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Doubt and Certainty

Authors : Tony Rotham and George Sudarshan

Source : Crosswords 
Price : Rs. 295
Pages: 320

 

 

 

 

 

 

Everyone of us has wondered at some point or other what the true meaning of life is. The answer to that question is the ultimate goal of philosophy. However, this book does not primarily address that question. What this book does is to try and find a deeper basis to science.

What is science really? Is what we know now the truth? or are we just as lost as the alchemists were when they tried to synthesize gold from baser metals? On a more fundamental level, does science exist at all? The last question may strike you as being exceedingly absurd. Science is after all "rational" thought which cannot be refuted. The question that the book poses is whether nature itself is rational.

The information in the book is presented as a series of debates between illustrious personalities from different fields (e.g Richard Fenyman arguing for quantum mechanics, Steven Weinberg arguing in support for "reductionism" , Aristotle for western philosophy and Deepak Chopra for Eastern Mysticism). Although it seems at the outset that such a format might disturb the narrative and make the book frivolous, the authors have taken great pains to avoid this. The "debates" in fact serve as an interesting diversion from the main topic as well as allow the authors to quote the relevant personalities in a believable manner in the context which those comments were made.

The topics debated include : "Why is there left and right?" , "Is nature Unreasonably mathematical?" , "How did we get here?" and "Is there an answer?". I would like to emphasize that these topics are NOT presented with a metaphysical mumbo-jumbo audience in mind. Each one of the debates is grounded in "Science" and rational thinking. This may also be inferred from the credentials of the authors, who are not philosophers themselves, but are world-renowned physicists. It would be impossible to give a gist of all the topics covered in the book, and hence I have tried to put into my own words a particular topic in the book which interested me the most. This brief gist (note : with no original contributions from me whatsoever), is given at the very end of this review.

The authors obviously know the subject matter well. George Sudarshan is one of the first persons to present an explanation for the weak nuclear force and is also an expert in Indian Philosphy, and Jack Rotham is also a renowned quantum mechanist. There are many references to the Bhagvad Gita and the Vedas in the texts, reflecting the authors' interest in the subject. Although these quotations might seem out of place at first, they are very relevant to the discussions being carried out, and the authors ensure that they are seen in the proper light.

The one negative point that I noticed about the book was that some of the concepts ( e.g "Synchronicity" ) are not lucidly explained. However, this might due to my own lack of knowledge about the subject. The authors assume sometimes (not frequently though... ) that the reader has some knowledge of the topic that they are discussing and hence, the reader might find it difficult to follow the discussion. In a book that is targeted at neophytes, this is a small but noticeable flaw. That being said, most of the debates are excellently presented and are accessible to everyone, including us doctors.

 

I have never read anything even remotely resembling philosophy in my entire life. I always thought of it as an arcane subject which was very interesting but which might be too difficult for me to understand and which would be of no practical use. This book changes that impression to a degree. This book has changed the way I look at science. I believed in God when I was in junior school. As I progressed to high school and beyond, I was overawed by science, science which left no place for God in the scheme of things. I became the "Arrogant Human being", who believed science explained everything.


As a reviewer on Amazon.com said : I was an atheist when I started reading this book. Now I no longer know what I am.


- Oncogen
( The review proper ends here. What  follows are my own impressions of  what the book debates..)

What exactly is mathematics???

The subject of the first chapter of the book is  "Is the Universe describable?". Even though science may claim to have described many natural phenomena, do these explanations really exist in nature? Mathematics is considered to be the highest form of rational science.  Andrew Wiles, a famous mathematician, once remarked that if a parallel universe existed somewhere " The mathematics would be the same". In short, the existing view (which we all accept, knowingly or unknowingly) is that Mathematics is "out there",  it is a basic inherent property of nature that we just "discover". We do not consider mathematics to be a "man-made law" like for example the laws governing the voting rights of Indians are. We consider it to be a "Natural Law", consistent everywhere and at anytime.As G H Hardy, another famous mathematician said "I believe that mathematical reality lies outside us, that our function is to discover or observe it, and the theorems which we prove , and which we describe grandiloquently as our "creations", are simply our notes of our observations" 

In turn, we believe that mathematics and physics govern chemistry, including organic chemistry which in turn governs the biological processes. Even though biology is not amenable to physical analysis right now, it is not entirely implausible that this is because of our inability to apply physics to such a complex subject. Nature, including biology, (we might assume) could possibly be explained in terms of physics if we had sufficient intelligence for the same.

However, is Mathematics really the gospel truth? There has always been a group of individuals who believed that it is not. The axioms of mathematics, they say, are no more than a group of mere conventions, no more fundamental than any other such conventions ( e.g. the voting rights..) . Mathematics is just an approximation of what is happening in nature, but it not mathematics which underlies nature.

This befuddled me for some time before I read the remaining part of the second chapter which gave me some food for thought (but sadly, did not resolve the matter):

 


Is mathematics consistent with itself? :
Eucledian or plain geometry has certain axioms, or principles that must be fundamentally accepted. One of them states that the measure of the interior angles of a triangle must be 180. However, in non-Euclidean geometry, this might not always be so.
Consider the globe and two lines of longitude making a triangle with the equator. Each of the basal angles of this triangle will be 90 . The total sum of all the angles would be 90 + 90 + X, where X is the angle made by both the longitudes at the point where they meet. This sum, obviously, is greater than 180.
Distance itself, which is taken to be unequivocally measurable ( remember (Hypothenuse)2 = a2 +b2, where and b are the lengths of the other two sides.) has now been "proven" by Einstenian physics to depend upon the observer, so that in certain cases, (hyp)2 is not equal to a2 + b2, even for the same observer

If both you and your friend came across a particular object on the road ,and you said "Why look! what a beautiful cup!" and your friend said " Why look! Isn't that a great looking glass?", both of you CANNOT be right. Two mutually inconsistent statements cannot describe the same thing.
If mathematics itself has disparate mutually inconsistent theories how can these theories describe the single consistent entity called nature?

 


Can Mathematics/Physics describe everything?
Mathematics/ Physics are "deterministic" sciences (with the notable exception of quantum physics). That is they allow for things to occur in only one way. Consider a group of particles in a vacum. If you are given the relevant information about the characteristics of each particle ( viz initial position and velocity) , you can supposedly predict with unerring accuracy the future of these particles, and state with unwavering conviction that the future you predict for these particles is the only future possible for them. If you accept this proposition, then it would be very simple to accept that given a sufficiently fast computer (or a great "super-intelligence"), it is THEORETICALLY possible to repeat this experiment for ALL the particles in the universe, including those in our brain.

However if this is true and mathematics is the science on which reality rests, then supposedly "indeterministic" realities in nature such as human choice cannot conceivably exist. Can human "Choice" be described by mathematics? If mathematics is the reality on which nature is based, why can't choice be explained by it?
And if choice CAN be described by a deterministic science like mathematics/Physics, does "free choice" really exist or is it an illusion?

 

 

Does mathematics reflect reality or just approximate it?
Supposedly, the three different happenings of a swinging pendulum, a satellite orbiting the earth, and a weight on a spring bouncing from a fixed support can all be explained by the same equation : that of simple harmonic motion.
These occurrences however are DISTINCT. It is difficult to accept the fact that one single equation describes all of these happenings. Does the equation only approximate what is happening in each of these individual cases?
If the equation is truly and completely correct, what made these three different occurrences to be so closely related to each other? Is God a mathematician?

 

 

Are all mathematical concepts based in nature?
Do imaginary numbers (derived from the square root of -1) exist in nature? Things like matrices seem to exist only in mathematical textbooks. One might argue that matrices and imaginary numbers are just tools invented by man to understand science.
If these "tools" have been invented, it probably means that these concepts are no more fundamental than other laws that mankind has laid down.
As a further deduction, it might be said that it is impossible to draw a line which distinguishes "Natural" mathematical laws from "Man-made" mathematical conventions.
If mathematics (at least in some parts) does not describe reality, what exactly does it describe?

 

 

All of which brings us back to the original question : "Does mathematics describe nature?" (or conversely, "Does nature work on mathematical principles?") , which is the heading of the second debate in the book....

 

The Origin of Everything:

Ok Mister Smarty pants... you still believe that science can make all things rational? Where do you think everything evolved from?

If you think of it, there are only 3 possibilities:

1) The something that we see around us ALWAYS existed. ( In that case, how did it get there in the first place?)
2) The something was created out of nothing.
3) Something or Someone who always existed made the something we see around us today.

Ha! Which of these possibilities do you think is the most comprehensible???

You know what... I think I should go out , get drunk, and forget about this book for some time...