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Posts Tagged ‘Quantum mechanics

Something Rather Than Nothing? Is Change always one generation away?

My opinion is that:

1. There are changes in every generation. Not necessarily significant in most issues.

2. The preponderant World Views could change in a couple generations, but these views are cyclical in nature and many older world views will resurface after 3 generations in different forms and contexts

My opinion is that:

1. The term Nothingness is an abstract notion.

2. Even when taken statistically, nothingness cannot be demonstrated or proven. Any substantial issue will not generate enough enthusiasm for the world community to invest in the latest precise measuring tools and observation of the entire earth or colony.

Physicist Lawrence M. Krauss said in a video:

Change is always one generation away…

If we can plant the seeds of doubt in our children, religion will go away in a generation, or at least largely go away. And that’s what I think we have an obligation to do.”

Krauss was addressing whether religion should be taught to children in school.

Though, as an atheist, he opposes religious education, he said he does support teaching comparative religion classes instead of completely “shying away” from the topic. (There are no differences among religions or sects: Simply a different political context in  historical and society conditions for power grabbing)

“What we need to do is present comparative religion as a bunch of interesting historical anecdotes, and show the silly reasons why they did what they did,” he remarked.

He said educators should force children to confront their own misconceptions.

“But you don’t shy away from religion any more than you shy away from the claim that Earth is the center of the universe. We laugh at that now, and we get kids to realize why that might be wrong… and so we should take other falsifiable facts, which are at the center of our society, which is religious doctrine, and make just as much fun of that.”

Watch video below.


    Why There Is Something Rather Than Nothing

    By Lawrence M. Krauss

    Illustrated. 202 pp. Free Press. $24.99.

Lawrence M. Krauss, a well-known cosmologist and prolific popular-science writer, apparently means to announce to the world, in this new book, that the laws of quantum mechanics have in them the makings of a thoroughly scientific and adamantly secular explanation of why there is something rather than nothing. Period. Case closed. End of story. I kid you not.

Look at the subtitle. Look at how Richard Dawkins sums it up in his afterword: “Even the last remaining trump card of the theologian, ‘Why is there something rather than nothing?,’ shrivels up before your eyes as you read these pages. If ‘On the Origin of Species’ was biology’s deadliest blow to super­naturalism, we may come to see ‘A Universe From Nothing’ as the equivalent from cosmology. The title means exactly what it says. And what it says is ­devastating.”

There are lots of different sorts of conversations one might want to have about a claim like that: conversations about what it is to explain something, and about what it is to be a law of nature, and about what it is to be a physical thing. But since the space I have is limited, let me put those niceties aside and try to be quick, and crude, and concrete.

Where, for starters, are the laws of quantum mechanics themselves supposed to have come from? Krauss is more or less upfront, as it turns out, about not having a clue about that. He acknowledges (albeit in a parenthesis, and just a few pages before the end of the book) that every­thing he has been talking about simply takes the basic principles of quantum mechanics for granted. “I have no idea if this notion can be usefully dispensed with,” he writes, “or at least I don’t know of any productive work in this regard.”

And what if he did know of some productive work in that regard? What if he were in a position to announce, for instance, that the truth of the quantum-mechanical laws can be traced back to the fact that the world has some other, deeper property X?

Wouldn’t we still be in a position to ask why X rather than Y? And is there a last such question? Is there some point at which the possibility of asking any further such questions somehow definitively comes to an end? How would that work? What would that be like?

Forget where the laws came from. Have a look instead at what they say. It happens that ever since the scientific revolution of the 17th century, what physics has given us in the way of candidates for the fundamental laws of nature have as a general rule simply taken it for granted that there is, at the bottom of everything, some basic, elementary, eternally persisting, concrete, physical stuff.

Newton, for example, took that elementary stuff to consist of material particles. And physicists at the end of the 19th century took that elementary stuff to consist of both material particles and electro­magnetic fields. And so on. And what the fundamental laws of nature are about, and all the fundamental laws of nature are about, and all there is for the fundamental laws of nature to be about, insofar as physics has ever been able to imagine, is how that elementary stuff is arranged.

The fundamental laws of nature generally take the form of rules concerning which arrangements of that stuff are physically possible and which aren’t, or rules connecting the arrangements of that elementary stuff at later times to its arrangement at earlier times, or something like that.

But the laws have no bearing whatsoever on questions of where the elementary stuff came from, or of why the world should have consisted of the particular elementary stuff it does, as opposed to something else, or to nothing at all.

The fundamental physical laws that Krauss is talking about in “A Universe From Nothing” — the laws of relativistic quantum field theories — are no exception to this. The particular, eternally persisting, elementary physical stuff of the world, according to the standard presentations of relativistic quantum field theories, consists (unsurprisingly) of relativistic quantum fields.

And the fundamental laws of this theory take the form of rules concerning which arrangements of those fields are physically possible and which aren’t, and rules connecting the arrangements of those fields at later times to their arrangements at earlier times, and so on — and they have nothing whatsoever to say on the subject of where those fields came from, or of why the world should have consisted of the particular kinds of fields it does, or of why it should have consisted of fields at all, or of why there should have been a world in the first place. Period. Case closed. End of story.

What on earth, then, can Krauss have been thinking? Well, there is, as it happens, an interesting difference between relativistic quantum field theories and every previous serious candidate for a fundamental physical theory of the world.

Every previous such theory counted material particles among the concrete, fundamental, eternally persisting elementary physical stuff of the world — and relativistic quantum field theories, interestingly and emphatically and unprecedentedly, do not.

According to relativistic quantum field theories, particles are to be understood, rather, as specific arrangements of the fields. Certain ­arrangements of the fields, for instance, correspond to there being 14 particles in the universe, and certain other arrangements correspond to there being 276 particles, and certain other arrangements correspond to there being an infinite number of particles, and certain other arrangements correspond to there being no particles at all.

And those last arrangements are referred to, in the jargon of quantum field theories, for obvious reasons, as “vacuum” states. Krauss seems to be thinking that these vacuum states amount to the relativistic-­quantum-field-theoretical version of there not being any physical stuff at all. And he has an argument that the laws of relativistic quantum field theories entail that vacuum states are unstable. And that, in a nutshell, is the account he proposes of why there should be something rather than nothing.

But that’s just not right. Relativistic-quantum-field-theoretical vacuum states — no less than giraffes or refrigerators or solar systems — are particular arrangements of elementary physical stuff.

The true relativistic-quantum-field-­theoretical equivalent to there not being any physical stuff at all isn’t this or that particular arrangement of the fields — what it is (obviously, and ineluctably, and on the contrary) is the simple absence of the fields!

The fact that some arrangements of fields happen to correspond to the existence of particles and some don’t is not a whit more mysterious than the fact that some of the possible arrangements of my fingers happen to correspond to the existence of a fist and some don’t.

And the fact that particles can pop in and out of existence, over time, as those fields rearrange themselves, is not a whit more mysterious than the fact that fists can pop in and out of existence, over time, as my fingers rearrange themselves. And none of these poppings — if you look at them aright — amount to anything even remotely in the neighborhood of a creation from nothing.

Krauss has heard this kind of talk before, and it makes him crazy.

A century ago, it seems to him, nobody would have made so much as a peep about referring to a stretch of space without any material particles in it as “nothing.” And now that he and his colleagues think they have a way of showing how everything there is could imaginably have emerged from a stretch of space like that, the nut cases are moving the goal posts.

He complains that “some philosophers and many theologians define and redefine ‘nothing’ as not being any of the versions of nothing that scientists currently describe,” and that “now, I am told by religious critics that I cannot refer to empty space as ‘nothing,’ but rather as a ‘quantum vacuum,’ to distinguish it from the philosopher’s or theologian’s idealized ‘nothing,’ ” and he does a good deal of railing about “the intellectual bankruptcy of much of theology and some of modern philosophy.”

But all there is to say about this, as far as I can see, is that Krauss is dead wrong and his religious and philosophical critics are absolutely right. Who cares what we would or would not have made a peep about a hundred years ago? We were wrong a hundred years ago. We know more now.

And if what we formerly took for nothing turns out, on closer examination, to have the makings of protons and neutrons and tables and chairs and planets and solar systems and galaxies and universes in it, then it wasn’t nothing, and it couldn’t have been nothing, in the first place.

And the history of science — if we understand it correctly — gives us no hint of how it might be possible to imagine otherwise.

And I guess it ought to be mentioned, quite apart from the question of whether anything Krauss says turns out to be true or false, that the whole business of approaching the struggle with religion as if it were a card game, or a horse race, or some kind of battle of wits, just feels all wrong — or it does, at any rate, to me.

When I was growing up, where I was growing up, there was a critique of religion according to which religion was cruel, and a lie, and a mechanism of enslavement, and something full of loathing and contempt for every­thing essentially human.

Maybe that was true and maybe it wasn’t, but it had to do with important things — it had to do, that is, with history, and with suffering, and with the hope of a better world — and it seems like a pity, and more than a pity, and worse than a pity, with all that in the back of one’s head, to think that all that gets offered to us now, by guys like these, in books like this, is the pale, small, silly, nerdy accusation that religion is, I don’t know, dumb.

David Albert is a professor of philosophy at Columbia and the author of “Quantum Mechanics and Experience.”

Note: All Religions are mental constructs to enslave the common people to the elite class and ruling classes that possess power. And the philosopher happily delved in those trove of constructs because they interested the intellectual people and the ruling classes in disseminating the necessary existence of religious beliefs.


It is Attitude, not ability: Doing math, physics, chemistry…

The proper attitude is to persist in solving a problem.

It doesn’t matter how difficult or complex is a problem: The more you try solving and figuring out various perspectives to tackling the difficulty, angles, and methods…the closer you are in resolving the problem.

With focus and perseverance, acquired in childhood, you reach this critical instant of eureka “Yah! I get it”

I recall that I never had the patience to sit down and solve math or physics exercises and problems. The easy exercises bored me and the difficult problems didn’t receive much focus and attention and energy to try harder: I would jump to the solution section if available…

Sure I understood the concepts and how to proceed, but what counted is exam time were the limited time, the patience to go on …

If your attitude was lousy during the entire semester, it isn’t going to change and make any difference at exam sessions: You are frantic, out of patience, and your mind wants to fly away and give up quickly on challenging problems…

I recall taking relativity and quantum mechanics courses. There were not books available for solutions of problems.  What I could find were books on the history and philosophy of the materials.  I would thoroughly read all these voluminous books, but the main question remained: “Can you solve the problems in the allotted time at exam sessions?

Maybe if I located solving manuals for exercises and problems I might have barely passed these courses from the first time. With this attitude of mine, I would have never been a mathematician or an efficient physicist…

Now, if you give me a 100-item questionnaire to fill, you can bet that no less than 20 questions would be left blank. And if I am required to fill every single question, the blank spaces would shine with utter cynicism and blunt falsehood

In cultures that pragmatically place the highest emphasis on effort and hard work, people are best in solving math problems...

Pragmatic cultures means to actually do and finish any task handed to you, whether you like the task or not…

And the reward? To be recognized by the community as a hard-working members you can be counted on to pursue difficult tasks and responsibilities…

No one who can rise before dawn, 360 days a year, can fail to make his family rich…” This is an idiom in south China around the Pearl River Delta of rice paddies…

These Far Asian cultures are renown for answering every question in lengthy questionnaire. Kind of if you want to know the details of an individual, all you have to do is to provide him with a questionnaire…

Math proficiency in Far Asian culture is high, in spite of lower IQ scores and other aptitude tests. But again, IQ tests are biased by western culture and idiosyncratic mentality

I recall a few of my cousins who were bright in math and in any course they have taken, even history, geography, literature…They would sit down for hours, strong with a pen, a notebook and a ruler…and solve every exercise and problem at the end of every chapter…and every manual with exercises and problems…

I know they could solve the hardest of math or physics problems, but they built this attitude of resolving every minor and simple exercises, as meticulously and clearly as any other harder problem…

You built-in the attitude and let ability and talent follow you throughout your life, and gathering and reaping success and awards on the way…

The Knowledge Is Power program (KIPP Academy) in the south Bronx believes that sustained learning, even in summer time, is the best responses to increasing students’ proficiency in any topic as the new scholar year starts.

School starts at 7.55 am and ends at 5 pm and extends till 7 pm for students engaged in theater, orchestra…

Every day, students have to attend a 90-minutes math course, 90 minutes of English, 25 minutes in reflective thinking (taking all the time necessary to solving a problem, and not just math…). The motto is smile, sit up, listen, ask questions, nod and track with your eyes…(SSLANT)

Note: Topic was inspired by a chapter in one of Malcolm Gladwell books

And Higgs enshrined a modern material God. The tiniest of all: The Boson

Last week, particle and nuclear physicists “discovered” that the theoretical notion of the particle boson, labelled the boson of Higgs does exist.  The British Higgs theorized in 1965 that this boson must exist if matters should gain any weight…the missing link to a cohesive theory for the creation of a universe…Higgs is jubilant that the discovery was conclusive while still alive…

After thousands of trials bombarding elementary particles of protons and neutrons and…5 bosons, the tiniest of all particles, materialized in a flickering fraction of a one millionth of a second, invisible to human eyes and other sensory organs.

And the new God turned out to be the smallest, the tiniest of all, and still the most invisible even to the most modern equipment in technologies, and still permeating everything, every particle…

And the new God turned out not to be One, but zillion of Gods, mostly identical though, zillion in every particle in the universe…

And the new God turned out to have some physical weight, physical gravity…And without Him nothing could have amassed any weight…And no Gravity, and no universe could have existed…

And it turned out that all He had to do is to show up for less than one millionth of a second after this mythical Big Bang for everything to take form and exist…to happen, to get bigger, to expand, shrink at incredible speed

And we thought that we are from dust and shall return to dust. Wrong! We are from bosons and shall return to bosons…

Mankind created a God to be far larger than the universe, far more powerful…Political scientists said the ancient God should had to be that powerful, liberal capitalists said so, multinational financial corporations said so, superpower imperialist political strategists said so, Einstein relativity theory said so, all the religions said so…

And it turned out that this ancient God was not that big, not so abstract, and hate to survive more than one millionth of second on His own, free from attachment to other particles…

What happened to this God who appeared to Charlton Heston Moses, who took all his time spelling the 10 Commandments to a flabbergasted Moses who finally fell asleep and went into deep coma?

Heston Moses died and was reincarnated into “Heston Higgs”…old in the picture, as it should be. Prophet Higgs has been screaming in the wilderness for over four decades on this British Desert: “God appeared to my mind. He is in my mathematical nuclear equation. God said: Call me Boson. Find me this Boson. I miss Him. Get in touch with this damned Boson…And for God sake, call Him Boson, not Boson of Higgs…Cannot stand blasphemy…”

The new God is a Heisenberg quantum particle that “cannot be seen and heard simultaneously…” (see note)

Trust the physicists, this highly religious sect, for searching for the absolute and the eternal God. They still believe in the Big Bang, another myth that acquired consensus certainty in this exclusive club.  As if the universe should be created “instantly” and with a Big Bang for it to make any sense…

All other scientific fields, natural and social, believe that development and creation is a time-consuming process…Not to nuclear and particle physicists: Everything must happen instantly and in no time…

Trust the physicists to claim that nothing would have materialized without the existence of this boson after the one millionth of a second of the Big Bang…In every second, many stars and galaxies disintegrate, emitting zillion of bosons, and still, the universe could not have existed if the boson failed to intervene and materialize right after the Big Bang

The new God is not even physics: He is still a philosophy of the sub atomic universe…He always was a concept to hold together our scattered brain, yearning for the Absolute and the Eternal

Note: Heisenberg restriction in the sub atomic universe was that no particle can be exactly located and timed simultaneously: If we focus on exactly measuring the location of a particle, then time is a statistics and vice versa.  Why? Any measuring instrument is bound to disturb the current state of any particle in the sub atomic world…

I have studied nuclear and atomic physics. I have studied relativity and quantum physics…I loved all these courses, except quantum.  I kept wondering: If we cannot measure exactly and simultaneous many parameters in the sub atomic universe then, why call it physics?

May be since I have taken quantum mechanics technology has advanced in such a way not to disturb particles in the sub atomic universe…May be the quantum convoluted equations are easier to compute by computer…May be Quantum mechanics can be inducted into the world of Physics…

And you have hundreds of theoretical physicists trying hard to discover a mathematical equation that would unify relativity and quantum physics…Why? Math is an abstract field by excellence, but when you intend on purpose to applying it in physics then you have got to be able to measure, test, and validate the equation…How can this be done in the subatomic universe?

Efficiency has limits within cultural bias; (Dec. 10, 2009)

Sciences that progressed so far have relied on mathematicians: many mathematical theories have proven to be efficacious in predicting, classifying, and explaining phenomena.

In general, fields of sciences that failed to interest mathematicians stagnated or were shelved for periods; maybe with the exception of psychology.

People wonder how a set of abstract symbols that are linked by precise game rules (called formal language) ends up predicting and explaining “reality” in many cases.

Biology has received recently a new invigorating shot: a few mathematicians got interested working for example on patterns of butterfly wings and mammalian furs using partial derivatives, but nothing of real value is expected to further interest in biology.

Economy, mainly for market equilibrium, applied methods adapted to dynamic systems, games, and topology. Computer sciences is catching up some interest.

Significant mathematics” or those theories that offer classes of invariant relative to operations, transformations, and relationship almost always find applications in the real world: they generate new methods and tools such as theories of group and functions of a complex variable.

For example, the theory of knot was connected to many applied domains because of its rich manipulation of “mathematical objects” (such as numbers, functions, or structures) that remain invariant when the knot is deformed.

What is the main activity of a modern mathematician?

First of all, they do systematic organization of classes of “mathematical objects” that are equivalent to transformations. For example, surfaces to a homeomorphisms or plastic transformation and invariant in deterministic transformations.

There are several philosophical groups within mathematicians

1. The Pythagorean mathematicians admit that natural numbers are the foundations of the material reality that is represented in geometric figures and forms. Their modern counterparts affirm that real physical structure (particles, fields, and space-time…) is identically mathematical. Math is the expression of reality and its symbolic language describes reality. 

2. The “empirical mathematicians” construct models of empirical (experimental) results. They know in advance that their theories are linked to real phenomena.

3. The “Platonist mathematicians” conceive the universe of their ideas and concepts as independent of the world of phenomena. At best, the sensed world is but a pale reflection of their ideas. Their ideas were not invented but are as real though not directly sensed or perceived. Thus, a priori harmony between the sensed world and their world of ideas is their guiding rod in discovering significant theories.

4. There is a newer group of mathematicians who are not worried to getting “dirty” by experimenting (analyses methods), crunching numbers, and adapting to new tools such as computer and performing surgery on geometric forms.

This new brand of mathematicians do not care to be limited within the “Greek” cultural bias of doing mathematics: they are ready to try the Babylonian and Egyptian cultural way of doing math by computation, pacing lands, and experimenting with various branches in mathematics (for example, Pelerman who proved the conjecture of Poincaré with “unorthodox” techniques and Gromov who gave geometry a new life and believe computer to be a great tool for theories that do not involve probability).

Explaining phenomena leads to generalization (reducing a diversity of phenomena, even in disparate fields of sciences, to a few fundamental principles).  Mathematics extend new concepts or strategies to resolving difficult problems that require collaboration of various branches in the discipline.

For example, the theory elaborated by Hermann Weyl in 1918 to unifying gravity and electromagnetism led to the theory of “jauge” (which is the cornerstone theory for quantum mechanics), though the initial theory failed to predict experimental results.

The cord and non-commutative geometry theories generated new horizons even before they verified empirical results. 

Axioms and propositions used in different branches of mathematics can be combined to developing new concepts of sets, numbers, or spaces.

Historically, mathematics was never “empirically neutral”: theories required significant work of translation and adaptation of the theories so that formal descriptions of phenomena are validated.

Thus, mathematical formalism was acquired by bits and pieces from the empirical world.  For example, the theory of general relativity was effective because it relied on the formal description of the invariant tensor calculus combined with the fundamental equation that is related to Poisson’s equations in classical potential

The same process of adaptation was applied to quantum mechanics that relied on algebra of operators combined with Hilbert’s theory of space and then the atomic spectrum.

In order to comprehend the efficiency of mathematics, it is important to master the production of mental representations such as ideas, concepts, images, analogies, and metaphors that are susceptible to lending rich invariant.

Thus, the discovery of the empirical world is done both ways:

First, the learning processes of the senses and

Second, the acquisition processes of mathematical modeling.

Mathematical activities are extensions to our perception power and written in a symbolic formal language.

Natural sciences grabbed the interest of mathematicians because they managed to extract invariant in natural phenomena. 

So far, mathematicians are wary to look into the invariant of the much complex human and social sciences. Maybe if they try to find analogies of invariant among the natural and human worlds then a great first incentive would enrich new theories applicable to fields of vast variability.

It appears that “significant mathematics” basically decodes how the brain perceives invariant in what the senses transmit to it as signals of the “real world”. For example, Stanislas Dehaene opened the way to comprehending how elementary mathematical capacity are generated from neuronal substrate.

I conjecture that, since individual experiences are what generate intuitive concepts, analogies, and various perspectives to viewing and solving problems, most of the useful mathematical theories were essentially founded on the vision and auditory perceptions. 

New breakthrough in significant theories will emerge when mathematicians start mining the processes of the brain of the other senses (they are far more than the regular six senses). Obviously, the interested mathematician must have witnessed his developed senses and experimented with them as hobbies to work on decoding their valuable processes in order to construct this seemingly “coherent world”.

A wide range of interesting discoveries on human capabilities can be uncovered if mathematicians dare direct scientists and experimenters to additional varieties of parameters and variables in cognitive processes and brain perception that their theories predict.

Mathematicians have to expand their horizon: the cultural bias to what is Greek has its limits.  It is time to take serious attempts at number crunching, complex computations, complex set of equations, and adapting to newer available tools.

Note: I am inclined to associate algebra to the deductive processes and generalization on the macro-level, while viewing analytic solutions in the realm of inferring by manipulating and controlling possibilities (singularities); it is sort of experimenting with rare events.

Ironing out a few chaotic glitches; (Dec. 5, 2009)

              Philosophers have been babbling for many thousand years whether the universe is chaotic or very structured so that rational and logical thinking can untangle its laws and comprehend nature’s behaviors and phenomena.

              Plato wrote that the world is comprehensible.  The world looked like a structured work of art built on mathematical logical precision. Why? Plato was found of symmetry, geometry, numbers, and he was impressed by the ordered tonality of musical cord instruments.  Leibnitz in the 18th century explained “In what manner God created the universe it must be in the most regular and ordered structure.  Leibnitz claimed that God selected the simplest in hypotheses that generated the richest varieties of phenomena.”  A strong impetus that the universe is comprehensible started with the “positivist philosophers and scientists” of the 20th century who were convinced that the laws of natures can be discovered by rational mind.

            Einstein followed suit and wrote “God does not play dice.  To rationally comprehend a phenomenon we must reduce, by a logical process, the propositions (or axioms) to apparently known evidence that reason cannot touch.” The pronouncement of Einstein “The eternally incomprehensible universe is its comprehensibility” can be interpreted in many ways. The first interpretation is “what is most incomprehensible in the universe is that it can be comprehensible but we must refrain from revoking its sacral complexity and uncertainty”.  The second interpretation is “If we are still thinking that the universe is not comprehensible then may be it is so, as much as we want to think that we may understand it; thus, the universe will remain incomprehensible (and we should not prematurely declare the “end of science”).

            The mathematician Herman Weyl developed the notion: “The assertion that nature is regulated by strict laws is void unless we affirm that it is related by simple mathematical laws.  The more we delve in the reduction process to the bare fundamental propositions the more facts are explained with exactitude.”  It is this philosophy of an ordered and symmetrical world that drove Mendeleyev to classifying the chemical elements; Murry Gell-Mann used “group theory” to predicting the existence of quarks.

            A few scientists went even further; they claimed that the universe evolved in such a way to permit the emergence of the rational thinking man.  Scientists enunciated many principles such as “the principle of least time” that Fermat used to deduce the laws of refraction and reflection of light; Richard Feynman discoursed on the “principle of least actions”; we have the “principle of least energy consumed”, the “principle of computational equivalence”, the “principle of entropy” or the level of uncertainty in a chaotic environment.

            Stephen Hawking popularized the idea of the “Theory of Everything TOE” a theory based on a few simple and non redundant rules that govern the universe.  Stephen Wolfran thinks that the TOE can be found by a thorough systematic computer search: The universe complexity is finite and the most seemingly complex phenomena (for example cognitive functions) emerge from simple rules.

            Before we offer the opposite view that universe is intrinsically chaotic let us define what is a theory.  Gregory Chaitin explained that “a theory is a computer program designed to account for observed facts by computation”.  (Warning to all mathematicians!  If you want your theory to be published by peer reviewers then you might have to attach an “elegant” or the shortest computer program in bits that describes your theory)

            Kurt Gödel and Alain Turing demonstrated what is called “incompletude” in mathematics or the ultimate uncertainty of mathematical foundations.  There are innumerable “true” propositions or conjectures that can never be demonstrated.  For example, it is impossible to account for the results of elementary arithmetic such as addition or multiplication by the deductive processes of its basic axioms.  Thus, many more axioms and unresolved conjectures have to be added in order to explain correctly many mathematical results.  Turing demonstrated mathematically that there is no algorithm that can “know” if a program will ever stop or not.  The consequence in mathematics is this: no set of axioms will ever permit to deduce if a program will ever stop or not. Actually, there exist many numbers that cannot be computed.  There are mathematical facts that are logically irreducible and incomprehensive.

            Quantum mechanics proclaimed that, on the micro level, the universe is chaotic: there is impossibility of simultaneously locating a particle, its direction, and determining its velocity.  We are computing probabilities of occurrences.  John von Neumann wrote: “Theoretical physics does not explain natural phenomena: it classifies phenomena and tries to link or relate the classes.”

            Acquiring knowledge was intuitively understood as a tool to improving human dignity by increasing quality of life; thus, erasing as many dangerous superstitions that bogged down spiritual and moral life of man.  Ironically, the trend captured a negative life of its own in the last century.  The subconscious goal for learning was to frustrate fanatic religiosity that proclaimed that God is the sole creator and controller of our life, its quality, and its destiny.  With our gained power in knowledge we may thus destroy our survival by our own volition; we can commit earth suicide regardless of what God wishes.  So far, we have been extremely successful beyond all expectations.  We can destroy all living creatures and plants by activating a single H-Bomb or whether we act now or desist from finding resolution to the predicaments of climate changes.

            I have impressions.  First, what the mathematicians and scientists are doing is not discovering the truth or the real processes but to condense complexity into simple propositions so that an individual may think that he is able to comprehend the complexities of the world.  Second, nature is complex; man is more complex; social interactions are far more complex.  No mathematical equations or simple laws will ever help an individual to comprehend the thousands of interactions among the thousands of variability.  Third, we need to focus on the rare events; it has been proven that the rare events (for example, occurrences at the tails of probability functions) are the most catastrophic simply because very few are the researchers interested in investigating them; scientists are cozy with those well structured behaviors that answer collective behaviors.

            My fourth impression is that I am a genius without realizing it.  Unfortunately Kurt Gödel is the prime kill joy; he would have mock me on the ground that he mathematically demonstrated that any sentence I write is a lie.  How would I dare write anything?




April 2023

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