The last century can be seen as the golden age of modern civilization. There has been exponential scientific growth and expansion of human knowledge about self and our surroundings. We can now predict the behavior of almost everything with a high degree of precision. Despite the extent of our knowledge there is still uncertainty prevalent in our science. Our understanding of the quantum realms and the obscure phenomena in the vastness of space is still hazy. Theoretically our equations give us a fair picture. Or at least that is what we think. The major part of the 20th century was spent in unifying the most successful theories we have - The general theory of relativity and the quantum mechanical theory. Even now our physicists are in pursuit of the grand unification theory, a theory that if formulated will govern the behavior of particles in both infinitesimal and the infinitely large realms.
Now here surfaces the major flaw. What exactly is the infinitesimal small and the infinitely large? Our mathematics focuses on the real number system as the superset. ( complex numbers are ignored here for the sake of practicality). The real number line is defined such that there are infinitely many real numbers between any two given real numbers. In other words the set of infinity is a subset of itself. ( You might argue saying that every set is a subset of itself but remember that here we talk about a bounded subset). This gives rise to a major anomaly. How can infinity be contained between two well defined finite real numbers, when the distance between them is also a finite real number?
Consider a line of finite length say 10cm. Lets call this line "line A". Consider another line, "line B" of length 5 cm. Based on inequality one can definitely say that line A is larger than line B.
Now, let me start my argument. I argue that both the lines are of the same length. My argument is backed by the fact that every point on the line A can be paired with a point on line B. This one-one correspondence is possible because both line A and line B contain infinite number of points. Due to this one-one correspondence we can also say that both the lines have the same number of points and hence they are of the same length.
You may call me insane, but before you do let me explain why and how this ambiguity prevails. Every object in this universe has an upper and lower limit of perception. All observations that can be made by that object lie within its own limits of perception or what I call the region of perception. These limits equally apply to all the dimensions perceivable by that object. We humans can only observe objects that are larger and more massive than photons. This is because only such objects can reflect photons back to our eye. Similarly we can extend this argument to the larger scales. after a certain point any object bigger than the limiting boundary value of perception seems equally big. Hence we cannot differentiate them. It is just not humanly possible. But you may say that we can build apparatus that can make these measurements for us but again remember that any apparatus that we may build wcertainly lie in our boundary of perception and hence cannot make observations beyond our scale.
So in order to completely understand our universe we require the ability to perceive in any scale. Un-defining infinity and eliminating it from our system of mathematics is the necessary condition to advance our knowledge. But the limits imposed on our region of perception prevent us from doing so. There may be ways to achieve this indirectly. The Vedas hold countless accounts about how our ancient sages freed their minds and opened the doors to the limitless knowledge. But the true essence of the Vedas is scarce in today's world. The translations to the original version are adulterated with the personal interpretations of the translators. The Vedas must be relished as they are, untouched. It is one of my goals to read them in their true form.
I do not assert that the Vedas hold the key to our advancement. But I certainly believe they can direct us in a right path and accelerate us towards achieving it. The top scientists and great thinkers of today might just rediscover this knowledge for us.