smell and arrange the objects, put things together or take them apart. Through such experience the children understand their world intuitively.

Dr. Thomas’ suggestions: collect beads of various colours and tell the kids to alternately string two beads of, say, two colours. Tell them to bring red and green balls and make two piles of equal number of balls. Another game could be to arrange playing cards in rows of three or four. These activities can enforce quantitative thinking and help make numbers our friend.

“While the other sciences have some amount of hands on activity included in the syllabus and the idea of a physics, chemistry or biology lab is common, maths is still taught only by the chalk and talk method,” says Dr. S.N.Gananath, recipient of Ashoka Fellowship for innovations in teaching activity-based mathematics. “This is particularly unfortunate as a subject like maths can be understood only when a child experiences, first-hand, the idea of weight and volume, shape and size, number and pattern,” he says.

Dr. Gananath has designed Maths Kits, with charts, diagrams and games, to explain various difficult concepts in Mathematics, like place-value, fractions or decimals. He takes a piece of paper, marks off lengths a and b and in minutes, by suitably folding the paper, arrives at formulas for (a+b) 2 and (a-b)2. Such activity-based teaching stimulates thinking, encourages discussion or search for alternate ways of solving problems. On the other hand traditional teaching in schools seems to give the impression that there is only one way to solve a given problem.

“Learning does not mean simply “knowing” facts; but understanding the underlying concepts that are anchored in experience,” says H.N.Parmesh, head-master of Born Free, a government school in the village of Banjarpalya, off Banaglore-Mysore road. His school has the rare distinction of all the students securing first-class in the VII standard public examination for several consecutive years. Parmesh and his team of dedicated teachers have used inexpensive materials like match-boxes and coloured beads made of baked clay to make educational aids that they affirm have helped the slow learners to understand maths better.

Several organizations like the Akshara Foundation and the Azim Premji Foundation, with support from corporate bigwigs, have collaborated with the government and used computers to capture the bored rural children’s attention, and spur their curiosity and imagination. However, using computer effectively to support teaching is no easy task. It needs good planning and design; otherwise it may end up as an expensive replacement for rote learning, if all it does is to replace dull text with colorful animations.

IT can be innovatively used to usher in interactive learning, as has been attempted by Oracle Education Foundation, which has designed a web-based educational environment – think.com for teachers and students in Bangalore, and elsewhere. This has enabled students and teachers to create personal Web pages and communicate or discuss with each other through message boards and e-mails. The website has made the students more creative and the teachers more responsive and accessible to students.

Games and puzzles are a sure way to aid learning. As children, we have asked each other the puzzle: a goat, a tiger and a bunch of grass should be transported across a river through a boat which can carry only one of the three at a time. Given that the goat will eat the grass and the tiger will eat the goat if left alone, how would you take them across one by one and save their lives? There is a similar exercise in logical thinking in the classic example of a village with two tribes – one which always speaks the truth and the other always tells lies. When you reach a point where the road forks into two paths, with one leading to treasure and the other to death, you see a member of each tribe. If you are permitted to ask only one of them a single question, who will you ask and what will you ask, so as to get the treasure?

Puzzles like this will initiate a lot of discussion. And the lessons learnt will not be easily forgotten; they will be applied when a similar situation occurs.

Learning must be guided by generalized principles in order to discover strategies for problem solving. Knowledge learned through rote memory rarely transfers to new, even though similar, situations.

Teacher-centric classrooms where teacher dominates the scene should soon become a thing of the past. Teachers should be facilitators of learning; they should stimulate thinking, which would lead to self-discovery, so that the child experiences the sheer joy of learning.



Source by Uma Shankari

04 Sep

Advantages of Mathematics

Many of us wondered about the advantages of Mathematics during our childhood days. Many of us were not able to comprehend the benefits of mathematics beyond the daily usage of calculating simple numbers. Let us see in detail what are some of the benefits of learning mathematics and marveling at this arduous subject at early age.

The importance of mathematics is two-fold, it is important in the advancement of science and two, it is important in our understanding of the workings of the universe. And in here and now it is important to individuals for personal development, both mentally and in the workplace.

Mathematics equips pupils with a uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem-solving skills, and the ability to think in abstract ways. Mathematics is important in everyday life, many forms of employment, science and technology, medicine, the economy, the environment and development, and in public decision-making.

One should also be aware of the wide importance of Mathematics, and the way in which it is advancing at a spectacular rate. Mathematics is about pattern and structure; it is about logical analysis, deduction, calculation within these patterns and structures. When patterns are found, often in widely different areas of science and technology, the mathematics of these patterns can be used to explain and control natural happenings and situations. Mathematics has a pervasive influence on our everyday lives, and contributes to the wealth of the individual.

The study of mathematics can satisfy a wide range of interests and abilities. It develops the imagination. It trains in clear and logical thought. It is a challenge, with varieties of difficult ideas and unsolved problems, because it deals with the questions arising from complicated structures. Yet it also has a continuing drive to simplification, to finding the right concepts and methods to make difficult things easy, to explaining why a situation must be as it is. In so doing, it develops a range of language and insights, which may then be applied to make a crucial contribution to our understanding and appreciation of the world, and our ability to find and make our way in it.

Increasingly, employers are looking for graduates with strong skills in reasoning and problem solving – just the skills that are developed in a mathematics and statistics degree.

Let us look at a few examples. The computing industry employs mathematics graduates; indeed, many university computing courses are taught by mathematicians. Mathematics is used to create the complex programming at the heart of all computing. Also cryptography, a form of pure mathematics, is deployed to encode the millions of transactions made hourly via the Internet and when we use debit or credit cards. Mathematics and Computer Science is a popular degree choice, and four-year degrees with a placement in industry are also available. The latter give graduates plenty of relevant experience to increase their employability.

Mathematics led to the perfect ratios shown in Renaissance painting. The study of astronomy in the early times of its inception demanded the expansion of our understanding of mathematics and made possible such realizations as the size and weight of the earth, our distance from the sun, the fact that we revolve around it, and other discoveries that allowed us to move forward in our body of knowledge without which we would not have any of our modern marvels of technology.

The computer itself is a machine built upon the principles of mathematics, being an invention so important as to bring about an economic revolution of efficiency in data communication and processing.



Source by Shilpa Rao

11 Aug

Math Tutoring – 3 Basics Steps to Master Reading Mathematics Formulas

Understanding how to read mathematics formulas requires a basic understanding of the formula vocabulary and how to recognize formula reading patterns. We will focus on how to read Mathematical formulas and learn how this formula reading pattern can be used with formulas from different subjects (i.e. Algebra, Geometry, Chemistry, Physics). Knowing how to read Mathematics formulas is essential for maximum understanding and easy memory recall.

It is my hope that you will see a pattern with reading formulas across different subjects. Why is seeing a pattern across subjects so important? Students often feel like they are learning something new each time they are introduced to a Math formula in another class or course. Fact remains, the same methods you use to read formulas in Algebra are the exactly same methods used to read formulas in Trigonometry, Physics, Chemistry, Economics, etc. So the key is mastery of reading formulas in Algebra.

Step 1: Understand what a formula is. What is a mathematical formula? An equation (i.e. F = ma) which expresses a general fact, rule, or principle.

Step 2: Identify and learn the basic Mathematics equation vocabulary and use as often as possible while doing problems. A good mathematics educator (e.g. tutor, mentor, teacher, …) will help you engage this vocabulary as you are working on your problems. This vocabulary is useful when reading Math instructions, doing word problems, or solving Math problems. Let’s define a basic set of basic Math formula (equations) vocabulary words below:

Variable – a letter or symbol used in mathematical expressions to represent a quantity that can have different values (i.e. x or P)
Units – the parameters used to measure quantities ( i.e. length(cm, m, in, ft), mass (g, kg, lbs, etc))
Constant – a quantity having a fixed value that does not change or vary
Coefficient – a number, symbol, or variable placed before an unknown quantity determining the amount of times it will be multiplied
Operations – basic mathematical processes including addition (+), subtraction (-), multiplication (*), and division (/)
Expressions-a combination one or more numbers, letters and mathematical symbols representing a quantity. (i.e. 4, 6x, 2x+4, sin(O-90))
Equation – An equation is a statement of equality between two mathematical expressions.
Solution – an answer to a problem (i.e. x = 5)

Step 3: Read formulas as a complete thought or statement-do not ONLY read the letters and symbols in a formula. What do I mean? Most people make the repeated error of reading the letters in a formula rather than reading what the letters represent in the formula. This may sound simple, but this simple step allows a student to engage the formula. By reading the letters and symbols only, one cannot associate the formula with particular vocabulary words or even the purpose of the formula.

For example, most people read the formula for area of a circle (A = “pi”r2) just as it is written – A equals pi r squared. Instead of just reading the letters and symbols in the formula, we propose reading formulas like A = “pi”r2 as a complete thought using all the descriptive words for each letter: The area (A) of a circle is (=) pi multiplied by the radius (r) of the circle squared. Do you see how the formula is a complete statement or thought? Therefore, one should read formulas as a complete statement (thought) as often as possible. It reinforces what the formula means in the mind of the reader. Without a clear association of Math formulas with their respective vocabulary, it makes applications of those formulas near impossible.

Example of formulas and the subjects where they are introduced:

PRE-ALGEBRA – Area of Circle: A = “pi”r2
The area (A) of a circle is pi multiplied by the radius (r) of the circle squared
o A- area of the circle
o “pi” – 3.141592 – ratio of the circumference to the diameter of a circle
o r- the radius of the circle

ALGEBRA – Perimeter of a Rectangle: P = 2l+ 2w
Perimeter (P) of a rectangle is(=) 2 times the length(l) of the rectangle plus 2 times the width (w) of the rectangle.
o P- perimeter of the rectangle
o l- measure of longest
o w- measure of shortest

GEOMETRY – Triangles Interior Angles Sum Theorem: mÐ1 + mÐ2 + mÐ3 = 180
The measure of angle 1 (mÐ1), plus the measure of angle 2 (mÐ2) plus the measure of angle 3 (mÐ3) of a triangle is 180 degrees.
o mÐ1 – perimeter of the rectangle
o mÐ2 – measure of a side
o mÐ3 – measure of the width

Knowing the units for each quantity represented in these formulas plays a key role in solving problems, reading word problems, and solution interpretations, but not merely reading the formulas.

Use these steps as a reference and learn how to read Mathematics formulas more confidently. Once you master the basics of formulas, you will be a Learner4Life in different subjects that use Math formulas!



Source by Avery Austin

08 Aug

Learn Mathematics

Education is one of the most important things here on earth; people are always searching for answers and education play an important role in this endeavor; education will help us discover and explore everything with the use of logic and reason. In this light, education should be prioritized by all individual and should be promoted by all states as well. Of course if the individual acquired certain education and knowledge, wider opportunities are in store for them right? Education is very crucial in the development and growth of every individual therefore the role of the state is to plan and implement programs to help and assist individual earn and have the education they deserve. As you may notice, the state is allotting budget every year for the education system to make improvements and make it better. In every sense of the word, education is defined as the process of the society that seeks to transmit every grain of knowledge to every generation; moreover it comprises acts that are geared toward molding the kid’s physical, mental and social functions.

The education system is providing their students with reliable people, equipments and materials that will surely help in the success of this endeavor. Educating a child happens in the classroom but modern teaching strategies consider immersing the child outside to learn and see the real world. In almost every learning experience of a child, there are experienced teachers to guide their way which makes it effective. Aside from teachers, the institution should give importance to learning the fun and dynamic way through some technologies, equipment and other tools available. Most importantly, there are materials that can help you in the process. These materials can be considered in many subject matters that include music, science, children’s literature, character education, puzzles, language arts, social studies and even mathematics.

It is important that the above mentioned subjects should be prioritized. For instance, mathematics. Mathematics transcend to more than traditional and simple counting for it encompasses analysis and critical thinking through the use of abstraction; it is a system that is widely used by almost every field such as natural science, engineering, social science, medicine and other crucial studies. There are people that consider math difficult but if you persist, everything will work out just fine. Learning mathematics is easy if you consider some help; there are quite a number of teacher supply. You can also provide your students with preschool furniture for their comfort.With the help of school supplies and furniture, learning math can be fun and interesting. Math will play an important part in our life so it should not be despised.

These materials are not that expensive so you can have many. Indeed education is more effective with the help of these materials. Remember that education is the most important thing in this world and as a parent and teacher, the least thing that you can do for your students is to provide them with a comfortable environment with equipment and materials necessary for the success.



Source by Andre Reynolds

09 Jul

Times Tables and the Vocabulary of Mathematics

How many times do you see people apologise for using mathematics in a television programme, book, discussion group etc? They apologise for using equations or mathematical terms as though they were talking Martian. Everyone these days has attended countless maths lessons at school and many have studied the subject to a higher level, so there really is no reason to avoid these terms and concepts.

Even Professor Hawking of Cambridge University, in his book ‘A Brief History of Time’ said he had been told to keep the number of equations to a minimum as every equation he included halved his potential readership.

What a crazy world we live in. You never hear a reviewer of a drama or fictional book apologising for using big words to describe the characters or the genre of the piece. Why do we do this in mathematics and why do we mathematicians put up with it?

Children love to learn and use new, often difficult, words. Watch them trying to get their tongues around words such as ‘Tyrannosaurus Rex’, ‘Diplodocus’ or the name of some Italian or Lithuanian football player. They love it!

So, listen out for mathematical language and make sure you are introducing it into your conversations with your youngsters whenever appropriate, just as you would any other term.

You can begin when they are very young and I should like to use the concept of multiplication as an example.

How many ways can we describe a simple sum such as ’12 x 6′?

All of the following statements involve this problem:

What is 12 times 6?
What is 12 multiplied by 6?
Find the product of 12 and 6?
What is 12 times more than 6?
What is 12 lots of 6?
What number is 12 times greater than 6?
What is 12 groups of 6?
What is the 12th multiple of 6?
Commutative Law (the law that says that 12 x 6 is the same as 6 x 12)

There are similar words and phrases for the other three processes:

Addition – total, sum, all together, plus, how many in all…

Subtraction – difference, how much more, subtract, take away, how many are left, how much less than, how many more to make…

Division – divided by, divided into, quotient, shared between, halve, one third of, how many 5s make 35?…

Once you introduce these terms into your everyday conversation, other mathematical terms such as ‘equilateral triangle’, ‘isosceles’, ‘quadrilateral’, ‘hexagonal’, ‘perimeter’, ‘millimetre’ and ‘enlargement’ will not scare the pants off them and will soon become part of their everyday language too.

Children’s brains are designed to learn new words quickly and they love trying, so please use this to your (and their) advantage.



Source by Alan Peter Young

09 Jun

Cancer, Ancient Atomic Mathematics and the Science-Art of Quantum Biology

As is commonly known, the pursuit of happiness ideal was fused into the basic design of the Constitution of the United States of America. Surprisingly, no one seems to know why and how that came about. Scholars knew it had something to do with a message from ancient Egypt’s ‘Eye of Horus’, depicted at the top of a pyramid as part of the Great Seal of America. They also knew that this all-seeing eye message had been linked to the work of the Greek mathematician, Pythagoras, who had studied political ethics in ancient Egypt.

Some thought that the message might relate to a happiness of acquiring wealth through mechanical industrialisation. However, the discovery of quantum biology during the 21st Century demonstrated that a far greater potential wealth exists within new technologies able to harness the previously unknown natural properties of carbon, belonging to human life forms. The old acquisition of wealth, derived from a mechanical mindset, is now well recognised as being the cause of a future unsustainable carcinogenic existence on planet Earth. Within Science-Art research, humanity has an innate non-mechanical association with Einstein’s protege, David Bohm’s holographic universe.

The first Science-Art discovery of a holographic living force occurred late in the 20th Century, and came about by reuniting science with artistic feelings. This unification led to the discovery of new physics laws governing optimum seashell growth and development through space-time. These physics laws appear to belong to the ancient mathematics governing the political ethics embedded into the ‘pursuit of happiness’ concept. The world’s largest technological institute, IEEE in Washington, reprinted this scientific breakthrough as one of the important optics discoveries of the 20th Century, placing it alongside such names as Louis Pasteur and Sir Francis Crick.

This historical event was fused into quantum biology research theory, by the recipients of the 2010 Gorgio Napolitano Medal, awarded on behalf of the Republic of Italy for their quantum biological physics and chemistry discoveries. The second discovery was that some artists throughout history had unconsciously depicted hidden stereoscopic, holographic images, in their paintings. While new technologies have developed infinite fractal logic techniques to manufacture such images, prevailing science remains completely oblivious to the fact that the human mind can create them. This is one example of the mathematician, Cantor’s observation, that the mindset of modern science is inhabited by an unnatural fear of infinity, denying Newton’s first principles of creative gravitational force by substituting the foolish falling apple myth in its place.

In order to provide a brief outline of this interesting, but very controversial story, a historical explanation appears to be warranted. Pythagoras’ research was a precursor to the Platonic tradition of ancient Greek mathematical culture. That tradition fused further ethical concepts into Egyptian ethical atomic mathematics, in order to invent ethical science during the 3rd Century BC. The Egyptian mathematics was about the purpose of sacred geometry within invisible atoms, to make tiny seeds from which forms of life throughout the universe emerged. During the Egyptian Second Kingdom, their sacred geometrical logic, concerning justice, compassion and mercy, had been fused into political law, and later copied by other civilisations, to legalise the construction of hospitals and policies of caring for the aged.

The founding fathers of the flawed American Democratic system of politics attempted to establish a greater ethical, scientific, political system from ancient Greek science. However, the Christian Church, during the 4th Century AD, had declared the pagan mathematics to be the work of the Devil. Saint Augustine had incorrectly translated the property of unformed chaos within the atom, as being the evil of female sexuality. He associated the mathematics with the mechanistic worship of Ishtar, the Babylonian Goddess of prostitution and war. However, this was not the mathematics that the Great Library of Alexandria was developing at the time. Nonetheless its Science-Art scrolls were destroyed by rioting Christian fanatics.

The linking of the Egyptian pursuit of happiness concept to quantum biological cancer research, during the 21st Century, was clearly predicted by the mathematician, Georg Cantor. Born in 1845, Cantor developed his infinite mathematical theories from the ancient Greek ethical science, derived from earlier Egyptian atomic mathematics. His work is now basic to modern scientific science. However, Cantor’s ability to intuit the future discovery of Mandelbrot’s infinite fractal logic, embraced ideas that prevailing Christian oriented science, finds completely incomprehensible.

Cantor knew that Aristotle was a central figure in the Platonic tradition of philosophy and investigated the mathematical theory upholding his research into the pursuit of happiness concept. Aristotle had linked the pursuit of happiness to a future science, to guide ennobling government for the health of the universe. This idea was obviously about a future medical science, using sacred geometrical logical ideas, beyond the limitations of our prevailing science, which considers that the only universal energy in existence flows from hot to cold. Cantor saw that the living process extended to infinity, in contradiction to this universal heat death concept, which condemns all life to eventual extinction. This universal heat death sentence became scientifically irrevocable after Charles Darwin used it as the basis of his evolutionary theory. Later, Einstein declared that this entropic law governed all aspects of science, including political, economic and medical.

When the framers of the American Constitution tried to bring Aristotle’s political vision into reality they defined the ethical idea of liberty incorrectly. Liberty embracing the pursuit of happiness within a medical science for universal health was assumed to obey Sir Isaac Newton’s emotionless laws governing the workings of his mechanical universe. The Founding Fathers, unaware of Newton’s more natural, profound theory of gravitation, erroneously based the concept of liberty only upon his mechanical description of the universe. Newton published his little known theory at the risk of being burnt alive by order of the Church. He insisted that gravitational force was a non-mechanical spiritual force evolving emotional consciousness within an infinite universe. As a result of publishing that opinion he was held by the Church to be criminally insane, and suffered a mental breakdown for which he was hospitalised.

Newton was most likely aware that his contemporary, the philosopher of science, Giordano Bruno, had been imprisoned by the Church in Rome, tortured, then burnt alive for teaching about the ethical Greek science at Oxford University. Newton’s published heretical gravitational theory was featured in his 28th Query Discussions in the second edition of his famous journal, Opticks, as anyone can easily verify. Also, his unpublished Heresy Papers and copies of his private letters, written during the height of his genius, demonstrate that Newton was not insane when he published his spiritual theory of gravity. Newton most certainly did not believe that reality was governed by the functioning of a clockwork universe, as modern quantum mechanics science had incorrectly assumed.

The Romantic era, from about 1800 to 1850, consisted of an artistic, literary and philosophical movement, which erroneously condemned Newton for promoting lifeless theories of science. The movement was ignorant that his first physics principles actually associated gravity with the living process, derived from ancient Greek Platonic science. William Blake, the poet and artist, along with other principle figures of the Romantic era, held Newton in contempt. They had not realised that Immanuel Kant, 1724-1804, one of the most influential philosophers of science in the history of Western philosophy, had given electromagnetic properties to Newton’s concept of emotional gravitational force. They were also unaware of the scientific insights of the poet, Alexander Pope, who had been greatly praised by Kant for his knowledge of ancient Greek philosophy.

Alexander Pope is considered one of the greatest English poets of the eighteenth century. His famous ‘Essay on Man’ consisted of four parts. The first Epistle, was about man’s place in the universe; Epistle II, was concerned with the individual person; Epistle III related to man within human society governed by political structures; and Epistle IV with the political ideal of the pursuit of happiness.

Alexander Pope’s concept of an ethical infinite universal purpose can be seen to be compatible to Newton’s theory of gravitational force, evolving ethical emotional consciousness within an infinite universe. Einstein modified Newton’s theory of light and later altered it to give more credence to Newton’s original concept. Some scholars have considered that Alexander Pope’s linking of Newton’s theory of light to an infinite ethical purpose, from the perspective of Kantian pure logic, explains why Immanuel Kant considered Alexander Pope to be a great genius. Pope’s ideas were well known to the leaders of the electromagnetic Golden Age of Danish Science.

In 2002, Harvard University and Massachusetts University held an international symposium to tell the world of the social importance of the message of the electromagnetic Danish Golden Age of Science. They noted that its crucial message had been written mostly in Danish and not translated, making it invisible to English speaking scholarship. However, Immanuel Kant, a leading personality of that Golden Age, had written that the English poet, Alexander Pope, had given the ancient Greek theories an artistic expression. The discoverer of the electromagnetic field, Hans Christian Oersted and his colleague, Friedrich Schelling, were also principle figures of the Golden Age. Their own Science-Art theories gave credence to Newton’s first principles, necessary for the healthy and ethical evolution of humanity. Their theories have been associated with Alexander Pope’s development of a similar concept.

Georg Cantor’s mathematical logic condemned the idea that all life in the universe must be destroyed after its heat had radiated away into cold space. This universal heat death law simply contradicted his discovery of mathematical infinity, which he had linked to the evolution of life. His work, attacked by many of the world’s leading mathematicians, led to his conclusion that the scientific mind was inhabited by a primitive, myopic fear of infinity. The solution to this emotionally traumatic, carcinogenic situation can be easily obtained in the light of advanced quantum biology cancer research. But it requires a more profound understanding about Aristotle’s concept of a medical science needed to guide ennobling government.

A first step is to produce evidence that this illogical scientific fear of infinity does exist. Modern science knows very well that an infinite fractal logic exists, but it is unable to allow for fractals to be part of the living process as it is obsessed with its falsely assumed thermodynamic extinction. This is completely illogical because the functioning of the molecule of emotion has been identified, beyond doubt, as obeying infinite fractal logic.

A second step is to refer to Sir Isaac Newton’s firm conviction that the universe is infinite. His first principles of gravitational force were not mechanical but belonged to the ancient Geek emotional atomistic science, as mentioned above. Whether or not this was a criminally insane reasoning, as claimed by the Church, is of no importance. Isaac Newton most certainly did not advocate a mechanical clockwork-like universe. Therefore, Einstein’s stating that the mechanical heat death law was the premier law of all the sciences, in particular political, economic and medical economic sciences, were based upon false assumptions. Isaac Newton wrote that such a pretentious scientific first principle logic would contaminate scientific philosophy, just as the mathematician, Cantor, discovered when he researched the origins of the concept of the pursuit of happiness.

In advanced quantum biology cancer research Einstein’s energies of mechanical quantum chaos are entangled with another universal energy, known as Shannon-Weiner information energy, which does not flow from hot to cold. The 1937 Nobel Laureate, Szent-Gyorgyi, noted that failure to visualise that consciousness evolved through such an energy entanglement depicted a primitive mindset associated with cancerous growth and development.

The book ‘Phantoms in the Brain’, written by V.S Ramachandran M.D., Ph.D., and Sandra Blakeslee, about how the brain works, was very highly acclaimed by Nobel Laureate, Francis Crick Ph.D.,. Within the book, mention is made of the mental affliction known as anosognosia, about which almost nothing is known. The question is raised as to why this affliction should exist when it seems detrimental to our survival. Anosognosis can be considered to present a model of denial that the mathematician, Georg Cantor, described as existing within the scientific mind, as a blind fear of infinity.

The human survival message contained in ‘Phantoms in the Brain’ is so advanced that it can be considered to readily apply to solving the current extinction obsession inhabiting the modern scientific mind. The funding to carry out this objective will come from a new understanding of first cause cancer research principles and this will be made possible by reuniting the culture of art with the culture of science. That project has been publicly classified by leading quantum biologists in Europe as being the rebirth of the lost original Greek science – the 21st Century Renaissance.

Quantum biology cancer research not only addresses this human survival problem but can be seen to be the foundation upon which an omni human survival technology can be constructed. This technology was clearly alluded to by the champion of American liberty, Ralph Waldo Emerson, during Georg Cantor’s lifetime. Emerson echoed Cantor’s concern that an association of infinite mathematical logic with human evolution was not tolerated within the American scientific mind. His logic argued that infinite Sanskrit mathematics, leading to a truly democratic technological culture, had been forbidden, because industrial mechanical greed had enslaved the minds of the American people to deny its very existence. He blamed this phenomenon upon America having inherited a false mechanical, mathematical worldview from ancient Babylonian culture.

The 1957 the New York University of Science Library published a book entitled ‘Babylonian Myth and Modern Science’ which stated that Einstein had developed his theory of relativity from the intuitive mythological mathematics of ancient Babylon. Unintentionally, Einstein’s great genius was only about the mechanical functioning of the universe, which can now be successfully modified through its entanglement with the information energies of quantum biology. Reference to ancient Mesopotamian cultures leads to a storybook tale of how and why the mental disease of anosognosis led to modern science worshipping the concept of human extinction. The worship of Einstein’s heat death law, sentencing humanity to extinction, was the one that the mathematician, Lord Bertrand Russell, advocated in his most famous essay, ‘A Freeman’s Worship’. Both Russell and Einstein were awarded Nobel Prizes for their mechanistic, entropic worldview theories.

The Pyramid Texts discovered by Gaston Maspero in 1881 were about the advanced sacred geometrical purpose within invisible atoms, depicted by the Egyptian god Atum. The god declared, from the dark abyss of initial chaos ‘Let there be light’, centuries before the Hebrew and Christian religions came into being. Atum decreed that all created life would eventually return back into the original state of chaos, which modern science now accepts as being inevitable.

During the reign of Pharaoh Akhenaten the various Egyptian gods were dismissed and the worship of one god, the sun god, Ra, was established. That period was short-lived and Akhenaten’s city, built to honour Ra, quickly fell into ruin. During the reign of Ramses the Great, the Egyptian religion governing political law followed the teachings of the Goddess, Maat, in which humans could become immortal within an infinite universe. The geometrical logic of the infinite Egyptian mathematics was further developed by Greek scholars, such as Thales during the 6th Century BC and Pythagoras in the 5th Century BC. The Platonic tradition of Greek philosophy used the ethical atomic mathematics to invent ethical science in the 3rd Century BC. The Greeks defined gravity as an emotional whirling force acting upon primitive particles in space, to make the worlds spin and generate harmonic knowledge to guide the evolution of ethical, emotional thought.

In 2008, The Times Literary Supplement included ‘The Two Cultures and the Scientific Revolution’ by C P Snow in its list of the 100 books that most influenced Western public discourse since the Second World War. It is crucial that we now heed the warning by the molecular biologist, Sir C P Snow, during his 1959 Reid Lecture at Cambridge University, that unless science and art are again reunited, despite modern science’s primitive belief in the universal heat death extinction law, then civilisation will be destroyed.



Source by Robert Pope

09 May

Ancient Greek Impact on Mathematics

Greek Impact on Western Civilization

Ancient Greece has been one of the greatest civilization’s to have ever flourished because of its enormous impact it had on Western Civilization.

The Classical Age of Greece (8th century BC – 146 BC) was characterized by colonization and Homer’s Iliad and the Odyssey were the first two greatest epics in world literature.

During the Golden Age of Greece in the 5th century BC, the greatest artistic, literary, architectural, scientific, philosophical and sporting achievements took place.

Historians, Herodotus and Thucydides, Hippocrates, the Father of Medicine and the philosophers, Plato and Socrates all lived and worked in 5th-century BC Athens.

Today, we can gaze at the arcthitectural wonders of ancient Greece and gain an insight to the wisdom of ancient Greek philosophers.

The Hellenistic Age (4th to 1st century BC) was Alexander the Great’s legacy to the world when Greek culture dominated the Mediterranean and Middle East and Greek became the international language.

Hellenistic Alexandria

From about 350 B.C. the center of mathematics moved from Athens to Hellenistic Alexandria, a port city in northern Egypt, founded in 331-BC by Alexander the Great and built by his chief architect, Dinocrates of Rhodes.

Rhodes Island is famous for the Colossus of Rhodes, a 33-metre-high statue of the Greek sun-god Helios which straddled the harbor of the city and was one of the Seven Wonders of the Ancient World.

The Greek, Ptolemaic dynasty ruled Egypt (from 305 to 30 BC) during the Hellenistic Period.

Cleopatra VII Philopator (69 – 30 BC), was a descendant of its founder Ptolemy I Soter, a Macedonian, Greek general of Alexander the Great.

The Great Library of Alexandria was one of the largest libraries of the ancient world and its Museum had scholars such as Euclid (Greek mathematician and “Father of Geometry”) and Eratosthenes (Greek mathematician, geographer and chief librarian) who worked there.

Importance of Mathematics

There are two periods of Greek mathematics:

1. The Classical Period (600-B.C. to 300-B.C.)

2. The Alexandrian or Hellenistic Period (300-B.C. to 300-A.D.)

The word “mathematics” is derived from the ancient Greek word “mathema” which means “knowledge or learning” and is the study of numbers, shapes and patterns.

It deals with logic of reason, quantity, arrangement, sequence and almost everything we do today.

Famous Greek Mathematicians and Their Contributions

Pythagoras of Samos (570 BC – 495 BC)

Pythagoras of Samos is the Father of the famous “Pythagoras theorem”, a mathematical formula which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

Samos was famous in antiquity for its navy, wine, and sanctuary to Hera, a goddess in ancient Greek mythology.

Pythagoras taught that Earth was a sphere in the center of the universe and that the paths of the planets were circular.

Pythagoreanism

Pythagoras founded Pythagoreanism which made important developments in mathematics, astronomy, and the theory of music.

Many 6th, 5th, and 4th-century’s most prominent Greek thinkers are labeled Pythagoreans such as Parmenides, Plato and Aristotle.

Plato (428/427 or 424/423 – 348/347-BC) was an Athenian philosopher during the Classical period in Ancient Greece who founded the Platonist school of thought and the Academy, the first institution of higher learning in the Western world.

Parmenides of Elea (late 6th or early-5th-century BC) was a pre-Socratic Greek philosopher from Elea in Magna Graecia (“Greater Greece,” meaning Greek-populated areas in Southern Italy) who founded metaphysics (branch of philosophy that examines the fundamental nature of reality).

Euclid of Alexandria (around 300 – 270-BC)

Euclid is the father of geometry (Euclidean geometry) who was active in Alexandria during the reign of Ptolemy I (323-283 BC).

He made revolutionary contributions to geometry and introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof.

His book, Elements, served as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the early 20th century.

Archimedes of Syracuse (287 – 212-BC)

Archimedes is the Father of mathematics and is considered the greatest mathematician of antiquity.

He lived in the Greek city of Syracuse, Sicily, his birthplace.

His father, Phidias was a mathematician and astronomer.

Archimedes revolutionised geometry and his methods anticipated the integral calculus (its applications include computations involving area, volume, arc length, center of mass, work, and pressure).

He is also known for the invention of compound pulleys and the Archimidean screw pump device (machine used for transferring water from a low-lying body of water into irrigation ditches).

Thales of Miletus (624-620 – 548-545-BC)

Miletus was an ancient Greek city in Ionia, Asia Minor (now modern Turkey).

Thales was a pre-Socratic philosopher, mathematician and astronomer, renowned as one of the legendary Seven Wise Men, or Sophoi, of antiquity.

He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry.

Aristotle (384 – 322-BC)

Aristotle was born in Stagira, an ancient Greek city near the eastern coast of the peninsula of Chalkidice of Central Macedonia.

Aristotle was a pupil of Plato and made contributions towards Platonism.

He was a polymath (knowledge spans many subjects) during the Classical period of Ancient Greece which included mathematics, geology, physics, metaphysics, biology, medicine and psychology.

He was the founder of the Lyceum, the Peripatetic school of philosophy, and the Aristotelian tradition.

Aristotle tutored Alexander the Great and established a library which aided in the production of hundreds of books.

From his teachings, Western Civilization inherited its intellectual lexicon on almost every form of knowledge.

Diophantus of Alexandria (around 200 – 214-AD – 284 and 298-AD)

Greek mathematician, known as the father of algebra and the compilation of a series of books called Arithmetica dealing with solving algebraic equations.

He was the first Greek mathematician to recognize fractions as numbers.

Eratosthenes of Cyrene (276 – 194-BC)

Cyrene was an ancient Greek city in Libya and founded in 631-BC.

Eratosthenes was a Greek mathematician, geographer, poet, astronomer, and music theorist who became the chief librarian at the Library of Alexandria.

His work involved the study of geography and he introduced some of the terminology still used today.

Eratosthenes correctly calculated the circumference of the earth and the tilt of the Earth’s axis.

Hipparchus of Nicaea (190 – 120-BC)

Nicaea was an ancient Greek city in Anatolia, Asia Minor (now modern Turkey).

Hipparchus was a Greek astronomer, geographer, and mathematician who made many mathematical contributions.

He was the founder of trigonometry and the first mathematical trigonometric table.

Hipparchus was also the first to develop a reliable method to predict solar eclipses.

Heron of Alexandria (10 – 70-AD)

Heron is considered the greatest experimenter of antiquity and is remembered for Heron’s formula, a way to calculate the area of a triangle using only the lengths of its sides.

He was also an important geometer (mathematician who specializes in the study of geometry) and who invented many machines including a steam turbine.

Ptolemy of Alexandria (100 – 170-AD)

Ptolemy was a Greek mathematician, astronomer and geographer who wrote several scientific researches.

The Great treatise is one of his renowned works now known as Almagest on astronomy.

His world map, published as part of his treatise Geography in the 2nd century, was the first to use longitudinal and latitudinal lines.

Hypatia of Alexandria (355 – 415-BC)

Hypatia, the daughter of a mathematician, was the first woman known to have taught mathematics and to make valuable contributions in the field of mathematics.

She was also a philosopher who taught as the head at a school, the knowledge of Plato and Aristotle.

Hypatia was the first woman to pursue her dreams and became an inspiration to many young women.

Antiphon of Rhamnus (480 – 411-BC)

Rhamnus, an ancient Greek city in Attica, a historical region of Athens, is situated on the coast, overlooking the Euboean Strait.

Antiphon was the earliest of the ten Attic orators, and an important figure in 5th-century Athenian political and intellectual life.

He was the first to give an upper and lower bound for the values of Pi by inscribing and then circumscribing a polygon around a circle and finally proceeding to calculate the polygons areas. The method was applied to squaring the circle.



Source by Andrew Papas

09 Apr

Mathematics and Physics Think Tanks – What is the Best Size of the Group?

Did you know a good many of the most influential think tanks in the world are all about the mathematical analytics involved in problem-solving? Indeed these think tanks use mathematical equations to figure out the most appropriate solution to the major economic, military, energy, and infrastructure challenges that face mankind. Why is this you ask? Well, it has a lot to do with coming to a conclusion without making a mistake, and stacking the deck in your favor based on probability of a positive outcome.

Of course, to do this, first you need to know which mathematical equations to use. But that requires an entirely different type of think tank. It requires a think tank that is all about the math, and not about the given problems. In other words you have to develop the proper math first, before you can solve anything. Therefore, if a group of individuals are trying to come up with the best solution they would first refer to the mathematics arm of the group to give them the proper analytical basis.

Now then, helping one determine what the size of a physics or mathematics think group should actually be is not so easy? Well it turns out that we need to refer back to the group iteself, and calculate what the best size group might be for that area of science. It turns out there is a mathematical equation which determines the best size for a mathematical mastermind group. Isn’t that interesting? And believe it or not, statistically it has been proven that the size of these groups matters more than you might ever believe.

In fact, there was an interesting article published recently in Physics World, written by the News Editor Michael Banks which was titled; “Why 13 and 25 are Magic Numbers for Physicists” and posted online on June 9, 2011. The article explained that there is actually a mathematical basis for the efficiency of success in experimental physics groups and mathematical think tanks. You see if the group is too small, there tends not to be the big breakthroughs, but if it is too large the personalities, egos, and debates take up too much time and less will get done, sometimes nothing gets done. The article states;

“Two physicists have, for the first time, quantified how the increasing size of research groups in physics affects the quality of the work it can produce. They conclude that the best group size for experimental physicists is around 25 researchers, while in theoretical physics the number is 13. Adding more researchers to the group over these sizes does not result in an increase in research quality.”

The other day, I was speaking to a College Professor working on a research paper that could revolutionize human mathematics, and introduce some rather intriguing geometrical shapes as the basis for calculating quantum computing problems, and also solving mathematical proofs that have been deemed nearly impossible to prove so far. Indeed, perhaps even come up with endless new proofs and launch a whole new branch of mathematics. In discussing this completely intriguing concept with him, we determined we needed a special think tank to do it.

In this case study it makes sense to find a 13 of the top analytical mathematics scientists if indeed we expect the project to be viable, and come up with adequate solutions. In any case, I hope you will please consider the importance of mathematics in the proper running of our civilization. Think on it.



Source by Lance Winslow

10 Mar

Should the Teaching of Mathematics in Secondary Schools Be Resource Based?

Traditionally, the teaching of Mathematics in secondary schools rarely included the use of resources other than a text book. This was “satisfactory” because most of the student body was academically included. In today’s jargon, using Gardener’s learning styles; they were most likely maths-logic learners.

The prevailing pedagogue was “Chalk and Talk”. In simple terms it was lecture style approach followed by lots of worked exercises from simple to harder (more complex) examples. There was little or no attempt to teach problem solving skills needed to solve unfamiliar problems.

With the introduction of all students into secondary education in the mid twentieth century, the steady raising of the school leaving age and the expectation of parents that their offspring get the opportunity to seek university qualifications mathematics teachers had to work with students who could not learn just with the “Chalk and Talk” approach. Many able learners found that Mathematics seemed to have no real life meaning to them and they sought, when allowed, to leave their Mathematics classes for other subjects.

The “Chalk and Talk” approach did not help the slow learner to absorb the Mathematics that they needed to survive as a citizen in modern society. Behaviour problems abounded in Mathematics classrooms.

It became obvious to teachers and administrators and syllabus writers that vast changes needed to be made in the teaching of Mathematics. In Australia, corporations were crying out for problem solvers. They found Mathematics graduates were not. This prompted syllabus writers to look at the teaching approaches that would not only lead students to become real problem solvers but pedagogue that would enhance the learning of those who were not maths-logic learners. This also meant that assessment procedures should reflect the ways in which particular topics were taught.

Added to all of this was the advent of the calculator, (four operations, scientific and graphics calculators) which meant that much more in the way of real life problems could be incorporated in a mathematics lesson. The computer added further to this. At the same time, the time allocated to the teaching of Mathematics was being reduced particularly in secondary schools with other subject disciplines gaining that time.

The technology revolution meant there were topics in the Mathematics syllabus that were redundant and thus removed. The field of Mathematics had expanded. The study of probability and statistics had expanded dramatically and was widely used in the community. Consequently, many new topics were added to the syllabus to reflect modern developments in Mathematics and its use in the community.

Many of these new topics were not conducive to “Chalk and Talk”. Some required a hands-on approach; others needed the use of multi-media; and still other required the use of technology. Internet became a valuable resource for real life problems. Technology often allowed the teacher to work at greater depth in less time with their students.

Some of these resources could be used successfully in non-traditional assessment items. These assessment techniques often allowed the non-maths-logic thinkers to gain greater success.

More importantly, more students were beginning to become more interested and more successful in Mathematics. Teachers began to see less behaviour problems in their classrooms and greater on task work by students.

Thus it became obvious to educators in Mathematics that the pedagogue required to teach Mathematics to all students in secondary schools required Mathematics department to create their own set of physical resources to create the best possible learning experiences for their students. So the answer to the title of the article “Should the Teaching of Mathematics in Secondary Schools be Resource Based?” must be an emphatic “YES”.



Source by Richard D Boyce

08 Feb

The Reality And Non-Reality Of Mathematics

There’s little doubt that mathematics rules the reality roost when it comes to the laws, principles and relationships within the sciences in general and the physical sciences in particular. Further, mathematics plays a dominant role when it comes to the purely economic aspects of our lives and where would sports be without statistics? However, when it comes down to brass tacks, how much of really real reality is actually reflected in our mathematics?

The Reality of Mathematics.

Mathematics is just a shorthand mental concept that simulates reality, or approximates reality or a possible reality or even an imaginary / impossible ‘reality’. Mathematics is NOT reality itself. You can mathematically manipulate the alleged extra dimensions in String Theory but that doesn’t mean of necessity that these extra dimensions actually exist.

Mathematics is a tool that at first approximation tries to reflect upon the nature of really real reality. Mathematics is not reality itself. Further, our mathematics are structured to reflect our version of reality based on our observations not of necessity what really happens. The perfect example is Quantum Mechanics. For example, we may not know, even cannot know even in principle, exactly where a particle is as well as at the same time where it is going with 100% precision. So we invent a form of probability mathematics like the Schrodinger Equation or the equation that governs the Heisenberg Uncertainty Principle. Those equations are for our edification but they don’t alter the really real reality fact that the particle has actual coordinates and is going from A to B. Probability in Quantum Mechanics, and the mathematical equations associated with it, are just reflections on the limits of the human observer and human instrumentation, not a reflection on Mother Nature’s really real reality. Our Quantum Mechanical equations are imposed approximations to really real reality much like Newton’s equation for gravitational attraction was really only in hindsight an approximation.

There can be multiple models of reality, each based on mathematics, but they can’t all be right. Cosmology is a case in point.

The phrase “but the mathematics works” means absolutely nothing. Just because mathematics predicts the possibility of some kind of structure and substance, or some law, relationship or principle that the Cosmos might have, does not of necessity make it so. A prime example where the mathematics worked but the Cosmos didn’t go along for the ride was the ad-hoc piling on those epicycles upon epicycles in order to explain the motion of the planets. It finally got so unwieldy that the baby was thrown out with the bathwater and a new baby conceived, that being that the Earth was just another planet and not at the center of life, the Universe and everything. Once it was postulated that the Earth went around the Sun, planetary motion fell into place – mathematically into place as well.

Take a more modern example. The mathematics works in String Theory, but to date String Theory remains a theorists’ theoretical dream (accent or emphasis on the word “dream”).

Probability theory is that branch of mathematics that interposes itself between the macro human and human comprehension and abilities and the micro world of quantum mechanics. That has way more to do with the macro than with the micro since the absolutes of the micro aren’t visible in the realm of the macro; they are beyond the realm of the macro to resolve through no fault by the way of human comprehension or abilities.

A prime example is that there is no probability in quantum mechanics, only probability introduced by the limitations of the conscious mind to get down and dirty to the level of detail required to eliminate the concept of probability from quantum mechanics.

Mathematics serves no purpose, useful or otherwise, outside of the context of the human mind (specifically) or outside of the intellectual conscious minds of other sentient species (in general), thus making allowances for E.T. and maybe the terrestrial great apes; whales and dolphins; and perhaps other advanced minds – perhaps elephants as well as some birds.

In the absence of any conscious minds, what use has the Universe for arithmetic, geometry, trigonometry, calculus, topology, statistics and the multi other branches of mathematics? Now 1 + 1 = 2 might be universally the case and logically true even in the absence of any conscious mind, or before any life form ever came to pass, but so what? That cuts no mustard with the Universe! There was nobody around to conceive of that or to make use of that or to equate the manipulation of numbers as a reflection of universal reality (or even non-reality*). There was no conscious or intellectual mind around to appreciate any mathematical utility or usefulness or beauty or elegance.

Mathematics in fact is not a reflection on or of reality, only that reality as observed or defined once having been filtered through sensory apparatus thus pondered over by the conscious mind. Reality as perceived in the mind is several transitional layers of processing removed from whatever pure external reality there happens to be. There’s even an additional layer if instrumentation is a middleman. So the conscious mind is thus limited in terms of its ability to come to terms with the full scope of really real reality.

Mathematics is the interface between humans and human comprehension, understanding, etc. of the Cosmos at large. Mathematics can tell you in actuality or theoretically the ‘what’ but never the ‘how’ or the ‘why’. For example, there’s Newton’s Law of Gravity, but even he realized that that equation just told you ‘what’, not ‘how’ or ‘why’.

The Non-Reality of Mathematics.

The following examples are some of what I term the non-realities of mathematics.

* Hyper-cubes are a nice abstract concept that mathematics / geometry can incorporate. However, while you might be able to play with real cubes, like dice, hyper-cubes will be forever beyond you.

* Stephen Hawking’s concept of negative time. Since IMHO time is just change and change is just motion, then negative time would have to be negative change and negative motion. That doesn’t make any sense at all. So while Hawking’s negative time might be useful in a mathematical sense, it has no bearing on our reality and can safely be ignored.

* Lots of quantum mechanical equations yielded up infinities so a sleight-of-hand concept called re-normalization was invented to deal with those cases involving infinities. That strikes me as dealing cards from under the table or otherwise known as a inserting a “fudge factor”. Does re-normalization represent really real reality?

* The mathematics of singularities inherent at the moment of the Big Bang or in Black Holes goes down the rabbit hole in that the laws, principles and relationships inherent in the physical sciences that are so otherwise adequately described mathematically now break down when trying to describe singularities and thus so does the accompanying mathematics that are involved as well. So what actually is the really real reality behind singularities?

* Mathematics are perfectly capable of dealing with alleged extra dimensions inherent in String Theory. However, that doesn’t make String Theory a reality, not does it make a half-dozen extra and hidden dimensions a reality.

* Mathematics is perfectly capable of dealing with an inverse cube law that has no correspondence with our physics. Just because a mathematical equation works doesn’t mean that there is a one-on-one correspondence to the real physical world.

* Mathematics are perfectly capable of dealing with zero, one and two dimensions yet these are just mental concepts that can’t actually be constructed and thus have no really real reality.

* Space-Time: Since space is just an immaterial mental concept (that imaginary container that actual physical stuff has to reside in) and since time is also just an immaterial mental concept (our way of coming to terms with change which is just motion – which is also an immaterial mental concept since motion itself isn’t composed of anything physical), then space-time has to be an immaterial mental concept. Neither space nor time nor space-time is actually composed of any material substance and the trilogy has no material 3-D structure. However, the mathematics involving the concept of space-time are a useful tool in describing reality, but not actually really real reality itself.



Source by John Prytz