Posts Tagged ‘rare events’
A few chaotic glitches in sciences and philosophy?
Note: Re-edit of “Ironing out a few chaotic glitches; (Dec. 5, 2009)”
This Covid-19 pandemics has forced upon me to repost this old article.
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 fond 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 nature 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 Hermann 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; Murray Gell-Mann used “group theory” to predict 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 Wolfram 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 meant 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.
Fourth impression is that I am a genius without realizing it. Unfortunately, Kurt Gödel is the prime killjoy; 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?
Einstein speaks on theoretical physics
Posted by: adonis49 on: February 16, 2010
Einstein speaks on theoretical physics; (Nov. 18, 2009)
The creative character of theoretical physicist is that the products of his imagination are so indispensably and naturally impressed upon him that they are no longer images of the spirit but evident realities. Theoretical physics includes a set of concepts and logical propositions that can be deduced normally. Those deductive propositions are assumed to correspond exactly to our individual experiences. That is why in theoretical book the deduction exercises represent the entire work.
Newton had no hesitation in believing that his fundamental laws were provided directly from experience. At that period the notion of space and time presented no difficulties: the concepts of mass, inertia, force, and their direct relationship seemed to be directly delivered by experience. Newton realized that no experience could correspond to his notion of absolute space which implicates absolute inertia and his reasoning of actions at distance; nevertheless, the success of the theory for over two centuries prevented scientists to realize that the base of this system is absolutely fictive.
Einstein said “the supreme task of a physician is to search for the most general elementary laws and then acquire an image of the world by pure deductive power. The world of perception determines rigorously the theoretical system though no logical route leads from perception to the principles of theory.” Mathematical concepts can be suggested by experience, the unique criteria of utilization of a mathematical construct, but never deducted. The fundamental creative principle resides in mathematics.
Logical deductions from experiments of the validity of the Newtonian system of mechanics were doomed to failures. Research by Faraday and Maxwell on the electro-magnetic fields initiated the rupture with classical mechanics. There was this interrogation “if light is constituted of material particles then where the matters disappear when light is absorbed?” Maxwell thus introduced partial differential equations to account for deformable bodies in the wave theory. Electrical and magnetic fields are considered as dependent variables; thus, physical reality didn’t have to be conceived as material particles but continuous partial differential fields; but Maxwell’s equations are still emulating the concepts of classical mechanics.
Max Plank had to introduce the hypothesis of quanta (for small particles moving at slow speed but with sufficient acceleration), which was later confirmed, in order to compute the results of thermal radiation that were incompatible with classical mechanics (still valid for situations at the limit). Max Born pronounced “Mathematical functions have to determine by computation the probabilities of discovering the atomic structure in one location or in movement”.
Louis de Broglie and Schrodinger demonstrated the fields’ theory operation with continuous functions. Since in the atomic model there are no ways of locating a particle exactly (Heisenberg) then we may conserve the entire electrical charge at the limit where density of the particle is considered nil. Dirac and Lorentz showed how the field and particles of electrons interact as of same value to reveal reality. Dirac observed that it would be illusory to theoretically describe a photon since we have no means of confirming if a photon passed through a polarizator placed obliquely on its path.
Einstein is persuaded that nature represents what we can imagine exclusively in mathematics as the simplest system in concepts and principles to comprehend nature’s phenomena. For example, if the metric of Riemann is applied to a continuum of four dimensions then the theory of relativity of gravity in a void space is the simplest. If I select fields of anti-symmetrical tensors that can be derived then the equations of Maxwell are the simplest in void space.
The “spins” that describe the properties of electrons can be related to the mathematical concept of “semi-vectors” in the 4-dimensional space which can describe two kinds of elementary different particles of equal charges but of different signs. Those semi-vectors describe the magnetic field of elements in the simplest way as well as the properties electrical particles. There is no need to localize rigorously any particle; we can just propose that in a portion of 3-dimensional space where at the limit the electrical density disappears but retains the total electrical charge represented by a whole number. The enigma of quanta can thus be entirely resolved if such a proposition is revealed to be exact.
Critique
Till the first quarter of the 20th century sciences were driven by shear mathematical constructs. This was a natural development since most experiments in natural sciences were done by varying one factor at a time; experimenters never used more than one independent variable and more than one dependent variable (objective measuring variable or the data). Although the theory of probability was very advanced the field of practical statistical analysis of data was not yet developed; it was real pain and very time consuming doing all the computations by hand for slightly complex experimental designs. Sophisticated and specialized statistical packages constructs for different fields of research evolved after the mass number crunchers of computers were invented.
Thus, early theoretical scientists refrained from complicating their constructs simply because the experimental scientists could not practically deal with complex mathematical constructs. Thus, the theoretical scientists promoted the concept or philosophy that theories should be the simplest with the least numbers of axioms (fundamental principles) and did their best to imagining one general causative factor that affected the behavior of natural phenomena or would be applicable to most natural phenomena.
This is no longer the case. The good news is that experiments are more complex and showing interactions among the factors. Nature is complex; no matter how you control an experiment to reducing the numbers of manipulated variables to a minimum there are always more than one causative factor that are interrelated and interacting to producing effects.
Consequently, the sophisticated experiments with their corresponding data are making the mathematician job more straightforward when pondering on a particular phenomenon. It is possible to synthesize two phenomena at a time before generalizing to a third one; mathematicians have no need to jump to general concepts in one step; they can consistently move forward on firm data basis. Mathematics will remain the best synthesis tool for comprehending nature and man behaviors.
It is time to account for all the possible causatives factors, especially those that are rare in probability of occurrence (at the very end tail of the probability graphs) or for their imagined little contributing effects: it is those rare events that have surprised man with catastrophic consequences.
Theoretical scientists of nature’s variability should acknowledge that nature is complex. Simple and beautiful general equations are out the window. Studying nature is worth a set of equations! (You may read my post “Nature is worth a set of equations”)
Ironing out a few chaotic glitches
Posted by: adonis49 on: December 9, 2009
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?
First Anniversary: I married wordpress.com
Posted by: adonis49 on: September 17, 2009
First Anniversary: I married wordpress.com; (September 18, 2009)
Thursday, September 18, 2008. The weather is mostly cloudy. I borrowed “Chroniques de Gaza” by Caroline Mangez at a private library. I removed to my study around 3 pm and saw my niece Joanna working on her portable. I reminded her that she promised to aid me open a blog; she selected wordpress.com on account that it is the most visited site. I sat by her side and we went through the queries. My site is adonis49.wordpress.com; the affix 49 is the year of my birthyear since Adonis was already taken.
I tried to start publishing articles on my blog of wordpress.com but the internet was acting up as I clicked on “publish”. I was wondering: “This might turn out to be a time consuming process of publishing what I have written”. It took me over an hour just for one article to go. Once I had ironed out the process I spent a hectic week publishing over five years of unpublished pieces of articles, book reviews, short stories, and novels. The published materials amounted to 600 posts: I had subdivided chapters of my novels to quicken the process.
I learned later that I should have subdivided even further so that readers won’t have to suffer more than two pages at a time. I also learned much later that it is preferable to assign a new title to every post and not the easy alternative of patching up part 1, part 2, or continue 1, continue 2, and the sort. Thinking up new titles are fun and a great learning processes. I discovered the value of assigning new titles for posts that did not generate hits: people have so many choices of posts to read that they prefer catchy titles.
In this year I added over 600 new posts to the ones I had written previously and generated 16,000 hits. Laws do not fail very often: maybe 20% of my posts generated 80% of hits even if I disagree with my readers on the value of their choices. Laws do not fail very often but when they do it is catastrophic; scientists, and especially financial analysts, fail to consider seriously the rare events and their dangerous potential consequences. They just take the easy way out by focusing on the average or most likely events. The latest financial crash is a striking example; it is not as if the financial analysts didn’t know about rare events: they preferred not to be considered the black sheep of doom. It is so much nicer to collect easy bonuses and let others suffer.
Actually, I am under the impression that a dozen of posts or 1% are generating a fourth of the total hits. Thus, I may retire for a whole year and still generate a substantial number of hits; that is not my purpose: I want people to read good stuff.
By and by I increased the number of categories to reach 25; if it were feasible to edit and re-shuffle the names of my categories I would have gladly invested time of this important factor. I would appreciate some aid in that domain.
Nick was very helpful in sending me a link to widgets when I asked for his advice to simplify navigating my cumbersome blog. So far, widgets have been great for my own navigation; I do not doubt that they’ll be helpful for my readers. So far, my posts do not include pictures or video: I lack the equipments and the patience for this important improvement. They say a picture is worth a thousand words; I am not so sure; it might be correct for the lazy minds or those who are more inclined to visual information. Anyway, rest assured that in due time my pictures would not be “stand-alone” dumb medium such as “No Comment”. Expressing your feelings, ideas, and opinions in words are great exercises for your own benefit: you refresh your memory and re-structure your ideas for better explanation and exposition.
I received a new release on life this fabulous year; discovering a free publishing site is like receiving grace. I need to read more so that I can publish at least one post a day; usually, I publish 10 posts per week. I learned to be concise and not surpass 1,000 words per posts. Thus, long articles are divided into parts with new titles. Every now and then, I regroup the parts into one lengthy article with a new title: it is beneficial to me to re-edit the main topic and present a comprehensive article for later use.
An excited reader was overwhelmed by the diversity and wealth of my book reviews in topics and in foreign sources (I do read and write in three languages Arabic, French, and then English); she encouraged me to patronize her site; she failed to know that I am a novice navigator and that I have no patience whatsoever for net navigation. I like hard cover materials. Bref, I sent her a message telling her that all that I have is a word processor; all that I know to do is to store my pieces on a USB and then locate an internet provider to publish my posts. I hope that I finally nailed down this troublesome acronym USB: I kept saying UBS until my nieces and nephews got bored of correcting me. I sometimes insist on UBS to express my displeasure for their behaviors.
Yes, all that I do is read a lot and then jot down sentences and ideas on a sheet of paper: public power is out over 12 hours a day in this part of a country. Once the electricity is on then my article is done within half an hour. I quickly store my piece on a USB for fear that the power does not fail me again, as it so often do. It is not so hard publishing but the public power hardly will improve in the foreseeable future. I firmly believe that if I enjoyed better amenities in electricity and equipments then my productivity might suffer accordingly. It does not mean that those patronizing my blog should pray for my situation to last: that would be cruel and inhuman. You might pray that I win big on the lotto or a publisher contacts me: I have so much to publish on hard covers: the medium that I cherish so much and that generates money.
WordPress.com board of directors must start thinking seriously how to help us bloggers make money for our hard and consistent work.
Adonis Diaries 