Subscribe Google Whatsapp Pinterest Digg Linkedin Stumbleupon Vk Print Delicious Buffer Pocket Xing Tumblr Mail Yummly Telegram Flipboard Advertisement We have become quite used to pronouncements of doom, from scientists predicting the sixth mass extinction due to the measurable effects of climate change, and from religionists declaring the apocalypse due to a surfeit of sin. But in the early days of the scientific revolutionthe days of Shakespeare contemporary Francis Baconand later 17th century Descartes it was not at all unusual to find both kinds of reasoning, or unreasoning, in the same person, along with beliefs in magic, divination, astrology, etc. Yet even in this maelstrom of heterodox thought and practices, Sir Isaac Newton stood out as a particularly odd co-existence of esoteric biblical prophecy, occult beliefs, and a rigid, formal mathematics that not only adhered to the inductive scientific method, but also expanded its potential by applying general axioms to specific cases.
However, this ebook will answer that question in a more complicated way. I am interested in how mathematics "works" -- in some sense I am interested in how Mathematics is implemented as a language, whereas most just "use" it and are not interested on examining it in detail or systematically.
On the other hand, I am very well aware of the many efforts within and outside of mathematics looking at notions of complexity or theoretical characterizations of logic that have been applied to mathematics and logic before.
For example, Kolmogorov and Chaitin complexity or Topos theorymodel theorydomain theoryand paraconsistent logic are interesting and useful knowledge domains that can contribute to an examination of mathematics.
However, what is the point of mathematics? Mathematics is a language. This issue will become more important as time goes on. The crisis in Physics, with string theory having no experimental basis other than what has been discovered before e.
All they can do is throw words at the problem -- those fuzzy meaning things -- those slippery things -- in the form of natural language, no different than lawyers and politicians or similar criminals.
Of course, they can ignore or be oblivious to the problem, like politicians.
Albert Einstein I quickly came to recognize that my instincts had been correct; that the mathematical universe had much of value to offer me, which could not be acquired in any other way. I saw that mathematical thought, though nominally garbed in syllogistic dress, was really about patterns; you had to learn to see the patterns through the garb.
I learned that it was from such patterns that the insights and theorems really sprang, and I learned to focus on the former rather than the latter. Richard Feynman In theory, there is no difference between theory and practice. In practice there is.
Yogi Berra Much of mathematics was developed by "non" mathematicians -- Archimedes, Newton, and Gauss are considered the giants of mathematics, significantly used the natural world to create their ideas in mathematics.
The problem of addressing "function" as opposed to structure has not been done well in mathematics. The field of economics has tried to use conventional mathematics, and has generated many baroque "theories" of little use except creating academic empires or meteoretic financial groups e.
Biology and evolution involve more dynamic and functional questions, and mathematics will need to go beyond structural ideas to progress significantly.
No doubt the vast majority of mathematicians will not be interested, hence it might be better to not characterize the development as mathematics or metamathematics. Maybe a neo-logism is more appropriate: There are many measures and characterizations of complexity and power of expressiveness that have been applied to both to computation, logic, and mathematics, but most of the time those characterizations or measures have concentrated on the thing that mathematics and logic tries to represent, rather than trying to look very closely at the thing mathematics and logic that it can represent -- the thing -- reality.
I will address these various incarnations as to their role, later. It should be noted that the more complex the numbers, as in quaternions or octonions, the more information that is embedded implicitly. However, how much of that information is random information?
And what does one MEAN by "random" -- again "random" is a "word. As a start, there seems a balance of information between order and disorder when generating mathematical ideas and looking at their consequences.
Gregory Chaitin has shown that within number theory some facts or "theorems" are essentially "random. Abandon the Shannon I am interested mathematics from a global informational and semantic point of view.
All of these approaches are important and I will eventually put them in context. One may think this is a bad rap, a glib strawman characterization on my part, but for now I ask you to suspend your suspicions, in this regard, for a while.
I will explore the notions of material complexityfunctional complexity and lastly comparative complexity. To explain what I mean by that last relatively obscure sentence, I need to delve into mathematics, physics, biology, computer science, and their history.
I will try to explain this in the ebook, but for now I will introduce a story about normed division algebras, that I think illustrates the circle of ideas that encompass the issue.
The interplay between tensorsa generalization of vectors, and the form of normed division algebrasis an interesting story to examine. It will take a few chapters to explain this, for this is the crux of the problem. To give you a flavor what I mean, in the realm of mathematics, I will briefly examine some of the pre-history of the concept tensor, and the opposing roles of W.
Hamilton and Oliver Heaviside. The quickest way to broach this problem is to quote John Baeztaken from his paper Octonions.John Napier: John Napier, Scottish mathematician and theological writer who originated the concept of logarithms as a mathematical device to aid in calculations. At the age of 13, Napier entered the University of St.
Andrews, but his stay appears to have been short, and he left without taking a degree. Little. Latest breaking news, including politics, crime and celebrity. Find stories, updates and expert opinion.
Mathematics Itself: Formatics - On the Nature, Origin, and Fabrication of Structure and Function in Logic and Mathematics. Yet faith in false precision seems to us to be one of the many imperfections our species is cursed with.
Leonhard Euler was born on 15 April , in Basel, Switzerland to Paul Euler, a pastor of the Reformed Church, and Marguerite née Brucker, a pastor's daughter. He had two younger sisters: Anna Maria and Maria Magdalena, and a younger brother Johann Heinrich.
. The Early Life of Leonard Euler and His Potential in Mathematics PAGES WORDS 4, View Full Essay. More essays like this: Not sure what I'd do without @Kibin - Alfredo Alvarez, student @ Miami University.
Exactly what I needed. - Jenna Kraig, student @ . The purpose of this paper is to highlight the work of an extraordinary mathematician Leonhard Paul Euler and thereby motivate the mathematics lovers to go through his works.