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BH
Torah and Chemistry
GALEINAI PUBLICATION SOCIETY
TTThhheee PPPeeerrriiiooodddiiiccc TTTaaabbbllleee ooofffttthhheee EEEllleeemmmeeennntttsss
from Harav Yitzchak Ginsburgh
1. Theoretical Background
Oneofthemostwellknownandubiquitoussymbolsofmodernscienceingeneraland
chemistryinparticularisthePeriodicTableoftheElements.Themodernperiodictablehas
beenalmost300yearsinthemaking.Earlyeffortstogroupelementsproducedthetables
ofGeoffroy(1718)andLavoisier(1787).TheatomictheoryformulatedbyDaltoninthe
early 1800s provided chemists with a solidbasis to classify elements, and the theory
stimulatedvigorousexperimentationthatculminatedinthedevelopmentofthemodernformoftheperiodictablein1869(Seefigure1).
1
H2
He3
Li4
Be5
B6
C7
N8
O9
F10
Ne11
Na12
Mg13
Al14
Si15
P16
S17
Cl18
Ar19
K20
Ca21
Sc22
Ti23
V24
Cr25
Mn26
Fe27
Co28
Ni29
Cu30
Zn31
Ga32
Ge33
As34
Se35
Gr36
Kr37
Rb38
Sr39
Y40
Zr41
Nb42
Mo43
Tc44
Ru45
Rh46
Pd47
Ag48
Cd49
In50
Sn51
Sb52
Te53
I54
Xe55
Cs56
Ba57
La72
Hf73
Ta74
W75
Re76
Os77
Ir78
Pt79
Au80
Hg81
Tl82
Pb83
Bi84
Po85
At86
Rn87
Fr88
Ra89
Ac
58
Ce59
Pr60
Nd61
Pm62
Sm63
Eu64
Gd65
Tb66
Dy67
Ho68
Er69
Tm70
Yb71
Lu90
Th91
Pa92
U93
Np94
Pu95
Am96
Cm97
Bk98
Cf99
Es100
Fm101
Md102
No103
Lr
Figure1
From the early rudimentary groupings of chemical compounds to our modern
classificationthatrecognizestheperiodicityofatomicelementstogether,chemicaltables
are usuallybased on an implicit theory of the compositionofmatter1. These theories
havesharedacommonaxiom: thatallof thematter in theUniverse iscomposedofa
finitevarietyofbasicbuildingblocks.Thesebuildingblockshavebeenknownfromthe
ancientGreekstothepresentasatoms.
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Inourmoderntableofthechemicalelements,thedifferentatomsareidentifiedand
orderedby theiratomicnumber.Atomsaredefinedas thesmallestunitofanelement
thatcancombinewithanotherelement.Atomsaretheorizedascomposingofanucleus,
madeofprotonsandneutrons,andelectronsthatmovearoundthenucleus.Theatomic
numberidentifiesthenumberofprotonsinanelementsnucleus.Atomscanloseorgain
electrons,andtheeasewithwhichtheydosoisameasureoftheirreactivity.In our modern periodic table of elements, elements are arranged in columns and
rows.Asitsnameimplies,themoderntableisperiodicinnature,meaningthatelements
areplacedinitbasedontheirsharedandrecurring(periodic)characteristics.Periodicity
of element properties is found tobe strongest down columns of the table. Primary
amongtheseperiodsisthatofthe6noble(orinert)gaseswhichpopulatethefarright
columnofthetable.Thepropertysharedbytheinertgasesisalackofreactivityensuing
fromtheirinabilitytogainorloseelectrons.
Anotherexample: the firstelement in thetable,Hydrogen (H) isagas, thesecond,
Helium(He),isanoblegas,andthethird,Lithium(Li),isasoft,reactivemetal.Going
downthetable,wefindeightelementslaterFluoride(F),Neon(Ne)andSodium(Na),agas,anoblegas,andasoft,reactivemetal,andeightelementslater,Chloride(Cl),Argon
(Ar)andPotassium(K)again:agas,anoblegas,andasoft,reactivemetal.
The remarkablepredictabilityof elementproperties revealedby the periodic table
allowed chemists to describe as yet unidentified elementsbased on their supposed
location in the table.Suchwas thecasewhen in1871DimitryMendeleev, theRussian
chemistwhooriginally formulated theperiodic law,correctlydescribed theproperties
oftheelementbetweenSilicon(14)andTin(50)whichhecalledekasilicon.Theelement
in question was not identified until 1886 by a German chemist who dubbed it
Germanium.
2. The Kabbalistic counterparts to the Periodic Table
Itisourgoalinthisarticletopresentanexactandfullanalogytothemodernperiodic
tablewithinTorah.Themotivationforthisgoal isexplained inprecedingchapters.To
doso inamethodologicalmanner,wemust firstascertain that theTorahdoes indeed
include examples of the two central concepts underlying the content and formof the
PeriodicTable:(1)atomsand(2)periodicity.
Thenotionoftheentiretyofcreationbeingconstructedoutofafinitevarietyofbasic
building blocks is central to the earliestKabbalistic sourceknown (and incidentally the
firstbookofHebrewgrammar)theBookofFormation (SeferYetzirah).From there this
notion assumes a central role throughout the entire Kabbalistic and esoteric traditionwithinTorah.2
Specifically, the Book of Formation turns to Genesis and, following a (spiritually)
linguistic perspective, identifies 32 noncorporeal elements or atoms. They are the 10
sefirot[whichcorrespondtothe10utterances(maamarim, )spokenbyGodwhen
He created the world3] and the 22 letters of the Hebrew alphabet [out of which the
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However,thoughtheBookofFormationprovidesuswiththenotionofbasicbuilding
blocks of the Universe, the atoms it identifies are ill suited for our purposes of
correspondence. First, because they are of two separate categories: one (utterances)
clearlyhierarchicallyabove theother (letters).Second,becauseweare searching foraonetoone correspondence between the atoms of the periodic table and some
correspondingunitinTorah.
However,onepieceofvaluableinsighttobegainedfromtheBookofFormationisthe
ideathatshouldtheTorahsequivalentofelementsoratomsbefound,itwouldbeinthe
first chapter of Genesis, where the act of creation is described. Whatbetter place to
searchfortheTorahatomsfromwhichCreationisconstructed?
* * *
Toexplainthecorrespondencewehavefound,letusfirstmentionthatofthemorethan
100elements,only92arenaturallyoccurring.Atomsofelementswithatomicnumber
higher than 92 canbe artificially synthesized,however, they are generally not stable4
and undergonuclear rearrangement resulting in radioactivedecay shortlyafterbeing
synthesized.
Andnowtoourcorrespondence:oneofthemostimportantcontributionstoJewish
scholarship in the recentpasthasbeen theworkofRabbiZalmanPinchasHorowitz5.
Rabbi Horowitz was (to thebest of our knowledge) the first to correctly count the
numberof times theTetragrammaton (YHVH)appears in thePentateuch:1820 times.
EvenmoresurprisingandinnovativewasRabbiHorowitzscatalogingofallthedistinct
words6inthePentateuch,whichhealsofoundtobeexactly1820innumber.
Thisequalitystillwarrantsmuchresearch,butherewewillnoteafactrelatedtoour
own particular interest: of the total1820 unique words in the Pentateuch, the section
describing creation (Genesis 1:1 to 2:3, inclusive) contains exactly 92 distinct words.
Indeed,asmentionedalready,thissectionoftheTorahliterallydescribesthecreationof
matter in the universeit is only fitting that it is here that we find our sought after
parallelforthe92naturalelementsidentifiedbymodernscience.
Before proceeding let us copy the familiar periodic table of elements with the 92
distinctwordsofGenesisplacedinorder:
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1
H2
He
3
Li4
Be5
B6
C7
N8
O9
F10
Ne
11
Na
12
Mg
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
34
Se19
K20
Ca21
Sc22
Ti23
V24
Cr25
Mn26
Fe27
Co28
Ni29
Cu30
Zn31
Ga32
Ge33
As35
Gr36
Kr
37
Rb38
Sr39
Y40
Zr41
Nb42
Mo43
Tc44
Ru45
Rh46
Pd47
Ag48
Cd49
In50
Sn51
Sb52
Te53
I54
Xe
55
Cs56
Ba57
La72
Hf73
Ta74
W75
Re76
Os77
Ir78
Pt79
Au80
Hg81
Tl82
Pb83
Bi84
Po85
At86
Rn
87
Fr88
Ra89
Ac
58
Ce59
Pr60
Nd61
Pm62
Sm63
Eu64
Gd65
Tb66
Dy67
Ho68
Er69
Tm70
Yb71
Lu
90
Th91
Pa92
U93
Np94
Pu95
Am96
Cm97
Bk98
Cf99
Es100
Fm101
Md102
No103
Lr
Followingourmethodology,weshouldnowseekperiodicity,thesecondorganizing
principleidentifiedabove.Todoso,wewillfirstexamineandunderstandindepththe
periodicnatureofthestructureandformofthetableofelementsandthemodelusedto
explain this periodicity. We will then explore parallel spiritual models found in
KabbalahandChassidut. Ina forthcomingarticlewewilluseour findings toexamine
theperiodicityinherentinourparallelTorahtableofelementspicturedabove.
3. On the relationship between spiritual and mundane in the Torah
Before startingouranalysis, lets take a few stepsback to say a fewwords about the
rationale for looking to theTorah formodels that candescribe (directlyor indirectly)
naturalphenomena.
The physical world and its attributes are often spoken of as a reflection or
manifestationofthespiritualrealm,andassuch,bystudyingthephysicalwemaycome
toknowmoreaboutthespiritualworlds,andultimatelyourCreator7.
ItisexplainedinJewishtraditionthattherearetwowaystodescribetherelationship
betweentheTorahandphysicalreality:
The first,morecommonlyheldview, is that theTorahspeaksofmundanematters
(e.g.lawsofcommerce,liability,etc.)butasitwere,thesemundanemattersarealsoto
be foundreflected in thehigher (or inner)spiritualdimensionsof theuniverse.Sowe
might say that the Torah canbe interpreted as saying something about the spiritual
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worldsaswellasthemundane.Thisinterpretationcanbeassimpleastalkingaboutthe
spirit of the law (as opposed to the letter or the law). Or, it can form thebasis of a
complexandintricate(anthropomorphic)analysisoftheDivine,basedontheTorah.
Thesecondapproach,advocatedbyH. assidism,holdsthattheTorahsactualsubject
matterare thehigher (or inner)spiritualdimensionsof theuniverse,and it isactually
they thatarealsoreflected,ormimicked, inthe lowermundanematerialdimensions8.ThuswemaysaythattheliteralmeaningoftheTorahisspiritual,whileanonliteral,or
allegoricalinterpretationofthismeaningteachesaboutthemundanephysicalworld.9
The second approach may seem troubling because the Torah does not seem to
employspirituallanguage(notethelackofmentionofangelsoranyotherheavenly
artifacts). In fact, the opposite is more the casethe stories related and the
commandmentsofGdfoundinitallseemtospeakdirectlyaboutphysicalrealityasit
was a few thousand years ago. The response to this point comes in the shape of the
TalmudicdictumthatTorahspeaksinthelanguageofmen10.Inotherwords,though
the subject matter of the Torah is indeed spiritual, its language is mundanethe
languageofmensuchthatitemployslanguagethatrefertoobjectsandstatesofaffairfamiliartohumans.11
Armedwith these twobasicnotions regarding the subjectmatterand languageof
Torah,weargue thatby studying thephysicalworldusing scientific methods (which
should hopefully give us a clear picture of physical phenomena) we expect to find
parallelsbetween theTorahs physical terminologyand the findingsofexperimental
science regarding those phenomena. Relating our knowledge about such physical
phenomenatotheTorahsvocabulary(orothernonlinguisticformsofcommunication,
as willbe explained) will, in turn, lead us toabetter understandingof the spiritual
issues,whicharetheTorahsactualsubjectmatter.Thuswecometolearnmoreabout
thespiritualrealmusingscientificknowledge.The Torah contains varied types of communicable information, alluded toby the
famous acronym: PaRDeS. PaRDeS stands for the four types of textual analysis
traditionallyusedtoexploretheTorahinordertorecoveritsinformativecontent.These
are:pshat (literalanalysis), remez (symbolic,ornumericalanalysis),drash (hermeneutic
analysis)and sod (associative,ormodelbasedanalysis). Inorder toquicklyorient the
reader we will note that drash (hermeneutic analysis) was utilized in the study and
developmentofHalachah(JewishLaw).Sod(associative,modelbased)analysiswasmost
fullydevelopedinLurianicKabbalah.Ourpresentstudywillmakeuseofallfourtypes
of textualanalysis.At times,werefer totheknowledgearrivedatusingremezandsod
analysis
as
the
inner
(or
esoteric)
wisdom
of
the
Torah.
4. Nature and the Divine
One of the mostbasic findings in the Torah using remez analysis (numerical, in this
case)isthatthenumericalvalueofthehebrewwordfornature( 12,hateva)=86is
equal to the numerical value of the name of Gd associated with the creation of the
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.
As we shall see, thisbasic equivalency will form thebackdrop for much of our
presentdiscussion.
5. 92 naturally occurring elementsThe firstpossibilitywouldbe tomapeachelement to itscorrespondingHebrew root,
simplybasedonorderofappearance(seeTable1inAppendixA).
Furtherreflectionthoughrevealsanalternative.The92distinctrootsofthestoryof
creationaredividedsuchthatthefirst86appearintheversesrelatingthefirstsixdays
ofcreation(Genesis1:1through1:31),whilethelast6arefoundintheversesrelatingthe
Sabbath (ibid2:1 through2:3).Thismotivatesus tocorrespond the6noblegaseswith
the 6 distinct roots found in the Sabbath section in Genesis, while the remaining 86
elementswillbecorrespondedinordertothedistinctrootsfoundinthe6Dayssection
ofGenesis.
Wemention thissecondpossiblemappingherebecauseofour interest in the inert
gases,asfollows.
6. Inert and non-Inert Elements
Scientifically speaking, there are many ways in which the chemical elements canbe
arranged to accent different attributes of their periodicity. Briefly, when looking at a
periodic table, the elements are normally presented with their name, atomic number,
andoften theirvalenceelectronconfiguration.Thecommonly found tableofelements
highlightsvarious typesofperiodicity,oneof themost centralonesbeing thatof the
noble
or
inert
gases.
One of the most importantand outstanding features of the 92 naturally occurring
elementsisthattheymaybedividedintotwogroups,basedupontheirabilitytoform
compounds:thereare6whichdonotformcompounds,alsoknownasinert(ornoble)
gases,whiletheother86doformcompoundswithotherelements.
On the periodic table inFigure 1, the inert gases form the far right hand column.
Graphically, our modern version of the table of elements is structured such that the
periodicity of the inert gases is highlighted, though, as we shall seebelow, the table
couldbe(andhistoricallywas)arrangedentirelyaroundthisperiodicity.
Thisbasicdivisioninto6and86observedinthenaturallyoccurringelementsistobe
found(again,usinganonliteralanalysisoftheTorahtext)intheveryfirstverseofthe
Torah: (usuallytranslatedasInthebeginningGd
created theheavensand theearth).The firstchapterof theTorah recounts theactof
creationofthenaturalworld.ItisimportanttonotethatGdhereisreferredtoasElokim
alone (andnotbyHisothernames), thus leading to theassociationof thisnamewith
nature.
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The6 lettersof the firstword,Bereishit ( )canbesplit into2separatewords,
eachwith3lettersandreadasbarahsheet( ),meaningcreatedsix(inAramaic,
thelinguafrancaoftheancientneareast).
Thenext twowords in theverseare barahElokim.Asnotedabove, thenumerical
valueofElokim,oneofthenamesofGdis86.Wehavethenthatthefirst3wordscanbe
understood to say: six were created (barahsheet) and 86 were created (barah
Elokim).Thesumofthesetwoactsofcreationis866=92,thenumberofthenaturally
occurringelements.
Asmentionedabove,86,thevalueofElokim,isalsothenumericalvalueoftheword
hateva inHebrew,or nature.ThusbarahElokim canbe readascreatednatureas
well.
ThereisyetanotherappearanceofthenameElokimregardingthe6inertgases:
Theatomicnumbersoftheinertgasesare2,10,18,36,54,86. Theheaviestinertgas,
radon(Rn),hasanatomicnumberof86=Elokim.
7. Spiritual WholenessWenow turn to reflecton thespiritualparallel to thepresenceofboth inertandnon
inertelementsinthenaturalworld.
Thespiritual(orpsychological)counterpartofphysicalinertnessintheelementscan
befoundintheTorahsdescriptionofJacobandLavans(Jacobsfatherinlaw)working
relationship. Regarding the wages thatJacob received for tending Lavans flocks the
Torahwrites(Genesis30:42):
Thisisusuallytranslatedliterallyas:
the weaker (atufim) [flocks] were to Lavan and the stronger(kshurim) [flocks] were to Jacob.The literalmeaning is that thesheepwerecharacterisedasstrongerorweaker; the
weakerremainedthepropertyofLavan,thestrongerweregiventoJacobaswages.
However,Rashi,thebasic(literal)MedievalcommentaryontheTorahinterpretsthe
meaningof atufim differently.14 ThisHebrew word canbeanalyzed to stem from the
rootatf( )thatyieldstheinfinitivelaatof,towrap.Itwouldthenmeanthosethatare
wrapped.
Likewise,KshurimthewordusedtodescribethetypeofflocksgiventoJacob,canbe
analyzedtostemfromtherootk.sh.r.( )andtheinfinitivelikshor,tobind.Itsmeaning
wouldthen
be
those
that
are
bound
Ifthesecharacteristicsofthesheepareseenasmetaphorsfortwodifferenttypesof
personalities, thenanatufdescribesonewho iswrapped inwool,keepingwarmallto
himself,whileakashursymbolizesonewhois incompletewithoutformingbondswith
others outside of himself. A wrapped (atuf) individual is not inneed of a mate and
finds sufficient warmth alone. Such an individual needs not receive from nor give to
another.Ontheotherhand,apersonwithatied(kashur)personalityseekscompletion
inrelationshipswithothers,attimesgivingattimesreceiving.
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For the sake of rigor we note that spiritually speaking, these two types of
personalities are usually associated with negative and positive qualities, respectively.
Anatufattitude(especiallyinthepresentcasewheretheseflocksareindicatedasbeing
thepropertyofLavan)isconsideredanalogoustothatfoundinBiblicalSodom15:That
whichbelongs to me is mine, that whichbelongs to you is yours.16 While a kashur
attitudeisnormallyassociatedwithholiness(thoughattimesitcandrifttoanextremeformofwantonnesswhichisofcoursenegative).
However, inH. assidicwritings it is explained thata trulywhole individual isone
who hasboth qualities. Tobetter understand why how this is so we may take the
kaballisticprinciplestatedbyRabbiAbrahamAbulafia(1240c.1291),the13thcentury
philosopherandmystic:beingwholeisbeingoneandahalf.Orinthefamouswordsof
RebbeNachmanofBretzlov:nothing ismorewhole thanabrokenheart.Wecoin the
term whole and half ( , shalem vachetzi) to designate this special quality of
wholeness.
Atrulywhole(andholy)personisdoesnotfeelselfsufficient,therebynotrequiring
others,but ratheronewho is,existentially speaking,bothcompleteand incompleteatthesametime.Byvirtueoftheirhalfness,theyneedtoconnectorbondwithothers.By
virtue of their wholeness they are able to offer support and help to others. Real
wholeness(andholiness)comesbyvirtueofanexistentialfeelingofincompletenessof
insufficiencyandinadequacytosinglehandedlyprevail,empoweredandstrengthened
byasenseofwholenesswhichsavesonefromasenseofaninabilitytorisetothetaskat
hand.
Scientifically speaking, we can immediately note the analogybetween these two
basic definitions of atuf and kashur and the distinctionbetween inert and noninert
elements.Bondformationispossibleonlywhenanelectronorbitalishalforincomplete.
Butwhenanorbitaliswholeorfilled,theelementinquestionisnotinneedofacceptingor receivingelectronsand thusdoesnot formbonds.Yet,bothexist innature.Nature
reflectsthesetwobasicqualities.
The inert gases are also called the Noble gases. The mark of nobility is the air of
wholeness surrounding it. The nobility of the elements do not react with any other
elements. It isonly the86,Elokim,elements thatcandoso.Nonetheless, thesixnoble
gasesformasortofaxisaroundwhichtheother86elementsrevolve.
8. Whole-ness of the Patriarchs
The attribute ofbonding is found tobe associated with the name Elokim in another
manner:ElokimisthenameofGdrelatedmostcloselywiththePatriarchIsaacasbothmanifestthequalityofjudgment(ordin ).WhendepartingfromLavan,hisfather
inlaw,Jacobsays:
,
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If the G-d of my father, the G-d of Abraham, the fear of
Isaac, was not with me, then you would have sent me away
empty-handed17Jacob refers to the way inwhich Isaac (his father) knewGdas the fear of Isaac
(pachadYitzchak, ).Thenumericalvalueofpachad,or fear, is92,which isagain
Elokim(86)plussixthetotalnumberofnaturallyoccurringelements.
Yet,Isaacwasnotalwayswholeinthesenseofbeingbothwholeandhalfatthesame
time.ThesagestellusthatIsaacwasactually37yearsoldatthetimethatAbraham(his
father)wascommanded tosacrificehim toGd (seeGenesis22),knownas the testof
theAkeida the test of thebindingof Isaac.TheZohar,18 thebasicbook of the inner
teachingsof theTorah, relates that Isaacwasentirelywhole,exclusivelyof noble,or
inert, character and was therefore not suited for marriage, not suited tobond with
another.ItwastheAkeidaliterally,thebindingwhichbroughthimtocompletehis
character with the quality of halfness. It was only then that he became suited for
marriage, tobond with a wife. ThuspachadYitzchak (= 92) canbe understood as the
attribute of Elokim (86) plus another 6, the addition of something to Yitzchaks ownwholeness.
BythesametokentheZoharexplainsthatAbrahamwasnottrulywholeeither,ashe
didnothavethequalityofMightorJudgment.ItwastheactoftheAkeidathebinding
ofJacobdoneoutof fearandaweofGod (as theangel spoke tohim following the
binding: for now I know that you are indeed fearful of God (Genesis 22:12) which
complementedhisessencewiththisquality.
9. Inert Periodicity Historically
Nowthatwehavespentsometimestudyingtheperiodicityoftheinertelements,letus
delveabitintoitshistory.Usingtheperiodicityoftheinertelementsasthebasisforthe
table of chemical elements was first proposed in 1895byJ. Thomsen19 and was itself
basedonanearliermodelbyT.Bayley(1882).AtablesimilartoThomsensappearsin
Figure2.Notethattheprincipaldisadvantagesofthistablewasthelargespacerequired
by theperiodof32elementsand thedifficultyof tracingasequenceofcloselysimilar
elements(forpurposesofillustrationtheinertelementshavebeenmarkedinblue,and
thenonmetals,markedingreen,inthecontemporarytableformatriangularshape,but
heredonotalignsimilarly).
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1
H2
He 3
Li4
Be5
B6
C7
N8
O9
F10
Ne 11
Na12
Mg13
Al14
Si15
P16
S17
Cl18
Ar
19
K 20
Ca 21
Sc 22
Ti 23V 24
Cr 25
Mn 26
Fe 27Co 28Ni Cu29 30Zn Ga31 32Ge 33As 34Se 35Gr 36Kr 37
Rb38
Sr39
Y40
Zr Nb41 42
Mo43
Tc44
Ru45
Rh46
Pd Ag47 48
Cd49
In50
Sn51
Sb52
Te53
I54
Xe 55
Cs56
Ba57
La58
Ce59
Pr60
Nd61
Pm62
Sm63
Eu64
Gd Tb65
Dy66 67
Ho68
Er69
Tm70
Yb71
Lu72
Hf73
Ta74
W75
Re76
Os77
Ir78
Pt79
Au80
Hg81
Tl82
Pb83
Bi84
Po85
At86
Rn87
Fr88
Ra89
Ac90
Th91
Pa92
U
Table 1
10. Orbital Filling of the 6 Inert Gases
Itwasonlyin1922thatNielsBohrproposedthequantumtheoreticalmodelthatforms
thebasisforourcurrentunderstandingofthesubatomicconstructoftheelements,and
explains the observed periodicity of the inert gases. According to Bohrs model, the
structure of each atom couldbe singularly described using 4 quantum numbers to
identify the orbitals in which electrons organize around the atoms nucleus. The
orbitals (sometimes called subshells) are grouped into shells, the shells being
designatedbytheletters:K,L,M,N,,orsimply1,2,3,4,.
Everyorbital isclassifiedby twoquantumnumbers: theprimaryquantumnumber
andtheangularmomentumquantumnumber.Theangularmomentumquantumnumber
isreplacedbytheletterss,p,ord.Twootherquantumnumbersthemagneticquantum
numberandthespinquantumnumberdeterminethenumberofelectronsthatcanfit
inanorbital.
Looking at the periodic table using Bohrs model, we find that the naturally
occurringelementscanbedescribedexhaustivelyusing7shellsand4orbitals,namely
(designatingtheshellsbytheirnumber,notletter):1s,2s,2p,3s,3p,3d,4s,4p,4d,4f,5s,
5p,5d,5f,6s,6p,7s.Thenumberofelectronsthatcanfitineachorbitalis:2insorbitals,
6inporbitals,10indorbitals,14inforbitals
To truly understand the theoreticalbasis for Bohrs model isbeyond our scope.
However,wewould liketotakeacloser lookatthemathematicalregularitiesthatthis
model produces. So let us order the elements in a table that will show us how their
electronsfillthevariousshellsandorbitals:
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1 1 2(2) H He
2 3 4 5 6 7 8 9 10(8) Li Be B C N O F Ne
3 11 12 13 14 15 16 17 18 21 30(18) Na Mg Al Si P S Cl Ar Sc Zn
4 19 20 31 32 33 34 35 36 39 48 57 70(32) K Ca Ga Ge As Se Br Kr Y Cd La Yb
5 37 38 49 50 51 52 53 54 71 80 89 92(50) Rb Sr In Sn Sb Te I Xe Lu Hg Ac U
6 55 56 81 82 83 84 85 86(72) Cs Ba Tl Pb Bi Po At Rn
7 87 88(98) Fr Ra
Shells
Orbitals s(2) p(6) d(10) f(14) g(18) h(22) i(26)
Table 2
TherowsdesignatetheShells,whilethecolumnstheorbitalsineachshell.Thusfor
instance, the firstshell (K)canaccommodateup to2electronsand thereforehasroom
for 2 elements. The second shell (L) can accommodate 8 electrons and therefore has
room for8 elements,and soon. In theK shell,all theelectronsareavailable in the s
orbitalonly.IntheLshell,electronsspotsareavailableinboththesandporbitals.
Notethatshellsarenotfilledentirelybeforethenextshellisstarted,duetothefact
thatelectrons inelementsalwaysseekthe lowestpossibleenergystate theycanreach.
Thisisclearifwefollowtheelementsinthistable.UptoArgon(Ar),thefirstshell(K)
and second shell (L) are filled completely. Then the sorbital of the third shell (M) is
filled,followedbyacompletefillingofitsporbital.Argonthenisthe18thelementinthetablewithelectronscompletelyfillingthe3p[3rdshell(M),porbital]orbital.Butthenext
element,Potassium(K)doesnotcontinuetofillthe3rdshellsdorbital,butratherskips
to the 4th shells (N) s orbital,because electrons in that orbital actually have a lower
energylevelthenelectronsinthe4dorbital.Thisisduetotheinteractionsbetweenthe
electronsthemselves,aneffectknownasshielding.SoPotassiumsextraelectronsdo
notlocateinthe3dorbitalbutratherinthelowerenergyorbital4s.Therestofthetable
follows this general trend, with electrons always vying for the lowest energy level
orbitals.
Therearetwointerestingfactsaboutthistablethatshouldbenotedare:
thatthenumberofspotsineachorbitalisequaltothedifferencesbetweenthe
totalnumberofelementsthatcanpopulateeachshell.
alltheorbitalsthatareusedarefilledorpopulatedtocapacitybyelements
exceptfor the5thshellsforbital.Though5fhasroom for14electrons,only4
spotsareusedby the heaviest naturallyoccurring elements from Actinium
(89)toUranium(92).
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The first fact is the reason thatwehavedrawn the tableas7x7even though the
entireg,handiorbitalshavebeenleftblank.Letusexplicitlywritethefirstfactout:The
totalnumbersofelectronsintheshellsare(WedesignatetheseassetA):
A={2,8,18,32,50,72,98}
Thenumbersofelectronsineachorbitalare(wewilldesignatetheseassetB):
B={2,6,10,14,18,22,26}NownotethatthenumbersinsetBarethedifferencesbetweenthenumbersinsetA.
Thiscanbeclearlyillustratedbywritingthetwosets,AandB,onebeneaththeother,as
follows:
totalelectronsinshells 2 8 18 32 50 72 98
electronsinorbitals 6 10 14 18 22 26
This is truly one of the most astonishing mathematical properties of the periodic
table.
But,arrangingtheelementsintheabovetablealsorevealsaninterestingpropertyoftheinertgasesandthatisthataninertgasisformedeachtimetheporbitalfills.Thep
orbitalofeachandeveryshellhasroomfor6electrons.Thatistosaythateachtime6
electronsfilltheporbital,aninertgasifcreated(excludingHelium,whichdoesnotuse
theporbital).
Recollect that above we noted that in the story of creation, the first word of the
Torah, Bereishit, which can be understood to mean created 6, should be seen as
corresponding to the formation of the 6 inert gases! In fact, the excluded inert gas
Helium, ishintedtointhewordBereishitastheletterbet,thefirst letterofthewordis
writtenintheTorahscrollasalargebet( ,betrabati)andthenumericalvalueof
the
letter
bet
is
2.
11. Mathematical Patterns in Inert Elements
Letusnowlookatthenumbersoftheinertgasesfromanotherperspective. Ifwetake
theatomicnumbersoftheinertelementsandnotethedifferencesbetweenthemwecan
constructthefollowingtable:
elementatomicnumber
difference inatomic number
n, wheredifference = 2n
2
He (Helium) 2 2 1
Ne (Neon) 10 8 2
Ar (Argon)18
8
2
Kr (Krypton) 36 18 3
Xe (Xenon) 54 18 3
Rn (Radon) 86 32 4
Table 3
The rightmost column shows that the differences between the elements are all
values,inorder,ofthemathematicalseriesf[n]=2n2(nstartingat0).
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Thesenumbersareknown in the inner teachingsof theTorahas thedoublesquares
( ,ribuimkfulim).Theirsignificanceisrelatedtothe32pathsofWisdom( "
,lamedbeitnetivotchochmah).TheBookofFormation,mentionedabove,begins:
--
'
Using 32 wondrous paths of wisdom Kah Havayah [God]
Lord of Hosts engraved and created His world, using
three books: author and book and story.20
ItisknownthatthetextualsourceintheTorahforthese32pathsofWisdomistobe
foundinthe32timesthatthenameElokimisusedintheversesdescribingthesixdays
of Creation.21 This, again, is the Name which we have recognized as central in our
discussionoftheperiodictable.WenotethatnootherNameoftheAlmightyappearsin
thecreationstory,22anditappearsexactly32times.
32 is thus thenumberassociatedwithWisdom (chochmah). In the inner teachingsofthetorahwefindthenumber50associatedwithUnderstanding:50GatesofUnderstanding
( ,chamishimshaareibinah).Thereisalsoanother,lesswellknownconcept
of72Bridges( " ,ayinbeitgesharim).23
Actually, all three of these concepts are closely related and are part of one larger
picture.Thisbasicconceptualschemeidentifiesthetypeofenergyrelatedtoeachsefirah
andthetypeofconduitthroughwhichitflows:
Thus the energy ofWisdom is identified as mind that flows through apath ( ,
nativ);theenergyofUnderstandingisidentifiedasintelligencethatflowsthroughagate
( , shaar); finally the energy ofKnowledge is termed psyche and flows through a
bridge( ,
gesher).
This
model
issummarized
in
Table
2.
sefirah energy type conduit type number of conduits
Wisdom mind Path 32
Understanding intelligence Gate 50
Knowledge psyche Bridge 72
Table 4
Ofcourse,72 isalsoadouble square (particularly,72=2 .62).Wehave thus,so far,
foundthementalsignificanceofthedoublesquaresforn=4,n=5andn=6.Tocomplete
ourunderstandingof thesignificanceofdouble squaresweneed tocomplete the series
beginningwith
n=1.
Thebasicmodelof the sefirot inKabbalah indicates thataboveWisdom resides the
Crown( ,keter)thatisexplainedintheZohartoconsistofthreeheads( ,
tlatreishinshebaketer).24Inourpresentmodelwewillmapthese3partsoftheCrownto
correspondtothefirst3valuesofn.
Continuingourpreviousdiscussion regarding thevariousmentalpowerswenote
thatWisdommarksthefirstconsciousmentalpower.Thus, theCrownwhichresides,
both figuratively and in our Kabbalistic model, above the head corresponds to the
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superconscious faculties.The threeheadsof theCrown,or the3superconsciousmental
powersareknownas:Belief( ,emunah),Pleasure( ,taanug)andWill( ,ratzon).
Table 3 illustrates the double squares for values of n from 1 to 6 with their
correspondingmentalfaculties.
sefirah mental faculty n f[n] = 2n2
belief 1 2
pleasure 2 8Crown
will 3 18
Wisdom mind 4 32
Understanding intelligence 5 50
Knowledge psyche 6 72
Table 5
Using the sefirotasamodel for the seriesofdouble squares,we could continue the
seriesuntiln=13.Forexample,correspondingtothedoublesquare128(n=8)wewould
havethe
sefirah
of
Might
( ,
gevurah).
For
338
(n
=13)
we
would
have
the
sefirah
of
Kingdom( ,malchut).
Wehavenowtakenalookattheseriesofdoublesquares,thedifferencesbetweenthe
atomicnumbersof the inertgases.Thisseries isessentially thebackboneof thewhole
periodictableoftheelements.
Extrapolating from our knowledge of double squares in the periodicity of inert
elementswewouldexpectthenextinertelementtobeofquantumnumber:
86 (Radon) 32 = 118. This element hasbeen dubbed Uuo (Ununoctium)by the
InternationalUnionofAppliedChemists(IUPAC)untilitsexistenceisprovenatwhich
timeitspropertieswillbeascertained.
Wewouldexpecttofindthenextinertelementatquantumnumber:
11850=168.ThiselementhasbeendubbedUho(Unhexoctium).
12. Metals and non-metals
Another important periodicity represented in the periodic table is that of the non
metallic elements. Whereas the periodicity of the inert elements was definedby the
doublesquares(asexplainedabove),theperiodicityofthenonmetalsisrecognizableby
the triangular shape they form on the periodic table, as highlighted in the next table
(nonmetalsareshadedinturquoise).
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1
H2
He3
Li4
Be5
B6
C7
N8
O9
F10
Ne11
Na12
Mg13
Al14
Si15
P16
S17
Cl18
Ar
19
K20
Ca21
Sc22
Ti23
V24
Cr25
Mn26
Fe27
Co28
Ni29
Cu30
Zn31
Ga32
Ge33
As34
Se35
Gr36
Kr37
Rb38
Sr39
Y40
Zr41
Nb42
Mo43
Tc44
Ru45
Rh46
Pd47
Ag48
Cd49
In50
Sn51
Sb52
Te53
I54
Xe55
Cs56
Ba57
La72
Hf73
Ta74
W75
Re76
Os77
Ir78
Pt79
Au80
Hg81
Tl82
Pb83
Bi84
Po85
At86
Rn87
Fr88
Ra89
Ac
58
Ce59
Pr60
Nd61
Pm62
Sm63
Eu64
Gd65
Tb66
Dy67
Ho68
Er69
Tm70
Yb71
Lu90
Th91
Pa92
U93
Np94
Pu95
Am96
Cm97
Bk98
Cf99
Es100
Fm101
Md102
No103
Lr
Table 6
Ofthe86noninertelements15areclassifiedasnonmetals.Theother71elements
areclassifiedasmetals.Wenotethathydrogenissometimesplacedinaclassofitsown,
somethingweshalladdressbelow.Generallyspeaking,thoughnotalways,metalsactas
electrondonorsandnonmetalsaselectronrecipientsinchemicalcompounds.
As mentioned above, the nonmetals form a triangle in the righthand side of the
periodictable:5elementsinthefirstrowofthetriangle,4inthesecond,3inthethird,2
inthefourthandfinally1inthelast.
5
B6
C7
N8
O9
F14
Si15
P16
S17
Cl33
As34
Se35
Gr52
Te53
I85
At
15isatriangularnumber.Thefunctionthatgeneratestriangularnumbersis:
n(n1)
2f[n]=
Wedesignatetriangularnumbersbythespecialsymboln.25Thus,5=15.Another
way todefine thenth triangularnumber isas thesumofallnumbers from1ton. It is
thereforealsotruethat:
n=n(n1)
Therefore,
5=54
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But,4=10,sothat5=510.
Thus,the5thtriangularnumberhasthepropertyofwholeandhalfthatwesawabove
(5).
Thenumber10, the4th triangularnumber (and thewholepartof5),hasa special
referenceintheinnerteachingsoftheTorah.Itissometimesasdesignatedas:
,,,
simple song, double song, triple song, quadruple songThis idiomalludes tothenumber10as thesumof1(simple),2(double),3 (triple)
and4(quadruple).
Inourparticularcase,wehave5elementsabove4,or inHebrew letterswehavea
heh( =5)overayud( =10).Recallthat86thenumberofnaturalelementsexcluding
theinertgasesisnumericallyequivalenttotheDivinename,Elokim( ).Thisname
hasfiveletters,withnumericalvaluesareasfollows:
letter in hebrew valuealeph 1
lamed 30
heh 5
yud 10
mem 40
The15nonmetalsthuscorrespond to thetwo letterheh( ,5)andyud ( ,10)ofthe
fivelettersofthenameElokim,theseminalnameoftheperiodictable.
13. Metals and Hydrogen
After accounting for the 15 nonmetals we now remain with 71these are known as
metals.However,inmanyrenditionsoftheperiodictable,hydrogen,theelementwithatomicnumber1,isclassifiedbyitself,implyingthathydrogenforvariousreasonsdoes
notfallwithinoneortheothercategoryofmetalsandnonmetals.
Howshouldweunderstand the roleofhydrogenamong theelements?Togivean
answer,wemustfirstreintroduce theclassicalmodelofthefourelementsofantiquity
anditsmoderndaycorrespondence.Asexplainedelsewhereinlength,26eachofthefour
classic elementsfire, air, water and earthcorresponds with a specific modern
chemicalelement(seetable6).
classicalelement
modern
element
atomic
numbersefirah
air oxygen 8 Crown( ,keter)water hydrogen 1 Wisdom( ,h. oh. ma)
fire carbon 6 Understanding( ,binah)
earth nitrogen 7 Knowledge( ,daat)
Table 7
Thiscorrespondenceisbasedontheessencethateachoftheclassicalelementswas
meant to represent,and themajor role thateachof themoderndayelementsplays in
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nature. Thus, oxygen is the most important component of Air for human beings;
hydrogen, our subject of interest (together with oxygen, which we have already
correspondedwithAir)makesupwater27,uponwhichwewillelaborateinamoment;
nitrogen is the earths major nutrient usedby plant life; and the earliest human fires
wereofthetypethatburnscarbon.
Looking at the atomic numbers of these elements we note that the sum of theirtriangularnumbers=86:
1 6 7 8=1212836=86!28
The classical element water naturally corresponds to hydrogen (e.g. in modern
nomenclature, the prefix hydro denotes a watery characteristic). During the time
periodthatKabbalahwasbeingdeveloped,theacceptedchemicalanalysiswasbasedon
the4classicelements.Classicwaterwasbroughtdownascorrespondingtothesefirahof
Wisdom.Thus, inour modern chemicalanalysis,hydrogen that corresponds to classic
water would also correspond to the sefirah ofWisdom. RegardingWisdom we find an
importantverse(Psalms104:24):
You made them all with WisdomAnalyzingthisusingsod,whereWisdomisthesefirahofhydrogen,wecansaythatall
chemicalelementsbeginwithhydrogen,butthathydrogenremainsinacategoryofits
own. Thus hydrogen would parallel the first letter, aleph, in the Name Elokim, the
essentialNameofthePeriodicTable.Moreover,thenumericalvalueofalephis1,asis
theatomicnumberofhydrogen,strengtheningouridentification.
Aswehavealreadyaccountedfor the lettersaleph,hehandyudof thenameElokim
we are left with two letters: lamed and mem. We are also left with 70 elements not
accounted for (aseither inertgases,nonmetals,orhydrogen).Thenumericalvalueoflamed is 30, the numerical value ofmem is 40, their sum equal to 70. Thus we can
completeourcorrespondenceof theelementswith thenameElokimbynoting that the
numberofmetalsequalstheletterlamedandmem.Ourcompletedanalysisispresented
inTable8.
letter(s) of nameElokim
in Hebrewnumerical
valuecorresponding
element(s)
aleph 1 hydrogen
heh yud , 15 nonmetals
lamed mem , 70 metals
Table 8
Elokim As Creative Consciousness
OuranalysisofthenameElokimasthecentralpivotoftheperiodictablewouldnotbe
completewithoutusspendingafewmomentslookingatthespiritualsignificanceofthis
phenomenon.
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ThoughtheusualusageofthewordElokim isasthenaturalnameofGod,itdoes
haveotherusesintheBible.Indiscussingcivilsuits,theTorahreferstothecourtorthe
judgeasan Elokim (Exodus22:8,22:27). In theBookofPsalms (82:6)we findanother
usageofthenameElokimtorefertoAdam,thefirsthumanbeing:
I had said, You are Elokim and all of you are sons of the
Most HighThisverse servesas the source fromwhich theArizal teaches thateachandevery
Jew literallyhasaDivineelementwithin them.Theverbsaid ( )heredoesnot
mean thatGod literallycommandedAdam tobe anElokim,but rather,as itat times
means in Biblical Hebrew, that God had wanted or had hoped that man would
ascendtotheheightsofbeinganElokimsonsoftheMostHigh.
The Edenic serpent, the catalyst for Adam and Eves downfall and transgression,
clearly voiced this destiny of mankind as a reason for eating from the Tree of
Knowledge(Genesis3:45):
.
And the serpent said to the woman: You shall not surely
die. For God knows that on the day you eat of it, then your
eyes shall be opened, and you shall be as Elokim, knowing
good and evil.Withoutgoing in length into thedifferencebetweenGodshope formankind,and
theserpentsdescriptionofmankindsdestiny,letusmerelysaythatduetoAdamssin,
thisdesireofTheHolyOneBlessedBeHewasnotyettoberealized.Godwilling,inthe
timesoftheMessiahitwillbefulfilled.
But how would we describe the state of humanity hoped forby God and termed
Elokim.Untilnowwehavestudiedthenatural(mundane)worldasareflectionofthe
spiritual worlds of the Divine. Here we find that an element of the mundane world,
albeit a spiritual elementthe soulshares the same nameElokimas the pivotal
nameofthePeriodicTable.IfuntilnowwehaveseenthePeriodicTableasreflectingthe
Divine,wenowunderstandthatitalsoreflectsthespiritualelementwithinman.Thisis
notentirelysurprisingasweknowthatthesoulisitselfapartoftheDivine.
AsthenameElokimisthecentralbuildingblockforthePeriodicTableofthephysical
elements,sowesaythatwithinmanthenameElokim is instrumental in theexpansion
anddevelopmentofconsciousness.Consciousnessistomankindasthephysicalworld
istoGod,andbothareconstructedusingthepivotalnameofElokim.Thisisthemeaning
ofthesayingofthesages:
Icreateworlds,youalsowillcreateworlds. IwantedthatjustasIcreate,youwill
create.TheserpenttrickedEveintothinkingthatshecouldreachthislevelofcreative
consciousnessthroughtheft. Thiscouldonlyfail. Yet,theCreatorwantsthis,forusto
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reachcreativeconsciousness. Thusallofourmeditationon theNameElokim is really
aboutoursouls ( ,neshamah). Each level,thealeph,thehei,theyud,the lamedmem,
andtheaxisofsixaboutwhichallthe86(86=Elokim)elementsrevolve,belongstothe
soulof theJew. By studying theperiodic table, weare studying aspectsofour own
souls.
14. Hydrogen As the Source of All Elements
ItwasmentionedabovethathydrogencorrespondstothesefirahofWisdom,andthatby
WisdomGodcreatedallintheuniverse,asnotedintheverse:Youhavemadethemall
withWisdom(Psalms104:24).
ThisideathatWisdom,oritselementalparallel,hydrogen,isthesourceofallother
matter in the universecorresponds to the accepted contemporary theory of
nucleosynthesis(elementformation),whichtheorizesthatallelementsarecreatedinthe
fusionreactionofhydrogenstars likeoursun. In thecoresofstars,hydrogen is fused
into helium, helium into carbon (and sometimes into oxygen) and may include the
formationofelementsasheavyasiron(atomicnumber26).
InouranalysisofthePeriodicTablewehaveseenthathydrogencorrespondstothe
letteralephof thenameElokim.TheBaalShemTov, the founderofChassidut, taught
that all the other 21 letters of the alphabet originate from the letter aleph, another
paralleltothetheoryofnucleosynthesis.
15. The Mathematical Series of the Element Groupings
We now have a complete structural scheme for understanding the spiritual
correspondenceofeachofthe92naturallyoccurringelementsinthePeriodicTable.We
haveseenthattheycanbedividedinto4basicgroupings:hydrogen,the6inertgases,15
nonmetalsand70metals.Wenowhaveaseriesof4numbers(whichwehavefoundby
categorizingthe92elements):1,6,15,70.
With this series in hand, we now turn to one of the most basic techniques of
numericalanalysisused inthe innerwisdomoftheTorah:seriescalculus.29Whenever
wehaveaseriesofnumberssuchas this, it is important, frombothmathematicaland
Kabbalistic perspectives, to find the base of the series. Doing this is technically very
simpleasallthatweneedtodoisfindthedifferencesbetweenthenumbersoftheseries,
then the differencesbetween the differences, and finally, in our case where webegin
with4numbers,thedifferencebetweenthose,asfollows:
numbersinseries 1 6 15 70differencebetweennumbersinseries 5 9 55
differencebetweendifferences 4 46
finaldifference/baseofseries 42
Thusthebaseofourseriesis42.TheNamewithwhichtheuniversewascreated,is
the42letterName. Theverynumberthatisthebaseofouranalysisoftheperiodictable
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is thenumber that is themost related to theCreationby thesages,ofwhich it issaid
thisisthegatetoGod,therighteouswillcomethroughit,30itisthenameof42letters,
withwhichthehigherandthelowerwerecreated.31
16. Group 1B Periodicity: Copper, Silver, and Gold
FollowingouranalysisofthemajorperiodsinthePeriodicTable,wenowturntoamore
local periodicitythat of the elements in Group 1B. Group 1B contains the three
preciousmetalsCopper(Cu),Silver(Ag)andGold(Au).Apartfromtheirbeingknown
as the 3 precious metals, these three elements were of particular significance in the
constructionoftheTabernacle(Exodus25:126:30)asweshallsee.
These elementsgroupnameIBsignifies that theelements in thegroup sharea
similarorbitalconfiguration to those inGroup1A (Hydrogen,Lithium,Sodium,etc.).
Morespecifically,elementsinGroupIBalwayshaveoneelectrontodonateor,inour
terminology,theyarealwaysjustalittlebitmorethanwhole(shalem).Theouterorbital
configurationsoftheseelementsare:
Cu 3d104s1
Ag 4d105s1
Au 5d106s1
Weseefromtheorbitalconfigurationthatthesemetals,copper,silverandgold,have
anaspectoffinishingacycleandbeginninganewone.Ineachofthem,thespecificd
orbitalisfilled(completed)whilethenextsorbitalcommencesfilling.
Naye saider is a Yiddish idiom that expresses this same sentimentwhere one
phenomenoniscompletedandanewonecommences,particularlyinregardstostages
orcyclesinhistory.WemightsayoftheIBelementsthattheyreflectsuchapointinthe
PeriodicTable,whereoneorbitalcompletesandanewonebegins.Atthispointanew
beginningismade,anewderech,path.ItisacknowledgedwithinthecirclesofChassidutthatwhentheBaalShemTovwas
born,aneworderbegan in theworld.Likewise,when theMessiahwill come,anew
orderwillbeginaswell32.
By having only one electron in the s orbital, these elements, like their Group 1A
counterparts, are the epitomic electron donors, or influencers (mashpiim). Due to the
outersorbitalhavingonlyoneelectron,thesethreemetalsofGroupIB,whichservedto
build the Holy Temple, combine in theory with oxygen in the same manner as
hydrogen,asexplainedabove.Morespecifically,theywouldcombinewithOxygenata
rationof2:1(2atomsfromgroupIB,foreveryOxygenatom).
NotingthateachofthegroupIBmetalscommencethefillingofanothersorbital,wemay take a closer look specifically at the outer orbital configurations of the transition
metalsbeforeandaftercopper(Cu):
element Sc(21) Ti(22) V(23) Cr(24) Mn(25) Fe(26) Co(27) Ni(28) Cu(29) Zn(30)
orbital 3d14s2 3d24s2 3d34s2 3d54s1 3d54s2 3d64s2 3d74s2 3d84s2 3d104s1 3d104s2
Table 9
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Precedingcopper (Cu),orbitalswhichhavebeen filledare1s,2s,2p,3s,and3p. In
copperwe find that3dthesixthorbital iscompletedwhile4stheseventhorbital
beginstobefilled.Thustheseventhorbitalisstartedwithcopper.
ThereisawellknownprincipleinTorahthatallseventhsarebeloved(
).Hereweseethisprinciplebeautifullyapplied.TheTabernaclesignifiesthemost
beloved place for God to dwell in the mundane world. It is only fitting that itbeconstructedfromcoppertheelementcommencingthefillingoftheseventhorbital.
Continuingourexaminationofcopperspecifically,letusquotefromExodus,where
theTorahdescribestheofferingrequiredbytheChildrenofIsraelfortheconstructionof
theTabernacle:
And God spoke to Moses, saying: Speak to the Children of
Israel that they should bring me an offering: of every man
whose heart prompts him to give, you shall take my
offering. And this is the offer that you shall take from them:
gold and silver and copper
IntheoriginalHebrewtext,thewordforcopper( )isthe29thwordfromthe
beginningoftheparshah.29is,ofcourse,theelementalnumberofcopper.
IntheTorah,inthetextjustquoted,thegroupIBelementsareorderedbyheaviness
(atomic mass): gold (79) silver (47) copper (29), the heaviestgoldlisted first. This
ordercorrespondstoreadingthegroupIBelementsfrombottomtotop.
InAramaic, theonlynonHebrew language towhich thesageshavecontributeda
measureofsanctity,theHebrewwordforheavy( ,kaved)meansprecious(inHebrew
,yakar). Some of this meaning has alsobeen retained in the Hebrew word kavod,
whichmeansimportanceorhonor.Inanycase,itisestablishedthatinHebrewthat
whichisheavyisalsoprecious.
WeseethisintheGroupIBelements.Theheaviertheelement,themorepreciousitisconsidered.Gold is themost treasured33, thensilver,and,copper, the lightest is the
leastprecious.
Another approach for analysing the significance of these three metals is their
correspondence with the sefirot. Indescending order of heaviness, gold is associated
with the sefirah ofMight ( ,gevurah); silver associated with lovingkindness ( ,
chesed); copper corresponds to Beauty ( , tiferet). It is well known that the 3
patriarchs,AbrahamIsaacandJacobalsocorrespondtothese3sefirot,asfollows:
lovingkindness(chesed) Abraham silver
might(gevurah) Isaac goldbeauty(tiferet) Jacob copper
Table 10
As we can see, gold the most precious corresponds with the patriarch Isaac. This
parallel between Isaac and gold becomes meaningful when considering the future
buildingofthe3rdHolyTemple.Ofthattimeitissaid(Isaiah63:16):
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For you are our father, for Abraham has not known us, and
Israel has not recognized us, You God are our father, our
savior, Your name is forever.Thesages(Shabbat89b)explainthisversetomeanthatofall3patriarchs(Jacob isalso
knownasIsrael),itwillbeIsaacthatwillshowspecialmercyontheJewishpeople,his
offspring, and will thusbe the primary patriarch. The sages also relate that the 3rd
Templewillbeconstructedentirelyofgold.
*BasedontwolecturesgivenbyRabbiGinsburgh,9thofElul5753(27/8/93)and15thofIyar5761
(7/5/01);TranscribedandtranslatedbyBatyaEshel.
1.Foramorethoroughdiscussionoftheseontologicalschemesinthe19thcenturyseeNye,ch.3.
2.Mostnotablyinchapter1ofpartIIIoftheTanya,thebasicworkofH. abadH. assidism.
3.Avot5:1;seeBTMegillah21bandelsewhere.Fortheidentificationofthe10sefirotwiththe10
maamarot,seeAlterRebbesTorahOr53a,82dandelsewhere.Foracorrespondencebetweenthe
the10maamarotandthe10AristotleanphilosophicalcategoriesseeMaimonides,Introductionto
Logic104.Foracorrespondencebetweenthese10philosophicalcategoriesandthesefirot,seeour
audiotape(Hebrew)TenTypesofConsciousness,(KfarH. abad:GalEinaiPublications,1998).
4.Recently,newexperimentationhasledtothediscoveryofsocalledislandsofstabilityinthe
superheavyelements;seeOganessianet.al.,VoyagetoSuperheavyIslandinScientificAmerican
282:1(January2000),pp.4549.
5.SeehisvolumeAhavatTorah(Podgorza,1905).
6.Meaningwordsthatstemfromdifferentroots( ,shorashim),the2or3lettercombinations
which serve to form words in semitic languages like Hebrew [technically, 2 letter roots are
knownasgates( ,shaarim)].
7.MarehHa
adamch.3(folio2a).
8.Basedon thisview,R. IsraelBaalShemTov, the founderof theChassidicmovement in18th
centuryUkraine,taughtthattheTorahisuniversalinthesensethatitisrelevanttoeveryperson
ateverymomentineverylocation(quotedubiquitouslyinToldotYaakovYosefbytheBaalShem
Tovsstudent,R.YaakovYoseftheMaggidofPolanah).
9.In theoriginalHebrew these twoviewpointsare:1) 2)
; these specific idioms are fromAsarahMaamarot,Maamar
ChikurDin, III, ch. 23by R. Moshe Azaria (Ramah) of Pano. They are originallybased on R.
YishayahHorowitz,authoroftheShneiLuh. otHabrit(Biozepaf,5639)folios10c11a.Thesecond,
Chassidic approach, seems to fit much better with the well known midrash (hermeneutic)
statement:He[God]lookedintheTorahandcreatedtheworld(seeBereisheetRabba1:1)
10. "" ;Berachot31bandelsewhere.
11.Notethatfollowingthefirstviewpoint,wheretheTorahisliterallyspeakingofthemundane,
thisTalmudicdictumhasno(oratmosttrivial)meaning.
12.ThesourceofthisnonBiblicalwordtodescribenaturewarrantsadiscussiontoitself,which
isunfortunatelybeyondthescopeofthepresentarticle.
13.Asthisnameisconsideredoneofthe7sacrednamesofGod,inmostcircumstances,itmay
notbe pronounced as it is written. We have thus used the usual substitution Elokim for the
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original lettering.Where thenumericalvalueofspecific letters in thisnameareused,wehave
resortedtotheoriginallettering,soasnottounnecessarilyconfusethereader.
14.Rashi,ad.loc.
15.Genesis18:1619:28.
16.See
Avot
5:10.
17.Genesis31:42.
18.SeeZoharI,120ab.
19.HansPeterJorgenJuliusThomsen(18261909),aDanishchemist,Professorofchemistryatthe
PolytechnicUniversityinCopenhagen,mostfamousforhisworkinthermochemistry.
20.SeferYetzirah1:1.
21.Genesis1:131.
22.MosttraditionalcommentariesontheTorahexplainthatchapter2ofGenesisdoesnotrelate
analternatestoryofcreation,butisratherasecondaccount,elucidatingthefirst.
23.SeeZoharIII,227a;AlterRebbesLikuteiTorahIII,36d.
24.Thesource for thesefirahofCrownbeingsubdivided into3 headsor crowns isZoharIII,
288aff.SeealsoMishnahAvot4:13:R.Shimonsays:thereare3crownstheCrownofTorah,
theCrownofPriesthoodand theCrownofSovereignty.InHassidut it isexplained that the3
headsorcrownsinthesefirahofCrownarealludedtointhe3laurelsfoundinthevesselsof
theHolySanctuarybuiltbyMosheinthedesert.TheselaurelsweremadetoencircletheArkof
theCovenant(seeExodus25:11),theTable(ibid25:24)andtheAltarofIncense(ibid30:3).
25.ConwayandGuy(1996:338)designatetriangularnumbersinasomewhatdifferentmanner
as:n.Weretainouroriginalnotationhereandthroughout.
26.IsraelOmerFromansky,TheFourElementsandtheSevenmetals.AudioTape(Rehovot,Israel:
GalEinaiPublications,1993).
27.Meiman( ),likeitsenglishequivalenthydrogen,actuallyderivesfromtheHebrewword
forwater( ,mayim).
28.AdditionalmathematicalequivalenciestothePeriodicTablearisefromthisequation:
Notethat86,thesumoftriangles,canbesplit: 1 6 7=50,while 8=36.Thisdivisionof86into50and36playsamajorroleintheKabbalisticexpositionoftheNameElokim(seeTikunei
Zohar49,folio85b;ZoharI,1b;ibidII,231b232a),basedontheverse:Liftupyoureyesonhigh
andbeholdwhohascreatedthesethings(Isaiah40:26),orintheHebreworiginal:
. (who)=50and (thesethings)=36.
Additionally,the sumofsquaresof1,6,and7=12 62 72=86;while82=64.Thisrevealsthe
important relationshipbetween86and64:86=Elokim ( )and64=Din ( ).TheNameof
ElokimisdirectlyrelatedtothethesefirahofMight( ,gevurah)itissometimesevencalled
theNameofMightwhichisalsoreferredtoasJudgment( ,din).
29.Foramorerigorousdiscussionofthismathematicaltool,seeappendixB.
30.Psalms118
31.ZoharII,234a; III,256b.One form [seeTikuneiZohar,69 (fs.103b104a)]of theNameof42
Lettersisrecitedanumberoftimesin thedailyprayers.In theTalmud(TractateKidushin71a),
wefindadirectreferencetotheNameof42letters:
SaidRavYehuda,saidRav: theNameof42 letters isnot tobegivenbut toonewhoismodest
andishumbleandstandsinmidlifeanddoesnotangernorgetdrunk,anddoesnotactharshly.
Andhewhoknowsthename,andiscarefulwithit,andkeepsitpure,isbelovedaboveandliked
belowandisfearedbyallcreaturesandinheritstwoworlds,thisworldandthecomingworld.
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32.TheMessiahisdestinedtorevealacompletelynewunderstandingintheTorah,aboutwhich
thesageshavesaidthattheTorahofourdayislikenaughtwhencomparedtotheTorahofthe
Messiah.Ofcourse,thetextoftheTorahwillnotchange,onlyitsunderstanding.
33.Itisinterestingtonotethattheobjectivebasisforthevalueweattributetogoldisnotclearat
all.For
more
on
this
question
see
Puzzling
Over
Golds
Allure
in
Johns
Hopkins
Magazine,
June 2000 (Baltimore: Johns Hopkins University) or internet,
www.jhu.edu/~jhumag/0600web/oncampus.html.
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