 # by Peter Plichta ### Return to Murrey Math ## Chapter 1 -- The End of All Dogma

• Without the existance of numbers as objects in reality, there could not be a universe.

• The collapse of accepted mathematical dogma will usher in an entirely new scientific situation. ## Chapter 2 -- Chemistry and Passion

• Numbers, space, and time are infinite.

• All matter is made up of atoms. The entire universe is composed of certain types of matter which are called chemical elements. Numbered with the cardinal numbers 1, 2, 3, 4, . . ., they are divided into groups (vertically) and periods (horizontally) according to similarity of characteristics. The chart showing all the chemical elements arranged in rows of sixteen is called the Periodic Table.

• An atom always consists of a nucleus and negatively charged particles, called electrons, which move around the nucleus as planets move around the sun. The chemical bond is effected by two electrons from the different atoms that hold each other. They are called electron pairs or twins.

• Ohm's Law:
• ohm = volt / ampere

• resistance = voltage / current

• The whole nature of electricity is wrapped up in this equation.

• If only one of the three dimensions is set to 1, the remaining two must be either equal or reciprocal. ## Chapter 3 -- The Beginnings of a Research Scientist

• Albert Einstein was the first to realize that the speed of light was a natural constant, the value of which never changes. This speed is almost exactly 300,000 km per second (186,283 miles per second).

• Scientists distinguish between the mathematical constants invented by man and natural constants. The mathematical constants include the geometrical number (pi = 3.14159...) and Euler's number (e = 2.718...). The whole edifice of physics is based on these "invented" numbers. Physicists doe not question the absolute value of natural constants. Mathematical constants are not obtained through measurements, but are "discovered" by calculation.

• I would later be able to prove that mathematical constants are also natural constants. They were therefore not invented, just discovered, by man.

• The essence of a natural constant is to be found precisely in the fact that it can be expressed with a single, unchangeable, numerical value.

• In 1906 Albert Einstein expresed the relationship between electromagnetic energy, E, and mass, m. The two basic constituents of the universe, energy and material mass, are linked in the equation to the two other basic fundamental elements, space and time.

Energy = mass * (speed of light)^2

• Einstein was the first to claim that the transmission of electromagnetic waves did not require any medium. Space itself would be the medium. Space must be more than just nothing.

• Space has a three-fold, qualitatively identical extension -- length, width, and height. Time, like space, has a three-fold nature -- past, present, and future.

• The stable elements in the periodic system are made up of the number series of 1 (hydrogen), 2 (helium), 3, ..., 83. Two elements do not exist in nature -- the elements with the atomic numbers 43 (technetium) and 61 (promethium).

• In addition to protons, the atomic nucleus also contains neutron particles -- particles with neutral charge. The atomic weight is the sum of the number of protons and neutrons. If an element can exist with more than one neutron-proton ratio, it is said to have stable isotopes. An element can have an absolute maximum of ten isotopes.

• Two elements beyond element 83 -- those with the atomic numbers 90 (thorium) and 92 (uranium) -- have a life of thousands of millions of years. Both elements are constantly decaying and thereby providing elements 91, 89, 88, 87, 86, 85, and 84.

• All components of our universe are divided into three categories:
• stable elements (1-83) [without 43 and 61]
• exclusively artificial elements (93-106)

• All elements are composed of three types of elementary particles -- protons, neutrons, and electrons. There are three types of radiation -- alpha, beta, and gamma. ## Chapter 4 -- Number and Plan

• At normal temperature all 81 stable elements are in one of the three states
• solid (e.g., sulphur)
• liquid (e.g., mercury)
• gas (e.g., nitrogen)

• The elements of the main groups are also categorized according to their material characteristics and chemical and physical behaviour:
• non-metallic (e.g., oxygen)
• mettalloid (e.g., arsenic)

• The elements of the subgroups are always metals. There are three kinds of bonds
• ionic bonds (e.g., common salt)
• atomic bonds (e.g., methane)
• metallic bonds (e.g., brass)

• There is a strict three-fold division in organic chemistry. Carbon can form three types of bonds
• single (simple) bonds
• double bonds
• triple bonds

• In all the universe there are only three elements capable of forming these three types of bonds
• carbon
• nitrogen
• oxygen

• There are 20 amino acids -- the building blocks out of which protein is composed. There are 19 left-oriented amino acids, and one amino acids which can have both a left and right orientation. There are 19 left-oriented amino acids, and there are 19 consonants. The number 19 is a prime number -- a number which is divisible only the the number 1 and the number itself.

• The total number of pure isotopes in all the stable elements is exactly 20. Of these 20 pure isotopes, the lowest element, beryllium, has the even atomic number 4. This is followed by the atomic numbers 9, 11, 13, 15, 21, 25, 27, 33, 39, 41, 45, 53, 55, 59, 65, 67, 69, 79, and 83.

• I now knew the same number sequence occurs in both biochemistry and nuclear chemistry:
1 + 19 amino acids
and
1 + 19 pure isotopes

• The three laws of thermodynamics are purely empirical. The first two laws preclude the existence of a perpetuum mobile; they state that energy is always lost when undergoing change or use. The third law says that at the lowest possible temperature of -273.2 deg C, or absolute zero, no more movement of atoms takes place and the value for entropy is thus zero.

• The experiments of Gay-Lussac proved that gases expand and contract by 1/273.2 of their volume for every degree of heating or cooling.

• The three forms of matter -- solid, liquid, and gas -- depend on pressure and temperature. All physical dimensions can be reduced to length (or distance), mass, and time. A chemical reaction has three results -- the final product, heat, and entropy. ## Chapter 5 -- Space and the Riddle

• Life is a community of three types of existence -- plants, animals, and humans. The plants manufacture three nutrients -- sugar, starch, and protein. Plants divide water into hydrogen and oxygen. Animals and humans then burn up the hydrogen and oxygen compounds of carbon to produce water again. This cycle is maintained by three porphyritic compounds -- chlorophyll, haemine, and cobalamine.

• If the Moon is actually a part of the Earth, the Earth-Moon system must consist of two planets.

• The Moon orbits the Earth in one sidereal month or 27.32 days. At the end of this period the Moon assumes the same position in relation to the stars.

• The synodic month of 29.53 days is used for calendars. This is the time the Moon needs to attain the same position in relation to the Sun.

• The period of growth in the human womb between conception and birth has a statistical duration of ten sidereal months, or 273 days. The female oestral cycle follows the true astronomical rhythm and not the cycle of full Moon to full Moon which is two days longer.

• Paracelsus believed that all materials were based on three materials -- mercury, sulphur, and salt. ## Chapter 6 -- Vision and Determination

• Orbiting electrons have precisely four features, which physicists call the four quantum numbers.

• The innermost orbit contains one pair of electrons, the next orbit has 4 pairs, the third orbit has 9 pairs, and the fourth orbit has 16 pairs. These numbers -- 1, 4, 9, 16 -- are the squares of the numbers 1, 2, 3, and 4. There are only four types of electrons in the shells.

• I began to notice four-fold phenomena in all types of fields
• four phases of the Moon
• four seasons
• four bases in DNA

• How can some phenomena be strictly triple whereas others are quadruple?

• If there is a divine plan, it is based on nothing else but numbers. This notion is in the classic platonic tradition.

• Hahn-Einstein equation
h * v = m * c^2 ## Chapter 7 -- The Final Question

• An infinite space cannot be three-dimensional.

• There are three major types of languages on the Earth
• isolating languages -- e.g., Chinese
• agglutinative languages -- e.g., Turkish
• inflected or fusional languages -- e.g., Latin

• Three main races exist on this planet -- Negroid, Mongoloid, and Caucasian.

• The original economic structures prevailing in all three races were hunting, tilling the soil, and animal husbandry. ## Chapter 8 -- Upside-down and Backwards

• Pharmacology merges major parts of the three natural sciences -- chemistry, physics, and biology.

• The same natural law must be at the foundation of all three natural sciences. And the plan must have been based on number theory. This means that no such thing as coincidence in the real sense can exist at all.

• Mathematicians deny that numbers exist at all. For them numbers are products of the human imagination. They maintain that scientists only imagine that they recognize natural constants.

• Oxygen is a paramagnetic (magnetic) molecule. The other three -- nitrogen, argon, and carbon dioxide -- are diagmagnetic (non-magnetic). Carbon monoxide is also paramagnetic. ## Chapter 9 -- The Queen of the Sciences

• The attraction between the Earth and the Moon is a function of the mass of each body and the distance between them. The power of attraction decreases as the distance between them increases. This relationship, 1/r*r, is called the reciprocal square law.

• A finite space, no matter how large, can have only one center. An infinite space has its center everywhere -- any point is its center. Leibniz described the center of infinity as "monads". Each single monad contains the reflection of the entire universe.

• It is a peculiar feature of infinity that it can be infinitely large as well as infinitely small. The natural numbers begin with 1, 2, 3, 4, 5, ..., and never end. The reciprocal numbers begin with 1/1, 1/2, 1/3, 1/4, 1/5, ..., and approach zero. The number 1 is therefore a frontier between the whole and the reciprocal numbers.

• In his book Timaeus, Plato describes a reflective surface consisting of two mirrors meeting at a right angle. Such a mirror reverses its image in space and always gives three reflections.

• The four-dimensional infinite space around a point does not possess a z axis, but only x*x*y*y plane geometry. This four dimensions has nothing to do with time.

• The atomic structure makes use of the numbers 3 and 4, and these are also the numbers used by our genetic material. DNA consists entirely of only three chemical components -- phosphoric acid (P), a sugar (S), and a base (B). There are precisely four bases -- thiamine, ademine, cytosine, and guanine.

• Gauss described number theory as the "queen" of all science. ## Chapter 10 -- Concerning Electrons and Prime Number Twins

• The usual sequence of prime number is 2, 3, 5, 7, 11, 13, ... . The number 1, the foundation of all numbers, was not usually found in the sequence.

• I began my examination of the prime numbers with the prime number 5. Prime numbers or prime number twins will always occur around a number divisible by 6 -- , 6, , and , 12, , and , 18, , etc. The product of 0 * 6 = 0 must be found at six to the left of the number 6. The number 0 must also be surrounded by a number twin -- [-1], 0, . The sequence of the first four number twins is therefore
(-1;1) ---- (5;7) ---- (11;13) ---- (17;19)

• What I discovered resembled a clock with a 24-hour division of time. The number zero was at the top of the innermost circle. The number 24 was directly above zero in the next larger circle.

• The numbers 1, 2, and 3 are the inital elements of the three number categories
• 1 --> 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, . . .
• 2 --> 4, 8, 10, 14, 16, 20, 22, 26, 28, 32, . . .
• 3 --> 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, . . .

• Since both the sum and the product of 1, 2, and 3 is equal to six, the number 6 is the scaffold on which the prime numbers within the natural numbers are built.

• The zeroth circle contained the values -1 and 0. The first circle contained the numbers 1 through 24. Eight rays went out though the center though the numbers 1, 5, 7, 11, 13, 17, 19, and 23 in the first circle. This shape looked like the cross of the Order of the Christian Knights. I decided to name this the "Prime Number Cross".

• Numbers are the third component of infinity. Only the concealed triplicate of space, time, and numbers can lead us out of the trap of finite concepts. Numbers must now be granted a real existance.

• Nature must itself be arranged according to the decimal system.
1/81 = 0.012345679012345679 . . .
100/81 = 1 + remainder 19
19/81 = 0.234567 . . . ## Chapter 11 -- Putting Bounds on the Infinite

• If numbers exist and if the decimal system is also not a coincidence, then the measurements of length, weight, and time could be identical with the absolute dimensions in which nature is arranged.

• The Babylonians set the length of a second as the 3,600th part of an hour. The value 3600 is the product of the square sof the Pythagorean numbers 3, 4, and 5.
3,600 = 3*3 + 4*4 + 5*5

• An hour was defined during the Babylonian period as the 24th part of a day (one rotation of the Earth). Twentyfour is the product of 1 * 2 * 3 * 4 and is the foundation of the natural prime number rhythm.

• All natural constant consist of the three units
• number (e.g., 2.9979 . . .)
• factor (e.g., 10^10)
• dimension (e.g., centimeters per second)

• Einstein's formula is usally quoted as follows: E = m * c * c. But it should actually be written as
E * E = (m * m) * (c * c * c * c)

• If the value c = 3 x 10^10 cm/sec is inserted, the following appears:
(E * E) / (m * m) = 81 * 10^40 cm^4/sec^4
or
(m * m) / (E * E) = 0.012345679... * 10^-40 sec^4/cm^4

• I now postulated that matter only fits into such space as is arranged according to the same principles as the matter itself. Something is either material and countable, or it disappears and dissolves. It then spreads out into infinity as a wave phenomenon, just as a number is a realization of a quantity and its reciprocal value is a diminution towards eternity.

• The infinity of space will exist reciprocally as points of matter. Protons and electrons exist because four-dimensional space requires by its very nature central points of finite size.

• The interface between the finity of observation and the infinite realm of the imagination is the human mind.
• matter and space
• energy and time
• quantity and numerical sequence

• If matter did not exist, not one single atom, there would also be no space. Where there is no movement, there is also no time. Energy can therefore be nothing else than the reverse of time. ## Chapter 12 -- The House of Cards That is Physics

• Along with the Euler number e, pi is the most important mathematical constant and occurs in physical equations and in physical natural constants with an amazingly precise "coincidence" again and again.

• The area of a circle with a radius of 1 is 3.14159. The surface of a sphere with a diameter of the circle measures exactly four times this dimension -- i.e, 4 * pi.

• The relationship between the area of a square and the surface area of its inner circle with a radius 1 is the ratio 4:pi.
4 : pi = 1.2732. . .

• The ratio of one quarter of this square and one quarter of the circle was 0.2732 -- the length of a sidereal month in days. This value might be another unnamed physical constant of nature.

• The length of an Earth-year is approximately 365.25 days. The reciprocal connection between the Earth and the Moon are confirmed to the fourth decimal place:
1/27.32 = 0.03660
1/366 = 0.002732...

• The acceleration of the Moon in its path around the Earth is measured as 0.273 cm/sec^2. The Moon's radius measures 0.272 Earth radii. The ratio of the mass of the Moon to that of the Earth is 1:81.

• After every 18 years and 11.33 days (6,585.78 days), the eclipse arrangement recurs with the greatest precision. The relationship between 6,585.78 days and the length of an eclipse year measuring 346.62 days is
6585.78 : 346.62 = 19 eclipse years.

• The Saros cycle contains a total of 8 eclipse occurrences in exactly 19 eclipse years.

• Some time in the future the Pythagorean notion that everyting is number and Kepler's notion that everything is geometry will finally be accepted. ## Chapter 13 -- The Law of Empty Space

• I added the numbers in each circle of the Primary Number Cross. The point of intersection between the two circles was counted twice as a starting and final number. I obtained the following values:
```1st circle:  0 +  1 +  2 + . . . + 24 =   300 = 1 * 300
2nd circle: 24 + 25 + 26 + . . . + 48 =   900 = 3 * 300
3rd circle: 48 + 49 + 50 + . . . + 72 = 1,500 = 5 X 300
4th circle: 72 + 73 + 74 + . . . + 96 = 2,100 = 7 * 300
```

• The sum of the uneven numbers 1, 3, 5, 7, 9, 11, ... always gives the series of squared numbers 1, 4, 9, 16, 25, 36.

• Because infinity has a triple nature (space, time, and number ), the numbers themselves evolve on the basis of the first three numbers. The basic constant of the Prime Number Cross is the number 3. The expansion constant of hte speed of light must also be 3.

• Shining objects are permanently emitting spheroid waves which diminish as they approach infinity with a fixed consistency through the reciprocal square law.

• The meter was established according to a decimal division of the Earth's axial circumference. The second was derived from the speed of the Earth's rotation. ## Chapter 14 -- Revelation

• Each individual atom contains the information and structure of the prime number space.

• If space expands according to the decimal system, then the material that fills this space must also be structured according to this system. The chemical elements are constructed according to the order of the natural numbers.

• Decimal fractions are divided into three types -- rational, irrational, and transcendental.

• The numbers e (2.718...) and pi (3.14159...) can be linked to each other by a formula discovered by Euler:
e^(i*pi) = -1 ## Chapter 15 -- The Order Within Disorder

• The number e (2.718...) was developed by Newton from a factorial series in 1665. In 1739 Euler found a second possibility for the number e by using binomials.

• The number e, which is the base constant of the universe, must have something to do with the order and combination of the number sequence.

• The Prime Number Cross offers the possibility of illustrating the six basic units of the universe -- e, i , pi, 1, 0, and -1.
• pi -- the number used in calculating circles
• i -- imaginary number which determines the cross structure of the zero shell
• e -- provides the order for the successive numbers

• Geometrically speaking, reciprocal numbers are located on a curve called a hyperbola -- the inversion of infinitely small sections of increasingly large circles.

• The Euler-Mascheroni constant is C (0.5772156649. . .).

• In modern physics, there are two wave models. The electromagnetic transverse waves run through empty space. The longitudinal (sound) wave is transported precisely by a gas medium and thus carries information of an incredible range.

• The two laws, 1/2^n and 1/n^2, describe the mutually reciprocal geometries of three-dimensional and four-dimensional space.

• The Mercator series is 1 - 1/2 + 1/3 - 1/4 + 1/5 - . . . = 0.69314. . . = natural logarithm 2.

• Three-dimensional gas-filled space is a reciprocal numerical space. It must be ordered by reciprocal prime numbers and be a geometric realization of the reversal of four-dimensional, empty, infinite space as ordered by prime numbers in the Prime Number Cross. ## Chapter 16 -- The Search for Reciprocal Geometry

• The numbers in Pascal's Triangle are calculated from binomials of the type (a+b)^n, e.g. [a + b]^2 = a^2 + 2ab + b^2.

• When the exponent of the binomial is a prime number, all coefficients -- except 1 -- are divisible by this prime number.

• Fractal geometry is coded in the prime numbers.

• The inversion of four-dimensional geometry which is derived from the base numbers 1, 2, and 3 and which contains eight rays must again produce a geometry which is constructed on the numbers 1, 2, and 3, is triangular, and has eight lines.

• "Nothing in nature is by chance . . . Something appears to be chance only because of our lack of knowledge." -- Spinoza

• Fractal geometry is not the only mathematical phenomenon that has a real existence in nature. Fractal geometry also explains why the musical note is transported with such beautiful precision.

• An Octave is compete after eight steps. The whole secret of music theory is contained in the fact that the halving, three-part, five-part, and seven-part of the string can be shown to result from there being two prime numbers which are not of the form 6n +/- 1.

• Two physical spaces have to exist. The four-dimensional space around a point transports electromagnetic waves according to the order of the whole numbers. If a three-dimensional body is filled with air in such a four-dimensional space, this air will transport heat or sound according to the order of the reciprocal numbers. Both spaces are pure inversions, since for each whole number the infinite reciprocal value also exists. Both types of space are formed on the base numbers 1, 2, and 3 and on the structural number 8. ## Chapter 17 -- God is Back!

• If there has to be a fourth dimension, this higher and final dimension must have a form of consciousness beyond the bounds of our consciousness. Since the dawn of time, this notion has gone under the name of "God".

• He has written a book called The Prime Number Cross.

• Only three elements can form three different types of bonds -- carbon, oxygen, and nitrogen. Chemistry is -- like the other two natural sciences -- the material costume for mathematics with which infinity is made finite.

• It was a decisive mistake that science began to interpret numbers as a human invention approximately 100 years ago, just so that mysticism could be expelled from science and mathematics. In this way God was also expelled from nature.

• There is a divine structural plan behind this world. ### Top of Page ### Return to Murrey Math  bonniehill@verizon.net last modified on February 11, 2020
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