Epistemology

“Some people have difficulty with accepting Plato’s mathematical world as being in any sense ‘real’, and would gain no comfort from a view that physical reality itself is constructed from abstract notions. My own position on this matter is that we should take Plato’s world as providing a kind of ‘reality’ as mathematical notions (and as I’ve tried to argue for forcefully for in the case S1.3) but I might baulk at actually attempting to physically identify physical reality within the abstract reality of Plato’s world. I think that Fig. 34.1 best expresses my position on this question, where each of three worlds, Platonic-mathematical, physical and mental-has it’s own kind of reality, and where each is (deeply and mysteriously) found in one that precedes it ( the worlds take cyclicly). I like to think that, in a sense the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very existence through logic alone. Be that as it may, there is a further mystery, or paradox, of the cyclic aspect of these worlds , where each seems to be able to encompass the succeeding one in its entirety, while itself seeming to depend only upon a small part of its predecessor.”
(Page 1028-The Road to Reality- Roger Penrose- Borzoi Book, Alfred A. Knoff- 2004)

It was important to me to understand the differences here, and how I derived the ability of information of entering the location of the Synapse. While I had called it the Thinking Mind in relation to what is at the "tip of the Pyramid," it had to of course, go through a methodology before it could have said that all elements of the intuitive information gathered, was from a "idea of probabilities" that existed, yet, it is from that same location that all memories are stored.

"It was a matter of putting things together and ‘seeing’ the answer!" Roger Penrose- Shadows of the mind

The "infinite regress," was an inductive/deductive stance to developmental possibilities without having a mentorship around for consideration, and by developing "adhoc methods" in my search for knowledge, it became apparent any intuitive deduction/induction would had to be in face of all the information available from our experience and senses, as well as, what could exist from that place of "memories stored."

While the limitations of a life could had amounted to what is learnt in that life, it did not encompass what was possible from the storing of information from all of our lives. It did not encompass all that is stored in the "collective unconscious."

"To answer ‘by intuition’, is hardly satisfactory."Paul Benacerraf and Hillary Putnam

This of course requires a deeper critical analysis for my own understanding and development.


According to Plato, knowledge is a subset of that which is both true and believed

Epistemology or theory of knowledge is a branch of philosophy concerned with the nature and scope of knowledge. The term was introduced into English by the Scottish philosopher James Frederick Ferrier (1808-1864).[2]

Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims. In other words, epistemology primarily addresses the following questions: "What is knowledge?", "How is knowledge acquired?", and "What do people know?"

A priori and a posteriori (philosophy)

The terms "a priori" and "a posteriori" are used in philosophy to distinguish between deductive and inductive reasoning, respectively. Attempts to define clearly or explain a priori and a posteriori knowledge are part of a central thread in epistemology, the study of knowledge. Since the definitions and usage of the terms have been corrupted over time and therefore vary between fields, it is difficult to provide universal definitions of them. One rough and oversimplified explanation is that a priori knowledge is independent of experience, while a posteriori knowledge is dependent on experience. In other words, statements that are a priori true are tautologies.

Innatism

Innatism is a philosophical doctrine that holds that the mind is born with ideas/knowledge, and that therefore the mind is not a 'blank slate' at birth, as early empiricists such as John Locke claimed. It asserts therefore that not all knowledge is obtained from experience and the senses.

See:

The Synapse is a Portal of the Thinking Mind

Dennis William Sciama

Dennis William Siahou Sciama FRS (November 18, 1926–December 18, 1999) was a British physicist who, through his own work and that of his students, played a major role in developing British physics after the Second World War.

Sciama also strongly influenced Roger Penrose, who dedicated his The Road to Reality to Sciama's memory. The 1960s group he led in Cambridge (which included Ellis, Hawking, Rees, and Carter), has proved of lasting influence.

Sciama was elected a Fellow of the Royal Society in 1982. He was also an honorary member of the American Academy of Arts and Sciences, the American Philosophical Society and the Academia Lincei of Rome. He served as president of the International Society of General Relativity and Gravitation, 1980-84.

In 1959 he married Lidia Dina, a social anthropologist, who survived him, along with their two daughters.

Alma mater
University of Cambridge

Doctoral advisor
Paul Dirac


Doctoral students

John D. Barrow
George Ellis
Gary Gibbons
Stephen Hawking
Martin Rees
David Deutsch
Brandon Carter

It was important that I understood the context of the entry by Phil Warnell.

Phil:

However, if the second is taken as truth and all is remembering, then what can the force of gravity do to a memory that is not in any, yet of all? So if all were to collapse would the memory not persist, since it is not of what vanished. Strangely, Hawking proved it so and yet he still denies his mentor who advised not only that it would be so, yet why

Acquiring Knowledge

True creativity often starts where language ends.Arthur Koestler

                    Probabilties
                 (The Fifth Dimension)
                         |
                         |
                  Idea of the pipe
                        / \
                       /   \
                      /     \
                 Picture of the pipe
                    /         \
                   /           \
                  /             \
               The real pipe and form  
                                         

See: Betrayal of Images" by Rene Magritte

IN a sense having already lived a life, one can say indeed that with what you learnt, you are able to make an assessment of life, and "in retrospective" lived life according to what you had learnt. But it's not always that easy. How was I suppose to know that life would turn out this way?

Life's simple moment of question about a whole life can be reduced to say "that in every moment" what shall I have done better? So we had to look at how we had lived, and only then, do we know "now," what we shall do different in the future.




So this is the quest you could say about "acquiring knowledge." Left to our own means, we can look at our environment, and one would have to wonder about your interaction with it. Left to your own means, without having the college degree, or the avenues to proceed under mentored tutorship, how is it that you could move yourself to the very "stop off points" for consideration, while you had lived your life, and advanced the knowledge?

Arthur Koestler CBE (September 5, 1905, Budapest – March 3, 1983, London)

As one discovers certain aspects of "the character of our heroes," it is not for me to judge their character in this blog piece, for they will be left to their own demise without my participation of condemning them.

IN "weighing the heart and the feather," the horrors of our own lives will have been left for us to "project forward," what we wish to correct again in another life. This does not ever diminish the wrongs done, but provides for a chance to move ever closer to that source, by acceptance of the "fate" by our choice of a new certain future?

Hall of Ma'at

In art, the feather was shown in scenes of the Hall of Ma'at. This hall is where the deceased was judged for his worthiness to enter the afterlife. The seat of the deceased's soul, his heart, was weighed on a balance against the feather of Ma'at. If the heart was free from the impurities of sin, and therefore lighter than the feather, then the dead person could enter the eternal afterlife. Other gods in the judgement hall who were part of the tribunal overseeing the weighing of the heart were also pictured holding a feather.

See:Egyptian Myths

In all the wrongs of that character was there ever a "light that shined in a piece of knowledge" whilst the lives struggled toward a future?

Of Koestler’s many books, his powerfully anti-Communist novel Darkness at Noon (1941) is still the most famous, but he wrote one book that focused squarely on the paranormal – The Roots of Coincidence (1972). Here, he attempts to find a basis for paranormal events in coincidence, or more precisely synchronicity, so that there is only one phenomenon to explain rather than many. He proceeds to seek the roots of coincidence in the Alice-in-Wonderland world of quantum physics, the infinitesimally small subatomic realm where our everyday logic no longer holds sway, where particles can be waves and vice versa, where forces that only mathematical equations can glimpse swim in the dark, unfathomable ocean of probability before the manifestation of either matter or mind. Towards the end of the book, Koestler pleads that parapsychology be made “academically respectable and attractive to students”, otherwise the “limitations of our biological equipment may condemn us to the role of Peeping Toms at the keyhole of eternity”.

In the Mean Time

This is the thing that people do not understand and our youth especially. That while one may of liked to have lived like a Garrett Lisi, one would had to have known that life can be lived very simply. So, there is an answering to the needs of the lifestyle one is accustomed, to have allowed oneself to live "freely in your thoughts," to "make room," to advance your knowledge, while taking care of these necessities of life.

There's no way around it. There are no freebies that life can be made so easy, that you could surpass all that life holds for your viewing and participation. Too know, that there are many things we had to learn, not just the acquiring of the knowledge, but to had lived that life, and to have lived it to a much "higher standard." One we had entered this life to accomplish. Who is it, for us to say, what that plan was?

See:

Arthur Koestler and Creativity
The Soul=λόγος,θυμος,ἔρως

Dark Energy: Beyond Einstein Missions

Adept

Charles L. Bennett

"ADEPT will measure these supernovae, but its real advance lies in a new, more powerful technique. Patterns in temperature of the very young universe provide a 'standard ruler' that is imprinted on the pattern of galaxies across the sky. ADEPT aims to map these through space and time," according to Bennett

ADEPT promises to provide the galaxy positions needed to follow the historical development of the universe, so that astronomers can determine the role played by the dark energy. Bennett says that the ADEPT mission will help answer many questions about the role played by dark energy in both fundamental physics and cosmology. Jonathan Bagger, chair of the Johns Hopkins physics and astronomy department, agreed. "Twenty-first century physics is at a crossroads," he said. "Our fundamental theories of gravity and quantum mechanics are in conflict. Dark energy might point the way out."

See: for Concept Development-Lisa De Nike">NASA Selects Hopkins-led "ADEPT" Space Mission
for Concept Development

Destiny

Artist's rendition of the Destiny spacecraft-Image Credit: NASA/GSFC

Known as Destiny, the Dark Energy Space Telescope, the small spacecraft would detect and observe more than 3,000 supernovae over its two-year primary mission to measure the expansion history of the Universe, followed by a year-long survey of 1,000 square-degrees of the sky at near-infrared wavelengths to measure how the large-scale distribution of matter in the Universe has evolved since the Big Bang. Used together, the data from these two surveys will have 10 times the sensitivity of current ground-based projects to explore the properties of Dark Energy, and will provide data critical to understanding the origin of Dark Energy, which is poorly explained by existing physical theories.

“Destiny’s strength is that it is a simple, low-cost mission designed to attack the puzzling problem of Dark Energy directly with high statistical precision,” said Tod R. Lauer, the Principal Investigator for Destiny and an astronomer at NOAO. “We build upon grism technology used in the Hubble Space Telescope’s Advanced Camera for Surveys to help us provide spectra of the supernovae as well as images. Spectra are critical to diagnosing the properties of the supernova, but are very difficult to obtain with more traditional cameras. Destiny’s grism camera, however, will take simultaneous spectra of all objects in its field. This is a major advantage of our approach, which greatly increases the ability to detect and characterize these distant stellar explosions.”

See:NASA Funds Development of Destiny: The Dark Energy Space Telescope

Snap

NASA will support the SNAP mission concept for probing dark energy by observing distant Type Ia supernova and studying weak gravitational lensing.

SNAP, the SuperNova/Acceleration Probe, is an experiment designed to learn the nature of dark energy by precisely measuring the expansion history of the universe. At present scientists cannot say whether dark energy has a constant value or has changed over time — or even whether dark energy is an illusion, with accelerating expansion being due to a gravitational anomaly instead.

"SNAP will investigate dark energy using two independent and powerful techniques," says Saul Perlmutter of Berkeley Lab's Physics Division, a professor of physics at the University of California at Berkeley who is principal investigator of SNAP and leader of the international Supernova Cosmology Project based at Berkeley Lab. "The best proven and most powerful current technique is to determine changes in the expansion rate by comparing the redshift and distance of Type Ia supernovae, but we are also targeting the most promising complementary technique, called 'weak gravitational lensing.'"

See: SNAP Wins NASA Support for Joint Dark Energy Mission

WMAP Reveals Neutrinos, End of Dark Ages, First Second of Universe

WMAP cosmic microwave fluctuations over the full sky with 5-years of data. Colors represent the tiny temperature fluctuations of the remnant glow from the infant universe: red regions are warmer and blue are cooler. Credit: WMAP Science Team

NASA released this week five years of data collected by the Wilkinson Microwave Anisotropy Probe (WMAP) that refines our understanding of the universe and its development. It is a treasure trove of information, including at least three major findings:

WMAP cosmic microwave fluctuations over the full sky with 5 years of data. WMAP cosmic microwave fluctuations over the full sky with 5-years of data. Colors represent the tiny temperature fluctuations of the remnant glow from the infant universe: red regions are warmer and blue are cooler.

* New evidence that a sea of cosmic neutrinos permeates the universe
* Clear evidence the first stars took more than a half-billion years to create a cosmic fog
* Tight new constraints on the burst of expansion in the universe's first trillionth of a second

"We are living in an extraordinary time," said Gary Hinshaw of NASA's Goddard Space Flight Center in Greenbelt, Md. "Ours is the first generation in human history to make such detailed and far-reaching measurements of our universe."

Relative constituents of the universe today, and for when the universe was 380,000 years old, 13.7 billion years ago. Neutrinos used to be a larger fraction of the energy of the universe than they are now. Credit: WMAP Science Team

The Synapse is a Portal of the Thinking Mind

Life must be understood backwards; but... it must be lived forward.
Soren Kierkegaard

Penrose's Bermuda Triangle?

A long time ago I learnt about using avenues to free the mind by doing different things in the face of adversities. One can not always gauge their reaction to what life throws at them. I found this for me most certainly, and in face of the understanding of the "emotive struggle," it is moving "clarity to such thinking" of the thinking mind, that one would like to at least understand what influences these emotive consequences have on their thinking space.

The brain is a matter defined state of existence and is furthest from the source of expression. Yet, it houses avenues within the very nature of it's structure, to allow processes that may be comparative to me of what spaces can be created, as we create an open portal for all thinking minds avenues to new possible changes.




So I of course like to use a bubble in this context to to display the field around that thinking brain/Body to know that the emotive consequences lie within this field of expression.

It wasn't enough then that what was apparent to me, that the continued struggle I have of dealing with these emotive fluctuations is in our thinking minds, that the reactive states, were held in a place of a deeper repose while the collection of these things come from a history of living.

It was not enough that I knew of a map created by another of psychological stature and lead by scientific valuation, that it would lead to the understanding of Penfield's work on the structure of the brain.

Source:McGill University ArchivesWilder Graves Penfield, OM, CC, CMG, MD, FRS (January 25/26, 1891 – April 5, 1976) was an American-born Canadian neurosurgeon. See also:Wilder Penfield

So while I had given Stefan of Backreaction "a brief summary of it" there in the following quote below, it is in such a way this unfolds I had developed this understanding of "historical context" and now, work toward the future. This is why I like history, and why I used David Hilbert's quote. It signals "advancements in thinking" as we explore history in not only the context of who we are, but of our predecessor's mathematical development as well. The "gap created for such ingenuities" had to realize a "stop off point" for further developments. So we develop from that point, forward.

At 11:08 AM, March 13, 2008, Blogger Plato said. Historical Meme: Seven Things about Richard Carrington

Often we say things in our own lives not aware of the context and influence our parents have on us, yet, such concepts themself are transmitted and unknowingly we become the parent of our raising.

To change the cyclical nature of such events, and move to our own adult situations requires a deeper insight into who we are, that we might change the circumstance and reveal who it is, is talking, when acting in this role of our day to day.

That you may not have children now is not the issue and any young person might know then that we are also our parent, as well as, the child of that experience. It is how we shall choose as an adult to address society, each other, in these ways, that we change the future.

A lot of time if you are not aware of the internal structure this information is transmitted how would you know that it follows "another's mindmap" and you were not aware of it? So as glossy as this sounds "my writing" about our individual histories, we now know that we transmit part of our histories into the future.

Parent ego state


This is a set of feelings, thinking and behaviour that we have copied from our parents and significant others.


As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.


As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.


Adult ego state


The Adult ego state is about direct responses to the here and now. We deal with things that are going on today in ways that are not unhealthily influenced by our past.


The Adult ego state is about being spontaneous and aware with the capacity for intimacy. When in our Adult we are able to see people as they are, rather than what we project onto them. We ask for information rather than stay scared and rather than make assumptions. Taking the best from the past and using it appropriately in the present is an integration of the positive aspects of both our Parent and Child ego states. So this can be called the Integrating Adult. Integrating means that we are constantly updating ourselves through our every day experiences and using this to inform us.


In this structural model, the Integrating Adult ego state circle is placed in the middle to show how it needs to orchestrate between the Parent and the Child ego states. For example, the internal Parent ego state may beat up on the internal Child, saying "You are no good, look at what you did wrong again, you are useless". The Child may then respond with "I am no good, look how useless I am, I never get anything right". Many people hardly hear this kind of internal dialogue as it goes on so much they might just believe life is this way. An effective Integrating Adult ego state can intervene between the Parent and Child ego states. This might be done by stating that this kind of parenting is not helpful and asking if it is prepared to learn another way. Alternatively, the Integrating Adult ego state can just stop any negative dialogue and decide to develop another positive Parent ego state perhaps taken in from other people they have met over the years.


Child ego state


The Child ego state is a set of behaviours, thoughts and feelings which are replayed from our own childhood.


Perhaps the boss calls us into his or her office, we may immediately get a churning in our stomach and wonder what we have done wrong. If this were explored we might remember the time the head teacher called us in to tell us off. Of course, not everything in the Child ego state is negative. We might go into someone's house and smell a lovely smell and remember our grandmother's house when we were little, and all the same warm feelings we had at six year's of age may come flooding back.


Both the Parent and Child ego states are constantly being updated. For example, we may meet someone who gives us the permission we needed as a child, and did not get, to be fun and joyous. We may well use that person in our imagination when we are stressed to counteract our old ways of thinking that we must work longer and longer hours to keep up with everything. We might ask ourselves "I wonder what X would say now". Then on hearing the new permissions to relax and take some time out, do just that and then return to the work renewed and ready for the challenge. Subsequently, rather than beating up on ourselves for what we did or did not do, what tends to happen is we automatically start to give ourselves new permissions and take care of ourselves.


Alternatively, we might have had a traumatic experience yesterday which goes into the Child ego state as an archaic memory that hampers our growth. Positive experiences will also go into the Child ego state as archaic memories. The positive experiences can then be drawn on to remind us that positive things do happen.


The process of analysis's personality in terms of ego states is called structural analysis. It is important to remember that ego states do not have an existence of their own, they are concepts to enable understanding. Therefore it is important to say "I want some fun" rather than "My Child wants some fun". We may be in our Child ego state when we say this, but saying "I" reminds us to take responsibility for our actions.

Transactional Analysis theory was developed by Dr Eric Berne in the 1950's.

Intuitive Light Switches

So you can start off with thinking all about what Penrose had to say, and Max may have pushed this further, to wonder, how his structural interpretation may be compared to what the actual Mathematical Universe is saying. A Square? A soccer Ball. So today, it may be some Easter Egg interpretation?:)





See:

Venn Logic and TA

The Plato’s Cave Study: Does Bullshit Truly Baffle Brains?”

The Continuum: The Interior of the Blackhole

The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighboring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." I am sure the reader will appreciate with sufficient clearness what I mean here by "neighbouring" and by "jumps" (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum.Albert Einstein p. 83 of his Relativity: The Special and the General Theory

How is it that time could have been a emergent process knowing full well that the measure, and the continued "half measure" we loose perspective on that space. So given the nature of the blackhole, how is it we see such smoothness geometrically developing, as the temperature values increase, according to the nature of the gravitational collapse? An energy valuation according to this radius allows one to think that "somewhere in this creation" the relativistic nature of the fluidity is taken to a point of that "emergent process." One had to account for the developing nature of the dark energy.

Phil Warnell:

If time is an emergent entity, rather then fundamental, then is perplexing why the universe had a beginning. For if time is both infinite and eternal and the universe is neither, it might be of reason to be limited in magnitude and yet why the wait? This also must form to be part of the explanation.

String theory and it first Three Microseconds by it's very nature pushes back perspective beyond Steven Weinberg's First Three Minutes. Consider Before 1 Planck Time

Before a time classified as a Planck time, 10-43 seconds, all of the four fundamental forces are presumed to have been unified into one force. All matter, energy, space and time are presumed to have exploded outward from the original singularity. Nothing is known of this period.

The Foundations of Mathematics, Invented or Discovered?

Mathematical ProblemsLecture delivered before the International Congress of Mathematicians at Paris in 1900By Professor David Hilbert

While insisting on rigor in the proof as a requirement for a perfect solution of a problem, I should like, on the other hand, to oppose the opinion that only the concepts of analysis, or even those of arithmetic alone, are susceptible of a fully rigorous treatment. This opinion, occasionally advocated by eminent men, I consider entirely erroneous. Such a one-sided interpretation of the requirement of rigor would soon lead to the ignoring of all concepts arising from geometry, mechanics and physics, to a stoppage of the flow of new material from the outside world, and finally, indeed, as a last consequence, to the rejection of the ideas of the continuum and of the irrational number. But what an important nerve, vital to mathematical science, would be cut by the extirpation of geometry and mathematical physics! On the contrary I think that wherever, from the side of the theory of knowledge or in geometry, or from the theories of natural or physical science, mathematical ideas come up, the problem arises for mathematical science to investigate the principles underlying these ideas and so to establish them upon a simple and complete system of axioms, that the exactness of the new ideas and their applicability to deduction shall be in no respect inferior to those of the old arithmetical concepts.

The original address "Mathematische Probleme" appeared in Göttinger Nachrichten, 1900, pp. 253-297, and in Archiv der Mathematik und Physik, (3) 1 (1901), 44-63 and 213-237. [A fuller title of the journal Göttinger Nachrichten is Nachrichten von der Königl. Gesellschaft der Wiss. zu Göttingen.]

Phil Warnell:For if time is both infinite and eternal and the universe is neither

So current understanding has been pushed to consider that there is no geometry which can be seen inside the blackhole? If this is not possible, then the very nature of the geometry is existing at "another level" has to be part of an "emergent process" before it manifests from it's previous state?

So what is that previous state that this universe came from? This universe then, is part and parcel of an "existing universe." While you may consider time as eternal, then what would allow for such a space to emergent within that universe to create a new beginning and another offshoot of it?

See:
What is Happening at the Singularity?

A New Cosmological View?

Glaucon

Glaucon (Greek: Γλαύκων) (born circa 445 BC) son of Ariston, was the philosopher Plato's older brother. He is primarily known as a major conversant with Socrates in the Republic (Plato), and the questioner during the Allegory of the Cave. He is also referenced briefly in the beginnings of the dialogues of Plato Parmenides (Plato) and the Symposium (Plato).

While I of course understood this conversation between Plato and Glaucon, there is a statement of reference that needs to be explained. So that it is not misunderstood that "the object" and "state of the one who questions and the one questioned," are shown to be like "God as the Geometer?" It is an "innate feature to the state of enquiry." That it follows alongside mapping, which advanced my own position of "methodology by intuition." An accumulated to a state called"Correlation of Cognition."

So by introducing "this brother"( a figure in mind to advance the developmental methodology,) to create this "state of being" within us, is much like an artistic endeavour of a plot, a writer, since one may not have had this conversation other then to move this story forward. How?:)

So I am glad there is a Glaucon who would move the conversation for advancement.

As Socratic method requires both a questioner and one questioned to move forward, Glaucon, who is the most honest about his ignorance amongst the friends, will help “build” the ideal philosophical city by engaging Socrates without fighting his ideas.

Self Evident

We hold (they say) these truths to be self-evident: That all men are created equal. In what are they created equal? Is it in size, understanding, figure, moral or civil accomplishments, or situation of life?Benjamin Franklin-The Gentleman's Magazine, vol. 46, pp. 403–404)

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.

"Deduction" is an interesting thing left on it's own. While we think it only as one avenue to the methodology of approach, it is not without pointing out that the "inductive part" is part of this philosophical adventure too. That it should leave one to understand that the "infinite regression" leaves one on a precipice of change. That what is self evident, becomes the "new stepping stone for advancement."

A VIEW OF MATHEMATICS by Alain CONNES

Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.

Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.

.......and again.

Alain Connes

Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition.

God the Geometer

Let proportion be found not only in numbers, but also in sounds, weights, times and positions, and whatever force there is.Leonardo Da Vinci

Vitruvian Man by Leonardo da Vinci.

Leonardo is clearly illustrating Vitruvius De Architectura 3.1.3 which reads:

The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square.

De Architectura, VitruviusFirst Milanese period 1481/2 - 1499

The first printed edition of the De Architectura (On Architecture) by the ancient Roman architect, Vitruvius, appears.

It is never easy sometimes to know what direction to go with these blog posts. What is being shown on the "screen of my mind" is a painting of Leonardo, and along with this idea about Coxeter's insight into what the geometer is really doing when he discovers aspects of what exists before it's manifestation in reality. As if, it is not enough to know what the Higg's is doing as it crosses the room in analogy with the great Professor Einstein.

Science takes us back to the very beginnings of the universe and how it is we know that such phases and transformational changes can be described, and behind it all, there is not some existing geometrical nature to the forms that manifest?

So from an historical perspective, the image set the pace for what discoveries become part of the blog entry. Who is to know what direction this may take me as I scour the internet and find the following.

Fol 79v-80r-Acoustics. Photo RMN © René-Gabriel Ojéda

Music

According to Leonardo, the musician composes harmony by the simultaneous conjunction of its “proportional parts”. The painter “grades the things before the eye as music grades the sounds that meet the ear”. On Ms. L. Fol 79v. Leonardo investigates sound and tries to establish strict mathematical proportions between the loudness of a sound at its origin and its range, the point in space up to which it can be heard. This “pyramidal law” was seen as a universal law of proportion that could be applied to other natural phenomena such as light, perspective and even mechanics.

Leonardo’s pyramidal law of proportional diminution did not always lead to fruitful conclusions. In the absence of knowledge of advanced mechanics, he attempted to apply it to the investigation of gravity, noting that every falling object acquires increments of impetus. He was obviously unaware of the Merton “mean speed theorem” which states that a body traveling at constant velocity will cover the same distance in the same time as an accelerated body if its velocity is half the final speed of the accelerated body.

Undeterred, Leonardo investigated the actions of levers, pulleys and balances at length according to medieval proportional laws, illustrating endless demonstrations of harmonic equilibrium. While most of the results had no practical purpose, Leonardo seems to have taken delight in demonstrating the certainty of proportional law for its own sake. Perhaps it confirmed his view of the inter-connectedness of all things in nature, which he so often disproved in the course of testing theory with experiment.

See Divine proportions as well.

Pyramidal colourings of our Emotive States

Photo RM -Hervé Lewandowski / Thierry Le Mage- Make Mona Smile here.

As you know I am using a comparative view of emotions which are much more subtle then the matter to which we assign our body. Earth is square. Plato points to heaven for a reason, and all things descend according to those things we assign emotive value which return to the matters defined. Alas, the human experience is emotive determined and our lives set in the direction we send it. All matters of due course, are heralded from a much finer level of thought.

See: The Triangle Descends into the Square

As many of you know I am not the great scientist that so many I follow are. Who have spent their times in the higher halls of learning. It is no less important to me that I work to the same vein of truth that they do in their pursuances for understanding and implementation of science under it's laws.

So too I work an area that would have been the decline of our scientist's credibility. The scientists who have suffered under the scorn of their own colleagues because of this divergence from what is known and understood. I do not have to worry, because I already work the lower echelon of the thoughts and feeling about those scorned. My immaturity perhaps and wonderment as to what purpose this lone blogger attempts, and I could be past off as some kook. I persevere, as we all do to understand life, reality and it's truths.

Mind Map: The Medicine Wheel

The Power of Myth With Bill Moyers, by Joseph Campbell , Introduction that Bill Moyers writes,

"Campbell was no pessimist. He believed there is a "point of wisdom beyond the conflicts of illusion and truth by which lives can be put back together again." Finding it is the "prime question of the time." In his final years he was striving for a new synthesis of science and spirit. "The shift from a geocentric to a heliocentric world view," he wrote after the astronauts touched the moon, "seemed to have removed man from the center-and the center seemed so important...

God as Architect/Builder/Geometer/CraftsmanEarly science, particularly geometry and astronomy/astrology, was connected to the divine for most medieval scholars. Notice, even, the circular shape of the halo. The compass in this 13th century manuscript is a symbol of God's act of Creation, as many believed that there was something intrinsically "divine" or "perfect" that could be found in circles The Circle

Going from 2 dimensional drawing to 3 dimensions has spherical relations in terms of it's mathematical development?

While I present a hint to the "explosion of the thinking mind," how is it such a transference to the actual processes in life could have equalled a "mathematical construct" that one might contend exists at the very beginning of this universe?




An Historical Version

Medicine Wheel Teachings by Thunderbird

The term "Medicine" as it is used by First Nations people does not refer to drugs or herbal remedies. It is used within the context of inner spiritual energy and healing or an enlightened experience, in other words, "spiritual energy." The Medicine Wheel and its sacred teachings assist us along the path towards mental, spiritual, emotional, physical balance and enlightenment.

A good starting point is to determine where you are on the Wheel by your birth date. The Medicine Wheel is walked in a clockwise direction (the direction of the Sun). The time needed to walk a complete circle is whatever time it takes - time, in other words, is relative to the process.

Now of course some feel very funny about using such things to represent something about themselves. Develop a map, that indicates some of one's own history according to someone's else method. What I mean here is that what you see of use in a historical method as per the Native Americans, then how would this apply to your own life?

I present this "from my own experience." How such ideas behind the mapping and mandalic interpretations are evidence for me of the complexity of the human mind. How is it we can create such a maps from the experience? One that can unfold for and from another more subtle recognition of the depth our natures. I believe that this process is inherent in each of us. The complexity of our human experiential existence makes this difficult to see. It is as if you "live a dream" and what does it mean at some other level? So you are confused about the chaoticness of the dream state?

A Tibetan interpretation of the Book of the dead would have it seem that confusion shall be the fog, our fog and any clarity of seeing would be to know what it is that causes this fog. Is it our emotive states of existence? Our emotive contaminants of the mental and spiritual state? What colour would these be if we had thought about what an emotive inflection had been given to an experiences of our own, as we speak and think about life?

So this journey of course took me back to Tibetan images, as well as Jung's interpretations of mandalas as expressions of the soul. The construction method and meanings associated with geometrical proportions to the division of the person. In terms of directions, north, south, east or west. These can have meanings to the idea of "seasons to our life" and this is, what going in a circle may mean in terms of the "totality of the life" of one person, from birth to death.

Does any of this seems familiar to you as it did to me. My natural inclination to mind mapping my experiences and developments of a philosophy according to what was being constructed, just arose from developing a "methodology to approach" intuitively.

See:

Mapping the Pathway Inside

The center and the whole-what it means?

Inside the Mathematical Universe