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Showing posts with label Raphael. Show all posts
Showing posts with label Raphael. Show all posts

Tuesday, February 11, 2014

The Monochord


Pythagoras in School of Athens
  
A monochord is an ancient musical and scientific laboratory instrument. It is also the class-name for any musical stringed instrument having only one string (such as the Vietnamese Đàn bầu). The word "monochord" comes from the Greek and means literally "one string." In a true monochord, a single string is stretched over a sound box. The string is fixed at both ends while one or many movable bridges are manipulated to demonstrate mathematical relationships between sounds.
[Slide 3-3: Closeup of Tablet, Bouleau. Janson, H. W. History of Art. (Fifth Edition.NY: Abrams, 1995). p.497
Raphael’s School of Athens shows Pythagoras is explaining the musical ratios to a pupil. Notice the tablet. It shows the words diatessaron, diapente, diapason. The roman numerals for 6, 8, 9, and 12, showing the ratio of the intervals, same as in the music book frontispiece.The word for the tone, ΕΠΟΓΛΟΩΝΕΠΟΓΛΟΩΝΕΠΟΓΛΟΩΝΕΠΟΓΛΟΩΝ, at the top. Under the tablet is a triangular number 10 called the sacred tetractys]

 The monochord can be used to illustrate the mathematical properties of musical pitch. For example, when a monochord's string is open it vibrates at a particular frequency and produces a pitch. When the length of the string is halved, and plucked, it produces a pitch an octave higher and the string vibrates at twice the frequency of the original (2:1) About this sound Play . Half of this length will produce a pitch two octaves higher than the original—four times the initial frequency (4:1)—and so on. Standard diatonic Pythagorean tuning (Ptolemy’s Diatonic Ditonic) is easily derived starting from superparticular ratios, (n+1)/n, constructed from the first four counting numbers, the tetractys, measured out on a monochord.[citation needed]


The Divine Monochord, from Fludd’s Utriusque Cosmi Maioris Scilicet et Minoris Metaphysica (1617)

The name "monochord" is sometimes incorrectly applied to an instrument with one open string and a second string with a movable bridge; however, such a two-string instrument is properly called a bichord. With two strings you can easily demonstrate how various musical intervals sound. Both open strings are tuned to the same pitch, and then the movable bridge is put in a mathematical position to demonstrate, for instance, the major third (at 4/5th of the string length) About this sound Play  or the minor third (at 5/6th of the string length) About this sound Play .

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SEE:Infinite Fire Webinar II - The Emblemata of the Atalanta Fugiens by Dr. Peter J. Forshaw



See: Atalanta fugiens

Saturday, February 08, 2014

Saturday, March 05, 2011

Novum Organum

The frontispiece of Novum Organum by Francis Bacon



The Novum Organum is a philosophical work by Francis Bacon published in 1620. The title translates as "new instrument". This is a reference to Aristotle's work Organon, which was his treatise on logic and syllogism. In Novum Organum, Bacon details a new system of logic he believes to be superior to the old ways of syllogism. This is now known as the Baconian method.

For Bacon, finding the essence of a thing was a simple process of reduction, and the use of inductive reasoning. In finding the cause of a phenomenal nature such as heat, one must list all of the situations where heat is found. Then another list should be drawn up, listing situations that are similar to those of the first list except for the lack of heat. A third table lists situations where heat can vary. The form nature, or cause, of heat must be that which is common to all instances in the first table, is lacking from all instances of the second table and varies by degree in instances of the third table.

The title page of Novum Organum depicts a galleon passing between the mythical Pillars of Hercules that stand either side of the Strait of Gibraltar, marking the exit from the well-charted waters of the Mediterranean into the Atlantic Ocean. The Pillars, as the boundary of the Mediterranean, have been smashed through opening a new world to exploration. Bacon hopes that empirical investigation will, similarly, smash the old scientific ideas and lead to greater understanding of the world and heavens.

The Latin tag across the bottom is taken from the Book of Daniel 12:4. It means: "Many will travel and knowledge will be increased".

Contents

Bacon and the Scientific Method

Many argue that Bacon's work was instrumental in the historical development of the scientific method. Association of Bacon's name and the modern conception of the scientific method is, however, to be treated with caution. No where in Novum Organum does Bacon even use the word "method" to describe his prescription for the exercise of natural philosophy.[1] That being said, it is undeniable that his technique bears a resemblance to the modern formulation of the scientific method in the sense that it is centered on experimental research. Bacon's emphasis on the use of artificial experiments to provide additional observances of a phenomena can often support the conclusion that Bacon's process and the scientific method are one, but Bacon himself should not be considered "the Father of the Experimental Philosophy (such expressions are egregiously outmoded)..." [1]

Preface

Bacon begins the work with a rejection of pure a priori deduction for the uses of discovering truth in natural philosophy. Of his philosophy, he states:

"Now my plan is as easy to describe as it is difficult to effect. For it is to establish degrees of certainty, take care of the sense by a kind of reduction, but to reject for the most part the work of the mind that follows upon sense; in fact I mean to open up and lay down a new and certain pathway from the perceptions of the senses themselves to the mind."

The emphasis on beginning with observation pervades the entire work. In fact, it is in the concept that the natural philosophy must begin from the senses that we find a revolutionary quality of Bacon’s philosophy, and its consequent philosophical method, eliminative induction, is one of Bacon's most lasting contributions to science and philosophy.

Instauratio Magna

Novum organum was actually published as part of a much larger work, Instauratio magna. Originally intending Instauratio magna to contain six parts (of which Novum organum constituted the second), Bacon did not come close to completing his metawork, as parts V and VI were never written at all. Novum organum, written in Latin and consisting of two books of aphorisms, was included in the volume that Bacon published in 1620; however, it was also unfinished, as Bacon promised several additions to its content which ultimately remained unprinted.

Book I

(Bacon titled this first book Aphorisms Concerning the Interpretation of Nature, and the Kingdom of Man)

In the first book of aphorisms, Bacon criticizes the current state of natural philosophy. The object of his assault consists largely in the syllogism, a method that he believes to be completely inadequate in comparison to what Bacon calls “true Induction:”

“The syllogism is made up of propositions, propositions of words, and words are markers of notions. Thus if the notions themselves (and this is the heart of the matter) are confused, and recklessly abstracted from things, nothing built on them is sound. The only hope therefore lies in true Induction.” (aph. 14)
In many of his aphorisms, Bacon reiterates the importance of inductive reasoning. Induction, methodologically opposed to deduction, entails beginning with particular cases observed by the senses and then attempting to discover the general axioms from those observations. In other words, induction presupposes nothing. Deduction, on the other hand, begins with general axioms, or first principles, by which the truth of particular cases is extrapolated. Bacon emphasizes the strength of the gradual process that is inherent in induction:
“There are and can only be two ways of investigating and discovering truth. The one rushes up from the sense and particulars to axioms of the highest generality and, from these principles and their indubitable truth, goes on to infer and discover middle axioms; and this is the way in current use. The other way draws axioms from the sense and particulars by climbing steadily and by degrees so that it reaches the ones of highest generality last of all; and this is the true but still untrodden way.” (aph. 19)

After many similar aphoristic reiterations of these important concepts, Bacon presents his famous Idols.

The Idols

Novum organum, as suggested by its name, is focused just as much on a rejection of received doctrine as it is on a forward-looking progression. In Bacon's Idols are found his most critical examination of man-made impediments which mislead the mind's objective reasoning. They appear in previous works but were never fully fleshed out until their formulation in Novum organum:
Idols of the Tribe

“Idols of the Tribe are rooted in human nature itself and in the very tribe or race of men. For people falsely claim that human sense is the measure of things, whereas in fact all perceptions of sense and mind are built to the scale of man and not the universe.” (aph. 41)

Bacon includes in this the idol the predilection of the human imagination to presuppose otherwise unsubstantiated regularities in nature. An example might be the common historical astronomical assumption that planets move in perfect circles.

Idols of the Cave

“Idols of the Cave belong to the particular individual. For everyone has (besides vagaries of human nature in general) his own special cave or den which scatters and discolours the light of nature. Now this comes either of his own unique and singular nature; or his education and association with others, or the books he reads and the several authorities of those whom he cultivates and admires, or the difference impressions as they meet in the soul, be the soul possessed and prejudiced, or steady and setteled, or the like; so that the human spirit (as it is allotted to particular individuals) is evidently a variable thing, all muddled, and so to speak a creature of chance...” (aph. 42)

This idol stems from the particular life experiences of the individual. Variable educations can lead the individual to a preference for specific concepts or methods, which then corrupt their subsequent philosophies. Bacon himself gives the example of Aristotle, “who made his natural philosophy a mere slave to his logic.” (Aph. 54)

Idols of the Market

“There are also Idols, derived as if from the mutual agreement and association of the human race, which I call Idols of the Market on account of men's commerce and partnerships. For men associate through conversation, but words are applied according to the capacity of ordinary people. Therefore shoddy and inept application of words lays siege to the intellect in wondrous ways.” (aph. 43)

Bacon considered these “the greatest nuisances of the lot” (aph. 59). Because humans reason through the use of words, they are particularly dangerous because the received definitions of words, which are often falsely derived, can cause confusion. He outlines two subsets of this kind of idol and provides examples (aph 60).

First, there are those words which spring from fallacious theories, such as the element of fire or the concept of a first mover. These are easy to dismantle because their inadequacy can be traced back to the fault of their derivation in a faulty theory. Second, there are those words that are the result of imprecise abstraction. Earth, for example, is a vague term that may include many different substances the commonality of which is questionable. These are terms are often used elliptically, or from a lack of information or definition of the term.

Idols of the Theatre

“Lastly, there are the Idols which have misguided into men's souls from the dogmas of the philosophers and misguided laws of demonstration as well; I call these Idols of the Theatre, for in my eyes the philsophies received and discovered are so many stories made up and acted out stories which have created sham worlds worth of the stage.” (aph. 44)

These idols manifest in the unwise acceptance of certain philosophical dogmas, namely Aristotle's sophistical natural philosophy (aph. 63) which was corrupt by his passion for logic, and Plato's superstitious philosophy, which relied too heavily on theological principles.

Book II

After enumerating the shortcomings of the current and past natural philosophies, Bacon can now present his own philosophy and methods. Bacon retains the Aristotelian causes, but redefines them in interesting ways. While traditionally the final cause was held as most important among the four ( material, formal, efficient, and final), Bacon claims that it is the least helpful and in some cases actually detrimental to the sciences(aph. 2). For Bacon, it is the formal cause which is both the most illusive and most valuable, although each of the causes provides certain practical devices. By forms and formal causes, Bacon means the universal laws of nature. To these Bacon attaches an almost occult like power:

“But he who knows forms grasps the unity of nature beneath the surface of materials which are very unlike. Thus is he able to identify and bring about things that have never been done before, things of the kind which neither the vicissitudes of nature, nor hard experimenting, nor pure accident could ever have actualised, or human thought dreamed of. And thus from the discovery of the forms flows true speculation and unrestricted operation” (aph. 3).

In this second book, Bacon offers an example of the process that of what he calls true induction. In this example, Bacon attempts to grasp the form of heat.

The first step he takes is the surveying of all known instances where the nature of heat appears to exist. To this compilation of observational data Bacon gives the name Table of Essence and Presence. The next table, the Table of Absence in Proximity, is essentially the opposite—a compilation of all the instances in which the nature of heat is not present. Because these are so numerous, Bacon enumerates only the most relevant cases. Lastly, Bacon attempts to categorize the instances of the nature of heat into various degrees of intensity in his Table of Degrees. The aim of this final table is to eliminate certain instances of heat which might be said to be the form of heat, and thus get closer to an approximation of the true form of heat. Such elimination occurs through comparison. For example, the observation that both a fire and boiling water are instances of heat allows us to exclude light as the true form of heat, because light is present in the case of the fire but not in the case of the boiling water. Through this comparative analysis, Bacon intends to eventually extrapolate the true from of heat, although it is clear that such a goal is only gradually approachable by degrees. Indeed, the hypothesis that is derived from this eliminative induction, which Bacon names The First Vintage, is only the starting point from which additional empirical evidence and experimental analysis can refine our conception of a formal cause.

The "Baconian method" does not end at the First Vintage. Bacon described numerous classes of Instances with Special Powers, cases in which the phenomena one is attempting to explain is particularly relevant. These instances, of which Bacon describes 27 in Novum Organum, aid and accelerate the process of induction. They are “labour-saving devices or shortcuts intended to accelerate or make more rigorous the search for forms by providing logical reinforcement to induction.” [1]

Aside from the First Vintage and the Instances with Special Powers, Bacon enumerates additional "aids to the intellect" which presumably are the next steps in his "method." In Aphorism 21 of Book II, Bacon lays out the subsequent series of steps in proper induction: including Supports to Induction, Rectification of Induction, Varying the Inquiry according to the Nature of the Subject, Natures with Special Powers, Ends of Inquiry, Bringing Things down to Practice, Preparatives to Inquiry, and Ascending and Descending Scale of Axioms. These additional aids, however, were never explained beyond their initial limited appearance in Novum Organum. It is likely that Bacon intended them to be included in later parts of Instauratio magna and simply never got to writing about them.

As mentioned above, this second book of Novum organum was far from complete and indeed was only a small part of a massive, also unfinished work, the Instauratio magna.

Bacon and Descartes

Bacon is often studied through a comparison to his contemporary René Descartes. Both thinkers were, in a sense, some of the first to question the philosophical authority of the ancient Greeks. Bacon and Descartes both believed that a critique of preexisting natural philosophy was necessary, but their respective critiques proposed radically different approaches to natural philosophy. While “one was rational and theoretical in approach and was headed by Rene Descartes; the other was practical and empirical and was led by Francis Bacon.” [2] They were both profoundly concerned with the extent to which human’s can come to knowledge, and yet their methods of doing so projected diverging paths.

On the one hand, Descartes’ begins with a doubt of anything which cannot be known with absolute certainty and includes in this realm of doubt the impressions of sense perception, and thus, “all sciences of corporal things, such as physics and astronomy." [2] He thus attempts to provide a metaphysical principle (this becomes the Cogito) which cannot be doubted, on which further truths must be deduced. In this method of deduction, the philosopher begins by examining the most general axioms (such as the Cogito), and then proceeds to determine the truth about particulars from an understanding of those general axioms.
Conversely, Bacon endorsed the opposite method of Induction, in which the particulars are first examined, and only then is there a gradual ascent to the most general axioms. While Descartes doubts the ability of the senses to provide us with accurate information, Bacon doubts the ability of the mind to deduce truths by itself as it is subjected to so many intellectual obfuscations, Bacon's “Idols.” In his first aphorism of New organum, Bacon states:

“Man, the servant and interpreter of nature, does and understands only as much as he has observed, by fact or mental activity, concerning the order of nature; beyond that he has neither knowledge nor power.” (aph. 1)

So, in a basic sense the central difference between the philosophical methods of Descartes and those of Bacon can be reduced to an argument between deductive and inductive reasoning and whether to trust or doubt the senses. However, there is another profound difference between the two thinkers' positions on the accessibility of Truth. Descartes was obsessed with absolute Truth—indeed it seems to be the object of his aims. It is slightly ambiguous whether Bacon believed such a Truth can be achieved. In his opening remarks, he proposes “to establish progressive stages of certainty.” For Bacon, a measure of truth was its power to allow predictions of natural phenomena (although Bacon's forms come close to what we might call "Truth," because they are universal, immutable laws of nature).

Original Contributions

An interesting characteristic of Bacon's apparently scientific tract was that, although he amassed an overwhelming body of empirical data, he did not make any original discoveries. Indeed, that was never his intention, and such an evaluation of Bacon's legacy may wrongfully lead to an unjust comparison with Newton. Bacon never claimed to have brilliantly revealed new unshakable truths about nature—in fact, he believed that such an endeavor is not the work of single minds but that of whole generations by gradual degrees toward reliable knowledge.[1]

In many ways, Bacon's contribution to the advancement of human knowledge lies not in the fruit of his scientific research but in the reinterpretation of the methods of natural philosophy. His undeniable innovation is best encapsulated in The Oxford Francis Bacon:

“Before Bacon where else does one find a meticulously articulated view of natural philosophy as an enterprise of instruments and experiment, and enterprise designed to restrain discursive reason and make good the defects of the senses? Where else in the literature before Bacon does one come across a stripped-down natural-historical programme of such enormous scope and scrupulous precision, and designed to serve as the basis for a complete reconstruction of human knowledge which would generate new, vastly productive sciences through a form o eliminative induction supported by various other procedures including deduction? Where else does one find a concept of scientific research which implies an institutional framework of such proportions that it required generations of permanent state funding to sustain it? And all this accompanied by a thorough, searching, and devastating attack on ancient and not-so-ancient philosophies, and by a provisional natural philosophy anticipating the results of the new philosophy?”[1]

External links

References

  1. ^ a b c d e Rees, Graham and Maria Wakely The Instauratio magna Part II: Novum organum and Associated Texts. Oxford: Clarendon, 2004. Print
  2. ^ a b Cantor, Norman F., and Peter L. Klein. Seventeenth-Century Rationalsim: Bacon and Descartes. Massachusetts: Blaisdell, 1969. Print
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In center, while Plato - with the philosophy of the ideas and theoretical models, he indicates the sky, Aristotle - considered the father of Science, with the philosophy of the forms and the observation of the nature indicates the Earth. Many historians of the Art in the face correspondence of Plato with Leonardo, Heraclitus with Miguel Angel, and Euclides with Twine agree.

See Also:

Inside Out

Monday, January 04, 2010

The Dance to Truth

While searching for familiarity on the terminology of Phenomenology, the greater question settled on my mind as to what Nature itself means.
Undoubtedly we have no questions to ask which are unanswerable. We must trust the perfection of the creation so far, as to believe that whatever curiosity the order of things has awakened in our minds, the order of things can satisfy. Every man's condition is a solution in hieroglyphic to those inquiries he would put. He acts it as life, before he apprehends it as truth. In like manner, nature is already, in its forms and tendencies, describing its own design. Let us interrogate the great apparition, that shines so peacefully around us. Let us inquire, to what end is nature  NATURE---Emerson, Ralph Waldo, 1803-1882

I would of course direct one's attention to the question of what Nature can mean here then. How we live with it and how it is applied to our circumstance for it to be "a truth for which we live and breathe."  "Walk the Talk" and live according too, is a measure of our judicial process  as to the finality of the road travelled with regards to our own life.

So what is the way in which you would perceive the road too, and how would you draw such a picture to best describe what you are seeing "as the way leading"  to a common front regarding predictions of science?

Dr. Roger Penrose, Oxford University

The idea of the predictions of science have to have a course in which to follow that accurately describes the process to which such predictions are made. Now, this kind of abstraction is correlated in my mind as to the way in which one could map the mind and the road toward such prediction,  and in following such a road, lead all to imagine that after such a journey, a verse can be expounded upon as to to what can possibly materialize out of such a "cloud gathering, " or a, "Light bulb" moment.


While giving this consideration,  such experimental processes were telling to me of where and what we were doing by focusing our attention directionally to a time in the fractions of second,  as to detail the very understanding of how the Universe came to be,  and how such correlation could have been spotted in the neural connection,  as if a space,  to which all information could enter.




But we know relatively little about how the circuitry of the brain represents the consonants and vowels. The chasm between the neurosciences today and understanding representations like language is very wide. It's a delusion that we are going to get close to that any time soon. We've gotten almost nowhere in how the bee's brain represents the simplicity of the dance language. Although any good biologist, after several hours of observation, can predict accurately where the bee is going, we currently have no understanding of how the brain actually performs that computation.

The thing was,  you had to provide that space in order to raise the question of what could have arisen out of it. What that space actually means. Now,  are these things real or imagined facets of the natural world,  or,  are they measurable things that we have been lead too, to direct our attention, and not call it some fictional representative of a wild Bumble bee Dance?

Thursday, August 13, 2009

Raphael's Dissertation on Age and Youth?



School of Athens by Raphael

In center, while Plato - with the philosophy of the ideas and theoretical models, he indicates the sky, Aristotle - considered the father of Science, with the philosophy of the forms and the observation of the nature indicates the Earth. Many historians of the Art in the face correspondence of Plato with Leonardo, Heraclitus with Miguel Angel, and Euclides with Twine agree.


In a reflective occasion drawn to the center of the picture of Raphael, I am struck by the distinction of "age and youth" as I look at Plato and Aristotle. Of what has yet to descend into the minds of innovative and genuine science thinkers to know that the old man/woman works in concert with the science of youth, and this is something yet has still to unfold.


This drawing in red chalk is widely (though not universally) accepted as an original self-portrait. The main reason for hesitation in accepting it as a portrait of Leonardo is that the subject is apparently of a greater age than Leonardo ever achieved. But it is possible that he drew this picture of himself deliberately aged, specifically for Raphael's portrait of him in The School of Athens.See:Leonardo da Vinci


Why, when it is understood that Leonardo Da Vinci's face is emblazoned on the likes of Plato by Raphael? It's to call attention to Leonardo's inventiveness that one might speculate as to what "descends into any mind" that has been prep by and stands in concert, side by side with Aristotle of science?


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PLato saids,"Look to the perfection of the heavens for truth," while Aristotle saids "look around you at what is, if you would know the truth" To Remember: Eskesthai

The ole wo/man represent all the possibilities of ingenuity as one moves to place their question. When it sinks deep into the vast reservoir of quantum descriptive world" it will then make sense that all things follow what has been put before the mind.

Friday, August 08, 2008

William Thurston

Xianfeng David Gu and Shing-Tung Yau
To a topologist, a rabbit is the same as a sphere. Neither has a hole. Longitude and latitude lines on the rabbit allow mathematicians to map it onto different forms while preserving information.


William Thurston of Cornell, the author of a deeper conjecture that includes Poincaré’s and that is now apparently proved, said, “Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide,” explaining that curiosity is tied in some way with intuition.

“You don’t see what you’re seeing until you see it,” Dr. Thurston said, “but when you do see it, it lets you see many other things.”
Elusive Proof, Elusive Prover: A New Mathematical Mystery

Some of us are of course interested in how we can assign the relevance to perceptions the deeper recognition of the processes of nature. How we get there and where we believe they come from. As a layman I am always interested in this process, and of course, life's mysteries can indeed be a motivating factor. Motivating my interest about the nature of things that go unanswered and how we get there.


William Paul Thurston
(born October 30, 1946) is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields medal for the depth and originality of his contributions to mathematics. He is currently a professor of mathematics and computer science at Cornell University (since 2003).


There are reasons with which I present this biography, as I did in relation to Poincaré and Klein. The basis of the question remains a philosophical one for me that I question the basis of proof and intuition while considering the mathematics.

Mathematical Induction

Mathematical Induction at a given statement is true of all natural numbers. It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.

The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science.

Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of deductive reasoning and is fully rigorous
.


Deductive reasoning

Deductive reasoning is reasoning which uses deductive arguments to move from given statements (premises), which are assumed to be true, to conclusions, which must be true if the premises are true.[1]

The classic example of deductive reasoning, given by Aristotle, is

* All men are mortal. (major premise)
* Socrates is a man. (minor premise)
* Socrates is mortal. (conclusion)

For a detailed treatment of deduction as it is understood in philosophy, see Logic. For a technical treatment of deduction as it is understood in mathematics, see mathematical logic.

Deductive reasoning is often contrasted with inductive reasoning, which reasons from a large number of particular examples to a general rule.

Alternative to deductive reasoning is inductive reasoning. The basic difference between the two can be summarized in the deductive dynamic of logically progressing from general evidence to a particular truth or conclusion; whereas with induction the logical dynamic is precisely the reverse. Inductive reasoning starts with a particular observation that is believed to be a demonstrative model for a truth or principle that is assumed to apply generally.

Deductive reasoning applies general principles to reach specific conclusions, whereas inductive reasoning examines specific information, perhaps many pieces of specific information, to impute a general principle. By thinking about phenomena such as how apples fall and how the planets move, Isaac Newton induced his theory of gravity. In the 19th century, Adams and LeVerrier applied Newton's theory (general principle) to deduce the existence, mass, position, and orbit of Neptune (specific conclusions) from perturbations in the observed orbit of Uranus (specific data).


Deduction and Induction



Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.


Back to the lumping in of theology alongside of Atlantis. Rebel dreams, it is hard to remove one's colour once they work from a certain premise. Atheistic, or not.

Seeking such clarity would be the attempt for me, with which to approach a point of limitation in our knowledge, as we may try to explain the process of the current state of the universe, and it's shape. Such warnings are indeed appropriate to me about what we are offering for views from a theoretical standpoint.

The basis presented here is from a layman standpoint while in context of Plato's work, brings some perspective to Raphael's painting, "The School of Athens." It is a central theme for me about what the basis of Inductive and deductive processes reveals about the "infinite regress of mathematics to the point of proof."

Such clarity seeking would in my mind contrast a theoretical technician with a philosopher who had such a background. Raises the philosophical question about where such information is derived from. If ,from a Platonic standpoint, then all knowledge already exists. We just have to become aware of this knowledge? How so?

Lawrence Crowell:
The ball on the Mexican hat peak will under the smallest perturbation or fluctuation begin to fall off the peak, roll into the trough and the universe tunnels out of the vacuum or nothing to become a “something.”


Whether I attach a indication of God to this knowledge does not in any way relegate the process to such a contention of theological significance. The question remains a inductive/deductive process?

I would think philosophers should weight in on the point of inductive/deductive processes as it relates to the search for new mathematics?

Allegory of the Cave

For me this was a difficult task with which to cypher the greater contextual meaning of where such mathematics arose from. That I should implore such methods would seem to be, to me, in standing with the problems and ultimates searches for meaning about our place in the universe. Whether I believe in the "God nature of that light" should hold no atheistic interpretation to my quest for the explanations about the talk on the origins of the universe.

See:

  • The Sound of Billiard Balls

  • Mathematical Structure of the Universe
  • Monday, February 11, 2008

    Inside Out

    3.1 As Cytowic notes, Plato and Socrates viewed emotion and reason as in a kind of struggle, one in which it was vitally important for reason to win out. Aristotle took a more moderate view, that both emotion and reason are integral parts of a complex human soul--a theory proposed by Aristotle in explicit opposition to Platonism (De Anima 414a 19ff). Cytowic appears to endorse the Platonic line, with the notable difference that he would apparently rather have emotion win out.




    I am trying to "create a image" that will use the one above. It is important that the select quoted comment below is understood. This can't be done without some reference.

    So while the exercise may be going on "inside" things are happening on the outside. Scientists have never been completely honest with themselves, while some may concern themselves with whose name said what?


    I use Plato as a namesake obviously, because of what I saw of some of our influential minds speaking, all the while making inferences to Plato. When ever you read something that resonates with you, it is of value because it correlates to something that you already know. This is what I tried to get across in the previous post, about what is "self evident." Little do some people recognize that while I may have inferred the point of some philosophical foundations, it is not without recognizing that the "qualitative phrases" have to be reduced as well to a logic. To reason.

    How do you do that? Well I'll tell you what I found and then you can think whether I understood reason in it's proper format. Whether I understood the "shadows of Plato" to mean something other then what could have been interpreted as being wrong. What is that analogy of the Cave really mean?

    Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.


    Yes I did not enter the halls of higher learning in the traditional ways. You can converse for many years, does not mean you become devoid of the lessons that spoken amongst the commentors. How is it you can think that while listening to scientists you cannot uncover the the processes they use? If I had given thirty years to study, what exactly had I studied? I am a doctor of nothing.:)

    This is a torus (like a doughnut) on which several circles are located. Unlike on a Euclidean plane, on this surface it is impossible to determine which circle is inside of which, since if you go from the black circle to the blue, to the red, and to the grey, you can continuously come back to the initial black, and likewise if you go from the black to the grey, to the red, and to the blue, you can also come back to the black.

    My quote at Backreaction on this and that, reveals not only part of the understanding gained through this "infinite regress," but also the understanding we have with the world around us. Some would be better served to see the image of the Klein bottle, but I wanted to show what is going on in a "abstract way" to what is happening inside of us, and at the same time, what is happening outside.



    I had used the brain and head as a place of our conscious awareness within context of our environment, our bodies. The topological explanations of the numbers above, and used them in the next paragraph. There will be confusion with the colour lines, please disregard that.

    While I talked of the emotive and mental realities. I included the spiritual development in the end. The way this interaction takes place, is sometimes just as the mental function(yellow). Other times, it is the emotive realization of the experience. It is coloured by our emotion(red).

    While we interact with our environment, there is this turning inside out, continuously. Sometimes we may say that "1" is the emotive realization, while the number 2 is seen as a mental extension of the situation. While the areas overlap each other, an outward progression may mean that the spiritual progress is numbered 4, while the interaction of the emotive, mental and spiritual progression may be number 3. Ultimately the spiritual progression is 4 (Violet). All these colours can mix and are significant in themself. They reveal something about our very constitution.

    While some may wonder how could any conceptualization ever integrate the "Synesthesia views" of the world when it sees itself presented with such a comparison? The journey of course leads to the "Colour of Gravity." Discard your body, and one will wonder about the "clear light." What it means, in the "perceptive state of existence." If one is prepared, then one shall not have "to much time on their hands" getting lost in the fog.

    Plato and Aristotle, Up and Down by Kelley L. Ross, Ph.D.

    Rafael has Plato pointing up and Aristotle gesturing down to indicate the difference in their metaphysics. For Plato, true existence is in the World of Forms, in relation to which this world (of Becoming) is a kind of shadow or image of the higher reality. Aristotle, on the other hand, regards individual objects in this world as "primary substance" and dismisses Plato's Forms -- except for God as a pure actuality, without matter.

    However, when it comes to ethics and politics, the gestures should be reversed. Plato, like Socrates, believed that to do the good without error, one must know what the good is. Thus, we get the dramatic moment in the Republic where Plato says that philosophers, who have escaped from the Cave and come to understand the higher reality, must be forced to return to this world and rule, so that their wisdom can benefit the state. Aristotle, on the other hand, says that the "good" is simply the goal of various particular activities, without one meaning in Plato's sense. The particular activities of most human affairs involve phronésis, "practical wisdom." This is not sophía, true wisdom, for Aristotle, which involves the theoretical knowledge of the highest things, i.e. the gods, the heavens, and God.

    Thus, for philosophy, Aristotle should point up and would represent a contemplative attitude that was certainly more congenial to religious practices in the Middle Ages. By the same token, Aristotle's contribution to what we now think of as science was hampered by his lack of interest in mathematics. Although Aristotle in general had a more empirical and experimental attitude than Plato, modern science did not come into its own until Plato's Pythagorean confidence in the mathematical nature of the world returned with Kepler, Galileo, and Newton. For instance, Aristotle, relying on a theory of opposites that is now only of historical interest, rejected Plato's attempt to match the Platonic Solids with the elements -- while Plato's expectations are realized in mineralogy and crystallography, where the Platonic Solids occur naturally.

    Therefore, caution is in order when comparing the meaning of the metaphysics of Plato and Aristotle with its significance for their attitudes towards ethics, politics, and science. Indeed, if the opposite of wisdom is, not ignorance, but folly, then Socrates and Plato certainly started off with the better insight.


    It is good that you go to the top of the page of the linked quotes of Kelley L. Ross. You must know that I developed this site without really understanding the extent Mr. Ross had taken this issue. There is much that is familiar, and with him, an opposing view too.

    See:

  • Induction and Deduction
    Intuitively Balanced: Induction and Deduction
  • Friday, April 13, 2007

    Housebuilding



    It all start off as "a dream" or "an idea." Where do these come from? Dialogos of Eide


    This is the house similar to what we will be constructing, with some modifications of course.

    Most know of my time helping my son last year constructing his home. The journey of pictures that I have here within this bloggery. It has also some "dimensional aspect" in it's development, so I thought this might help those who are working Euclidean coordinates, may help to seal this process in some way, by being introduced to house construction.

    This is the home that my wife and I had built in 1998. It was built on ten acres of land with a wide sweeping view of the mountains in the background. Although not seen here, you may have seen some of my rainbow pictures that I had put up over the years to help with the scenery we had.

    Well the time has come for my wife and I to be entering into the venture ourselves. You will notice that the model we choose above is one floor. We thought this suitable for the coming years as when we move into retirement.

    Here is a picture of my daughter-in-law and son's house in the winter of this last year. He still has some work to do, but as per our agreement, I help him, he is helping me.

    I think I am getting the better of the deal, as he has taken the time to write me a 17 page step procedure with which I must follow. I thought this will become part of the journey for my wife and myself, so that everyone may see the process unfolding and maybe learn something about home construction. The plans of course change from country to country, while this plan is unfolding in Canada.

    We purchased a 2 acre parcel of land with which to build the new home up top. I went into the bush with the camera and with about 2 feet of snow. It was not to easy to get around, so as time progresses,and as I put in the roadway and cleared site, you will get a better idea of what it looks like.



    We had to contend with where we will live. We wanted the freedom and space to be close to where we will be building, so we bought a 19' foot travel trailer and will be putting it on the acreage while we build our new home. We thought of "renting" and our son of course offered for a time to let us live with him. We thought all around with the new baby Maley, we would leave them have their space as well.

    Laying the Foundation

    Articles on Euclid

    See No Royal Road to Geometry?

    I would like people to take note of the image supplied on the website of Euclides.Org, as it is one that I have used showing Plato and Aristotle. The larger picture of course is one done by Raphael and is painted on the wall in the "Signatores room in the Vatican."

    The Room of the Segnatura contains Raphael's most famous frescoes. Besides being the first work executed by the great artist in the Vatican they mark the beginning of the high Renaissance. The room takes its name from the highest court of the Holy See, the "Segnatura Gratiae et Iustitiae", which was presided over by the pontiff and used to meet in this room around the middle of the 16th century. Originally the room was used by Julius II (pontiff from 1503 to 1513) as a library and private office. The iconographic programme of the frescoes, which were painted between 1508 and 1511, is related to this function. See Raphael Rooms

    While one may of talked abut the past, or use a name like Plato of the past does not mean that what is being supplied from that position is not dealing with information for the 21st century. I would like you to think that while speaking about models that what the house is doing in "a psychological sense" is giving you a method by which all that you do in your life will materialize in consciousness and digs deep into the unconscious.

    How often had you seen yourself in dream time, doing something or other, in the living room, kitchen, or anything that deals with the current state of mind, that you of course will see in this house? They are the many rooms of the mind.

    All those who have written histories bring to this point their account of the development of this science. Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of those of Theatetus, and putting in irrefutable demonstrable form propositions that had been rather loosely established by his predecessors. He lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. It is also reported that Ptolemy once asked Euclid if there was not a shorter road to geometry that through the Elements, and Euclid replied that there was no royal road to geometry. He was therefore later than Plato's group but earlier than Eratosthenes and Archimedes, for these two men were contemporaries, as Eratosthenes somewhere says. Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)


    See also Laying the Foundation with Respect While one indeed had to start somewhere I thought I would start here with, "Foundational Perspectives."

    I choose this as an introduction, whilst I will be starting from the ground up. This will include the planning of road way and building site. Since I have this interest about physics and where science is going these days, how could I not incorporate these things into what I am doing currently with my life now? So while I speak about the science end, I am encapsulating "this process" with regard to how I will construct my home.

    Is this possible?

    Well having spoken of the "Euclidean reference" one would have to know how one departs form such a scheme of Euclid, to know that this graduation to Non-Euclidean geometries was somehow related to the "fifth postulate" written by Euclid.

    So of course, we had those who were involved in this development historically, which serve to remind us about where someone like Dali may of been as a visionary, in terms of Time. Or "geometrically inclined" to higher dimensional figures.

    It definitely had it's connotations to "points of view." I mentioned religion, but for the nature of Salvador Dali, and his lifestyle, one would have to wonder where he was going with the Tesserack and his painting of Jesus on the Cross?

    While I do not subscribe to any religion per say, I do subscribe to the finger of Plato pointing up. Have you for one moment you thought to roll your eyes up in your head, and think of what is up their in your mind? Assign our highest values to goodness. Surely you would enlist the "Colour of gravity" in all situations as you choose to live your life? It's there for the choosing.

    Surely, that if you wore a hat on your head, or thought, to think of the roof of your house, you may indeed think of the highest ideals with which you choose to live your life. It's not my job to tell you what that is, that is yours alone.

    You will be involved with aspects of the "universal language" that knows no boundaries, no matter your race, gender, or nationality. Yet, it will be specific to you. It will have "probabilistic outcomes" according to the life you are living regardless.

    The Secret of the Golden Flower

    When ever you walk the pathways in your mind of what ever model, you are laying the road work for that which you will travel through. Why, I may have referred to the title of the "Golden Flower in the Bee story," is a result, that the probabilistic outcome of life calls upon this "chance meeting" to come to what is held in mind. So what's new having the honey of the Bee community?

    Do the Bee dance, and you learnt from others what this model is doing. So you travel. You get the benefits of the honey sometimes in new thoughts? There had to be a point "like the blank slate, glass room, a pen and paper ready" in order for the mind to be receptive to what already exists out there in the "form of ideas." How will these manifest? So indeed, it came from deep inside/outside you?

    I never thought this inductive/deductive method while thinking it topological smooth in it's orientation, was not the exchange going on with our environment. That if you live your life according to your principles, then the principles would become part of your life. That on a level not understood to clearly, the "colour of gravity" was what we could evolve too? What is our own dynamical makeup, to become part of the ideals we had set for ourselves. We set our own ship in life. The boat or vehicle, becomes part of the way we will travel in our dream time. The airplane we ride.

    Friday, April 06, 2007

    Craftsman of Plato

    Time is of your own making;
    its clock ticks in your head.
    The moment you stop thought
    time too stops dead.
    Angelus Silesius
    See Status of Warp Drive Smolin had some deep questions and relevance "about" time? :)

    Some "updates" within this article. Mainly for all those "couch potatoes" who watch Law and Order. I remembered Sean Carroll's portrayal as well on Preposterous Universe when Clifford showed the picture from "the lecture" Clifford is showing today.

    Dark Matter and Dark Energy: from the Universe to the Laboratory-Conclusion

    See comment here

    Good show


    Are Cosmologists Couch Potatoes?

    Your asking for simplicity and without a geometrical/topological approach(quantum gravity), the cosmos from surveillance and interrogation, and without further introspection, it leaves one with a nice comfortable view, as is.

    That's nice, for those who want to sit back and watch the show:)

    That fellow, does he have his binoculars backwards!Hmmmmm:)How would this lensing affect his view of the stake out? So close, yet so far away?
    plato | Homepage | Mon, February 21, 2005 @ 3:22 pm | #


    Maybe Clifford is a Seer? Or, is he a Craftsman who became a seer, like Lee Smolin? Well, we'd have to delve into the reason a seer "became" or could possibly "become?"

    The Craftsman

    BEHOLDING beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities, for he has hold not of an image but of a reality, and bringing forth and nourishing true virtue to become the friend of God and be immortal, if mortal man may. Would that be an ignoble life? PLATO


    If one had given their whole life to rote and memorization, how much smarter would they be, if they did not allow themselves to be "filled?" It is as if the universe said "look at the emptiness. This cannot be so?" It was at that moment the mind fills with all these "wonderful things" as if all that had taken place was ignited into a new view of the world. It is literally not the same world for them?

    Tabula rasa (Latin: scraped tablet or clean slate) refers to the epistemological thesis that individual human beings are born with no innate or built-in mental content, in a word, "blank", and that their entire resource of knowledge is built up gradually from their experiences and sensory perceptions of the outside world. See Tabula rasa: The Glass Room

    Predictions? Every tone spoken as if this new change took place, realized, that having enter a part of reality that was somehow away from, yet, existed in the reality until discovered. Coxeter shared these same views? So, every kind of geometry you know of, already exists, and is just waiting to be discovered. You had to be able to tap into the probabilities. You were always preparing the stage.


    Timaeus:

    Genesis Timaeus 27c-34a

    First then, in my judgment, we must make a distinction and ask, What is that which always is and has no becoming; and what is that which is always becoming and never is? That which is apprehended by intelligence and reason is always in the same state; but that which is conceived by opinion with the help of sensation and without reason, is always in a process of becoming and perishing and never really is. Now everything that becomes or is created must of necessity be created by some cause, for without a cause nothing can be created.
    See Timaeus:Laying the Ground rules on Genesis

    The Mechanism

    See "The Cosmological Constant and the String Landscape by Joe Polchinski (UCSB, KITP)"

    So one has to take into account the perspective being developed by others before we get to where we have some kind of mechanism of tunnelling the landscape? Is it right or not, to have a "potential hill" have evidence of some kind, having been traverse? You would then think, hmmm... the blackhole as a horizon?

    Three Ring Circus: Dark Energy

    "Of course this information is based on 2003 data but the jest of the idea here is that in order to go to a "fast forward" the conditions had to exist previously that did not included "sterile neutrinos" and were a result of this "cross over."


    What reason did Lee Smolin called the string theorists craftsman? I think part of the fun for me is when somebody who sits out front in terms of being a science director of a kind, then one is immediately thinking "okay, why did he say this."

    See The Entropic Principle by Raphael Bousso (UC Berkeley)

    Now, why did he say that? Yes, it would be easier to go to him and get the reason right from the person's mouth. But hey their busy, and I do not want to be on the list of those knocking on doors being pesky. Besides, that's part of the fun of doing the detective work and trying to understand the basis of any argument they may have.

    The Demiurge (Creator)

    Literally, “craftsman.” The creator of Plato’s physical world is not a divine intelligence or a personal ruler, but (as it were) a manual laborer. Cf. Vlastos, Plato’s Universe (pp. 26-27):

    That the supreme god of Plato’s cosmos should wear the mask of a manual worker is a triumph of the philosophical imagination over ingrained social prejudice. ... But this divine mechanic is not a drudge. He is an artist or, more precisely, what an artist would have to be in Plato’s conception of art: not the inventor of new form, but the imposer of pre-existing form on as yet formless material.


    The Seer

    So we now know to a degree how Lee Smolin assigned the Craftsman, but little is said about the Seer? The Seer, is one who knows how to use that blank slate. Knows how to find the departure point and is asking to be filled?

    If there are any runners out there, you might know the "depletion point" one can reach after having expended the energy, one gains a sense of this new influx of energy and well being? Having once know these times in my youth, I am sad to say, I am to old to be ever running like I did.

    So one sees the community is suffering and leaders in despair as to how new ideas can be generated and new ways to invigorate science come to the forefront. Is the privileged few who see themself pertaining to some model, that one would now say, hey they are getting all the incentives and the idea here about nurture is suffering?

    No, there must be special way to invigorate the scientists of the future? Allow them to empty themselves after the intense involvement, to allow the mind, when empty to be filled?

    (Thanks Bee for asking the question By the way, "Happy Easter" to you and Stefan)

    Thursday, April 05, 2007

    Nurturing Creativity

    See here and here


    It looks as if moderation, or maybe technical problems, has set in for me at Cosmic Variance. So I have to go from the last statement made there by Lee that I was allowed to contribute. To continue with the points I am making.

    I was glad to see Jacques was continuing where David B seems to have decided the futility of dealing with these issues of the String theory backlash.

    Lee Smolin:When there was little selection we naturally got a wide diversity of types of scientists, which was good for science. My view is that we need that diversity, we need both the hill climbers and the valley crossers, the technical masters and the seers full of questions and ideas.

    Raphael Bousso and Joseph Polchinski in "The String Theory Landscape" September 2004 Scientific issue speak exactly to what Lee is saying and descriptively allow us to see the pattern underlying Lee's comment. Maybe George Musser will release it for the group to inspect here

    Take full note of the diagrams.

    See OFF THE HOOK. Line-by-line crocheting instructions that tell where to increase or decrease numbers of stitches create the global shape of the Lorenz manifold.Univ. of Bristol

    Clifford:Hooking Up Manifolds
    The artlcle goes a great deal into the story of how mathematician Hinke Osinga and her partner mathematician Bernd Krauskopf got into this, and why they find it useful. You’ll also hear from mathematicians Carolyn Yackel, Daina Taimina, and Sarah-Marie Belcastro. This has been going on for a while, and there are even published scientific papers with crocheting instructions for various manifolds! How did I miss out on this?! This is great!


    If you did not continue with understanding the "topography of the energy involved" in terms of what the string theory landscape was doing, then you would have never understood the "hills and valleys" in the context of string theory landscape being described?

    HYPERBOLIC FABRIC. Many of the lines that could be inscribed on this crocheted hyperbolic plane curve away from each other, defying Euclid's parallel postulate.
    Taimina


    IN retrospect decisions we make will always resound with what we should have done, but that misses the boat when coming to the "creative abilities?" What we see may "institute a productive research group?" You exchange one for another?

    Lee Smolin:Is string theory in fact perturbatively finite? Many experts think so. I worry that if there were a clear way to a proof it would have been found and published, so I find it difficult to have a strong expectation, either way, on this issue.

    The fact that a way had been describe in terms of developing the "Triple Torus" speaks to the continued development of the string theory landscape? How could you conclusively finish off this statement and then from it describe the state of the union, when this had already been explained technically?

    We say that E8 has rank 8 (the maximum number of mutually commutative degrees of freedom), and dimension 248 (as a manifold). This means that a maximal torus of the compact Lie group E8 has dimension 8. The vectors of the root system are in eight dimensions, and are specified later in this article. The Weyl group of E8, which acts as a symmetry group of the maximal torus by means of the conjugation operation from the whole group, is of order 696729600.


    You had to see the context of the triple torus in relation too where the string landscape places were placing these modular forms. If I had said E8 and the continued development of modular form, what would this represent?

    The complexity of the forms themself are limited and finite so how could one claim that such work on the landscape is futile in regards to infinities?