'Names' for the powers of two
For exponents which are nonnegative integers the powers of two are in
English: one, two, four, eight, sixteen,
thirty-two, sixty-four, one hundred (and)
twenty-eight, two hundred (and) fifty-six and so on.
These words for numbers are often called "names", which they are not,
because for each number the expression for the next number in the sequence
follows strict rules.
The number 64 could not have been called "one hundred twenty-eight"
instead, and the word for it is not consistently capitalized, as a name
Moreover, in principle, names remain the same, regardless of the language
used, altho unknown phonemes in the one language may be replaced with
familiar phonemes in the other.
Words for numbers, however, differ like those for plants, animals and
In spoken Putonghua Chinese the powers of two are: yī, èr,
sì, bā, shí-liù, sānshí-èr, liùshí-sì,
yìbăi èrshí-bā, èrbăi wŭshí-liù et cetera.
(You will also need qiān, thousand, jiǔ, nine, for
2^12=4,096 and qī, seven, for 2^15=32,768.)
However much this Chinese may seem to differ from English, it is basically
the same in that it uses the base-10, 'decimal' or denary system
with it finite terminology.
These expressions for numbers may not be as arbitrary as names usually are,
they still use the standard number of fingers on a standard number of
human hands per specimen as their quasi-universal frame of reference in
Yet, except in a few very specific cases, perhaps, the number of ten or
shí human fingers is entirely irrelevant, and so is the use of the
denary numeral system.
In the context of two-sex procreation the base which stands out is the
number two of the binary system.
The written mathematical base-2 numbers may be many times longer than
base-10 numbers, on the whole systematic verbal expressions for binary
numbers (based on 2, 4 and 16 together) need not be longer than those for
The words or phrases for significant numbers in the binary system will even
be shorter than in the denary system (but, in general, those for
significant numbers in the denary system will, of course, be longer).
In my The Completion of the Binary System (not yet published) i have
developed an 'omnilingual' infinite binary terminology of numbers in which
the first nine powers of two are: sa, ko, to,
pu, mu or (sa) suten (which rimes with
refrain), ko suten, to suten, pu suten and
Some of these terms you may find in these pages of The Powers of Two; in
italics, that is.
Here, their occasional use is meant in the first place to wake the most
naive among ten-fingered devotees from their deep number slumber.
There are quite a few parameters which are supposed to describe the real
or expected growth of a two-gendered population in the course of time:
for example, the birth rate, the so-called '(total (period)) fertility
rate', the net reproduction rate and the replacement rate.
A parameter such as the 'fertility rate' deals with women of age 15 to 44
or 49 only; others, such as the net reproduction rate, can be useful when
there is a gender imbalance between the numbers of male and female babies.
Not only can a parameter take too little into account, it may, from a
global point of view, also take too much into account.
Thus, when a country's population growth is mentioned or shown this will
include a net change in immigration and emigration, but so long as human
beings migrate only terrestrially that change has no relevance to the
growth of the world population.
What actually counts with respect to overpopulation is the figure which
indicates with how many other human beings a human being is replaced at the
time of 'er (her or his) death.
In this figure neither gender nor migration counts.
(There is at least one complication: a human being may have had one or more
children who died without having children themselves before that human
being, that is, the parent, died.)
For a group of two or more it does not matter whether one individual is
replaced by no-one and another individual by two, because in the end it is
only the average which counts.
Purely from the point of view of overpopulation it does not matter either
if the reproduction takes place by two-sex procreation or by cloning.
In the case of two-sex procreation it only makes more sense to think in
terms of male-female couples that eventually are replaced with two human
beings, instead of one.
Dependent on the degree of accuracy needed it may make sense to consider
the number of births per woman only.
However, the number of human beings that replace a woman at her death need
not be the number of children she gave birth to, especially not in
countries or parts of countries with poor medical conditions or with
rampant civil or international warfare.
Moreover, the mother's own death may be premature, long before she has
reached the age at which she cannot reproduce anymore.
Factual, modal or normative
In any reasonable discussion, we must always distinguish reality as it is
(was or will be) from reality as it can be and from reality as it should
or ought to be.
Any adequate ontology must recognize (at least) three different spheres:
a factual sphere of facts (that is, things as they were, are and/or will
be), a modal sphere of possibilities or chances and a normative sphere of
values, rights and/or duties.
In the field of reproduction reproducing (having reproduced or going to
reproduce) yourself is something entirely different from being able to
reproduce yourself, and these two, in turn, entirely different from having
a moral right or duty to reproduce yourself.
Being able to produce young (a modal concept) is something different
from producing young (a factual concept); and something extremely
different from producing as much offspring as possible!
The words and phrases of natural language, however, do not always follow
these distinctions: one and the same word may be used for both something
factual and something modal; or with the more or less objective denotation
of a word a subjective normative or otherwise evaluative connotation may
Judging by their lexical definitions, both fertile and
fecund, for instance, may apply to human beings and nonhuman animals
able to produce or capable of producing young (a modal
notion); they may also apply to any organism producing or reproducing in
great quantities or having produced many offspring (a factual notion).
(The word fecund may just be defined as very fertile.)
In addition, the two words definitely have a favorable connotation, if only
because no-one considers 'infertility' or 'infecundity' an ideal in itself.
Hence, in fertile and fecund the factual and the modal, and
the conceptual, which gives us the denotation, and the emotive, which gives
us the normative or otherwise evaluative connotation, are all mixed
In certain ideologies such a ragbag of meanings may be a heavensent
opportunity for prevarication, but the fake and the vague will not save
nature from destruction.
Demography by stipulative
English has a special suffix to express ability or capacity.
It is the affix -able in a word such as approachable
(also written -ible, as in reproducible).
Neither fertile nor fecund contain this affix.
The meaning of the Latin suffix –(c)undus in fecundus is too
unclear to be of any use: it may refer to something factual, to something
modal, or again, some 'convenient' mixture of the two.
(And if the Latin suffix does have a modal meaning unambiguously, it will
immediately put an end to the sensible use of the English fecundable
defined as capable of conceiving.)
In this respect, a language such as German seems luckier with its word
fruchtbar for fertile, in which -bar has the same
meaning as the English -able.
(Alas, i know from Dutch that vruchtbaar, in spite of its similar
modal affix, is used most prolifically to refer to plain facts too.)
Demographers have attempted to clarify the issue by explicitly
defining fecundity as the physiological capability to
reproduce (the modal notion) and fertility as the actual
reproductive output of an individual, couple, or group (the factual
That all ordinary people, even those with a medical profession, use
fertile instead of fecund is their problem, if not error.
(Or, the Romance languages are blamed for having a bad influence on English,
since they have reversed the meanings of fecundity and
True, theoretically a scientist may call a table "a chair" and a chair "a
table" by stipulative definition.
But the two must have the same or, preferably, no or a neutral
connotation, then; otherwise the person in question will be an ideologue
(in this respect) instead of a scientist.
However, what the users of fertility as a factual instead of
modal term do is, knowingly or not, to transplant the favorable connotation
of fertility in the colloquial, modal sense to a 'fertility'
in the factual sense, regardless of the number of children involved or,
worse, in such a way that a woman's fertility is suggested to increase (in
favor) for every child she bears.
Doing this will only cater to people who know no equilibrium, who may even
embrace an immoderate, if not extremist, ideology.
It would be disastrous if we ourselves used a terminology in our fight
against human overpopulation in which no heed is given at all to the
difference between the denotation or conceptual meaning of a word and its
connotation or emotive meaning.
In a connotation-conscious terminology we may use fertility with its
favorable emotive meaning for the ability to produce young, for it is
good to have that capacity, which is needed for the survival of the species.
We just cannot use that term with its favorable emotive meaning in a factual
sense such as producing young in great quantities, because young
cannot be produced in quantities which are too big to be sustained by the
natural environment, certainly not if nonhuman species have a right to
survival as well.
So is there any alternative term?
Feracious and feracity
It is not easy to find a viable substitute for the term fertility
in the irresponsible sense demographers have used it until now.
There are numerous terms to take into consideration besides
fertility and fecundity; for example, abundance,
copiousness, fruitfulness, natality, potency,
productivity, prolificity and uberty.
When studying such terms, there are at least four points to give heed
- Can the word be used purely factually for both sexes in two-sex
reproduction to refer to the quantitative aspect of the production of
(On the basis of these criterions we should already have thrown out
expressions such as generative capacity and
- Does the term have no or a neutral connotation?
(For it cannot be used if it clearly has a positive or negative
- Is the term used for plants and/or nonhuman animals in one sense and
for human beings in a different sense?
(For here we are not interested in words like prolific when
used to refer to the many works of an author, artist or composer or
to the high scores of a sports player.)
- Is the term used for plants and/or nonhuman animals exclusively for
a valid reason, or in the same sense for human beings as well?
(For it may be used for all, or, if not used for human beings in the
same sense, we might still be able to use it in that sense.)
The word fertility is a noun, and therefore i have only listed
nouns until now, assuming that for any adjective (in the semantic field of
procreation) a noun can be found.
This may seem reasonable, but it bypasses one aspect of words and phrases:
that not only the frequencies of occurrence of such terms vary in general,
but that also the current frequency of occurrence of the adjective may be
markedly different from the current frequency of occurrence of the
The noun may be nonexistent or 'obsolete' nowadays, whereas the adjective
still exists, altho, perhaps, used rarely.
This precisely is the case with feracious, which just like
fertile means productive with respect to generative
(Even the fer- in both words derives from the same Latin
ferre meaning to bear, to carry.)
Dictionaries may mention fruitful, prolific and
(producing) abundant(ly) as synonyms of feracious, while at
the same time noticing that its occurrence has become rare these days.
It seems that the corresponding noun feracity has not been used
anymore for sixty years or so.
This, however, is an advantage, because with such a long-time nonuse, the
(possibly strong positive) connotation it may once have enjoyed will have
ebbed away too, making it suitable for a more objective contemporary use.
There is only one requirement left unfulfilled: from an etymological point
of view the fer- in feracious is not really sex-neutral and
(The woman bears the child, the man begets it.)
But so long as men, just as women, may be said to be 'fertile' too, this
should be acceptable as a broadening of the semantic scope of words
starting with the fer- of ferre in the past.
Moreover, the demographers' traditional 'fertility rates', for which we
needed a better term in the first place, are also expressed in the average
number of children born to a woman (not a man or couple) over her lifetime.
Indeed, these rates are no less and no more than female lifetime