The organisation of thought, educational and scientificWhitehead, Alfred North
Philosophy
The organisation of thought, educational and scientific
Whitehead, Alfred North
Education
For example, consider an electron. There is a scalar distribution of
electricity, which is what is ordinarily called the electron. This
scalar distribution has a volume-density ρ at the time _t_ at any
point (_x_, _y_, _z_). Thus ρ is a function of (_x_, _y_, _z_, _t_),
which is zero except within a restricted region. Furthermore, at
any time _t_, as an essential adjunct, there is a continuous space
distribution at each point of the two vectors (_X_, _Y_, _Z_), which is
the electric force, and (α, β, γ), which is the magnetic force. Lastly,
individuality is ascribed to the scalar electric distribution, so that
in addition to its conservation of quantity--involved in the assumed
laws--it is also possible to assign the velocities with which the
various individual parts of the distribution are moving. Let (_u_, _v_,
_w_) be this velocity at (_x_, _y_, _z_, _t_).
This whole scheme of scalar and vector quantities, namely, ρ, (_X_,
_Y_, _Z_), (α, β, γ), (_u_, _v_, _w_) is interconnected by the
electromagnetic laws. It follows from these laws that the electron, in
the sense of the scalar distribution ρ, is to be conceived as at each
instant propagating from itself an emanation which travels outwards
with the velocity of light _in vacuo_, and from which (_X_, _Y_,
_Z_) and (α, β, γ) can be calculated, so far as they are due to that
electron. Thus the field, at any time, due to the electron as a whole
depends on the previous history of the electron, the nearer to the
electron the more recent being the relevant history. The whole scheme
of such a field is one single thought-object of science: the electron
and its emanations form one essential whole, namely one thought-object
of science, essentially complex and essentially filling all space. The
electron proper, namely, the scalar distribution ρ, is the focus of the
whole, the essential focal property being that the field at any instant
is completely determined by the previous history of the focus and of
its space relations through all previous time. But the field and the
focus are not independent concepts, they are essentially correlated in
one organised unity, namely, they are essentially correlated terms in
the field of one relation in virtue of which the entities enter into
our thoughts.
The fields of a group of electrons are superposed according to the
linear law for aggregation, namely, pure addition for analogous scalar
quantities and the parallelogram law for analogous vectors. The changes
in motion of each electron depend entirely on the resultant field in
the region it occupies. Thus a field can be viewed as a possibility of
action, but a possibility which represents an actuality.
Public-domain text, read in full here on John Shaqi.
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