The Light Cone (Brian's space-time)

The previous results might be improved by keeping track of the signs of the inner products. A large, positive inner product means that two vectors are nearly aligned. A large negative inner product means that two vectors are nearly opposite in direction. A small inner product means that two vectors are almost perpendicular (orthogonal), and the sign means that any residual projection is either aligned (positive) or opposing (negative). Here are the signed results for הלך:

יאר    1    {irrigate,collect water,river}
יאש    -1    {despair}
יבש    1    {firm up,dry up,lose hope}
כול    1    {contain a measured quantity,measure,vessel,enclosure}
כום    -1    {venerate,constellation as a deity}
כמר    -1    {excite deep emotions,singe,blacken,catch in a net}
כנר    1    {harp,lyre,string instrument,emit sounds}
לכד    1    {seize,capture,set traps}
לעט    1    {swallow greedily,gulp down}
לשן    1    {tongue,language}
לתע    -1    {destroy,uproot,deadly fangs}
מרא    -1    {expand,enlarge,unfold wings in flight,well-fed animal,crop of animal holding food}
מתג    -1    {control,direct,bridle}

אקה    301    {wild,wild goat}
ארב    309    {restrain urge to penetrate,lie in wait,barrier,windows of heaven,lair,artifice,lattice,sluice}
ארג    307    {weave,loom,red-colored thread,join parallel threads}
ארה    303    {contain,pluck,barn stall,stable,powerful leaders,lion,take and hold}
אשד    307    {outflow,slope,pour out of}
אשה    305    {create material,be,exist,fire-shaped material,supporting pillar}
אתה    307    {come to someone,entrance}
תאר    -311    {harmonize,draw in outline,circle,harmonious form and shape of limbs}
תור    -301    {search for separate items,explore,search,seek knowledge,arrange,plan,migrating turtledove,forage for grass,stringed jewelry,appointed time}
תוש    -303    {romp,he-goat}
תחת    -301    {place below,underneath,in place of,instead of,in return for,lower level}

and for בוא, "come," "harvest:"

הצן    -1    {arm,equip}
טמם    -1    {dull,fill up,close off}
מום    1    {fault,disable}
עצד    1    {strike down,smithy,axe}
ערג    -1    {thirst for water,irrigate}
פתא    1    {surprise,sudden,unaware}

אבב    1007    {ripen,absorb nutrients greedily,stalk,springtime}
אדב    963    {pain,distress}
בדא    967    {fabricate,lie,create untruths}
גבא    973    {concentrate fluids,pool}
רתת    -995    {tremble,shake}
שרת    -989    {free from labor,give personal service,serve,attendant,s:serve,s:serving pot}
שתת    -1033    {set out,s:threatening power,s:exert power}
תרש    -985    {search,aquamarine stone,trading port shipping mined silver}

Suppose we ordered the Hebrew letters from א to ת, as usual, mapped them to the numbers -21/44 to 21/44, and interpreted the three letters of each shoresh, ignoring sofet letters, as components of a vector in 3-space. כ would have value -1/44 and ל would have value 1/44. We would expect the shoresh כלל, meaning "rules," "complete," "sustenance," and "daughter-in-law" (!) to have square-magnitude 3/44, one of the smallest magnitudes. We would expect אתת, meaning "sign," "with," "you" to have the largest possible value of 3*(21*21) = 1323. 

Here is a plot of the vectors for the entire Hirschian etymology of 1985 shoreshim (out of the theoretical number of 10,648)



We can now look at dot products, and ask, given a shoresh, what are the ones almost orthogonal to it or almost parallel to it. Here is a plot of the dot products of all Hirschian shoreshim with הלך, which means "go," "walk:"



I'll close with a two lists of Hirschian shoreshim: "almost orthogonal" to הלך and "almost parallel" to הלך, meaning "have an absolute dot product of 1" and "have an absolute dot product greater than 299" (in units of 44 squared)

First, most "unlike" הלך by this measure:

יאר    {irrigate,collect water,river}
יאש    {despair}
יבש    {firm up,dry up,lose hope}
כול    {contain a measured quantity,measure,vessel,enclosure}
כום    {venerate,constellation as a deity}
כמר    {excite deep emotions,singe,blacken,catch in a net}
כנר    {harp,lyre,string instrument,emit sounds}
לכד    {seize,capture,set traps}
לעט    {swallow greedily,gulp down}
לשן    {tongue,language}
לתע    {destroy,uproot,deadly fangs}
מרא    {expand,enlarge,unfold wings in flight,well-fed animal,crop of animal holding food}
מתג    {control,direct,bridle}

Next, most "like" הלך by this measure:

(אקה    {wild,wild goat}
ארב    {restrain urge to penetrate,lie in wait,barrier,windows of heaven,lair,artifice,lattice,sluice}
ארג    {weave,loom,red-colored thread,join parallel threads}
ארה    {contain,pluck,barn stall,stable,powerful leaders,lion,take and hold}
אשד    {outflow,slope,pour out of}
אשה    {create material,be,exist,fire-shaped material,supporting pillar}
אתה    {come to someone,entrance}
תאר    {harmonize,draw in outline,circle,harmonious form and shape of limbs}
תור    {search for separate items,explore,search,seek knowledge,arrange,plan,migrating turtledove,forage for grass,stringed jewelry,appointed time}
תוש    {romp,he-goat}
תחת    {place below,underneath,in place of,instead of,in return for,lower level}