Richard Suchenwirth 2002-11-10 - In the beginning there are Tohu (T) and Vohu (V): two very little things ("rishons" because they're the first (Hebrew)), of which T has an electric charge of 1/3 and V has none. And, as symmetry goes, there are also their anti-rishons - conventionally written with a bar over the abbreviation letter, but I use lowercase for easy keyboard input: t (with -1/3 charge) and v.

Rishons (and anti-rishons) always come in groups of three, and if order doesn't matter, we have four distinct triplets of each:

 Rishons: TTT, TTV, TVV, VVV; anti-rishons: ttt, ttv, tvv, vvv

Now let's enter the realm of elementary particles (for which a language named Tcl may have some uses ;-), which come in three weight classes: light, medium, and heavy (or scholarly Greek: Leptons, Mesons, Baryons). The particular theory that I'm retelling here says that leptons consist of just one Rishon triplet, if their charges sum up to an integer:

 ttt  -1  e-  Electron (finally, an old acquaintance...)
 VVV   0  ve  e-Neutrino
 TTT   1  p   Positron
 vvv   0  -ve Electron anti-neutrino

The other four have fractional charge sums, and thus can only be used as building blocks for bigger structures, the so-called quarks (and the complementing anti-quarks):

 TTV  +2/3 u  u-Quark ("up")
 tvv  -1/3 d  d-Quark ("down")
 TVV  +1/3 -d Anti-d
 ttv  -2/3 -u anti-u

There are more quarks postulated, with names like "charm", "strange", "top", "bottom", but my physics book didn't tell me how they map to rishons...

Mesons (middle-weight particles - although D-mesons are double as "heavy" as neutrons) consist of one quark and one anti-quark, and also sum up to an integer charge, here demonstrated on "Pions":

 u-u   0   pi0
 u-d   1   pi+
 d-u  -1   pi-

The really heavy guys, Baryons, are made up of three quarks, or three anti-quarks, and here we meet old acquaintances again:

 uud     1 p  Proton
 -u-u-d -1 p- Antiproton
 udd     0 n  Neutron

Neutrons and protons make up most of all matter. The bad news is that neutrons don't survive long in freedom - typically after 932 seconds(~15 min), the following happens:

 n -> p + e- + -ve

The neutron turns into a proton, emitting an electron and an electron anti-neutrino (please pardon my typography - originally there are bars over anti-particles, Greek letter nu where I put the v, and subscripts). Expressed in terms of quarks, the above becomes

 udd -> uud + e- + -ve

Or, back to rishons from where we started, the change is only in the second "d" quark, so in rishons that makes:

 tvv -> TTV + ttt + vvv

Finally, enter Tcl. Such process descriptions are strings, and Tcl is particularly (if you excuse the pun) good at strings. Here's some code to check whether a process abides by the Rules (which I don't know all, but two are:

• at one time you may add a rishon and its anti-rishon, e.g. Tt
• the end result must be a valid set of rishon triplets.)

Instead of inserting rishons, I start backward by removing matching rishon/anti-rishons from the postulated result, and see whether we get back to the start. But first, some helper routines:}

 proc rishon'charge rishons {
    # computes the electric charge of a rishon triplet
    expr [string map {T +1./3 V "" t -1./3 v ""} $rishons+0]
 }
 proc rishon'translate rishons {
    # turn a rishon sequence to more conventional particle names
    set tmp [string map {
        TTT e+ TTV u TVV -d VVV ve ttt e- ttv -u tvv d vvv -ve
    } $rishons]
    string map {
        uud p -u-u-d p- udd n u-u pi0 u-d pi+ d-u pi-
    } $tmp
 }
 proc rishon'reduce formula {
    regsub -all {[^TtVv]} $formula "" rishons
    set rishons [split $rishons ""] ;# turn into a rishon list
    while {[has T $rishons] && [has t $rishons]} {
        lremove rishons T
        lremove rishons t
    }
    while {[has V $rishons] && [has v $rishons]} {
        lremove rishons V
        lremove rishons v
    }
    regsub -all (...) [join [lsort $rishons] ""] {\1 } res ;# group triplets
    set res
 }
 proc has {element list} {expr {[lsearch $list $element]>=0}}
 proc lremove {listVar element} {
    upvar 1 $listVar list
    set pos [lsearch $list $element]
    set list [lreplace $list $pos $pos]
 }

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Testing:

 % rishon'reduce {TTV + ttt + vvv}
 tvv ;# so the neutron decomposition appears well-formed
 % rishon'reduce {ttv + TVV + TTT}
 TTV

The latter case is controversial: it describes (backward) how a proton decomposes into a pair of Pi-mesons and a positron - which violates the rule that the number of baryons should remain constant. I can't tell - particle experts, please comment (also on "superstrings", which sound as if they may be food for Tcl too...)

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The names tohu and vohu are quotes from the Hebrew Bible, meaning "desert and empty" (1.Moses 1,2).

LeRoi: Are you sure about that? That doesn't sounds like an accurate translation... also, Which book of the bible is called "Moses" ?

RS: I retranslated from the German translation, "(die Erde war) wüst und leer" 1. Moses is the very first book of the (German) bible, Old Testament.

LeRoi: I see. In english, the first book of the Bible is called "Genesis". Not knowing any german, I cannot comment on your translations, but "Tohu" and "Vohu", I recall being translated as "formless and void". Hmm, it looks like you came pretty close, then. I withdraw my suggestion of inaccurate translation.

AK: See also the german word Tohu/wa/bohu which describes the state of a children's room, if the mother does not put her foot down and says clean up here or else.

TV Very essential and fundamental to the basis of contemporary theoretical physics are the ideas of throw a dice or Gaussian Distribution and conditional probability functional integrals. The idea of linear systems like in Tcl based signal processing fundamentals: Additive Wave Synthesis, and frequency modulation like in Tcl based signal processing fundamentals: Frequency Modulation are also important in various types of nuclear physical model analysis methods. Of course that all is fairly unrelated to language..

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Arts and crafts of Tcl-Tk programming - Category Science