system,
between the dead and the living, runs counter to this tendency at once.
Thus it happens that we find it equally difficult to imagine that the
organized has duration and that the unorganized has not. When we say
that the state of an artificial system depends exclusively on its state
at the moment before, does it not seem as if we were bringing time in,
as if the system had something to do with real duration? And, on the
other hand, though the whole of the past goes into the making of the
living being's present moment, does not organic memory press it into the
moment immediately before the present, so that the moment immediately
before becomes the sole cause of the present one?--To speak thus is to
ignore the cardinal difference between _concrete_ time, along which a
real system develops, and that _abstract_ time which enters into our
speculations on artificial systems. What does it mean, to say that the
state of an artificial system depends on what it was at the moment
immediately before? There is no instant immediately before another
instant; there could not be, any more than there could be one
mathematical point touching another. The instant "immediately before"
is, in reality, that which is connected with the present instant by the
interval _dt_. All that you mean to say, therefore, is that the present
state of the system is defined by equations into which differential
coefficients enter, such as _ds_|_dt_, _dv_|_dt_, that is to say, at
bottom, _present_ velocities and _present_ accelerations. You are
therefore really speaking only of the present--a present, it is true,
considered along with its _tendency_. The systems science works with
are, in fact, in an instantaneous present that is always being renewed;
such systems are never in that real, concrete duration in which the past
remains bound up with the present. When the mathematician calculates the
future state of a system at the end of a time _t_, there is nothing to
prevent him from supposing that the universe vanishes from this moment
till that, and suddenly reappears. It is the _t_-th moment only that
counts--and that will be a mere instant. What will flow on in the
interval--that is to say, real time--does not count, and cannot enter
into the calculation. If the mathematician says that he puts himself
inside this interval, he means that he is placing himself at a certain
point, at a particular moment, therefore at the extremity again of a
certain time _