Why is the science of chaos (ie complex systems) important: because it refutes the assumptions of reductionist science





IONS willis Harman: paradigm shift


Roger sperry<

Nobel prize for work characterizing the left and right brain

Put thoughts into a lead article for the 1981 Annual review of NeuroScience Changing Priorities


Says we are leaving behind determinism,  behaviorism,  and the materialism of the science of the past


we are having to recognize the primacy of inner conscious awareness as a causal reality”

Harmon says our minds effect reality; and it is often said we create our own reality;

He says he thinks the solution to our global problems lies in recognizing consciousness is a primary cause of reality.

In the early years of science, there wqas a  Tacit agreement with the church that science would not stray too far into the areas of soul ad spirit. Science was characterized by 3 assumptions:

Objectivist,  positivistic and  reductionist; basic to western thinking; lead to great technological achievement, undermined our understanding of values. Short term economic gains


Prigogene; theory of disapative structures




Freud traumaatic events in childhood an be repressed

William James: prof  of philosophy; psychology; different approach; labeled “expansion of consciosness almost 100 years ago; changing inner attitudes



Frederick    W H Meyers          wrote   the book   Human Personality and its Survival of Bodily Death  which came out    in 1903

Sleep & Dreams

Unconscious processes



Psychic phen


William James had high regard for Meyers work




                                                               World Views: The Quest for Fundamental Reality



Mathematicians such as the French Simeon-Denis Poisson, Andre-Marie Ampere, and the German Wilhelm Weber, assumed that electrical charges and magnetic poles act on one another at a distance, while Michael Faraday believed electrical charges and magnets  infuse all space with lines of force, through which the electric and magnetic charges work. Many scientists of Newton’s time believed that Newton had explicitely rejected the possibility that gravity acted through a distance through some medium. But he appears to have taken the opposite view, based on a letter written to a colleague: “That gravity should be innate, inherent, and essential to matter, so that one body can act on another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into  it “. [2]


Newton assumed that both absolute time and location are quantities which cannot be observed, but must be inferred from relative time and location [2a] http://plato.stanford.edu/entries/newton-principia/


In 1801, the British physicist Thomas Young appeared to prove light was a wave from the results of his “Double Slit Experiment” which showed that multiple light sources produce interference patterns ; yet in 1839, it was first shown that light waves falling on metal caused the emission of electrons, which suggests that  light has particle properties.


Einstein (German)
As science progressed, it was found that Newton's Laws did not give the right answers under certain circumstances: It did not work for objects moving very fast, nor for very small particles, nor for non-uniform motion.



Einstein’s theory that nothing could exceed the speed of light flew in the face of Newton’s law of gravity, which said that gravity could be felt instantly. Einstein resolved the dilemma by proposing that gravity is the warpage of space time. Einstein calculated that ripples of gravity travel at exactly the speed of light.: The result was his general theory of relativity.


Einstein was not satisfied with general relativity; he wanted to expand his general theory to include electromagnetism, which had been unified from  electricity and magnetism by James Clerk Maxwell only about 50 years before Einstein.


The EM force is billions and billions of times stronger than the force of gravity. That is why the atoms of earth or concrete stop an object which is falling due to the force of gravity.


Einstein brooded over an apparent conflict between Maxwell’s equations and Newton’s laws of motion. It stemmed from the Michaelson Morley experiment which suggested that light always travels at the same speed, no matter how fast or in what direction the observer is moving. This could be explained if distances and times appeared different to observers traveling at different speeds. A formula for converting the times and distances measured by one observer to those measured by another (traveling at different speeds) was put forward by  Hendrik Antoon Lorentz. Maxwell’s equations worked perfectly under this transformation, but Newton’s did not. Einstein solved the problem with his special theory of relativity. He took the constancy of the speed light as a starting point and worked out the consequences. He arrived at Lorentz’s transformation from a new direction and gave it a new perspective. There were no absolute  measures of space or time. A corollary was that Maxwell’s equations were the basic laws of the physical world. Newton’s laws were an approximation. From E=MC (squared), mass is just an immensely concentrated form of stored energy. All this based on the assumption that C is constant, and C is ratio  of electromagnetic and electrostatic units of charge. Einstein’s theory explained perfectly the way atomic particles behave when traveling close to the speed of light, and accounted for lost mass when a radioactive atom decays into two smaller ones. [3]


Einstein Believed time is not absolute due to the behavior of light; space is also not absolute. Einstein's theories worked better for objects moving very fast.  The two theories were: 1) the Special Theory of Relativity: Speed of light constant; as material objects approach the speed of light, they become more massive and shorter.  Traveling at the speed of light, a material object would have infinite mass and zero length. 2) General Theory of Relativity: Gravity is the curvature of space.

Einstein's universe contains two fundamental types of stuff; matter and energy, related by the famous equation


Einstein's laws still did not give good results for very small particles. In addition, photons and electrons exhibited anomalous behavior.


Einstein and Maxwell’s theories were useless at defining what goes on inside atoms.

In the late 1920s, new developments in science showed that what happens inside  atoms is governed by probability. Quantum physics was very successful in predicting what happens inside the quantum world, but is bases in probability. Einstein was very uncomfortable with this notion, insisting that god does not play dice with the universe.


The combined theories of kinetic theory of gasses, thermodynamics, and Maxwell’s equations seemed to indicate that all of the kinetic energy of molecules should long ago have been radiated away, leaving a cold dead universe. What was missing? Nature seemed to have some hidden mechanism which allowed a balance to be reached between the radiation  that matter emitted and absorbed.


These anomalies finally lead to the development of the theory of Quantum Mechanics

Max Plank  produced a formula in an “act of desperation” which  allowed matter to absorb radiant energy only in discreet amounts, or quanta. Einstein completed the coup in 1905 by asserting that radiation itself comes in discreet packetd, now called “photons”. Maxwell made  the point that although the things we call photons and electrons appear to us to behave sometimes like particles and sometimes like waves, we should not make the mistake of thinking that they are either. [4]

Einstein rejected quantum mechanics, noting that “God does not play dice with the universe”.

The Oddities of Spin

Electrons and quarks (thought to make up protons and neutrons) posses a property called “spin”. Experimenters have long accepted that the spin of a particle will always be found to point along whichever axis is chosen by the experimenter as his reference. Further, only when an elementary particle is rotated two complete revolutions of 360 degrees, will it have properties indistinguishable from those of the initial particle. [4+1]

The EPR thought experiment was devised by Einstein Podolsky and Rosen to discredit the new quantum physics. This thought experiment said that if quantum theory were correct, a change in spin of one particle in a two particle system would effect its twin simultaneously, instantaneously, even if the two had been widely separated in space. A mathematical proof of this was produced by JS Bell in 1964, and experimentally confirmed in 1972. This effect is probably not the result of a transfer of information, but rather a consequence of the one-ness of apparently separate objects. According to Gary Zukav, "Bell's theorem not only suggests that the world is quite different than it seems, it demands it". But others would argue that macroscopic reality may be quite different from subatomic reality.



Probing the structure of the atom, scientists found two more forces: the strong nuclear force holds the protons and neutrons of the nucleus  together; the weak nuclear force allows neutrons to turn into protons, giving off radiation in the process.


Gravity is completely overshadowed by EM, strong and weak nuclear forces. The atomic bomb releases the power of the string nuclear force.


Where does gravity fit in?


For the last 20 years of his life, Einstein secluded himself in a modest house in  Princeton NJ, devoting all his energy to try to write an equation that united gravity and EM. He virtually ignored QM .




In 1982 a remarkable event took place. At the University of  Paris a research team led by physicist Alain Aspect performed what may turn  out to be one of the most important experiments of the 20th century.  Aspect and his team proved J.S. Bell’s Theorem: they discovered that  under certain circumstances subatomic particles such as electrons are  able to instantaneously communicate with each other regardless of the distance separating them. Their experiment showed that the material universe is "non-local."


University of London physicist David Bohm, has suggested that Aspect's findings imply that objective reality does not exist, that despite its apparent solidity the universe is at heart a phantasm, a gigantic and splendidly detailed hologram. 

To understand why Bohm makes this startling assertion, one must first understand a little about holograms. A hologram is a three- dimensional photograph made with the aid of a laser. To make a hologram, the object to be photographed is first bathed in the light of a laser beam. Then a second laser beam is bounced off the reflected light of the first and the resulting interference pattern (the area where the two laser beams commingle) is captured on film. When the film is developed, it looks like a meaningless swirl of light and dark lines. But as soon as the developed film is illuminated by another laser beam, a three-dimensional image of the original object appears. The three-dimensionality of such images is not the only remarkable characteristic of holograms. If a hologram of a rose is cut in half and then illuminated by a laser, each half will still be found to contain the entire image of the rose. Indeed, even if the halves are divided again, each snippet of film will always be found to contain a smaller but intact version of the original image. Unlike normal photographs, every part of a hologram contains all the information possessed by the whole. The "whole in every part" nature of a hologram provides us with an entirely new way of understanding organization and order. For most of its history, Western science has labored under the bias that the best way to understand a physical phenomenon, whether a frog or an atom, is to dissect it and study its respective parts. [5]

In a series of landmark experiments in the 1920s, brain scientist Karl Lashley found that no matter what portion of a rat's brain he removed he was unable to eradicate its memory of how to perform complex tasks it had learned prior to surgery. The only problem was that no one was able to come up with a mechanism that might explain this curious "whole in every part" nature of memory storage. Then in the 1960s Pribram encountered the concept of holography and realized he had found the explanation brain scientists had been looking for. Pribram believes memories are encoded not in neurons, or small groupings of neurons, but in patterns of nerve impulses that crisscross the entire brain in the same way that patterns of laser light interference crisscross the entire area of a piece of film containing a holographic image. In other words, Pribram believes the brain is itself a hologram. Pribram's theory also explains how the human brain can store so many memories in so little space. It has been estimated that the human brain has the capacity to memorize something on the order of 10 billion bits of information during the average human lifetime (or roughly the same amount of information contained in five sets of the Encyclopaedia Britannica).


Similarly, it has been discovered that in addition to their other capabilities, holograms possess an astounding capacity for information storage--simply by changing the angle at which the two lasers strike a piece of photographic film, it is possible to record many different images on the same surface. It has been demonstrated that one cubic centimeter of film can hold as many as 10 billion bits of information. Our uncanny ability to quickly retrieve whatever information we need from the enormous store of our memories becomes more understandable if the brain functions according to holographic principles. If a friend asks you to tell him what comes to mind when he says the word "zebra", you do not have to clumsily sort back through some gigantic and cerebral alphabetic file to arrive at an answer. Instead, associations like "striped", "horselike", and "animal native to Africa" all pop into your head instantly. Indeed, one of the most amazing things about the human thinking process is that every piece of information seems instantly cross- correlated with every other piece of information--another feature intrinsic to the hologram. Because every portion of a hologram is infinitely interconnected with every other portion, it is perhaps nature's supreme example of a cross-correlated system.

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The storage of memory is not the only neurophysiological puzzle that becomes more tractable in light of Pribram's holographic model of the brain. Another is how the brain is able to translate the avalanche of frequencies it receives via the senses (light frequencies, sound frequencies, and so on) into the concrete world of our perceptions. Encoding and decoding frequencies is precisely what a hologram does best. Just as a hologram functions as a sort of lens, a translating device able to convert an apparently meaningless blur of frequencies into a coherent image, Pribram believes the brain also comprises a lens and uses holographic principles to mathematically convert the frequencies it receives through the senses into the inner world of our perceptions. An impressive body of evidence suggests that the brain uses holographic principles to perform its operations. Pribram's theory, in fact, has gained increasing support among neurophysiologists.


Argentinian-Italian researcher Hugo Zucarelli recently extended the holographic model into the world of acoustic phenomena. Puzzled by the fact that humans can locate the source of sounds without moving their heads, even if they only possess hearing in one ear, Zucarelli discovered that holographic principles can explain this ability. Zucarelli has also developed the technology of holophonic sound, a recording technique able to reproduce acoustic situations with an almost uncanny realism.

Pribram's belief that our brains mathematically construct "hard" reality by relying on input from a frequency domain has also received a good deal of experimental support. It has been found that each of our senses is sensitive to a much broader range of frequencies than was previously suspected. Researchers have discovered, for instance, that our visual systems are sensitive to sound frequencies, that our sense of smell is in part dependent on what are now called "osmic frequencies", and that even the cells in our bodies are sensitive to a broad range of frequencies. Such findings suggest that it is only in the holographic domain of consciousness that such frequencies are sorted out and divided up into conventional perceptions. But the most mind-boggling aspect of Pribram's holographic model of the brain is what happens when it is put together with Bohm's theory. For if the concreteness of the world is but a secondary reality and what is "there" is actually a holographic blur of frequencies, and if the brain is also a hologram and only selects some of the frequencies out of this blur and mathematically transforms them into sensory perceptions, what becomes of objective reality?

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By Michael Talbot, from The Holographic Universe



Put quite simply, it ceases to exist. As the religions of the East have long upheld, the material world is Maya, an illusion, and although we may think we are physical beings moving through a physical world, this too is an illusion.


Looking for a GUT:


String Theory [6]


Four known types of force in the universe: gravity, EM force, weak and strong nuclear forces.


Superforce: The world of subatomic particles. p 80-100


Although Gravity is extraordinarily weak; billions of times weaker then EM force; it is also universal. The weak force is much stronger than gravity, but much weaker than the EM force. The weak force is confined to individual subatomic particles, while gravity and EM are long range. The weak force results in spontaneous transmutations of atoms. It was discovered that, left to themselves, neutrons disintegrate after several minutes into a proton, electron, and neutrino. The weak force is responsible for this. The Strong force holds protons together; this force is stronger than EM, but like the weak force, is confined to a very short distance. Neutrons and protons are subject to the strong force, acting to hold them together, but electrons are not; nor are neutrinos or photons.  In the 1960s, quark theory was proposed, which held that each proton and neutron is made of 3 quarks, held together by the strong force. This theory made the strong force easier to understand.


The product of high speed particle collisions include several hundred types. These are not the “constituents” of the collided particles, but rather resultant debris created on site. In the 1960s, physicists were completely bewildered by the seemingly endless variety of particles being discovered in these accelerator experiments. “Today, (1984) there is no longer any doubt.  There is a deep and meaningful order in the microcosmos” which we are only beginning to understand. The varying quantities are mass, charge, and spin, and lifetime. Particles with 0, 1, or 2 spin are called Bosons, after Satyendra Bose; ˝ and 3/2 spin are Fermions. Big particles which couple to the Strong force are called hadrons; those which feel the weak force but not the strong are are called leptons (“light thing”) only a handful of Leptons, which include electron and Neutrino.   Nutrinos feel neither the strong force nor the EM force, almost oblivious to matter they pass right through it. They are harmless so the neutrino experiments require no shielding. They are the most common objects in the universe, outnumbering electrons or protons by a thousand million to one: the universe is a sea of Neutrinos punctuated by other particles.  Hundreds of types of Hadons. The decisive step in unraveling the hadron mystery came in 1963, when Murray Gell-Mann and George Zweig invented the quark theory. Three flavors of quark are used; up, down, and “strange”. The strong force cannot change the flavour of quarks; only the weak force can do that. Without a flavour change to convert a strange quark to an up or a down, no particle decay an occur. In 1974 the simple version of the quark theory was dealt a sharp blow. A new particle (called psi) was discovered by two independent researchers. There was no room in the quark theory for this new particle.   The situation was resolved by postulating a fourth quark flavour: “charm”. A rerun occurred in 1977, when a fifth quark flavour was postulated; bottom or beauty. The original quark theory was supposed to simplify, but we again have proliferation.


All ordinary matter is made form the two lightest leptons (electron and neutrino) and the two lightest quarks (up and down), called the “top level structure”. All remaining quarks and leptons  are unstable and rapidly decay into the top level structure. Why does nature bother with them?


Viewed at the quantum level, two electrons in a collision path would result in a scattering event in which a photon is emitted by one electron and absorbed by another, and then the two particles diverge. ( I thought a photon WAS an electron) Schematic diagrams may be used to represent this activity, and were first used by Richard Feynman to represent terms in an equation. The emitted photon can be thought of as a “messenger particle” It is important to note that this exchange is not observed in the interaction, it is  only a conceptual way of thinking about it. This type of photon is called “virtual”.


The description of electromagnetic activity in terms of virtual messenger photons is a highly sophisticated and detailed mathematical theory known as quantum electrodynamics (QED) This theory is consistent with the principles of both quantum theory and relativity theory. This theory allows a procedure for calculating the results of any interaction between photons and electrons, however complicated.


QED passed two decisive tests:

According to QED, energy levels of the hydrogen atom ought to be slightly shifted from where they would be if virtual photons did not exist. Willis Lamb of U of Arizona conducted an experiment to look for the shift and measure its value showed the measured and calculated values matched exactly. The second test involved a small correction the magnetic field carried by the electron. Once again theory and experiment matched exactly. QED is the most successful quantitative theory in existence. QED became the model for the quantum description of the other 3 forces. For gravity a particle called the “graviton” messenger particle was invented, analogous to the photon. When two particles exert a gravitational influence on each other, thye exchange gravitons. Photons and gravitons travel at the speed of light, so are “zero rest mass’ particles. The messenger particles which hold quarks together are called “gluons” gravitons are classed real and virtual. Weak force messengers are the Z and W particles. Z is identical to the photon except rest mass, and is a new form of light. Quarks, leptons and messengers completes the list of known subatomic particles.


George Keyworth, science advisor to the US president, at a lecture in Baltimore (1984?) said that the US had to regain her particle physics supremacy.  A new monster accelerator was being planed by the US to dwarf CERN, called the “superconducting super collider”, or the “Desertron”.  Keyworth’s address coincided with a wave of publicity over the Regan anti-missile project, also known as the beam weapon program. “Certainly most particle physicists found the idea both absurd and abhorrent, and reacted strongly against the presidents proposal.  Keyworth castigated them… and appealed to each member of the physics community  ‘to consider what part you can play in making beam weapons a working proposition.’ p. 99.




p. 93 davies fenyman diagrams





Much has been learned about the universe in spite of the fact that we do not have a GUT. However, some parts of the universe will never be understood without understanding how gravity, EM, and QM are related; that is, without a “GUT”


In 1916, German astronomer Carl Swarchfield proposed what we now call black holes. He postulated these would arise in cases where the mass was so concentrated that gravity was strong enough to prevent even light from escaping.


Today, satellite telescopes are discovering regions with enormous gravitational pull. Most scientists believe these regions are under the influence of black holes.


So,  what equations do you use for something that is both very massive (gravity usually rules) or very tiny (QM usually rules) Here is a case where physical reality provides us with something we have no equations to describe. 


20th century physicists have now joined  in a  search to find a way to mathematically describe both the very large (massive) and very small.



The primary contender is “String” theory, or “Super String” theory, which asserts that all phenomena are made up of very tiny strings of energy, which vibrate in varying ways.


Problems: the strings, if they exist, would be so small there would be little chance of ever seeing them.

So how do you test this theory?


( this is a lot like just creating another type of “atom”, or smallest particle.)


Einstein’s theory says that space can stretch or warp, but it cannot tear, so a “worm hole “ cannot be created.


At the level of the quantum, the fabric of space is chotic, so it might rip.

But that might be catastrophic.

This is where strings come in. they have a “calming” effect; they make rips in space possible

(this is getting on pretty thin nice)


modeling of atom went from protons & neutrons in nucleus & electrons orbiting, to a nucleus made of quarks of various flavors.


The next iteration was “String Theory”


By the mid  1990’s, 5 different string theories evolved, involving 10 dimensions.


 Edward Witten regarded as standing head & shoulders above other physicists in mastery of mathematics; considered a successor to Einstein




At a world conference on string theory in 1995, Witten presented his work, which showed the 5 different versions of string theory were merely different perspectives on the same thing; his theory was called “M” theory, and requires 11 dimensions. Some string theory advocated


speculate the simple strings can now be membranes (Branes) that can be “as big as the universe”

and that our perceivable universe could be merely one “slice” of a “bulk” of parallel universes


The weakness of gravity confounded scientists for decades. String theory suggests gravity is not really weak, but “seeps” off of our universe like  the sound of billiard balls seeps off the billiard ball table.


In early string theory, the strings were all closed loops. Later string theory has all the forces except gravity be un-looped strands hooked to out universe, while gravity is closed loop form which can freely escape into parallel universes. These closed loop strings  are called gravitons.


It is also speculated by some that the “big bang” was due to the collision of two “membranes” (slices of toast)


It is noted that if you can’t test it in the lab, it’s not science, but philosophy.


Fermi lab has a 4 mile circuit atom smasher: looking for evidence of a graviton escaping our universe membrane


CERN is working on a much larger one.


String theory predicts supersymmetry: every proton electron grtaviton associated with “accompanying “sparticle


String theory is predicted by mathamatics


Our picture of the universe has been revised several times to reveal new complexities


Scientists agree: string theory could be wrong


Kaluza-Klein Theory

The Modern Kaluza-Klein Theory unifies Maxwell's Theory of Electromagnetic and Einstein's Theory of General Relativity & Gravity. The theory provides the scientific and technical basis for modeling galaxies, solar systems, and spacecraft for traveling to the stars.



Zero point field


Paul Davies: Superforce

Paul Davies wrote:  that the advances in theoretical understanding are made spectacular due to the rise of GUTs and supersymmery, which suggest that all nature is ultimately controlled  by a “superforce. In the late 1960’s it was shown that electromagnetism can be mathematically combined with the weak force. The new theory predicted a new type of light, made up not of photons, but “Z” particles. In 1983, Z particles were produced in a subatomic particle accelerator.

It is from insights into the relationship between force fields, particles, and symmetry that there has come the conjecture that we live in an 11 dimensional universe. [7]

“The act of observation in quantum physics is not just an incidental feature, a means of accessing information already existing in the external world; the observer enters the subatomic realityh in a fundamental way and the equations of quantum physics explicitely encode the act of observation in their description . An observation brings about a distinct transformation in the physical situation.”[8]

Notes the relationship between the exponential and sine/cosine functions is an example of a kind of symmetry which physicists look for. [9]

Newton’s laws were completely reformulated by the French physicist Joseph Louis Lagrange and the Irish physicist  William Rowan Hamilton in the 19th century. Hamilton’s work contained an unexpected pointer to quantum theory. Hamilton found that the most succinct expression for the laws of motion were contained in a mathematical statement identical to the minimum time principle for light waves. Thus, both material particles and light waves  actually move in similar ways, mathematically. From this one might conclude that particles have a wave like property. [10]


Davies on Symmetry

The conservation laws follow directly from Newton’s laws of motion, but the reformulation of these laws by Lagrance and Hamilton reveal a deep and powerful connection between the conservation of a quantity and the presence of symmetry. For example, if the system is symmetric when rotated, then it follows from Hamilton’s or Lagrange’s equations that angular momentum will be conserved. [11]


When Maxwell initially wove the equations of electricity and magnetism thgether, he  thought they looked unbalanced, He therefore added an equation to make the equations more symmetric. The extra term could be interpreted as creation of a magnetic field by varying an electric field. This turned out to actually exist. Inclusion of the second term allowed trig functions to be solutions to the equations, or electromagnetic waves.


Around 1900, Henri Poincare and Heinrich Lorentz investigated the math structure of Maxwell’s equations. The celebrated “extra term” turned out to give the EM field a subtle but powerful form of symmetry: a rotation not in space, but in space-time. The effect of rotating in space-time is to  project some spatial length into time and vice-versa. It took Einstein’s genius to drive home the full implications. Space and time are not independent, but interwoven. The “rotations” Poincare and Lorentz  found in Maxwell’s equations can occur in the real world, through motion. The key to the weird space-time projections lies in the speed of EM waves. Thus there is a deep relationship between EM wave motion and the structure of time and space.


Even though the mathematical symmetries may be hard, or even impossible to visualize physically, they can point the way to new principles in nature. Searching for undiscovered symmetries has thus become a major tool of modern physics.


If electric charge is conserved,  the question naturally arises as to the nature of the symmetry associated with it. The energy required to lift a weight depends only on the difference in height it is raised; it is independent of route, and of the initial height.  “There is a  symmetry, therefore, under changes in the choice of zero height. A similar symmetry exists for electric fields. Here voltage is analogous to height. Height and voltage are considered gauge symmetries. It is precisely the gauge symmetry for voltages that assures the conservation of electric charge. [12]


The French Mathematician Henri Poincare discovered that for formal mathematical reasons, Newton’s equations become unsolvable for three bodies; the answer can only be found by a series of approximations. Poincare’s discovery was an early step in the development of Chaos theory. [13]


Newton published his Principia in 1687. In it, he not only put forward a theory of how bodies move in space and time, but also developed the math to analyze these motions. He also postulated a universal law of gravitation, according to which each body in the universe is attracted to every other body by a force proportional to their mass and distance apart. He went on to show that according to his law, gravity causes the moon to move in an elliptical orbit around the earth, and the earth and planets to follow elliptical orbits around the sun. [14]


The questions of whether the universe had a beginning in time, and whether it was limited in space was extensively examined by philosopher Immanuel Kant in his Critique of Pure Reason, published in 1781. He called these questions “antinomies”, that is, contradictions to pure reason, because he thought there were equally compelling reasons for believing the thesis and antithesis of each question.


The concept of time has no meaning before the beginning of the universe. This was first pointed out by St Augustine. When asked what did God do before he created the universe, he did not reply. He said time was a property of the universe that God created, and thet time did not exist before the beginning of the universe.


In 1929, Edwin Hubble made the landmark discovery that wherever you look, galaxies are moving away from one another. Based on this, one could predict a time when the galaxies were all in one location; the time of the “big bang”, when the universe was infinitesimally small and infinitely dense 





[1] Using "dot" notation for motion with respect to time. Leibnitz (German)
Is also thought to have invented caluclus at about the same time as Newton. His notation was dx/dy, which was more general, since it allowed change of any variable with respect to any other variable, not just time.


In reality, calculus was developed incrementally:

ref: Change and motion: Calculus made clear the teaching company


derivative: deltax/deltat as t gets smaller: defnition of instantaneous velocity


Aristotle said "motion is the fulfillment of what exists  potentially insofar as it exists potentially"


Zeno' s paradoxes about motion starts off development of calculus:

at one instant,is a moving object movng? at every moment it is not moving

dicotamy paradox: moving object will never reach it's destinations.


these paradoxes bring up idea of infinity. instantaneous.


200 years after calculus invented, was "intantaneous" understood.


zeno 500 BC


Eudoxus 400 BC developed  method of "exhaustion", which is similar to the integral


Archimedes uses the method of exhaustion to calculate volumes




: kepler and Galilei worked on motion of planets 4 developing formulas for htese motions


pierre de fermat developed methods for determining maxima & minima; very close to deveoping derivitive


Cavalieri invented a "method of indivisibles"


newtons teacher Isaac Barrow expressed fundamental theorem of calculus, but did not realize it's significance.


most closely associated with calculus: newton & leibniz; the systematized it;


still took many years to be understood.



Euler: infinite series se of calculus


lagrange calculus of variations


laplace Partial dif eqs; applied to probability theory


fourier circular functions series


cauchy infinite series; tried to formalize the idea of limit


neither newton nor leibniz were able to master the concept of limit;

too another 180 years


Rieman developed modrn definition of integral


Karl Weierstrass developed rigorus definition of limit about 1850






[2] The Man Who Changed Everything: The Life of James Clerk Maxwell Basil Mahon


[3] ibid p180 f


[4] ibid p182 f


[4 +1] ]  Superforce Paul Davies Touchstone Books 1984  p. 32f.


[5] The Holographic Universe Michael Talbot Harper Collins 1995 p. 52 f.


[6] From The Elegant Universe, by Brian Greene


[7]  Superforce Paul Davies Touchstone Books 1984  p.5 f.


[8] Superforce Paul Davies Touchstone Books 1984  p.39 f.


[9] Superforce Paul Davies Touchstone Books 1984  p 56.


[10] Superforce Paul Davies Touchstone Books 1984  p.57 f.


[11] Superforce Paul Davies Touchstone Books 1984  p.59 f.


[12] Superforce Paul Davies Touchstone Books 1984  p. 60 f.


[13] Turbulent Mirror John Briggs and F.David Peat Harper Row, 1989 p.27


[14] A Brief History of Time: From the Big Bang to Black Holes  Stephen Hawking Bantam Books 1988 p. 4-5


[15] A Brief History of Time: From the Big Bang to Black Holes  Stephen Hawking Bantam Books 1988 p. 8.