Active Learning

Learn, UnLearn, Learn.

Understanding should never stay put. It is important to get a new understanding. Understanding can always be improved. 

There are two ways to do good science.
The first is to be smarter than everybody else.
The second way is to be stupider than everybody else—but persistent in the cycle of learn, unlearn, learn.

Hacked from Raoul Bott’s quote.

My father died on July 30th, 2013 and I intend to honor him, if I can, by writing a blog about him and the consequences of me integrating his ideas every year.  First year,  Second YearThird Year, Fourth YearFifth YearSixth Year, Seventh Year. This is the eighth year.

On Gestalt Science: Relational Complexity and Comparative Science
David West Keirsey and David Mark Keirsey

On the nature of ideas: almost right, almost wrong, brilliantly confused, sloppy confused.

On Ansatz and Ersatz Ideas

Feynman Diagram

No ideas are absolutely right. Good Ideas, that are almost right, model the world well. However, words are slippery and ambiguous, open to misinterpretation for those who are ill informed or misinformed. Ideas are model metaphors, limited in context.

Almost Right.

Green Ideas sleep furiously

There are almost right ideas that are complex ideas. These almost right ideas are a mixture of fast and slow ideas in a circumcised context. These ideas take time to be developed and are not the complete answer. These ideas are opposed or ignored by society in general. Moreover, the incumbent experts of the fast ideas vehemently oppose the incorporation of the slow ideas, but eventually accepted when their time has come.

Keirsey Temperament

The Keirsey Temperament Model (KTM) is a framework for understanding yourself and others. Millions of people have benefitted from the KTM, even though there was no advertising of it, except through word of mouth.

Keirsey Temperament Model’s Top Matrix

The Keirsey Temperament Model does not address, explicitly, the effect of gender, culture, and other environmental factors and influences on a person’s character, which are important factors in the development of an individual. On the other hand, understanding a person’s Temperament often can help in understanding these other factors and influences.

Quantum Mechanics and Quantum Potential

Quantum mechanics is the most accurate approximate theory in Science. Heisenberg’s Uncertainty Principle is correct but incomplete in understanding, because it is a principle (an assumption) not an explanation.  The debate between QM (ala Schrodinger, Heisenberg (Born), Dirac) versus the “hidden variable” QM Bohm-Einstein, both assume the continuity of the speed of light relative to the Planck scales (time, mass, energy, distance, spin, and charge). David Bohm’s new Quantum Potential (via The Undivided Universe) is a better ontological model than conventional QM; however, still doesn’t address the digital (Diophantine) nature of reality.

Quantum Potential

Quantum mechanics does not predict the right magnetic moment of the muon or tauon. And there are the three neutral leptons that have no explanation. Moreover, there is no set of relations, at this point of time (2020), that conventional physics has any hope of using to bridge that Fermi-Dirac-Landau gap. The Ersatz concepts of Dark Matter and Quantum Entanglement are vacuous rhetorical concepts pushed by the neo-Ostwaldian prophets. Quantum entanglement is a real phenomena, but the popular explanations are nonsensical. Formatics will hopefully address these issues.

Almost Wrong.

Give me a fruitful error any time, full of seeds,
bursting with its own corrections.
You can keep your sterile truth for yourself.
Vilfredo Pareto

There are almost wrong ideas that are much better than vague or confused ideas. These almost wrong ideas often are ground breaking for a time, and they are crucial in the evolution of science and ideas. These are the fast ideas or slow ideas of yesteryear. They’re the best science at the time, limited in the scope, and clearly to some degree very incomplete.

Personality Types

Isabel Myers created the Myers-Briggs Type Indicator (MBTI) and helped millions of individuals understand themselves better as individuals. Most people are not very good at introspection, but the MBTI although atomistic in its approach, the four linear factors [E-I,N-S,T-F,P-J], provided a better set of factors to see the People Patterns, than looking to doGs, daemons, tea leaves, 2000 year old texts, or dead ancestor’s droppings, to understand and as a guide to operate in the past, present, and future.

Isabel Myers modification and adding to Carl Jung’s vague and sloppy ideas was a major improvement. The idea that people are inborn in their different wants, needs, and styles of behavior, often contrary to their families, friends, and communities, was a game changing idea against the early and dominant 20th century blank slate ideas of Watson/Skinner or simplistic primal instinct theories of Freud and Pavlov. Can the individual be explained by four factors? No, but as an initial way of looking at an individual for the “content of their character”

Relativity and Particle Types

Energy/Matter: Isaac Newton was extremely successful when he invented differential and integral calculus to model Kepler’s concept of the motion of the heavens. Newton used his newly coined (mathematical) concepts of mass and fluxons to generate a simple equation relating these two to universal gravity. He also was the first to guess that light was a particle. He obviously had no idea of electrons, protons, and the particle and force zoo that his followers would expand upon.

Space/Time: Einstein, abandoned his work on Brownian motion and the photoelectric effect (involving a Planck constant), to concentrate on the mismatch between Hamiltonian mechanics and Maxwell’s equations. With the use of covariant tensors and the formalism of the Minkowski space, Einstein generated an approximate model of Newton’s guess at gravity that has been excellent in predicting interesting phenomena such as the bending of light waves, time dilation, gravity waves, and phenomena such as black holes. On the other hand, Einstein’s field equations cannot explain the rotation of galaxies and the evolution of the universe without numerous fudge factors (the Gravitational “constant”, the Hubble “constant”, “Dark Matter”, and “Dark Energy”). Einstein’s equations do not involve the Planck (finite) constants, in some sense hiding behind infinity.

From all this it is to be seen how much the limits of analysis are enlarged by such infinite equations; in fact by their help analysis reaches, I might say, to all problems, the numerical problems of Diophantus and the like excepted. [Editor’s emphasis]

Isaac Newton (Letter to Gottfried Leibniz on the advantages of infinitesimal calculus)

Ersatz Ideas: Brilliantly Confused or Sloppy Confused.

“Nothing is more obstinate than a fashionable consensus

Margaret Thatcher

These ersatz “confused” ideas are to be explored in more detail in a later blog; however, what follows is a short introduction of the concepts to be developed further. My father spent most of his life combating or ameliorating the effects of confused ideas. But it is not enough to criticize ideas that one considers wrong or confused, better ideas must be built from from old ideas and new ideas that address the issues finessed or ignored by the ideas of the current time.

Das ist nicht nur nicht richtig; es ist nicht einmal falsch!

Wolfgang Pauli

Almost Right and Almost Wrong Ideas are the bulk of science; however, there are ideas that arise that are either Brilliantly Confused or Sloppy Confused, that contribute to the evolution of science. These ideas are a little more complex to describe in their role in the evolution of science.

“What you said was so confused that one could not tell whether it was nonsense or not.”

Wolfgang Pauli (to Lev Landau)

Brilliantly Confused ideas often open up new vistas implicitly. To a degree the Brilliantly Confused ideas are partially right, but typically, for wrong reasons. Archetypes of Jung and Freud’s “talking cure” were better than the torture methods of the medics of the first half of the twentieth century, but ultimately have no scientific basis other than vague metaphors. String Theory was promising in the beginning, once Green and Schwarz figured out the right scale, but it rested on a bad assumption: mass and energy are continuous and proportional factors in non-equilibrium circumstances. These ideas eventually fade, but seem to never die.

Sloppy Confused Ideas are wrong turns on bad assumptions (often seen in hindsight, but sometimes obvious to a silent or silenced minority). The “Mental Illness” metaphor used to rationalize psychiatry’s and the pharmacological industry to drug their patients or clients, often compounding the problems of these victims of abuse from dysfunctional families and/or institutions. In the science of cosmology, Steven Hawking used his credibility and dominate position in the field to speculate about how the world works, the popular media loving to advertise his every word. However, Steven Hawking and David Deutsch’s Multiverse is more religion than science.

Active Learning: Learn, Unlearn, Learn

The thing I miss about my father, besides our spirited and long debates, was his interest in ideas. He was always up for discussing them. Looking at them and examining the pros and cons of ideas: how they are almost right, almost wrong, brilliantly confused, and sloppy confused. Understanding can always be improved.

I bailed out of Chemistry and Electrical Engineering as undergraduate to go into computing; however, I never gave up on trying to learn more and understand more, like quantum computing. With a fifth watching of Andrea Morello’s interview, I am still learning, unlearning, learning.

I also didn’t continue to learn more “mathematical” (non-discrete) concepts beyond my BS and MS degrees. Only in the last couple of decades I have gone back to learning, unlearning, learning other mathematical domains. For example, in understanding internal structure and dynamics, Peter Scott’s article The Geometries of 3-Manifolds has valuable information about the eight kinds of geometries in three dimensions.

Architect Rationals include: Mary SomervilleDavid Mark KeirseyJames MadisonSrinivasa RamanujanEmmy NoetherPaul DiracRobert RosenDavid West KeirseyAlbert EinsteinLonnie AthensDavid Bohm

Conway’s Mesh of Life

I saw him there as he sat, with his classic slightly bemused grin before his lecture.  I had never got a book autographed, until then. I am not easily enamored by fame, scientific or any other knowledge or skill domain. But I powered through my natural enryo, for I had brought his book with me intending to get him to sign it. I thought his book as one key to unlocking an important question.

I have studied the contents of the book for years. And continue to revisit and re-cycle his ideas contained within.


To Subquotient, or Not Subquotient,
That is the question!

The divisor status, of the lattice, oh my, Times, Rudvalis.
Crack the Dirac, Landau beseech the damp Leech.
It’s a Monster Conway Mesh, Mathieu’s Stretch, Jacques’ Mess, Janko’s Sprains, and Einstein’s Strain…

He had given me a quizzical look, since my hair was graying and I didn’t say anything.  He said it was his “best book.”  I nodded and I didn’t say anything.  I am not a mathematician by training, and I was working on a slow idea, not ready for Prime time On the nature of the universe.

Never mind the mock theta, Ramanujan’s gap, Namagiri dreams.
No Tegmark or Linde, but
Verlinde in name. It’s all but Feynman’s streams,
and weigh.

Such a Prime rank, any such Milnor’s exotic sank
No mess, no Stress, but Strain.
Tensors Bohm and bain

John Horton Conway, Inventor Rational, FRS (/ˈkɒnweɪ/; born 26 December 1937 – April 11, 2020) was an English mathematician active in the theory of finite groupsknot theory, number theory, combinatorial game theory and coding theory. He had also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Conway was Professor Emeritus of Mathematics at Princeton University.

He was the primary author of the ATLAS of Finite Groups giving properties of many finite simple groups. Working with his colleagues Robert Curtis and Simon P. Norton he constructed the first concrete representations of some of the Sporadic groups. More specifically, he discovered three sporadic groups based on the symmetry of the Leech lattice, which have been designated the Conway groups. This work made him a key player in the successful classification of the finite simple groups, which is considered one of the greatest quests in mathematics.

Now that John has passed from the scene, his Game of Life has ended, a new requestion will be continued. Conway’s Monster Mesh needs to be fleshed out and explained in more simple and complex terms: 1) in in-form-ation terms, 2) in phys-ical terms, 3) in mathe-mat-ical terms, 4) in in-volut-ionally and en-volut-ionally terms. But also explained with these four towers of Babel — integrated.

My slow idea was to use as a Framework based on Conway’s work on Symmetry and the Sporadic Groups, but also other mathematicians and scientists.

Many mathematicians including Conway regard the Monster Group as a beautiful and still mysterious object. Since there is no “physical meaning” attached to mathematical concepts and percepts, these “conceptual ideas” in mathematics will continue to be “beautiful and mysterious” and ABSTRACT. However, one can be more systematic in the use of ideas. It is about that Relational Thing: not only about Conway, Dirac, Einstein, Newton, or Hawking ideas.

Life Itself

When looking both at the details and the overall Gestalt, patterns can be seen. It might be called Existence Itself More and Less, A Gain.

The 27 Sporadic Groups with corresponding
Physical Ansatz Concepts and Percepts
Gestalt Science

Gestalt Science related blogs: Gestalt ScienceReimaginingFeynmanThat Relational ThingThe Digital Sand ReckonerTowards Quantum FormaticsThe Ring that Binds and GrindsPrimeOn the Question of Learning WordsOne Ring that Binds Them AllThe FunctionalWithin the Edge of…

Inventor Rationals include: Feynman, Atul GawandeLarry PageElaine MorganLynn MargulisElon MuskSteve JobsJoseph James SylvesterFrances CrickPaul AllenWerner Von BraunWolfgang PauliAbraham LincolnMark TwainHedy LamarrJulius Sumner Miller, and Zhang Xin

Using Reasoning to Learn New/Old Words

“Only strong characters can resist the temptation of superficial analysis.”

Albert Einstein

Quantum mechanics, with its leap into statistics,
has been a mere palliative for our ignorance.

Rene Thom

When logic and proportion fall soggy dead,
and the white knight is talking backwards,
with the Red Queen is on her head,
Remember what the dormouse said:
Feed your head.
Feed your head!

We typically learn many words from context, rather than looking them up in a dictionary. Each person knows and uses many words which they cannot define exactly. Most of the words we know are not learned by someone telling us the definition. More typically, we learn words by extracting its meaning from context. The first encounter with a given word is usually not sufficient to gain any real understanding of the word.

Understanding can be achieved by comparing several examples. Each successive example can either augment understanding, confirm the understanding, or in some cases, uncover misunderstanding.

Learn, Unlearn, Learn

If you don’t understand something said,
don’t assume that you are at fault.
David West Keirsey

Wandering towards Scientific Enlightenment

Understanding can always be improved.

Problem comes when learning old fast ideas.

The trouble with specialists is that they tend to think in grooves
Elaine Morgan

In 1900, Max Planck had created a theoretical explanation of Wien’s formula on black body radiation. But in that process, experimentalists aware of Planck’s interest in the matter, had recently looked into the matter at longer wavelengths and higher temperatures, and told Planck that the infrared region at high energies violated Wien’s formula — so his original explanation was wrong. To quickly solve the problem, Planck added a “correction” to his analysis. A resulting derived formula proved to correct, no matter the increase in frequency (looking at a wider range of energies) and the improved accuracy of experimental results. Planck went back to his quickly modified analysis and reformulated his ideas to justify the semi-ad-hoc correction and found that it implied that energy was emitted or absorbed in discrete units based on Boltzmann’s combinatorics. He had solved a problem by simply creating a “chimera:” adding a factor in his equation — but he did not realize its consequent was as significant until he tried to justify his change theoretically. Even then, he did not consider it as profound, until Niels Bohr and others started to apply his new idea “a quantum action” to atoms and molecules. Another problem was there was a flaw in Planck’s reasoning for which Satyendra Bose corrected later, but the idea of quantum action has proved to be one of the two key and major ideas of physics in the 20th century.

Niels Bohr became very successful in applying Planck’s quantum action idea when examining the spectrum of the hydrogen atom. The failure of Rutherford’s simple analog “orbit” model, whereas the precise predictions of Bohr using Fraunhofer spectral lines, signaled the death of 19th century physics in the realm of small. However, for more complicated atoms, Bohr’s model wasn’t as accurate, so his original fast idea [quantum theory] needed modification or to be added to. The initial progress of the ideas: Einstein’s 1) lichtquanten, 2) special relativity, 3) general relativity; 4) Schrodinger’s recursive function equation; and 5) Dirac’s delta functional; petered out into the “particle and force zoo” ending up with the not very well understood statistical and probability based Standard Model of particle physics.

Wandering towards Scientific Enlightenment 2.0

Time, Space, Mass, Energy, Charge, Spin? What do these words mean?

Gestalt Science related blogs: Gestalt Science, Reimagining, Feynman, That Relational Thing, The Digital Sand Reckoner, Towards Quantum Formatics, The Ring that Binds and Grinds, Prime, On the Question of Learning Words, One Ring that Binds Them All, The Functional, Within the Edge of…

Gestalt Science

modeling_relationA Viking Reader

Fearless Asymmetry and Symmetry

order_chaos_particle_biform
Chaos to Order,                                 Order to Chaos

My father died on July 30th, 2013 and I intend to honor him, if I can, by writing a blog about him and the consequences of me integrating his ideas every year.  First year,  Second YearThird Year, Fourth YearFifth Year, Sixth Year. this is the Seventh Year.

keirsey_seaweedMy father, near the end of his life, considered himself the last Gestalt Psychologist. When I was very young I was fearful of kelp seaweed: my father showed me that it couldn’t hurt me, so I shouldn’t be afraid of it.   I learned from him. If you understand something, you can reason about it.   If you only have a correlation, you can’t be sure of the factors. He was never afraid to question conventional wisdom or the current fashionable and entrenched ideas (however old or fast those ideas were).

As a clinical school psychologist he was on the front line against invasion of chemical psychiatry into K-12 schools, and he saw how they used “their pseudo-scientific expertise [and argot]” to fool and trap kids and parents into approving the use of brain disabling drugs, within the “educational system” and with the implicit pressure and blessing (and relieving of responsibility) of the teachers and administrators.  He also didn’t buy into the dominant paradigms of the first half of 20th century of Freudian psychology and the correlational “blank slate” behaviorism of Watson and Skinner.

“If you don’t understand something said, don’t assume you are at fault.”
— David West Keirsey

Throughout my discussions and debates with him in my lifetime, he talked about ideas.   We talked about philosophy, science, mathematics, computers, people, and life. 

to_explain_the_world_cover 

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More Moore

I don’t remember exactly how it happened, but I was in his office.  I remember it to this day.  Think it was Sue Lapin who directed me to his room, but that’s another story.

wizard_child

He was a classic example of a gray haired, balding, absent-minded professor, his office shelves stuffed to the ceiling with books, papers, and other flotsam and jetsam of an academia life. There we were: two different generations —  he, my father’s generation, and me, a 50’s nerd baby boomer. The commonality was we were both computer nerds, interested in ideas and the nascent computer science field.   At the time I was just trying to get a job to support my education: a Masters degree at University of Wisconsin, Madison, far from my home in sunny SoCal.  I had driven the two thousand miles or so across the US for the first time in my life to get there.

We talked for about four hours non-stop about all kinds of things, the Chinese language is the only subject I remember: he was a fountain of knowledge, and both us could have gone on many Moore hours.  I probably didn’t know the significance of it at the time, except he did point me to a job which I got to support myself in that strange land.  A year and half later, I got a Masters in Computer Science, and left Madison to wander towards Enlightenment for the next 46 years, and hopefully beyond.

dmk_library_physics_math

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The Digital Sand Reckoner

To see a World in a Grain of Sand

And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour

— William Blake

dave_grad_schoolarchimedes
New scientific ideas never spring from a communal body, however organized,
but rather from the head of an individually inspired researcher
who struggles with his problems in lonely thought and unites all his thought
on one single point which is his whole world for the moment.
Max Planck

elkies_power_five_formula

Connecting precise physical relationships between the finites and the infinites.

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Slow Ideas

Comparative Science and Relational Complexity

We would debate for hours.

Over decades.

Only the educated and self-educated are free.

My father died on July 30th, 2013 and I intend to honor him, if I can, by writing a blog about him and the consequences of me integrating his ideas every year.  First year,  Second YearThird Year, Fourth Year, Fifth Year  This is the sixth year.

When I was young, my father would introduce and discuss, around the dinner table, the ideas of philosophers, scientists, and historians: like Adam Smith, Charles Darwin, Herbert Spencer, John Stuart Mill, Georg Hegel, William James, Arthur Schopenhauer, Bertrand Russell, Oswald Spengler, Will Durant, Ayn Rand, Milton Erickson, and Jay Haley, to name a few.

I had a question early on “How and Why does the World Work?” He had a more difficult question: “What are the long-term patterns of an ‘Individual’s Human Action?” He was clinical school psychologist, who was identifying deviant habits of children, parents, and teachers. He was developing techniques aimed at enabling them to abandon such habits. His methods of research and reasoning enabled him to evolve his ideas into a coherent system. His model of Human Temperament has helped many people to better understand themselves and others.

He was good at qualitative reasoning, wholistic thought: the Gestalt (despite [and because] of having lots of training in statistics). I became good at quantitative reasoning: conventional science and mathematics. Between the two of us, as we debated, I realized that there was a middle way, much more powerful than ad hoc wholistic reasoning or ad hoc atomistic reasoning, when they are used separately. The new middle way, The Slow Idea, is using Comparative Science and Relational Complexity in conjunction as fields of scientific endeavor using systematic qualitative and quantitative reasoning together. To some extent: (hard and soft) science, mathematics, and computer science are towers of Babel, not able to understand each other’s argot and considered irrelevant to other.

The idea ofSlow Ideas <=> Fast Ideas

The root of this idea appeared just recently, thanks to Atul Gawande. He and Matt Ridley noted that ideas operate very much in an evolutionary manner.

Fast Ideas and Slow Ideas

FAST IDEAS WORK

eventually, SLOW IDEAS WORK BETTER, and longer

Atul Gawande introduced the idea of slow and fast ideas with an example from the 19th century. The fast idea was anesthesia and the slow idea was antiseptics. To quote him:

“Why do some innovations [ideas] spread so swiftly and others so slowly? Consider the very different trajectories of surgical anesthesia and antiseptics, both of which were discovered in the nineteenth century.”

“The first public demonstration of anesthesia was in 1846…”

“The idea [anesthesia] spread like a contagion, travelling through letters, meetings, and periodicals. By mid-December, surgeons were administering ether to patients in Paris and London. By February, anesthesia had been used in almost all the capitals of Europe, and by June in most regions of the world.”

Antiseptics, on the other hand, was a slow idea. It took decades for antiseptics to accepted by doctors, who had no incentives to change their practices that didn’t help them immediately. Blood stained clothes was a sign of a experienced surgeon; and washing hands, sterilizing instruments, and keeping hospitals clean seemed unnecessary. Germ theory was dismissed by doctors because the “germs” were not readily observed. Miasma Theory still was used as an excuse to not change.

Hey buddy, can you spare a Para-digm?

“Science advances one funeral at a time.” — Max Planck

“The trouble with specialists is that they tend to think in grooves” — Elaine Morgan

Establishment science needs to protect themselves from quacks, but it also resists slow ideas that are not easily incorporated into the current fashionable (often fast) ideas. This is natural, this is the way evolution works. However, Kuhnian revolutions (as in Margulian-Darwinian evolution) are necessary in science to progress and leap across the Quantum Gap.

Form

He didn’t get it.

I was surprised, kinda.  But it made sense, why he didn’t think much of my suggestion.  In fact, in his seminar at UCIrvine Information and Computer Science department (as tactic to get MIT to give him a better offer as a tenured faculty member), he dismissed my “idea”, quickly, even though he had asked (obviously rhetorically, in hindsight) for suggestions as a kind of Socratic presentation tactic in his talk.

My mentioning of Kirchoff’s law as a parallel in regards into information flow, he thought irrelevant, and was rather dismissive.  But who was I, just a graduate student from a west coast Podunk U [which eventually was a key university in the development of the World Wide Web].  He was an assistant Professor from MIT, angling for tenure.

kirchoff_law_1

This time I understood.  Although I didn’t have a name for it at the time.  I just shut up.

Now, I call it eucaryotic hubrisWe all have it, in the area of our expertise and our vast areas of ignorance.

This time, I had had enough encounters with these kind of guys to not be in awe of them. I didn’t assume I was at fault in not understanding, and not smart enough it “get what they are promoting”.  They were just as ignorant as I was, despite being a “MIT Professor”.

And, Stupid, as me.  So when I was watching one of Geoffrey Hinton’s youtube talks…

carl_hewitt_stupid

I had interacted this “professor” before, in that seminar.   And I had listened to some of his other conference talks, he is very very very smart and accomplished.  So smart, these days, he is a distinguished emeritus faculty member, at the institution he got his BS and PhD at.  He has never had to move out of Massachusetts, or MIT.  No, this guy wasn’t Marvin Minsky, but his student.  So when Hinton told his offhand story, about Professor Carl Hewitt, I had to laugh.  Deja vu, all over again.

“Indeed, in their later years (after finding out that most others are faking an understanding of the laws of nature), INTPs [Architect Rationals] are likely to think of themselves as the master organizers who must pit themselves against nature and society in an unending effort to create organization out of the raw materials of nature.” – Please Understand Me II,  Keirsey, David. Please Understand Me II (Kindle Locations 4099-4107). Prometheus Nemesis Book Company. Kindle Edition.

As scientists, we all are struggling with understanding:

Formatics: Precise Qualitative and Quantitative Comparison. Precise Analogy and Precise Metaphor: how does one do that, and what does one mean by these two phrases? This is an essay, in the form of an ebook, on the nature of reality, measure, modeling, reference, and reasoning in an effort to move towards the development of Comparative Science and Relational Complexity. In some sense, this ebook explores the involution and envolution of ideas, particularly focusing on mathematics and reality as two “opposing” and “fixed points” in that “very” abstract space. As Robert Rosen has implied there has been (and still is going on) a war in Science. Essentially you can view that war as a battle between the “formalists” and the “informalists” — but make no mistake the participants of this war are united against “nature” — both are interested in understanding the world and sometimes predicting what can and will happen, whether that be real or imagined. So… I will ask the questions, for example, of “what could one mean” precisely by the words: “in,” “out,” “large,” and “small.” The problem is both Science and Mathematics are imprecise — but this sentence contains fighting words and is impredicative, to say the least. In my father‘s terms, it is important to distinguish between order and organization, and understand the difference. Lastly, for now, the concepts and their relations, in the circle of ideas of “dimensions of time” and dimensions of energy along with the dimensions of space and dimensions of mass will be explicated, as I evolve (involute and envolute) this ebook. SO WHAT IS HE TALKING ABOUT? Let me try to explain.

Formatics

Other Architect Rationals include: Mary SomervilleDavid Mark KeirseyJames MadisonSrinivasa RamanujanEmmy NoetherPaul DiracRobert RosenDavid West KeirseyAlbert EinsteinLonnie AthensDavid Bohm

Gestalt Science and Formatics related blogs: Gestalt ScienceReimaginingFeynmanThat Relational ThingThe Digital Sand ReckonerTowards Quantum FormaticsThe Ring that Binds and GrindsPrimeOn the Question of Learning WordsOne Ring that Binds Them AllThe FunctionalWithin the Edge of…

Inventor Rationals include: Feynman, Atul GawandeLarry PageElaine MorganLynn MargulisElon MuskSteve JobsJoseph James SylvesterFrances CrickPaul AllenWerner Von BraunWolfgang PauliAbraham LincolnMark TwainHedy LamarrJulius Sumner Miller, and Zhang Xin

Prime

Partitions: Exact Approximations

… there is something strange going on with Primes
Paul Erdös

champagne_bubbles

Never mind the mock theta, Ramanujan’s gap, Namagiri dreams.

ramanujan_book

When Srinivasa Ramanujan wrote to G. H. Hardy in the 16th of January 1913, he had some remarkable formulas in that letter.  So remarkable are some of his formulas that mathematicians have been studying Ramanujan’s notebooks of formulas for new mathematical insights to this day, more than a hundred years later.
I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras… I have no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as “startling”. 
Hardy invited him to England because some of the formulas “had to be true, because no one could have the imagination to make them up”.   But there were no proofs.  However, when this poor vegetarian Indian Hindu came to England, eventually Hardy showed Ramanujan (thru Littlewood) that his formula on Primes was not EXACTLY correct. So Ramanujan had to bend to Hardy and work on his proofs of some of his formulas, so when they tackled the function of Partitions P(n), Ramanujan with the help of Hardy got to point where they “cracked” Partitions (and could prove it). They developed a direct formula that computed the number of partitions pretty accurately, and at the limit (infinity) it was “perfect” — and, could by truncating the number for high partition number to an integer could guarantee to be exact: since the number of partitions of integers is an whole number (i.e., the real number series “formula” converges with an deceasing error rate). Together they “cracked” the problem where neither man could do it alone. Ramanujan supplied the “intuition” (the finding of the hidden pattern) and Hardy provided the rigor to explain why the pattern is true.  The method they created, in this instance, was called the “circle method” — and it has been used ever since by numerous mathematicians for various other results.

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Thanks, I needed that.

Seasons change with the scenery
Weaving time in a tapestry

I was surprised.

I was just eating lunch by myself in the cafeteria.  I am attentive, not expressive, kind of guy.  Besides this was the first time I was visiting MIT, as a part of Artificial Intelligence (AI) conference.  No, my SATs were not good enough to get into CalTech (or MIT), and I am a west coast guy, anyway.

But, lo and behold.  He sat down next to me.  Obviously, to strike up a conversation.

Marvin Minsky.

Ok, now I wasn’t a kid anymore.  I was industry-based AI researcher (Hughes Research Labs, HRL) working at the time on Autonomous Vehicle research.   Minsky didn’t know me, but, I knew a fair amount about him.

Marvin Minsky, full professor at the Massachusetts Institute of Technology, and “one of fathers of Artificial Intelligence”, came to my table clearly because he was curious.  Minsky, a Fieldmarshal Rational, had been very successful in promoting his graduate students to getting academic professorships across the lands. The list of his PhD students is more than impressive. He had government and university funding. MIT is a technological power house.  Money, People, and Companies have been flocking to MIT well before I was born.

I tried to make our conversation as interesting as I could.  Hey, Marvin was a legend in my field: Artificial Intelligence.

After about 5-10 minutes of conversation, me doing most of the talking about the autonomous vehicle project that I had been involved with, Marvin excuse himself, and wandered over to another table with a couple of people and joined in that conversation.

He didn’t get any useful out of me, in his mind, no doubt.
Next.
He moved on.

Thanks, I needed that.

I did get something useful out of the encounter.
A slow idea. But not a fast idea.  A hint on a part of an idea on how the world works.
It was a Kuhnian moment for me, I knew some things that Marvin couldn’t imagine.

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