First Principals of Quantum Mechanics

Of course the discussions are leading me to gather my thoughts on things, as they are being spoken too, by Bloggingheads.

A Life of the Genius Ramanujan
by Robert Kanigel



Srinivas Ramanujan (1887-1920)In the past few decades, we have witnessed how Ramanujan's contributions have made such a profound impact on various branches of mathematics. The book, "The man who knew infinity", by Robert Kanigel reached out to the general public the world over by describing the fascinating life story of Ramanujan. And now, in the form of a play, the public is made aware, once again, of this wonderful story. This is a very impressive play and I had the pleasure of seeing it with Prof. George Andrews, the world's greatest authority on Ramanujan's work and on partitions.

I am some what disappointed that Sean Carroll deleted my response to Lawrence Crowell and Rebel dreams.

Lawrence referenced GH Hardy, and I expanded on this in relation to Ramanujan. The point is in regards too pure mathematics. Some might have become offended by my saying "one's God" too imply, that one can idolize and put into stone, graven images of God, yet, this is so far from the truth of my statement that I hope the post I wrote was kept and seen in this light that I am to explain.

Some would never recognize the developmental aspect of a "higher self" and what images that we unconsciously induce to allow this communication within to take place.

It is not the forgetfulness with which one would like to make those graven images and form, "but the realization" that what ever we attach to something being meaningful, becomes meaningful, and pray too, can come through with an extraordinary amount of wisdom.

IN this context I would not judge another human being on the position they hold too in life, as this sets the stage for what is to come. In Ramanujan's case, the information of his mathematics came through in such a form.

My point is that while we build the inductive/deductive application to our "principals of infinite regress" that ultimately such an exercise is reduce too, yes, the mathematical framework that lies very close to that light.

While in relation to creation stories, such responsibility is on the adherence that we adopt to scientific endeavour, with which we place observation and experimentation to understanding what reality is about. I do not advocate irresponsibleness in this regard, but push to rigour that science requires.

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

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 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.

See:

The Man Who Knew Infinity

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

Memories Arise Out of a Equilibrium

Sean Carroll of Cosmic Variance, California Institute of Technology and David Albert-Columbia University Science Saturday: Time’s Arrow

Some highlights at different spots of the exchange.

How a philosopher of science spends his time (08:34)

David describes his run-in with the “What the Bleep!?” cultists (11:56)

Is good science too disturbing to make good entertainment? (04:46)

Sean and David take on John Horgan’s critique of string theory (10:54)

String theory’s predictive power (or lack thereof) (06:04)

Why is the past so different, in so many ways, from the future? (12:20)

I selected the title for a reason. I will have to go back and record the exact time of this comment as it arises. Time 53:48 David mentions the point about a memory forming out of a equilibrium which not only encompasses the future, but can also include the past.

The integration of a philosophy of science alongside of a person in theoretics seems like a good idea to me. There is something to be said about this language used even though used in the conceptual performance of this collaboration.



Now you must know, that I speak from a position of one that is of discovery about the nature of the mathematics, as I have come to understand it. Yes sure I may cloud the interpretation of the mathematical deduction with the idea of a regress to an ultimate position in mind, that we might compare such relations to what the cosmos is saying and what we are saying about the future and past.

I will not discount the very fabric such psychologies might go too, to develop concept maps themselves, to map the thinking being as to the regress of reason, and it's ultimate fate resting in such a mathematical description.

When I point out the relation to WMAP and the idea of this mathematical relationship, one might see the underlying method with which Sean and David intermingle conceptually. To bring forward a clear and consistent description of what begins and ends in the universe, might mean in relation to the past and future. What it means in relation to the memory that arises

I am looking to define such a shape as well as to the very nature of this universe.

Incompatible Arrows

I link the previous blog entry above for consideration, in line with the topic of this post, so that the "continuance of this position" describes the other half of the talking heads, that Sean Carroll represents.

Sean Carroll has a interesting set of four entires about the backwardness of the arrow of time and how it would appear. This is an interesting exercise for me on how perception about the current direction of the universe could have represented "the Egg before the chicken" scenarios.

Incompatible Arrows, I: Martin Amis
Incompatible Arrows, II: Kurt Vonnegut
Incompatible Arrows, III: Lewis Carroll
Incompatible Arrows, IV: F. Scott Fitzgerald

Chicken or Egg

Illustration from Tacuina sanitatis, Fourteenth century

Reverse chronology — narrating a story, or parts of one, backwards in time — is a venerable technique in literature, going back at least as far as Virgil’s Aeneid. Much more interesting is a story with incompatible arrows of time: some characters live “backwards” while others experience life normally.

Update:

One should be aware that there are a series of bloggingheads up and coming that are being exchanged here.

Sean Carroll

This raises all sorts of questions, the most basic of which are: “What counts as `looking’ vs. `not looking’?” and “Do we really need a separate law of physics to describe the evolution of systems that are being looked at?”

See:Quantum Diavlog

Light House Keeper

Some will reconsider the effect that is portrayed here in terms of a mirror directed and reflects to one eyes, can cause an unsettling effect because of the focus of the beam.

IN nature such a thing is an everyday occurrence as we catch such glimpses not only here in our everyday lives, but assign them to a cosmological occurrence as well. Now as illusive as the God nature of particles from space, whose energy considerations may be of value, they are very odd to such glimpses contained, and maybe even called "God particles.":)

There is a limit to the knowledge, you have to remember and what is one to do when they invoke such a statement, to realize our knowledge is indeed limited? We theorize and we built gigantic devices for such measures, as to the certainty of our values assigned to those theoretics. It has to appear in some intellectual form before we can say yes they exist and the dependence on measure is what we are willing to build to become such realistic people.

I tend to think such a thing is a "direct connection to to what the event is saying" not only in our lives as the decay process is the effect of all our psychological actions(emotive intellectual or spiritual), it is also the elemental consideration that such constituents are held together by "such a glue" whose measure is affected, and measured, by such a light.

If light bends, what is it we are to saying about the path such a light has travelled that we would say "the light has an energy valuation to it" and such lensing occurs?

The light then, becomes a gravitational indication of the space it travels through?

Black Hole-Powered Jet of Electrons and Sub-Atomic Particles Streams From Center of Galaxy M87

NASA's Hubble Space Telescope Yields Clear View of Optical Jet in Galaxy M87

A NASA Hubble Space Telescope (HST) view of a 4,000 light-year long jet of plasma emanating from the bright nucleus of the giant elliptical galaxy M87. This ultraviolet light image was made with the European Space Agency's Faint Object Camera (FOC), one of two imaging systems aboard HST. This photo is being presented on Thursday, January 16th at the 179th meeting of the American Astronomical Society meeting in Atlanta, Georgia. M87 is a giant elliptical galaxy with an estimated mass of 300 billion suns. Located 52 million light-years away at the heart of the neighboring Virgo cluster of galaxies, M87 is the nearest example of an active galactic nucleus with a bright optical jet. The jet appears as a string of knots within a widening cone extending out from the core of M87. The FOC image reveals unprecedented detail in these knots, resolving some features as small as ten light-years across. According to one theory, the jet is most likely powered by a 3 billion solar mass black hole at the nucleus of M87. Magnetic fields generated within a spinning accretion disk surrounding the black hole, spiral around the edge of the jet. The fields confine the jet to a long narrow tube of hot plasma and charged particles. High speed electrons and protons which are accelerated near the black hole race along the tube at nearly the speed of light. When electrons are caught up in the magnetic field they radiate in a process called synchrotron radiation. The Faint Object Camera image clearly resolves these localized electron acceleration, which seem to trace out the spiral pattern of the otherwise invisible magnetic field lines. A large bright knot located midway along the jet shows where the blue jet disrupts violently and becomes more chaotic. Farther out from the core the jet bends and dissipates as it rams into a wall of gas, invisible but present throughout the galaxy which the jet has plowed in front of itself. HST is ideally suited for studying extragalactic jets. The Telescope's UV sensitivity allows it to clearly separate a jet from the stellar background light of its host galaxy. What's more, the FOC's high angular resolution is comparable to sub arc second resolution achieved by large radio telescope arrays.

See:Hubble Site>

Just to draw further comparison here for consideration in light of this thread I apologize, but it is of importance, just not in that blog posting space.

The significance in our every day life of such a thing "catches the eye,"( thanks again Paul in regards to Snowboarders.) and we do not realize it. To find such cosmological comparisons is really interesting in the unfolding of the events. How significant?

We see a pulsar, then, when one of its beams of radiation crosses our line-of-sight. In this way, a pulsar is like a lighthouse. The light from a lighthouse appears to be "pulsing" because it only crosses our line-of-sight once each time it spins. Similarly, a pulsar "pulses" because we see bright flashes every time the star spins.

See: Pulsars
Link to tutorial site has been taken down, and belongs to Barb of  http://www.airynothing.com
See Also:Pulsars and Cerenkov Radiation

So What Did I mean By Olympics?

Smoky Comes to Visit Again

We built a patio to the one side of the house that allows us to watch the birds feed, and some of these pictures I have shown on this site. We found that quite a variety were coming as long.

While the birds still do come, the squirrel population is doing well, as they come to these feeders. It seems to attract our friend Smokey too.



This is a black bear, and you wouldn't know it. My wife shot this photo, as I was talking to her from work. The cub was apparently interested on what was inside the house. Good thing the patio doors were not left open like we usually do.



The interesting thing was the bear was actually coming to the patio window to have a look inside, and at one point actually stood on the house with it's front paws while leaning against it.

This is the little bears second season.

Not fifteen minutes before this little one showed up, my wife seen a Mother bear and her cub. It was obvious that Smoky was causing some distraction for the mother as the cub was chased up a tree.