Euclid taught me that without assumptions, there is no
proof. Therefore, in any argument, examine the assumptions. (Eric Temple Bell,
1883-1960)
Today we have an appreciable scientific body of thought
built up, with questions addressed right from the microscopic to the
macroscopic world. There is a massive industry which is running its course
every day, with thousands of papers published in various disciplines, and huge
amounts of money being poured into certain fields for the purpose of research. The “scientific method” is the prevailing
agreed upon method of approaching the truth of the world. How does one know if
the scientific method provides us with the true perception of reality? Well,
technically, we do not know that, but it is possible to subject that idea to
the self-same test of scientific validity. What will be attempted hereon will
be to highlight the approach by means of encountering certain facts, in a more
or less haphazard order, and then work towards the conclusions.
With that in mind, let us make ONE single assumption right
away, regarding the approach which one is using -- that the World or Universe
of our experience can be understood via a rational approach, and it is possible
to obtain a true perception of the world being led by facts, to the limits of
accuracy to which we are able to perceive them. Although assumptions by
definition do not require previous reasoning, I think we can postulate this general
statement simply because rationality is the essential feature of the scientific
method which we will here set out to examine, and to the best of our knowledge,
experience is a good indicator of reality. Note that the core of the statement
is the principle of rationality, coupled to experiential facts. Also note, that
“setting out to examine” itself embodies the same principle, so we are
consistent.
A second concept which is largely called upon to verify the
truth of phenomena is proof. At this point, we are already on territory that is
a bit more uncertain, as this is only the requirement for mathematical
treatment, where a certain relation among magnitudes, with the assumptions of
mathematics being used, brings out a certain other relation among magnitudes as
an inherent necessity. Let us allow certain facts to throw some light on this
requirement of truth.
Rewind the clock a hundred years back, towards the latter
decades of the 1800’s, and it was well known that the only “minor problems” with
physics for example, was with respect to a blowing up of the UV spectrum
predicted for a blackbody, as well as certain small (note that keyword)
corrections being required to account for the movement of Mercury around the
sun. A look at theories of later time shows that two offshoots have been
derived from those apparently innocuous discrepancies, one being the concept of
the quantum, and thereby to quantum mechanics… and the second paving the way to
general relativity.
We will not concern ourselves with whether or not the above
theories are correct, and to what extent, because the point to be noted is with
regard to the mathematics. The mathematical assumptions were changed, at quite
a profound level, introducing Lorentzian metrics and for the first time ever, complex
numbers to describe the physics of real quantities (as a preliminary
look at the Schrodinger equation reveals). This means that no one who had not
made the connection with this sort of mathematics, in the years preceding this,
could ever PROVE that the existing set of laws are inadequate, and not just in
a minor way but to quite a large extent (in retrospect). One has to restrict
oneself to the existing set of mathematical assumptions in order to even set
out to prove something to the scientist of the day. Also note that from the
point of view of that particular time, the scientist would be attempting what
would be seen as a wholesale revision of existing concepts merely to account
for some “small” discrepancies. I shall come back to this point in a later
article.
What can we take away from this idea? The fact that “proof”
is valid only for the mathematical aspect of a theory, and NOT for the coupling
of experience with the mathematics. Since mathematics does not require the
adherence to reality or experience, but science does, it follows that one
cannot disprove a scientific theory on mathematical grounds, unless, of course
there is a mistake in the mathematics itself… at which point the laws of
mathematical necessity are enough to demolish the theory. A contradiction is
all it takes. What this means is that no one can prove, for example, that
Newton’s theory is wrong mathematically.
This means that in order to examine the scientific validity
of science, we are to direct our sights elsewhere, out of the domain of proof.
That is quite a big step, so let me reiterate, it is NOT necessary beforehand
that one is able to PROVE that a particular theory or view of the world is
wrong, in order to bring forward changes into the world-view. And the more
massive a paradigm shift, the tougher it is to prove the previous worldview as
being inadequate. Absence of disproof is NOT a test of scientific validity.
So how then are we to judge the validity of our scientific
examination of science? It has to be from experience, and the coupling of
mathematical ideas to experience must reveal whether or not we are on the right
track. It is here that we approach another turning point: how much of the
mathematical treatment must adhere to experience? What is the connection
between the two?
Let me illustrate this with an example. It is commonly
known, that in Newtonian dynamics, physics does not change under time reversal.
What does this mean? This is actually a mathematical statement, it means that
if we flip the sign on the term having time from +t to –t, the dynamics is
essentially unchanging, or as it is fancily called, invariant. What this is
then said to represent is that instead of going from initial to final
conditions, one can easily think of going from the final to the initial
conditions, with essentially the same physics coming into play. Hence
“dynamics” is closely connected here with our perception of time, +t represents
time moving forwards, and –t represents time moving backwards.
Pause. There is another explanation. When we look at time,
as represented by ‘t’, is just a count. It is a number that counts a periodic
occurrence. Since this count is linear, we are at perfect liberty to be
notoriously pessimistic and choose to count BACKWARDS. Let us assume that
instead of time starting from (for example) 1 AD and going to 2010 AD, it
instead starts at what we mark as 2010 AD counting DOWN to 1 AD. In that sense,
the future would go towards negative numbers! It is entirely up to us whether
we count it by adding an increment, or subtracting an increment, as long as we
do it periodically. But what happens in the case of (tfinal – tinitial)
in the case that the counting is downwards? It turns out to be negative. The
number line mathematically offers us this freedom, and it is the same freedom
that is reflected in the change of sign. The only conclusion that can be drawn
in that case is that in classical mechanics, time enters as a linear quantity.
However, note the connection generally made in physics, with
-t and time flowing from future to the past. Here, a physical perception (or
mental qualitative perception, if you will, both being valid in our
examination) of time is allowed to go totally reverse, and is then taken as
reality and applied to concepts such as causality, its violation, etc. There is
absolutely NO evidence of time ever ‘flowing’ backward, and about that, all the
scientists naturally agree. Not just that, quite apart from the absence of
evidence, it offers a way to understand that there are various ways to couple
mathematics to reality. Hence, the coupling of mathematics with experience here
is vital to re-examine, as it offers the ONLY corrective factor any theory has.
Mathematics says time can be counted downwards. That stands to experience. The
reversal of time, or processes, or any of our experiences, is not subject to
the same law.
As you have seen, a simple argument such as the above has
far reaching consequences. What about
causality then? What about the second law of thermodynamics? How about time
reversal symmetries in recent theories? … and so on. We’ll examine the process
of these questions in the next article, but here we note that this happens
because it deals with the basis of the sciences, which is the area from where
the revolutions in thought generally come about. It is indeed encouraging that
there is an avenue open for each one of us to explore independently, where we
connect the mathematics to the outer world.
To summarize, the criteria we apply on science is that it
must explain things rationally, quantitatively for the time being. In view of
that quantitative aspect, it is seen that in shift of viewpoints, it is
generally the relation between mathematics and reality that is remolded, and
hence disproof of an existing theory is not a good criteria. At this point we necessarily
reach the question: How do we overcome
the limits of human perception? We cannot obviously perceive electricity in the
same way as we do light, and we are pretty far from experiencing any nuclear
force, which nevertheless offers considerable explanation to physical
phenomena. We must be able to decide scientifically, the amount of leeway we
offer to mathematics when it comes to our perceptions and intuitions, and hence
put them “on hold” when we make our calculations.
We shall consider that next.
