Volume 64       July 22, 2019


By Professor  Dr. Tan Man-Ho

(An excerpt from the original work, Real World Views, Book 2 by Professor  Dr. Tan Man-Ho entitled "Biocosmic Nervo-Reflectant and the Theory of Material Reflection in Man, Inner Development and Social Upheavals",  July  1972 ~ September 1973 Discourses, Chapter 3, Section F: "The Tri-Octave Movement of the Allotropic Elements", pp. 71~79)





1   Allotropes are created as a result of quantitative changes to the number of atoms and bonding structures of the atom group under certain external conditions of pressure, light and temperature which lead to qualitative changes in the physical and chemical properties of the element.  Allotropes are the inner stopinders of an element within the World of Chemical Elements which is classified in the Periodic Table of Elements, and they function within the Octave of Elements and within this frame of reference.  It is still within the dimensions of the elements.  They are not within the World of Elementary Particles nor are they in the Periodic Table of the Elementary Particles (Subatomic Particles or the Octave of Atomic particles), or within the Octave of the Microcosms.  The general laws of dialectics and the general laws of octave apply to both these worlds.  These same laws also apply to the tri-octave movements of isotopes whereby the quantitative changes are in the number of neutrons in the nucleus of an atom which produces various types of heavy elements of the same atom being - examples are the carbon isotope octave notes such as carbon-12, carbon-13 and carbon-14 and they have qualitative leap points from between the stable isotopes and the unstable radioactive isotopes.

Allotropes are different structural forms of the same element and can exhibit quite different physical properties and chemical behaviors, whether in the solid, liquid or gaseous states.  Allotropes are the forms or appearances and the elements (the simple matters) are the essences - the general law that matter must appear in forms is implied here.  The change between allotropic forms is triggered by the same external forces that affect other structures, i.e. pressure, light, and temperature.  The stability of any particular allotrope depends on these particular conditions.  Iron, for example, changes from a body-centered cubic structure (ferrite) to a face-centered cubic structure (austenite) above 906 °C, and tin undergoes a transformation known as tin pest from a metallic phase to a semiconductor phase below 13.2 °C.  These points of “qualitative” changes are nodes of the dialectic process of allotropic motion.  However, according to the laws of uneven development of the dialectics, these points can just be “quantitative” nodes for minor “qualitative” changes of the same elements.

Typically, elements capable of variable coordination number and/or oxidation states tend to exhibit greater numbers of allotropic forms.  Another contributing factor is the ability of an element to catenate into stopinder-like long chains through its covalent bonding ability.  Allotropes are typically more noticeable in non-metals (excluding the halogens and the noble gases) and metalloids.  Nevertheless, metals tend to have many allotropes.



Among the naturally occurring metallic elements (up to U, without Tc and Pm), 28 are allotropic at ambient pressure: Li, Be, Na, Ca, Sr, Ti, Mn, Fe, Co, Sr, Y, Zr, Sn, La, Ce, Pr, Nd, (Pm), Sm, Gd, Tb, Dy, Yb, Hf, Tl, Po, Th, Pa, U.  Considering only the technologically-relevant metals, six metals are allotropic: Ti at 882˚C, Fe at 912 and 1394˚C, Co at 422˚C, Zn at 863˚C, Sn at 13˚C and U at 668 and 776˚C.

Below is a list of the Inner Octaves (inner stopinders) allotropic elements:

Allotropic Element Incomplete Inner Octave(Inner Stopinders) of a Non-Metallic and metalloidal Allotropic Element
Non-Metals and Metalloids


  1. Diamond - an extremely hard, transparent crystal, with the carbon atoms arranged in a tetrahedral lattice. A poor electrical conductor.  An excellent thermal conductor.
  2. Lonsdaleite - also called hexagonal diamond.
  3. Graphite - a soft, black, flaky solid, a moderate electrical conductor. The C atoms are bonded in flat hexagonal lattices (graphene), which are then layered in sheets.
  4. Amorphous carbon
  5. Fullerenes, including "buckyballs", such as C60.
  6. Carbon nanotubes - allotropes of carbon with a cylindrical nanostructure.
  7. Carbyne - or linear acetylenic carbon (LAC). Here carbon is in linear modification with sp orbital hybridisation.


  1. White phosphorus - crystalline solid P4
  2. Red phosphorus - polymeric solid
  3. Scarlet phosphorus
  4. Violet phosphorus
  5. Black phosphorus - semiconductor, analogous to graphite
  6. Diphosphorus, P2


  1. Dioxygen, O2 - colorless
  2. Ozone, O3 - blue
  3. Tetraoxygen, O4 - metastable
  4. Octaoxygen, O8 - red


  1. Dinitrogen, N2
  2. Trinitrogen, N3
  3. Tetranitrogen, N4
  4. Two solid forms: one hexagonal close-packed and the other alpha cubic


  1. Plastic sulfur (amorphous) - polymeric solid
  2. Rhombic sulfur - large crystals composed of S8 molecules
  3. Monoclinic sulfur - fine needle-like crystals
  4. Other ring molecules such as S7 and S12


  1. Red selenium, cyclo-Se8
  2. Gray selenium, polymeric Se
  3. Black selenium


  1. Amorphous boron - brown powder
  2. Crystalline boron - black, hard (9.3 on Mohs' scale), and a weak conductor at room temperature.


  1. α-germanium
  2. β-germanium - at high pressures


  1. Amorphous silicon - brown powder
  2. Crystalline silicon - has a metallic luster and a grayish color. Single crystals of crystalline silicon can be grown with a process known as the Czochralski process


  1. Yellow arsenic - molecular non-metallic As4
  2. Gray arsenic, polymeric As (metalloid)
  3. Black arsenic (metalloid) and several similar other ones.


  1. Blue-white antimony - the stable form (metalloid)
  2. Yellow antimony (non-metallic)
  3. Black antimony (non-metallic)
  4. Etc.



  1. Grey tin (alpha-tin)
  2. White tin (beta tin)
  3. Rhombic tin (gamma)


  1. alpha iron (Ferrite) - forms below 770°C (the Curie point, Tc ); the iron becomes magnetic in its alpha form; BCC
  2. Beta iron- forms below 912°C (BCC)
  3. Gamma iron- forms below 1394°C; face centred cubic (FCC) crystal structure
  4. Delta iron- forms from cooling down molten iron below 1538°C; has a body-centred cubic (BCC) crystal structure
Lanthanides and Actinides
  1. Cerium, Samarium, Terbium, Dysprosium and Ytterbium have three allotropes.
  2. Praseodymium, Neodymium, Gadolinium and Terbium have two allotropes
  3. Plutonium has six distinct solid allotropes under "normal" pressures. Their densities vary within a ratio of some 4:3, which vastly complicates all kinds of work with the metal (particularly casting, machining, and storage). A seventh plutonium allotrope exists at very high pressures, which adds further difficulties in exotic applications. The transuranium metals Np, Am, and Cm are also allotropic.
  4. Promethium, Americium, Berkelium, Californium have 3 allotropes


2   Different substances have different powers of attraction and repulsion.  If the attraction is strong enough, chemisorption results and new compounds are formed.  If the attraction is weak, the attractive bonds will “break” and elements are physically absorbed.  Suppose we have a substance of mixed amount of various elements are allowed to pass through the absorbent with the help of a medium.  In order for a substance to move through the absorbent, a medium or solvent is required.  This absorbent must not “react” with the substance.  As the substance passes through the absorbent those strongly attracting atoms chemisorb to form another chemical compound, and those weakly attracting atoms remain separated and stay at a greater distance from the atoms of chemisorbed compound.  These various elements absorb and emit waves of varying but definite frequencies for different kinds of element and on reaching the eyes they produce the effects of colors to our eyes.  A spectrum of colors can be observed.

In nature, there existed various elements such as copper, sulfur phosphorus, carbon, tin, etc.  These elements, of course, have different physical properties.  In elements with different physical properties (or crystallized in) said to exhibit allotropy.  Sulfur, for example, has two types of allotropes – monoclinic and the rhombic sulfur.  At a certain temperature 98 °C rhombic sulfur is stable while all the others formed allotropes are said to be metastable.



At a certain temperature, say 95.5 °C, it is possible for two forms of sulfur to form (six or s).  Experiment shows that the s is formed.  This phenomenon is summarized in a form of a lower.  When it is possible for a stable and a metastable form of a substance to form be produced, the metastable form is produced first this law is called Newale’s law of success reaction.  All the metastable form of a substance will eventually changes to the stable form.

According to the laws of dialectic, the L-sulfur at first undergoes quantitative changes until it reaches 95.5 °C.  At this temperature the L-sulfur is observed to undergo qualitative changes.  It is transforming into B-sulfur.  There is no quantitative change that is the temperature remains 95.5 °C.  This is in accordance with the laws of dialectic.  This temperature is the transition temperature – the temperature whereby L-sulfur is transformed into B-sulfur.

Let us now begin our frame of reference with an initial temperature slightly above of 95.5 °C.  In this case, L-Sulfur still transforms into B-Sulfur.  If the temperature is altered slightly below say 98 °C, the transformation to B-sulfur still occurs.

It is seen that white phosphorus “stubbornly” insists on transforming into red phosphorus quite independent of the forced quantitative changes in temperatures by the experimenter himself.  It is imagined that there is no transition temperature.  There is no transition temperature because sender the condition of the , the white phosphorus has already in its stage of transition to red phosphorus recalling the above phenomenon in L-Sulfur; while B-Sulfur is in its stage of transformation the quantitative changes are very badly interpreted.  It appears like at 95.5 °C.  If the temperature is increased, the L-Sulfur will be seen to transform to B-Sulfur quite independently of the temperature.  From this a 5th principle of dialectics can be deduced:

While a substance is undergoing qualitative changes or is in the stage of qualitative changes the changes are quite independent of the quantitative changes.


White phosphorus, under laboratory condition, is undergoing qualitative changes.  The change is quite independent of the quantitative forced changes such as temperature.

While in the transition stage, there are always two different qualities in co-existence (equilibrium) and which proportions can be changing with time and with the possible changes in the transition point.

“Two forms of phosphorus red and white phosphorus also differ chemically.  White phosphorus is poisonous, burns spontaneously in oxygen and chlorine, and gives phosphine with caustic soda.  Red phosphorous is non-poisonous, combines with oxygen and chlorine only when heated, and does not read with caustic soda.”  (Hey)

If the red phosphorus is heated, it would be changed into yellow phosphorus and even before it vaporizes, yellow phosphorus has already being form.  Therefore, it is hard to understand how red and white (or yellow) phosphorous can differ in chemical properties.




Home Matrix Chart Founder
Activities Seminars Publication
Odyssey Holistic Point E-Journal
Stopinder Announcement FM Studio
Links Contact  

Tel/Fax: +607-590 9688              Mobile: +6012 245 5127
Homepage:   E-mail :  
Copyright © Fourthway ManHo Center  Electronic Publishing,  All rights reserved