Adonis Diaries

Posts Tagged ‘Laplace

Einstein speaks his mind processes on the origin of General Relativity; (Nov. 21, 2009)

This article is on  how Einstein described his mind processes that lead to the theory of restricted relativity and then his concept for General Relativity. In 1905, restricted relativity discovered the equivalence of all systems of inertia for formulating physics equations.

From a cinematic perspective, there was no way to doubting relative movements. Still, there was the tendency among physicists to physically extend privileged significance to system of inertia.  The question was “if speed is relative then, do we have to consider acceleration as absolute?”

Ernest Mach considered that inertia did not resist acceleration except when related to the acceleration toward other masses. This idea impressed Einstein greatly.  Einstein said: ” First, I had to establish a law of gravitation field and suppress the concept of absolute simultaneity. Simplicity urged me to maintain Laplace’s “scalar gravity potential” and fine tune Poisson’s equation.

Given the theorem of inertia of energy then, inertia mass must be depended on gravitation potential; but my research left me skeptical. In classical mechanics, vertical acceleration in a vertical field of gravity is independent of the horizontal component of velocity; it follows that vertical acceleration is exercised independently of the internal kinetic energy of the body in movement.

I discovered that this independence did not exist in my draft theory; this evidence did not coincide with the affirmation that all bodies submit to the same acceleration in a gravitational field. Thus, the principle that there is equality between inertia mass and weight grew with striking significance. I was convinced of its validity, though I had no knowledge of the results of experiments done by Eotvos.”

Consequently, the principle of equality between inertia mass and weight would be explained as follows: in a homogeneous gravitational field, all movements are executed in relation to a system of coordinates accelerating uniformly as if in absence of gravity field. I conjectured that if this principle is applicable to any other events then it can be applied to system of coordinates not accelerating uniformly.

These reflections occupied me from 1908 to 1911 and I figured that the principle of relativity needed to be extended (equations should retain their forms in non uniform accelerations of coordinates) in order to account for a rational theory of gravitation; the physical explanation of coordinates (measured by rules and clocks) has to go.

I reasoned that if in reality “a field of gravitation used in system of inertia” did not exist it could still be served in the Galilean expression that “a material point in a 4-dimensional space is represented by the shortest straight line”. Minkowski has demonstrated that this metric of the square of the distance of the line is a function of the squares of the differential coordinates.  If I introduced other coordinates by non linear transformation then the distance of the line stay homogeneous if coefficients dependent on coordinates are added to the metric (this is the Riemann metric in 4-dimension space not submitted to any gravity field). Thus, the coefficients describe the field of gravity in the selected system of coordinates; the physical significance is just related to the Riemannian metric. This dilemma was resolved in 1912.

Two other problems had to be resolved from 1912 to 1914 with the collaboration of Marcel Grossmann.

The first problem is stated as follows: “How can we transfer to a Riemannian metric a field law expressed in the language of restrained relativity?”  I discovered that Ricci and Levi-Civia had answered it using infinitesimal differential calculus.

The second problem is: “what are the differential laws that determine the coefficients of Riemann?”  I needed to resolve invariant differential forms of the second order of Riemann’s coefficients. It turned out that Riemann had also answered the problem using curb tensors.

“Two years before the publication of my theory on General Relativity” said Einstein “I thought that my equations could not be confirmed by experiments. I was convinced that an invariant law of gravitation relative to any transformations of coordinates was not compatible with the causality principle. Astronomic experiments proved me right in 1915.”

Note:  I recall that during my last year in high school my physics teacher, an old Jesuit Brother, filled the blackboard with partial derivatives of Newton’s equation on the force applied to a mass; then he integrated and he got Einstein’s equation of energy which is  mass multiplied by C square. At university, whenever I had problems to solve in classical mechanics on energy or momentum conservation I just applied the relativity equation for easy and quick results; pretty straightforward; not like the huge pain of describing or analyzing movements of an object in coordinate space.

The illusion of knowing is the major obstacle to discovery; (October 4, 2009)

Even a century ago, a scientist would publish a single manuscript after a life time of research and toiling.

Transmission of opinions and suggestions among scientists were sent via long erudite letters by peers.

Translators of these remarkable books didn’t go unnoticed as today, but they were rewarded academically. Nowadays, any “respectable” scientist works for several institutions, private and public, and at various nations.

Even two centuries ago, scientists did not need to refer to Pythagoras or Archimedes.  Modern scientists have no time or need to refer to more recent scientists such as Copernicus, Galileo, Newton, Laplace, Lavoisier, or Kelvin. Soon Einstein and Heisenberg will be outmoded.

The team of the geeks in “Sciences and Future” met in August for brainstorming in “pause mode” to deliberate on the unique question confronting the team:

In the last few decades, what discoveries were true breakthroughs?”  The team reached an understanding on 5 scientific fields: climatology, neuroscience, astronomy, cellular biology, and Internet.

Consequently, I will answer a few of the questions that you might think you know in these fields so that our knowledge is no longer an illusion.

The internet shifts from the virtual to the real

There are 3 generations of internet or Web.

The first generation or Web1.0 was created from 2003 to 2005 and is represented by MySpace, Facebook, and YouTube that gathers people on common interest social aspects or making “friends”.

The second generation or Web 2.0 is represented by Twitter or the microblogging platform for messages restricted to 140 characters. Thus, these micro messages can be regrouped and analyze to constitute a story contributed by many Twitter bloggers.

The third generation of Web 3.0 is ready technologically; this generation is already labeled object oriented intelligence sources.  For example, you record a message on your cell phone and then stick a yellow sticker on a wall or an object. The next visitor will pass his cell phone over the sticker and copy your message of whatever you have seen or appreciated. This generation can zip all kinds of products and gather intelligence and compare with other resources.

Personally, I think that even the Twitter is already a perfect source of information by intelligence agencies; these centers can hire thousands of Twitter users and direct them on specific topic of interests in many countries.

Cells can be rejuvenated to its embryo stage

The lab technician would take samples of your skin. The skin cells can be treated to reach its first born state.

Whatever genetic diseases that cell inherited it will take another 30 years for the disease to emerge.  All the while you are thirty years younger. Better, skin cells can be treated to isolate a specific cell for any body member like liver, heart, brain, or whatever.

The sick tissue in any part of your body can be rejuvenated within a month. This biomedical technique of treating adult cells into embryo state was made possible because many laws prohibited using fetus embryo on the ground that the cell belonged to another person.

Is man’s activity altering nature more than geophysics?

Man feared the return of the ice age; it turned out that the climate is getting hotter and the poles are melting.

The emergence of urban and industrial societies as a geophysical force is altering the environment power for rejuvenation according to human threshold for survival.

Since 1824, Joseph Fourier theorized that gases in the atmosphere have the potential to increase surface temperature.

Even in 1896, John Tyndall predicted that the concentration of CO2 will increase temperature to 5 degrees by the end of the 20th century. Now, this is a fact and each year the casualties in man and nature are increasing by the violence of climatic changes. People are waiting anxiously the international summit on the environment in Copenhagen this December.

Awareness of man effective participation in climatic changes was proven when the ozone layer of O3 in the stratosphere was depleting. Seas level is increasing 3 mm a year since 1993.  So far, only Danemark produces the fourth of its power using eoliens or wind turbines.

Ex-President Bush Junior said in 1992: “The American way of life is not negotiable.”

The philosopher Michelle Serres said in 1990: “This world that we treated as an object is returning as a subject; capable of vengeance.

The humorist Coluche said: “For an ecologist to be elected as President, trees should be allowed to vote.”

The brain is in perpetual re-structuring

There are specialized neurons that can be activated when an action is executed or when an action is also observed (mirror neurons).  These mirror neurons are the biological basis for empathy, imitation, and training; almost every decision is influenced by our emotions.

Neurons have the potential to flow or transfer from one brain to another when recycling cognitive aptitudes such as reading and writing are elevated.  Neurons and connections are modified when training tasks are memorized.

We have 8 varieties of intelligence; mainly the visual, spatial, naturalist, logic-mathematics, corporal, musical, inter-personal, and intra-personal intelligences.

The new battery of experiments for testing cognitive and movements capabilities are designed to account for our eight kinds of intelligences. It is the quantity of synapses (connections) and not the weight of the brain that differentiate among the various intelligences.

There are phases in our sleep when brain activities are most intense while muscular activities are extremely inhibited; this phase is called “paradox sleep”.  We produce new neurons at every stage of growth, especially in the hippocampus and the smell brains.

Almost 10% of our synapses are established when we are born and they increase with our activities and cognitive demands (efforts, mental and physical, mean increase in fresh synapses and neurons).

Hormones or chemical messengers for the brains

Serotonin is a chemical messenger to the brains; it is implicated in sleep, feeding and sexual habits. A decrease in its production is associated to depressive moods. Anti-depressant drugs increase the concentration of serotonin in the blood.

Dopamine is a chemical hormone that controls movements, moods, addiction, and the circuit of pleasure; its deficiency generates rigidity in the muscles which is the symptoms of Parkinson disease.

Adrenaline is a chemical hormone that is secreted at moments of stress and is attached on large numbers of receptors to re-enforce cardiac functions, accelerate the heart beats, elevate arterial pressure, inhibit digestion and increase the level of glycemy.

Cortisol is secreted in moments of stress to increase the rate of glucose in the blood stream and liberating energy to counter dangers.

Insulin enhances the stock of glucose in the tissues and thus decreases glycemy.

Acetylcholine is a neuro-transmitter that excites the targeted brain when acquiring new training and for enhancing memory; its deficiency is the origin of Alzheimer disease.

Erythropoietin stimulates the synthesis of red blood cells; its deficiency results in anemia.  The word “doping” is related to sport competitors abusing of this hormone.

Article #30 of “What is Human Factors in Engineering?”;  December 27, 2005

 “How objective and scientific are experiments?”

If we narrow this article to the statistical analysis of experiments and without going into details suffice us to mention a few controversies.  First, let us do a chronology of the various paradigms in statistics and statistical algorithms.  From a European perspective Pascal is believed to have started probability theory in1654.

LaPlace and Legendre contributed to the Least-Squares algorithm for how to fit a model to data (1750-1810)

Gauss developed the geometry and algebra of the multivariate normal distribution (1800’s)

Galton studied regression between two variables (1885) and Pearson the correlation coefficient in 1895.

Fisher, Snedecor and Sheffe concurrently worked on experimental design and analysis of variance algorithm (ANOVA) to statistically test the population distribution under the assumptions of normality in the 1920’s.

The data analyses of non distribution base samples to fit models to data showing structural features were developed by Thurstone in Factor Analysis, by Young and Householder (1935) in Multidimensional scaling and Cluster analysis algorithms.

Joreskog, K. G developed in 1973 the algorithm of a general method for estimating a linear structural relational equation labeled LISREL that analyses the relationships among latent variables linked to operationalized indicators. This general method considers as special cases path analysis recursive or non recursive as well as Factors analysis.

John Tukey and Mosteller concentrated on studying exploratory data analysis to fit mathematical and geometric models to data showing both structural and residual, and thus complementing confirmatory or inferential analyses.

There are divergent paradigms in the following concepts:  first, the suitability of data measurements according to measurement theory versus the distribution properties of the variable of interest (S. S. Stevens versus I. R. Savage in the 60’s); second, the need to investigate real world data prior to applying any statistical package (data snooping) so that if you perform serious detective work on the data and torture it long enough it will confess and open many ways to understand its underlying behavior (John Tukey); thus increased emphasis on graphs of individual data points and plotting to investigate the preliminary screening so as to ensure that the summary statistics selected are truly relevant to the data at hand. 

Third, the application of the Bayesian approach from the consumer or decision maker viewpoint which provide the final probability against evidence instead of the investigator standard acceptance of a p-value to rejecting a hypothesis (read the “Illusion of Objectivity” by James Berger and Donald Berry, 1988).

Fourth, the selection of an investigator for a statistical package that he is familiar with instead of the appropriate statistics for the research in question;  The acceptance of untenable assumptions on population distributions and computing unrealistic parameters simply because the investigator is not trained to understanding or interpreting alternative statistical methods of nonparametric or distribution freer population methods.

Fifth, there are examples of investigators adopting explanatory statistical packages to torture data into divulging confusing causative variables while, in fact, the science is already well established in the domain to specifically determine exhaustively the causative factors simply because the investigator is not versed in mathematics or physics (“Tom Swift and his electric factor analysis machine by J. Scott Armstrong, 1967).

Sixth, there is a need to the “mathematization of behavioral sciences” (Skelum, 1969) which involves the development of mathematically stated theories leading to quantitative predictions of behavior and to derivation from the axioms of the theory of a multitude of empirically testable predictions. Thus, instead of testing verbal model as to the null hypothesis, an adequate mathematical model account for both variability and regularity in behavior and the appropriate statistical model is implied by the axioms of the model itself.  Another advantage is that attention is turned to measuring goodness of fit, range of phenomena handled by the model and ability to generating counterintuitive predictions.

This discussion is an attempt to emphasize the concept of experimentation as a structured theory and that the current easy and cheap computational potentials should be subservient to the theory so that data are transformed to answer definite and clear questions.  The Human Factors practitioner, whom should be multidisciplinary in order to master the human and physical sciences, is hard hit by the need of performing complex scientific experiments involving human subjects and yet required to yield practical recommendations for the applied engineering fields.

No wonder Human Factors professionals are confused in their purposes and ill appreciated by the other discipline unless a hybrid kind of scientists are generated from a structural combination of engineering discipline and modern experimental methods and statistical algorithms. 

However, Human Factors engineers who have an undergraduate engineering discipline and a higher degree in experimental research and statistical analyses training can be better positioned to handle research involving mathematical modeling of theories in sciences.

The fixed mindedness in adolescents reminds us of the mind fix of old people with the assumption that the mind has the potential flexibility to grow while young.

You may look young masking and old mind or look older and exhibiting a younger mind; it is your choice how much time and energy you are willing to invest for acquiring knowledge.


adonis49

adonis49

adonis49

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