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Patterns in Nature and Myth

The Periodic Table of the Elements was perhaps the first time science found a pattern in nature of the kind so often previously postulated by people proposing mystical schemes for organizing the Universe:

                                                                                 H
*                                                                                         *  He
Li Be                                                                         B  C  N  O  F  Ne
Na Mg                                                                         Al Si P  S  Cl Ar
K  Ca Sc                                           Ti V  Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y                                            Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe
Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac Th Pa U  Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mr Ds Rg

After Lawrencium, element 103, elements 104 and 105 were called Un-nil-quadium and Un-nil-pentium, but now elements 104 through 109 are officially named Rutherfordium, Dubnium, Seaborgium, Bohrium, Hassium, and Meitnerium, and apparently the next two elements are known as Darmstadtium and Roentgenium as well.

There are names for the groups of elements in the Periodic Table:

  -----  Alkali Metals
 /   --  Alkaline Earth Metals
|   /                                                                     --- Coinage Metals
|  |                                                                     /                   He
Li Be                                                                   |     B  C  N  O  F  Ne
Na Mg                                                                   |     Al Si P  S  Cl Ar
K  Ca Sc                                           Ti V  Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y                                            Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe
Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac Th Pa U  Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mr Ds Rg    |  |  |  |  |  |
     |                                                                       ||  |  |  |  |   \
      \                                                                     / |  |  |  |   \   ---  Inert Gases, Noble Gases
       ------------------------- Transition Metals -------------------------  |  |  |   \   ------  Halogens
                                                                              |  |   \   ---------  Chalcogens
                                                                              |   \   ------------  Pnictogens
                                                                               \   ---------------  Tetrels
                                                                                ------------------  Triels, Boron Group Elements
    ---- Rare Earths: Lanthanides plus Scandium and Yttrium
   /
  |-  Sc
  |-  Y
   -  La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu  -- Lanthanides
      Ac Th Pa U  Np Pu Am Cm Bk Cf Es Fm Md No Lr  -- Actinides

The lighter halogens are stronger than the heavier ones, whereas the heavier alkali metals are stronger than the lighter ones; that is, they are more reactive.

This is a consequence of a general property of how electronegative and electropositive ions behave chemically, and thus this property tells us about the behavior of elements in other columns of the Periodic Table as well.

Carbon is obviously not a metal; Tin and Lead, on the other hand, have always been recognized as metals, but they're all in the same column in the Periodic Table.

So, while the metals are on the left of the Periodic Table, and the non-metals are on the right, the boundary between them is not vertical but slanted.

Li Be                                                                        |B ]C  N  O  F  Ne
Na Mg                                                                         Al|Si]P  S  Cl Ar
K  Ca Sc                                           Ti V  Cr Mn Fe Co Ni Cu Zn Ga[Ge|As Se]Br Kr
Rb Sr Y                                            Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn[Sb|Te]I  Xe
Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi[Po|At]Rn
Fr Ra Ac Th Pa U  Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mr Ds Rg

There is no universally agreed-upon boundary between metals and nonmetals.

One conventional line includes Aluminum, Germanium, Antimony, and Polonium as metals, and Boron, Silicon, Arsenic, Tellurium, and Astatine as non-metals.

Other chemists include a group of semi-metals or metalloids between the metals and non-metals.

Boron, Silicon, and Astatine are sometimes included in this group, and sometimes classed as non-metals.

Germanium, Arsenic, Antimony, Tellurium, and Polonium are usually included on most lists of semi-metals or metalloids.

Since Selenium is shiny and metallic in appearance, I'm somewhat surprised, despite its position in the Periodic Table in the same column as oxygen and sulfur, that it, too, isn't recognized as a semi-metal.

Also, there were different systems of numerical designation for the columns of the Periodic Table:

IA IIA                                             IVA   VIA   VIII     IB    IIIB  VB    VIIB      European, former IUPAC
      IIIA                                            VA    VIIA           IIB   IVB   VIB   0
1A 2A 3A                                           4A 5A 6A 7A 8...  8  1B 2B 3B 4B 5B 6B 7B 0

IA IIA                                             IVB   VIB   VIII     IB    IIIA  VA    VIIA      American
      IIIB                                            VB    VIIB           IIB   IVA   VIA   VIIIA
1A 2A 3B                                           4B 5B 6B 7B 8...  8  1B 2B 3A 4A 5A 6A 7A 8A

 1  2  3...                                      3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18  Current IUPAC

H                                                                                            He
Li Be                                                                         B  C  N  O  F  Ne
Na Mg                                                                         Al Si P  S  Cl Ar
K  Ca Sc                                           Ti V  Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y                                            Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I  Xe
Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W  Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac Th Pa U  Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mr Ds Rg

In order to let the table fit, I've just used the two-letter symbols for the elements, but of course not all of them will be familiar, so here is a key:

                                                             1 H  Hydrogen                                                                2 He Helium
  3 Li Lithium        4 Be Beryllium      5 B  Boron         6 C  Carbon        7 N  Nitrogen        8 O  Oxygen         9 F  Fluorine   10 Ne Neon
 11 Na Sodium        12 Mg Magnesium     13 Al Aluminum     14 Si Silicon      15 P  Phosphorus     16 S  Sulfur        17 Cl Chlorine   18 Ar Argon
 19 K  Potassium     20 Ca Calcium       31 Ga Gallium      32 Ge Germanium    33 As Arsenic        34 Se Selenium      35 Br Bromine    36 Kr Krypton
 37 Rb Rubidium      38 Sr Strontium     49 In Indium       50 Sn Tin          51 Sb Antimony       52 Te Tellurium     53 I  Iodine     54 Xe Xenon
 55 Cs Cesium        56 Ba Barium        81 Tl Thallium     82 Pb Lead         83 Bi Bismuth        84 Po Polonium      85 At Astatine   86 Rn Radon
 87 Fr Francium      88 Ra Radium

 21 Sc Scandium    22 Ti Titanium         23 V  Vanadium     24 Cr Chromium      25 Mn Manganese     26 Fe Iron         27 Co Cobalt        28 Ni Nickel          29 Cu Copper         30 Zn Zinc
 39 Y  Yttrium     40 Zr Zirconium        41 Nb Niobium      42 Mo Molybdenum    43 Tc Technetium    44 Ru Ruthenium    45 Rh Rhodium       46 Pd Palladium       47 Ag Silver         48 Cd Cadmium
 57 La Lanthanum   72 Hf Hafnium          73 Ta Tantalum     74 W  Tungsten      75 Re Rhenium       76 Os Osmium       77 Ir Iridium       78 Pt Platinum        79 Au Gold           80 Hg Mercury
 89 Ac Actinium   104 Rf Rutherfordium   105 Db Dubnium     106 Sg Seaborgium   107 Bh Bohrium      108 Hs Hassium     109 Mr Meitnerium   110 Ds Darmstadtium   111 Rg Roentgenium

 58 Ce Cerium     59 Pr Praesodymium   60 Nd Neodymium   61 Pm Promethium   62 Sm Samarium     63 Eu Europium    64 Gd Gadolinium    65 Tb Terbium      66 Dy Dysprosium     67 Ho Holmium        68 Er Erbium     69 Tm Thulium        70 Yb Ytterbium    71 Lu Lutetium
 90 Th Thorium    91 Pa Protactinium   92 U  Uranium     93 Np Neptunium    94 Pu Plutonium    95 Am Americum    96 Cm Curium        97 Bk Berkelium    98 Cf Californium    99 Es Einsteinium   100 Fm Fermium   101 Md Mendelevium   102 No Nobelium    103 Lw Lawrencium

Later on, particle physics found a symmetry in the properties of heavy short-lived particles that eventually was explained in terms of the quark model...

and the arrangement of ten items in a triangle was considered to be the holy Tetractys by the Pythagoreans. Another famous set of ways to link ten items together is discussed in the page entitled A Peculiar Deck of Cards

The binary number sequence, now so frequently encountered in connection with computers, also forms the basis of the I Ching or Book of Changes (perhaps more literally, the Change Classic). The order in which the hexagrams are discussed in the I Ching is not the numerical binary order, but the following:

While no simple mathematical rule has been found to account for this complete sequence, it certainly does have many symmetries.

The hexagrams in this sequence are clearly grouped into 32 pairs. In each pair, the second hexagram is usually the result of reversing the sequence of solid and broken lines in the first one; only if the sequence of the first one would be the same when reversed is the second one, instead, inverted from the first one by replacing solid lines with broken lines, and broken lines with solid ones.

The first two hexagrams are all solid lines and all broken lines, and the last two both consist of alternating solid and broken lines.

A Western form of divination based on binary sequences is known as Geomancy; not the Feng Shui of China, but rather the Ilm al-Raml of the Middle East.

Copyright (c) 2005 John J. G. Savard


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