[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]
 }
if 0 {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...)
----
[Arts and crafts of Tcl-Tk programming]
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