Lack of variety; constancy: The principle that some things, properties and
relations do not change with time, and remain the same as long as they last.
It is hard to deny that there is some sort of invariance in
nature and in our
experience (and indeed someone who denies there is any invariance insists
on the invariance of the lack of invariance!), but it is difficult to pin it
down both in general and in particular cases without making mistakes.
1. Invariance in general: There are several principles of invariance
that deserve serious consideration. First, there is Newton's
A. First law of motion: 'Every body
continues in its state of rest, or uniform motion in a right line, unless it
is compelled to change that state by forces impressed upon it.'
This may be supplemented by a similar principle that Newton included in his
Rules of Reasoning in the
2nd edition of his Principia, which is very similar to
B. Rule I of
We are to admit no more causes of natural things than such as are both true
and sufficient to explain their appearances.
Similarly there is Newton's third rule, in which 'admit
neither intensification nor remission of degrees' indeed also
may be read as 'are invariant' or 'are unchanging' or 'are constant':
C. Rule III
: The qualities of bodies, which admit neither
intensification nor remission of degrees, and which are found to belong to
all bodies within the reach of our experiments, are to be esteemed the
universal qualities of all bodies whatsoever.
Then there is the following principle
D. The principle of sufficient reason:
Nothing happens without a reason.
which was ably and interestingly considered by
Schopenhauer, but has the set-back
that it does not allow for real chance.
It is interesting to note, also with respect to both Newton's First Law and
First Rule above, that Needham found that the Chinese arrived much earlier at
a similar principle:
E. Chinese law of motion: "The
cessation of motion is due to the opposing force... If there is no opposing
force ... the motion will never stop. This is as true as that an ox is not a
This dates from the third or fourth century BC,
i.e. almost 2000 years before Newton, and is quoted from p. 161 of
Robert Temple's "The genius of China"
that summarizes and popularizes Needham's volumes on science and civilization
Considering these principles of invariance, some
of which concern motion (A and E), some happenings (D), some causes (B), and
some explanations (C), we may propose a general principle:
Principle of Invariance: Nothing that
exists changes without reason - but things may come into being that
have no reason (and happen by chance) and certain things may have happened and
may happen always, without any reason or cause.
Thus, this concerns changes of existing entities,
but it allows for chance and indeed allows that
something that changes may have as a reason for some of its changes that it is
subject to chance (of a certain kind, with a certain probability
It is also important to note that what is invariant may be local and temporal.
This as discussed by Poincaré for natural laws and is briefly considered
below for living things and
2. Invariance in particular: There are many instances of particular
kinds of invariance, that may be called invariants, from human faces
and characters, to natural species, natural kinds, and natural laws, and thus
these particular instances of particular invariants may have different kinds
of reasons and explanations, that may or
may not be known.
As Santayana said: "Repetition is the only form of permanence that nature can
achieve" - but then that is reason we may know nature, for a reality where
everything changes unpredictably no human mind can understand.
Note though that as suggested above, the sort of invariance proposed also covers invariant
One may not know whether a particular item in a
random set will belong to a certain subset
of the set, but one may have excellent reasons to believe that this kind of
change does conform to a certain probability distribution, with a definite
probability to happen, that one may know
well enough to rely and confidently bet on.
And indeed, framed in these terms, what science
tries to establish are first and foremost nature's
invariants of all kinds, and next to its invariants, or included in
these as a special case, its invariant probability distributions, that
represent chance events of definite kinds.
3. Chance and invariance: As formulated, chance, supposing that it
exists, is also subject to invariance, in that if chance events exist, as seems
very probable given quantum mechanics, that works in practice and is
well-supported experimentally, and cannot do without chance events, these
chance events will have some particular probability distribution, that will
invariantly characterize it, unless this too is subject to change.
4. Invariance, exhaustion and death: It is also interesting to note that
- it would seem that - living things invariantly die, though they may last a
long time, and that as long as they live they have certain invariant
characteristics, and more generally that there are things, kinds and processes
that last for some time, but not forever.
Indeed, it may well be that the invariant characteristics of living things are
the cause of their death: Once produced these characteristics are not
maintained by a living organism, but are subject to random damage from the
environment, that in the end destroys them, as securely as a stone is hollowed
by an incessant sequence of drops of water that falls on it.
Similarly, and more simply, there are quite a few cases of processes that
exhaust themselves, and that while they exist seem to conform to Newton's
Third Rule of Reasoning (principle C above) and thus to allow
the simple induction that they may be invariant
for ever, which nevertheless is not so.
Two simple and physically well-understood examples are the bending of a metal
wire (one may bend and unbend it many times, but eventually it will break) and
the elasticity of rubber (it remains elastic a long time, but grows brittle
and hardens with age).
It would seem that there are more complicated processes of this kind, both for
living organisms, and for complex kinds of things like civilizations and
cultures that also tend to grow, flower, decline and perish, though so far no
one has explained these well, even though there are fine descriptions, like
Gibbon's 'The Decline and Fall of the Roman Empire'.