Irreversibility in mathematics.
V.Gopal
division.
These are the only four operators we are able to use in a sensible
manner. Is there any any mathematical formula or calculation that
permits us to justify irreversibility in nature. OR, is
irreversibility an illusion?
Hugh Denoncourt
I'm not sure what you mean by "sensible" but, to me, there are many
many more operations that we can use sensibly. One such irreversible
(in the sense of lacking a strict inverse function) operation is
squaring. If someone told you that they squared a number and got 9,
you do not know whether the number they squared is 3 or -3. You do
know its one of those two, but you cannot reverse the process only
with the information "I squared some number and got 9". There are
much worse examples.
For instance if someone told you they took the sine function of a
number and got 0, there are infinitely many possible numbers they
could have applied sine to. Typically, irreversibility in nature is
justified mathematically (entropy has a mathematical justification,
for example, though it is statistical in nature).
Hugh
Mark
You might want to x-post to sci.physics. They love this topic. I think
irreversibility in nature is the offspring of quantum mechanics
(built-in probability), statistical mechanics (entropy) and chaos
theory ("it's all downhill from here").
-mark
V.Gopal
demonstrated'. 2+2=4 can demonstrated. Addition, subtration,
multiplication and division can be demonstrated and the results can be
proved to be true. In all these mathematical operations we use the
LOGIC OF our SENSE OF SIGHT. But 'differentiation' and 'integration'
cannot be demonstrated; 'I' cannot use the logic of 'MY' sense of
sight in order to reject or accept integral and differential calculii.
Therefore I can find no reason to accept it. To me calculus is
'insensible'.
In mathematics we make a statement or proposition that begins. But
every statement that begins does not end. But are able to find a
finite 'value' for a statement that begins but does not end - like
convergent series. Here the 'proposition' is irreversible. I am sure
that 'irreversible' propositions represent irreversible processes in
nature like natural radioactive decay, chain reaction etc. Is
'inegration' a reversible mathematical calculation?
V.Gopal
through quantum theory. The idea of quantum is definitely useful in
explaining the reality. But, just as we cannot integrate particles we
cannot integrate variuos quanta. Quantum theory cannot re-create the
same sensible/concrete reality that it explains. We cannot
re-construct reality from knowledge knowledge about it. Therefore I do
not think that we should accept that irreversibility is an illusion.