Mathematical Alchemy

Pyrite cubic crystals

Many alchemists have dreamed of turning base metal into gold.

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, the ability to transform base metals into the noble metals, gold or silver; and the elixir of life, which confers youth and longevity.

Similarly, mathematicians have dreamed of turning base metal into gold.

Newton’s writings suggest that one of the main goals of his alchemy may have been the discovery of The Philosopher’s Stone (a material believed to turn base metals into gold), and perhaps to a lesser extent, the discovery of the highly coveted Elixir of Life.

The alchemists have been unsuccessful [so far] in turning base metal in gold.

However, the mathematicians have had more success.

The mathematician, astronomer and astrologer Johannes Kepler [1571-1630] established three laws of planetary motion by mathematically analyzing the planetary observations made by Tycho Brahe.

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing orbital motion, originally formulated to describe the motion of planets around the Sun.

1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

The planetary laws developed by Johannes Kepler laid the foundations for modern astronomy and defined the Gold Standard for the application of the scientific method.

Gold Standard
1. A monetary system in which the unit of currency is defined with reference to gold
2. The supreme example of something against which others are judged or measured

Collins English Dictionary – Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

Unfortunately, successive generations of mathematicians have abandoned the scientific method and have only succeeded in turning Kepler’s Gold Standard into Fool’s Gold.

The mineral pyrite, or iron pyrite, is an iron sulfide with the formula FeS2. This mineral’s metallic luster and pale brass-yellow hue have earned it the nickname fool’s gold because of its superficial resemblance to gold.

Understanding how this mathematical alchemy is performed requires a basic understanding of a very simple technique [used in solving equations] that allows the mathematician to “add, subtract, multiply, or divide both sides of the equation by the same number”.

Solving Equations

A more sophisticated form of this technique enables the mathematician to introduce any other variables [of their own choosing] into an equation provided they keep to the established mathematical rule of doing the same thing to both sides of the equation.

Mathematical Alchemy

Unfortunately, the result is mathematically correct but it may be just meaningless nonsense.

This is the case in the above example where TIME is being added to a DISTANCE.

The following example is [again] mathematically correct but is pure fantasy because it is based upon the concept that the “magical powers” of 1 wizard equals the “magical powers” of 7 fairies.

Mathematical Alchemy - Fantasy

Now let’s back to some of the mathematical alchemy performed in “science”.

One of the most popular targets for mathematicians has been Kepler’s Third Law of Planetary Motion because this scientific “gold standard” adds a gloss of respectability to their alchemy.

Kepler's Third Law of Planetary Motion

For further supporting evidence see:

Jupiter’s Moons:

Saturn’s Moons

Uranus’ Moons

Let’s start with a clear case of mathematical alchemy that is clearly documented.

Firstly, we have the setup that introduces Kepler’s Third Law.

Pari Spolter - Kepler
New Concepts in Gravitation – Pari Spolter

Secondly, we have the mathematical alchemy where the mathematician substitutes in their chosen variables and values by performing operations on both sides of Kepler’s formula so that it is “shorn of its mystery”.

Pari Spolter - Mathematics
New Concepts in Gravitation – Pari Spolter

Unfortunately, this mathematical manipulation does not mean the result is valid in the real world.

Anything can be substituted into Kepler’s formula using this technique [like wizards and fairies].

This only demonstrates that the mathematician knows the rules of mathematics.
This is not science.
This is mathematical alchemy.

However, it is the believers in Newtonian Gravity who really excel at mathematical alchemy.

Returning to the Wikipedia page on Kepler’s Third Law we can step through the alchemy.

Firstly, they avoid showing Kepler’s formula because they need to avoid the word “constant”.

Wikipedia Alchemy - Step 1

Secondly, they force Kepler’s formula to produce the answer “1” by using AU and Year values.

Wikipedia Alchemy - Step 2

Thirdly, they rearrange the forced formula [prior to substitution].

Wikipedia Alchemy - Step 3

Fourthly, they shoehorn [substitute] unconnected values and variables into the forced formula.

Wikipedia Alchemy - Step 4

Unfortunately, this mathematical manipulation does not mean the result is valid in the real world.

Anything can be substituted into Kepler’s formula using this technique [like wizards and fairies].

This only demonstrates that the mathematician knows how to bend the rules of mathematics.
This is not science.
This is not even mathematically valid alchemy.
This is just Fool’s Gold.

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6 Responses to Mathematical Alchemy

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  4. Pari Spolter says:

    Equal areas are swept in equal intervals of time only near perihelion and aphelion, and that is all that Kepler himself has claimed. Please see “Kepler’s Second Law and Conservation of Angular Momentum” In PHYSSICS ESSAYS, volume 24 (2011) pp. 260-266 and
    Equating the gravitational force with the quantity or density of inert matter is incorrect. The correct interpretation of Kepler’s third law is: Gravitational force is equal to acceleration times the area: F = a . A. The weight of a body is equal to its mass times the acceleration: W = m . a. Weight is not Force. Please see the book GRAVITATIONAL FORCE OF THE SUN, (1994 first edition and 2015 second edition), and articles “New concepts in Gravitation” in PHYSICS ESSAYS, Volume18, (2005), pages 37–49, “Problems with the Gravitational Constant” in INFINITE ENERGY, Volume 10, No. 59, (2005), page 39.
    Pari Spolter
    P.S. Biography of Dr. Pari Spolter is in Contemporary Authors, Volume 163.

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