Maintaining order in the classroom is no problem for Helen
Hecksenbasen, or 'Miss Hecksenbasen', as she is called at
school. The days when the children used to get six of the best
for bad behavior passed a long time ago. Especially during their
daily hour of arithmetic it is the computer that keeps Miss
Hecksenbasen's pupils busy. Even tho they are some 40 or 50 in
number, she does not have to do much more than to look over
their shoulders occasionally, and to check whether everything is
alright. Nearly all teaching chores are done by the computer
nowadays. When a pupil makes a mistake the computer gives him or
her a chance to try again. In the meantime it analyzes the mistake,
and if necessary, puts the pupil back on the right track.
Little John, behind whom Miss Hecksenbasen is standing, never
makes a mistake. On the monitor screen he reads "How much is
22 + 13?", he presses the  key (between the  and  keys)
and the  key (between the  and  keys), and the computer
confirms his answer on the screen:
Yes, that's correct, 22 + 13 = 35.
The next question is How much is 22 + 14?. John
first types in "4" and then "0" by pressing two keys next to
each other. And, again, the computer confirms it with
Yes, that's correct, 22 + 14 = 40.
Miss Hecksenbasen smiles, pats
John on the back and moves on, for John certainly does not need
Little Phyllis, sitting in front of John, is not very good at
her sums. She has to calculate how much is 15 + 15. After quite
a bit of hesitating she fills in "30" on the screen.
That's not correct. Please, try again.
is the computer's reaction. She
tries  and , but the same message reappears. She is given
one more chance, and Miss Hecksenbasen, who fears that Phyllis
has no head for figures, is pleased to see that she now presses
the fifth and the third number key from the left.
Yes, that's correct, 15 + 15 = 34
the computer replies in 2,103 brightly
lighted pixels, feeling practically as much satisfaction as its
(For these inexperienced children part of the problem is, of
course, that the number keys, like those with the letters of the
alphabet, have been put on every which way. The [QWERTY\254031]
keyboard in front of them was introduced a few centuries ago to make
it impossible to type faster than a typewriter could manage.
Altho this technological constraint is a thing of the distant
past now, the same antique keyboard is still used by warlocks
and nonwarlocks alike, in spite of more user-friendly
alternatives having been suggested in its place, one being the
After this period Miss Hecksenbasen's day at school is over. She can go
home now, but this does not mean that she is free already. There are
again a couple of adjustments in the program and data of tomorrow's
software to be made. Such adjustments, altho usually looking very minor,
always tend to be much more time-consuming than expected. However, still
in the prime of life --she has just turned one hundred and
five-- Miss Hecksenbasen is full of energy and never
One hour after dinner she is not yet finished but decides to
go to her weekly meeting first. The meeting is in Twelfour
Sweets, a town 120 kilometers from the village of Eleven Elves,
where she lives and teaches at Holy Number Elementary School.
Tonight she will have to go by car, but she often takes her
bicycle, especially in the warmer time of the year when it is over
seven degrees Centigrade and she can leave her coat at home. It
is only half-an-hour's ride, and she needs the exercise. (A
weight of 31 kilograms is too much for a woman her height.)
Until about a millennium ago, Miss Hecksenbasen has been
told, the assemblies were held on the heath in the middle of the
forest between Eleven Elves and Twelfour Sweets. There used to
be a hallowed spot then with exactly 42 cypresses. Tall and
straight, they were symbolic of the enduring, essential unity of
the material world. The spot itself has been preserved, but
because of pollution --also here, so far from the big
cities-- the condition of the grove had rapidly deteriorated,
and it became impossible to save even six cypresses. Five of them
still stand up, now representing the transitory in life. And,
perhaps, even their days are numbered.
Miss Hecksenbasen's destination this evening is a modern
building of the last century, with an entrance flanked on both
sides by newly-planted witchhazels. Shortly after midwinter,
while the ground may still be covered with a thick whitening of
six-sided snowflakes, these whitchhazels welcome the visitors in
a marvelous glow of myriads of sulfur-yellow flowers.
The building has a peculiar shape. Two equilateral triangles
of the same dimensions are superimposed on each other in such a
way that they form a regular polygon on the inside, the walls of
it supporting a flat roof which is several meters higher than
the roofs of the smaller triangles on the outside. Under the
high roof in the center of the hexagram --for that is the
shape of the total structure-- there is a small varnished
table on a raised floor. The sole function of this table is to support
a tome of formidable size with a black cover and gold-edged pages.
Clearly visible from a distance, it carries the name HEXABOOK
in large golden letters. Obviously, here, in the temple's inner
shrine, lies a holy writ.
Looking from the entrance, the back of the hexagon (the
regular polygon on the inside) is closed off by walls separating
this space from three adjacent triangular rooms on the outside.
On the middle wall a huge display of 144 figures in a
square of 12 by 12 catches every visitor's eyes. The figures
appear, on closer inspection, to have been arranged in a certain
order, judging by the alternation of broken and unbroken lines
painted above one another. As each figure is made up of six
lines, no fewer and no more, they turn out to be 'hexagrams' as
well, albeit in a sense quite different from the one in which
the whole temple is a 'hexagram'.
Despite coming by car Miss Hecksenbasen is late tonight. On
the highway she got stuck behind a wheezing truck, an old Super-Six
sedan, and could not drive at her usual speed of 1300 km/h.
And then, traffic in Twelfour Sweets itself is always so slow.
At each intersection in this town there is at least one red
hexagon for which everyone has to stop before proceeding.
Miss Hecksenbasen thus almost misses the prayer at the
beginning of the meeting. This would definitely have upset her,
because for her a day of five prayers, instead of the normal
six, is lacking in something essential. She is not one of those
mystics, according to whom every text of the Holy Writ has 1 or
10 or 100 layers of interpretation, the first, superficial
meaning being merely for the vulgar populace. Like all genuine
believers she is certain that there is only one correct reading
of the Hexabook for both the ignorant and the wise, namely the
literal one. And it is written literally that the People of the
Book shall pray six times between sunrise and sunset, which
should be clear and easy enough for everyone who is, like her,
so lucky not to live too near to the polar regions.
When the prayer is finished, the chairman of the meeting gets up first,
as usual. He walks to the little platform in front of the central wall
with the display of hexagrams on it, and commences:
"My dear brothers, my dear sisters, every week, and also
tonight, we're gathered together under the shelter of the
Six-Pointed Star, in the presence of the Six Testaments, to
celebrate the eternal hexadic nature of reality: God, Man and
Society, and Devil, Woman and Progeny. To celebrate the eternal
hexadic nature of the whole of reality, not only physical
reality, because physical reality is, as we all know, merely a
paper-thin shadow of the godliness that is the crown of all
being. One of the white witches of yore used to formulate it so
sagely, so sagaciously: "Even glory and victory in the world of
science, technology and politics come to naught if they lack
the wisdom and understanding that fall to those who live the
true tree of life". The top of that tree is not reached by dint
of a broomstick, not even by dint of the most sophisticated
contemporary device, for, paradoxical as it may seem to the
uninitiated, matter is immaterial.
I don't have to tell you, who always read the Hexabook with
pleasure and attention, that mankind's path of righteousness
and salvation is the Noble Sixfold Path of Creation, Worship
and Charity, and of Reception, Submission and Chastity, the
three masculine and the three feminine pillars of religion. The
cosmic dynamics of the light, active, creative forces of life
and affirmation that oppose the dark, passive, receptive forces
of matter and negation are clear to you. And so is the
mechanism by which a continuous sexual, intellectual and moral
flux eventually turns into an equilibrium which endures. The
Sixth Testament, that most extraordinary book of changes,
describes very well how the unbroken lines of masculinity and
the broken lines of femininity combine to produce the final,
sixfold permutations of which the sacred hexagrams on this wall
behind me are the precious fruits.
My dear brothers and sisters you know that I do not like to discuss
the profane with you and that I almost never bother you with what does
not deserve our interest. But unfortunately, my dear brothers and
sisters, there's one thing which you may not yet be aware of, and which
I'll therefore have to bring to your attention this evening.
Three days ago, a small, insignificant group of naturalists,
skeptics, atheists, freethinkers, humanists, agnostics,
nihilists and a few others of that ilk held a special
conference on education. At that conference they launched a
plan to persuade the government not to teach senary mathematics
and creation science in public schools anymore. They denigratingly
refer to the former subject as 'the hexes' hokum' and to
the latter as 'the creation myth'. They even venture to
claim that there isn't a whisper in the Hexabook forbidding us
to use the denary system and to count decimally.
Their mystic fiddling with numbers and rules is indeed
unheard of. The world has been created by our Master in no fewer
and no more than six days. He blessed and sanctified the sixth
day, as everyone can verify by reading the First Testament, and
He gave us no fewer and no more than Six Commandments, as
everyone can verify by reading the Third Testament of the Holy
Book. Six is the beginning of a new cycle; it is completion;
the one and the many at once. Nonetheless, this cabal of
blackhearted, empty-headed pagans, numberless as they are, want
to teach this nation's children arithmetic on the basis of the totally
arbitrary number ten --yes, 14 of all numbers!
And this is only the beginning, because it won't make sense
to keep our present system of weights and measures while doing
all our calculations the decimal way. With decimalization the
decametric system is bound to be thrust down our throats
Some of you may not realise what is at stake, for the metre
will remain practically the same, give or take a few millimetres,
and a gramme will still be the exact weight of one
cubic centimetre of water. Yes, brothers and sisters, but one
cubic centimetre in their system, in which 1 cm is approximately
2 mm. Their decametric gramme is hardly more than 14 mg, and
their kilo less than a quarter of our kilo.
Then, you may think, we just multiply each unit with some
number from a conversion table, as was done in the old days to
convert stones into litres and gallons into grammes. No, my esteemed
brothers and sisters, for there is no constant correlation
between their decametric and our hexametric system. The metres
may be almost the same, but that's because ours is equal to the
one-billionth part of an earth quadrant and theirs to the
ten-millionth part. They say that the length of a quadrant is
10,000 km and not 1,000,000 km, even though the quadrant and
the metre don't differ. We'd be walking something like 5 km/h
instead of 40 km/h; or cycling 20 km/h instead of 240 km/h; or
driving 100 km/h instead of the 2100 km/h we're used to. Would
you like to return to the time when you had to inch your ways
from your homes to the assembly?
And this is only distance we are talking about. Should this
Gang of Ten succeed in their scheming, I'll be weighing
something far more than the 24 kilos I and my doctor are so
content with now. They'd have us all overweight in a jiffy
without offering us anything digestible whatsoever. They'd
also have us boiling in temperatures of far over 20 degrees
Centigrade in summer, while we're now used to calling eleven
degrees or more "a heat wave".
And this is only the material aspect of going decimal: I
haven't yet mentioned how it would impoverish us and our
children and our children's children culturally and spiritually!
Future generations couldn't read our great literature
anymore, because what author in his right mind would describe
an adult person of 'only' 31 kg as 'weighing too much'? Or what
author in his right mind would say that it took only half an
hour to travel 120 km by bike -- an ancient thinking in
furlongs, perhaps? Most importantly of all, how could anyone
understand the Hexabook, without realising that our Master
didn't designate five, didn't designate seven, and certainly
didn't designate ten as the holy number to guide our lives,
but six? The inestimable value of the Hexabook can solely be
fully appreciated by believing six, by feeling six and by being
six, at home, at work and at school. Just imagine, dear brothers and
sisters, the incalculable damage done to our faith, and
the great unnumbered multitude of innumerate and illiterate
wretches that would roam this country if the Gang of Ten had it
their way. We should decimate them --
that's what we should!"
Her sixth sense tells Miss Hecksenbasen that there are few
things in life as wicked and destructive of the fabric of society
as religious intolerance, most of all intolerance towards
religion in general. If anger were not one of the six deadly
sins, she would have been really angry. How can this bloody pack
of tenfold calculating wolves say such biting things and show so
damn little respect for her feelings and those of other People
of the Book? It must be particularly painful to Sixth-Day
Adventists who sincerely believe that the Creator will very soon
come again for the sixth time. These despicable naturalists seem
to forget that senary mathematics is based not just on a
doctrine but on the doctrine which supersedes at least two major
cabalas of the past, one which used to have five and the other
which used to have seven as its divine or magic number.
Six is not only the golden mean between five and seven, it is
also the first perfect number, that is, the smallest number of
which the sum of its divisors is equal to itself. That is
why those who believe in the hexadic nature of reality are
numerically superior beyond doubt. Is not the Six-Pointed Star,
the magical symbol of the Hexabook, a pentacle of perfection,
pure, beautiful and sublime like the six-winged seraphs of
heaven? Does not each part of the day (forenoon, afternoon, the
part of the night before and that after midnight) last exactly
six hours? Does not it take exactly six months for the Sun to
travel from the one tropic to the other?
Even the dice which naturalists use to play their games is
not ten- but six-sided, simply because space does not have
five but three dimensions.
In the wisest words of the most ancient of philosophers we
earthlings have always lived between six cardinal points:
north, south, east, west, zenith and nadir.
(Miss Hecksenbasen is familiar with the idea, not with
liuji, the term for it.)
And when the game of games is over and we proceed beyond the bounds
of the six extremes, it is not to end up in a
five-dimensional world of ten, but to enter a realm of
no such extremes at all.
Already in secondary schools every student
is taught that nothing is more logical than to use base 2n in
n-dimensional space. By doing so the perimeters, surfaces and
n-dimensional volumes of regularly-shaped objects with side or
diameter s are simple multiples of 10 and s. Moreover, there
emerges a constant relation then between the values of rectangular
objects like squares and cubes, and all the corresponding
values of radial objects like circles and spheres. Using base
six this radial coefficient is 0.305 in the kind of space in
which all human beings live, deca buffs with their silly pi of
Altho languages, unlike mathematics, are not Miss Hecksenbasen's
forte, she knows that a fully developed language like
Latin has six cases: Dominus is Master;
Domine, Master!; Dominum, Master;
Domini, of the Master;
Domino (the dative) to or for the Master;
and Domino (the ablative) by, with or from
the Master. In olden days famous poets
used to write sonnets in Latin and other languages. They had 22
lines with five iambs, that is, ten syllables, each. Nowadays,
however, every self-respecting poet writes poems of 10 lines
with six syllables, called "sestets". (The Six By Six, the
best-known children's song, is such a hexadic sestet.) Some very
old-fashioned poetasters first add an octet to their sestet, so
that they do not have to part with the perpetual sonnet. But
even those poems have six-syllable lines throughout, and not
the entirely artificial ten-syllable ones.
Altho Miss Hecksenbasen is not strong in biology either, she
too knows that bees, those industrious insects she always
mentions as an example to her pupils, store their honey and
leave their brood in honeycombs constructed on the unvarying
principle of the regular, six-sided hexagon. The wax the bees
secrete to build all the hexagonal cells consists of hydro-carbons,
among other substances. On the chemical level the
hexagon of the beehive is the structure of benzene
cyclic hydrocarbons used in organic synthesis,
as motor fuel, as solvents for resins and ... waxes. A
hexachloro derivative called "lindane" once served as an insecticide
against agricultural pests, but had to be banned, because
it turned out to be too poisonous. It is still used in medicine
tho; as a remedy to treat schoolchildren against scabies, for
instance. The sixless and ruthless mite that causes the itch
is no match for the highly efficacious hexachlorocyclohexane
in which another six atoms of chlorine reinforce the six of carbon.
These are only a few examples of the hexadic nature of what
is, perhaps, not reality but the better part of reality. There
are many, many more.
True, Miss Hecksenbasen has not always been that respectful
to dissenters and dissidents herself. She used to laugh at the
Witnesses For The Prosecution whose Holy Book reveals that
eventually 144,000 souls will rule the entire world together
with a Heavenly Judge. Why 144,000? The number certainly is a
pathetic brew of decimal and duodecimal ingredients. And she
used to laugh at those pitiable devotees of denary numerology
who argued that a number like foursix-one, which was first
called "five-and-twenty" and later "twenty-five", possessed some
kind of a felicific quality because its denary ciphers added up
to seven. However, this was really hilarious, for not only did
not their senary ciphers add up to six, they did not even add up
It is not that Miss Hecksenbasen does not have an eye for the occult
significance of numbers. On the contrary: people's personality
traits and secret ambitions are doubtless derived from the
numbers in their birth dates and the letters in their names,
which hold the keys to understanding both their circumstances
and their potentials. It is rather that everyone utilizing the
standard system ought to know that the true lucky numbers under
one hundred are eleven (15), twelve-four (24), threesix-three
(33), foursix-two (42) and fivesix-one (51), as their ciphers
add up to 10. That is, for example, why the age of majority is
33 in this country.
The proposal put forward by the Gang of Ten would affect Miss
Hecksenbasen as a teacher at a public school more than anyone
else. Teaching arithmetic may be one of her six pleasures in
life, teaching denary arithmetic definitely is not. While she
contemplates the unfairness of the proposal, a politician in the
audience takes the floor:
"Mister Chairman, why all this commotion? This is a free
society and naturalists and their lot may come up with any
concoction they like. Times without number they've actually
done so before. But this is also a democracy, and in a
democracy the majority rules, in particular where it concerns
public funds and schools supported by public funds. You know,
as well as I do, Mister Chairman, that a majority of at least
31% of our population are true believers who've sworn allegiance
to, and will continue to swear allegiance to, the
Hexabook; that a majority of at least 31% of our population
visit, and will continue to visit, a hexagram temple every
Sabbath. Therefore there are souls enough for the number. We
don't only have our number, we'll also win by sheer force
of numbers. There isn't any reason for panic, as there's no danger
whatsoever of Parliament ever acceding to the deletion of
senary mathematics, or, for that matter, creation science, from
the public school curriculum. Should they persist in attacking
us from such a heathenish decimal position, we'll knock them
for six. You can count on that, Mister Chairman! And I'll be
glad to let them know then that their number is up!"
"Let Our Master send wild beasts among 'em which will rob 'em of
their children, and destroy their goods and chattels, and make
'em few in number", says the ubiquitous Mr Leviticus, almost
literally quoting passage 42:34 of the First Testament.
Another elderly gentleman remarks that he and his neighbor had
an argument the other day. They live in an apartment building
which is twelve stories high. His neighbor had said that their
building did not have a ninth floor, because 13, or 'thirteen',
is an unlucky number in the denary system. He had told his
neighbor in no uncertain terms how zany this decimal superstition
is, for that so-called 'number thirteen' is twelve-one, and
there is nothing unlucky about twelve-one at all. He had made it
clear to him that the reason why there is not a ninth floor in
the building is simply that 13 is an unlucky number in the
senary system. No sane soul relishes living on a floor with such
A young lady remarks, much more to the point, that it says
nowhere in the Constitution that public schools should teach
denary, rather than senary, mathematics.
Also Miss Hecksenbasen is now convinced that there is nothing
to worry about. Were she ever to grow as old as Megahexannum,
she would still be teaching senary arithmetic. (Every educated
warlock m/f knows that Megahexannum, a patriarch who believed in
immortality, managed to prolong his life for 4253 years.)
Before leaving the meeting Miss Hecksenbasen personally
thanks the politician for his wise and forceful words. The
politician feels flattered and says:
"If our Master has created us in His image on the Sixth Day,
then we must not only be as good but also as strong as Him. A
school that eschews the supernatural teaches children how to
sweep when they need to be taught how to fly".
"Yes, that's correct, a school that eschews the supernatural
teaches children how to sweep when they need to be taught how to
fly", replies Miss Hecksenbasen, who from now on will number
this man among her closest friends.
Back home she does not go to bed immediately. Over a glass of
resinated wine she writes a few new senary sums to be fed into
The next day little John is as clever as ever in class. The
computer asks him how much is 45 + 31, and he answers almost
without delay "one hundred and twelve" by pressing the , 
and  keys.
Poor little Phyllis tho is making numerous
mistakes and not getting any better. When asked to add 32 and 24
she first types in "5" by pressing the second number key from
the left. Then she looks for a figure which has the shape of a
capital C curving back to the left so that its lower half
resembles a small o. Miss Hecksenbasen, who has been watching
her, asks what figure is next. Phyllis says "this one", and
draws the figure with her finger on the table.
Miss Hecksenbasen is furious and suspects Phyllis' parents of
indoctrinating their daughter with decimal numbers. She holds out her
finger in the direction of the point on the table where Phyllis has just
drawn the invisible digit, and shouts:
"Gracious me! What ridiculous character is that? This is
numbers, not history or art or something! What the heck comes
Phyllis makes an attempt to cipher it out, says that she does
not know and starts to cry. The scene of pandemonium around
Phyllis and her computer has distracted the other pupils from
their own sums. They begin to come to her table; first only 2 or
3; then 4, 5, 10, 11 and still more.
Miss Hecksenbasen now realizes that she must keep calm and
not lose her composure. After all, Phyllis cannot help it that
the computer is not programed to deal with mistakes of a decimal
type. This time she will have to do the instruction herself, and
in an age-appropriate way.
"Listen, Phyllis", she says in a voice as friendly as possible,
"What figures come after 5?"
"1 and 0", answers Phyllis.
"And we call it?"
"Six", answers Phyllis.
"That's correct, 10, and we call it "six". And what after 15?"
"2 and 0".
"And we call it?"
"That's correct, 20, and we call it "twelve" instead of "twosix"
or something. You see, it's very simple. Now, 10 comes after 5.
So what comes after 55?"
While Phyllis is deep in thought, Miss Hecksenbasen produces
a thin stick which looks like a magic wand but may just be a
teaching aid. Lightly she strikes it against the table, three
times. Then all of a sudden, albeit still rather insecure,
Phyllis spells "100".
"And the word for it is?"
"Hundred", Phyllis says, a lot more self-confidently this time.
"Great!" exclaims Miss Hecksenbasen, in her excitement entirely
forgetting to repeat the right answer, as she always does.
Everyone is in the sixth heaven and starts laughing.
Since most of her pupils are now standing together anyhow,
and as Phyllis deserves a little rest, Miss Hecksenbasen poses a
general, open question directed towards all of them:
"Who knows what is the first lucky number after 51?"
"I know", cries little John, a wizard with numbers.
However, Miss Hecksenbasen decides that someone else should have
a try at it first. Paul believes that it is one hundred. Miss
Hecksenbasen asks the others why that is wrong.
"Because the sum of 1, 0 and 0 is not 10", John replies.
Then Miriam explains that it is one hundred and five, because 1,
0 and 5 add up to 10, the holy number. It is soon clear to all
the children that this is indeed the case.
Filled with joy Miss Hecksenbasen suggests that the whole
class sing the Six By Six to conclude the interruption:
One, two, three,
four, five, six,
This is ma-
the- ma- tics.
Three come af-
ter se- ven,
Be- fore lu-
cky 'le- ven.
Our num- ber's
per- fect, pure,
And ho- ly,
that's for sure.
After having finished the song by repeating the last two
lines the children return to their own monitors, delightedly but
Complete order has been restored.
APPENDIX TO TALE SIX|
List of senary numbers used in the text
with their denary equivalents
0:0; 0.305:0.524; 1:1; 2:2; 3:3; 4:4; 5:5; 10:6;
11:7; 12:8; 13:9; 14:10; 15:11; 20:12; 22:14;
24:16; 25:17; 30:18; 31:19; 32:20; 33:21; 34:22;
35:23; 40:24; 41:25; 42:26; 45:29; 50:30; 51:31;
54:34; 55:35; 100:36; 105:41; 120:48; 144:64;
240:96; (300:108; 1,000:216;) 1,300:324; (2,000:
432;) 2,100:468; 2,103:471; (4,000:864; 4,100:
900; 4,200:936; 4,250:966;) 4,253:969; (10,000:
1,296; 100,000:7,776;) 1,000,000:46,656
List of senary percentages with their denary
(0%:id; 30%:50%;) 31%:52.8%; (100%:id)
Lists of 'hexametric' weights and measures with
their metric, that is 'decametric', equivalents
1mg:97.0mg; 14mg:970.0mg(=1.0g); 1g:20.9g; 1kg:
4.5kg(=4523.4g); 24kg:72.4kg; 31kg:85.9kg
1mm:4.6mm; 2mm:9.2mm; 1cm:2.8cm(=27.6mm); 1m:
1.0m (=992.3mm); 1km:214.3m; 40km:5.1km; 120km:
10.3km; 240km:20.5km; 1,300km:69.4km; 2,100km:
100.3km; 1,000,000km:10,000km (exactly)
(1 year:id;) 1 century:36 years;
1 millennium:216 years