Alchemy is an influential philosophical tradition whose early practitioners’ claims to profound powers were known from antiquity. The defining objectives of alchemy are varied; these include the creation of the fabled philosopher’s stone possessing powers including the capability of turning base metals into the noble metals gold or silver, as well as an elixir of life conferring youth and longevity. Western alchemy is recognized as a protoscience that contributed to the development of modern chemistry and medicine. Alchemists developed a framework of theory, terminology, experimental process and basic laboratory techniques that are still recognizable today. But alchemy differs from modern science in the inclusion of Hermetic principles and practices related to mythology, religion, and spirituality.

 

 

 

 

 

The defining goals of alchemy are often given as the transmutation of common metals into gold (known as chrysopoeia), the creation of a panacea, and the discovery of a universal solvent.  However, this only highlights certain aspects of alchemy. Alchemists have historically rewritten and evolved the explanation of their art, making a singular definition difficult.  H.J. Sheppard gives the following as a comprehensive summary:

Alchemy is the art of liberating parts of the Cosmos from temporal existence and achieving perfection which, for metals is gold, and for man, longevity, then immortality and, finally, redemption. Material perfection was sought through the action of a preparation (Philosopher’s Stone for metals; Elixir of Life for humans), while spiritual ennoblement resulted from some form of inner revelation or other enlightenment (Gnosis, for example, in Hellenistic and western practices).

In the eyes of a variety of esoteric and Hermetic practitioners, the heart of alchemy is spiritual. Transmutation of lead into gold is presented as an analogy for personal transmutation, purification, and perfection. This approach is often termed ‘spiritual’, ‘esoteric’, or ‘internal’ alchemy.

Early alchemists, such as Zosimos of Panopolis (c. AD 300), highlight the spiritual nature of the alchemical quest, symbolic of a religious regeneration of the human soul.  This approach continued in the Middle Ages, as metaphysical aspects, substances, physical states, and material processes were used as metaphors for spiritual entities, spiritual states, and, ultimately, transformation. In this sense, the literal meanings of ‘Alchemical Formulas’ were a blind, hiding their true spiritual philosophy.

 

 

 

 

The origin of Western alchemy may generally be traced to Hellenistic Egypt. The Hellenistic city of Alexandria was a center of Greek alchemical knowledge, and retained its preeminence through most of the Greek and Roman periods.  Here, elements of technology, religion, mythology, and Greek philosophy, each with their own much longer histories, combined to form the earliest known records of alchemy in the West. Zosimos of Panopolis wrote the oldest known books on alchemy while Mary the Jewess is credited as being the first non-fictitious Western alchemist. They wrote in Greek and lived in Egypt under Roman rule.

 

 

 

 

 

 

Technology – The dawn of Western alchemy is sometimes associated with that of metallurgy, extending back to 3500 BCE.  Many writings were lost when the emperor Diocletian ordered the burning of alchemical books after suppressing a revolt in Alexandria (292 CE). Few original Egyptian documents on alchemy have survived, most notable among them the Stockholm papyrus and the Leyden papyrus X. Dating from 300 to 500 CE, they contained recipes for dyeing and making artificial gemstones, cleaning and fabricating pearls, and the manufacture of imitation gold and silver.  These writings lack the mystical, philosophical elements of alchemy, but do contain the works of Bolus of Mendes (or Pseudo-Democritus) which aligned these recipes with theoretical knowledge of astrology and the Classical elements. Between the time of Bolus and Zosimos, the change took place that transformed this metallurgy into a Hermetic art.

 

 

 

 

 

The demise of Western alchemy was brought about by the rise of modern science with its emphasis on rigorous quantitative experimentation and its disdain for “ancient wisdom”. Although the seeds of these events were planted as early as the 17th century, alchemy still flourished for some two hundred years, and in fact may have reached its apogee in the 18th century. As late as 1781 James Price claimed to have produced a powder that could transmute mercury into silver or gold.

 

 

 

 

 

 

Have to put on your thinking caps for this one.

The Mandelbrot set is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoît Mandelbrot, who studied and popularized it.

More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial z_n+1 = z_n² + c remains bounded.  That is, a complex number c is part of the Mandelbrot set if, when starting with z₀ = 0 and applying the iteration repeatedly, the absolute value of z_n remains bounded however large n gets.

                                                                                                                                                                                                                                                           

                                                                                                                                                                                                                                                        

The Mandelbrot set is defined by a family of complex quadratic polynomials

given by

where is a complex parameter. For each , one considers the behavior of the sequence

obtained by iterating starting at critical point , which either escapes to infinity or stays within a disk of some finite radius. The Mandelbrot set is defined as the set of all points such that the above sequence does not escape to infinity.

More formally, if denotes the nth iterate of (i.e. composed with itself n times), the Mandelbrot set is the subset of the complex plane given by

As explained below, it is in fact possible to simplify this definition by taking .

Mathematically, the Mandelbrot set is just a set of complex numbers. A given complex number c either belongs to M or it does not. A picture of the Mandelbrot set can be made by colouring all the points which belong to M black, and all other points white. The more colourful pictures usually seen are generated by colouring points not in the set according to how quickly or slowly the sequence diverges to infinity. See the section on computer drawings below for more details.

The Mandelbrot set can also be defined as the connectedness locus of the family of polynomials . That is, it is the subset of the complex plane consisting of those parameters for which the Julia set of is connected.

                                                                                                                                                                                                                                                           

                                                                                                                                                                                                                                                           

The Mandelbrot set is a compact set, contained in the closed disk of radius 2 around the origin. In fact, a point belongs to the Mandelbrot set if and only if

for all .

In other words, if the absolute value of ever becomes larger than 2, the sequence will escape to infinity.

The intersection of with the real axis is precisely the interval [-2, 0.25]. The parameters along this interval can be put in one-to-one correspondence with those of the real logistic family,

The correspondence is given by

In fact, this gives a correspondence between the entire parameter space of the logistic family and that of the Mandelbrot set.

The area of the Mandelbrot set is estimated to be 1.50659177 ± 0.00000008.

                                                                                                                                                                                                                                                       

 

 

What an eye-opener.  M

 

Dangerous Minds

Mudra chakra.

By curling, crossing, stretching and touching the fingers and hands, we can talk to the body and mind as each area of the hand reflexes to a certain part of the mind or body.

 

 

                                                                                                                                                                                                                                                          

 

                                                                                                                                                                                                                                                         

 

Philip K. Dick was one of America’s most progressive Science Fiction writers of the 20th century.

This is an abbreviated transcript of the closing words of Philip K. Dick’s speech given at the 1977 Metz Sci-Fi Convention, where he is describing his creative process in his 27 years of writing science fiction novels:
“At no time did I have a theoretical or conscious explanation for my preoccupation with these pluriform pseudo-worlds. But now, I think I understand. What I was sensing was the manifold of partially-actualized realities lying tangent to what evidently is the most actualized reality – the one which the majority of us agree on by ‘consensus gentium’ [Latin for the "agreement of the people"]…
“I wrote out these dreams in novel after novel; to name two in which this prior ugly present obtained most clearly, I cite the man in the High Castle and in my 1974 novel about the US as a police state called ‘Flow My Tears, the Policeman Said.’ I’m going to be very candid with you. I wrote both novels based on fragmentary residual memories I had of such a horrid slave state world.
“People claim to remember past lives. I claim to remember a different – very different – present life. I know of nobody who has ever made this claim before but I rather suspect that my experience is not unique. What perhaps is unique is my willingness to talk about it. We are living in a computer-programmed reality and the only clue we have to it is when some variable is changed and some alteration in our reality occurs. We would have the overwhelming impression that we were living the present deja vu – perhaps precisely in the same way, hearing the same words, saying the same words – I submit that these impressions are valid and significant. And I will even say this: such an impression is a clue that, at some past time point, a variable was changed – reprogrammed as it were – and that because of this, an alternative world branched off.”