The Impossible Machine
VOLITIONAL MATHEMATICS
Based on a letter (5/4/07) to
Donald Simanek, an
extrapolation from talk about
the laws of nature, whether
mathematics changes, etc.
Donald:
Examples don't prove
generalities
Terrapin:
Then how can you say that
experiment is evidence of a
general law?
Donald Simanek, an
extrapolation from talk about
the laws of nature, whether
mathematics changes, etc.
Donald:
Examples don't prove
generalities
Terrapin:
Then how can you say that
experiment is evidence of a
general law?
The conclusion, that either (some) examples DO prove
generalities, or the scientific method is wrong (in basing
general proofs on experience), leads to the reasoning that in
order to find all laws, we must conduct all experiments (the
fault may be that physics is not in fact based on experiment,
but is only confirmed by experiment. But it is hard for me to
conceive how all of mathematics, as a form of experience,
could be explored, since infinity is one of its concepts). The
statement that some laws are universal then amounts to the
assumption or at least assertion that all relevant experiments
have been conducted.
It is still valid to conclude that the laws are valid within the
range of conventional experiments, and within all experiments
if the laws are categorical. However, my intuition is that no
mathematics could be categorical without admitting both the
positive and negative of any given value, e.g. accepting
energy loss is also accepting energy
gain (to say
otherwise, in my mind, is to reject the concept of zero, and
claim that negative one and one are not opposites, what I
presume a mathematician would call madness).
CONTINUE TO VOLITIONAL ENERGY
generalities, or the scientific method is wrong (in basing
general proofs on experience), leads to the reasoning that in
order to find all laws, we must conduct all experiments (the
fault may be that physics is not in fact based on experiment,
but is only confirmed by experiment. But it is hard for me to
conceive how all of mathematics, as a form of experience,
could be explored, since infinity is one of its concepts). The
statement that some laws are universal then amounts to the
assumption or at least assertion that all relevant experiments
have been conducted.
It is still valid to conclude that the laws are valid within the
range of conventional experiments, and within all experiments
if the laws are categorical. However, my intuition is that no
mathematics could be categorical without admitting both the
positive and negative of any given value, e.g. accepting
energy loss is also accepting energy
gain (to say
otherwise, in my mind, is to reject the concept of zero, and
claim that negative one and one are not opposites, what I
presume a mathematician would call madness).
CONTINUE TO VOLITIONAL ENERGY
VOLITIONAL ENERGY
VOLITIONAL EQUILIBRIUM
CALCULATING EQUILIBRIUM
CALCULATING VOLITION
CALCULATING EFFICIENCY
VOLITIONAL EQUILIBRIUM
CALCULATING EQUILIBRIUM
CALCULATING VOLITION
CALCULATING EFFICIENCY
