As usual Lord Sapota and Venkster, the second last devil were making conversation and they landed up in defining basic laws and where does all theory comes from? So here is the conversation between Monsieur Sapota and Venkster, the second last devil.

Venkster, the devil: Yes, but one can always hypothesize.

Monsieur Sapota: i shun from such practice, there is no practical importance of such theoretical formulation. I believe either we should know or we must think that it is an unknown fact or may be it can be proved by some possible method with a interpolation of existing fact, either way it is either known or proved.

Venkster, the devil:But all proof begins with a hypothesis doesnt it..

Monsieur Sapota:well they do, but those are in form of postulates and then some mathematical or theological or some other form of proof or atleast a draft of proof is attached to them.

Venkster, the devil: Sir every form of proof comes from atleast one base hypothesis that cant be proved but is just assumed to be true...even mathematics, for example it is very easy to prove that 2+2 is not always 4, even though we know mathematically for it to be true...

Monsieur Sapota: see all things are proved with respect to some elementary results.

for example summation of integers ought to be an integer, now that is an adopted convention and proved by many real world situation. now once basic abstract form is proved, you move over to new forms. People say maths use some assumptions, but those assumptions are real world scenarios, for example in case of whole numbers, if you add two shirts to two more existing shirt in ur wardrobe, they ought to be four shirt and that is one elementary result and all equations afterwards will assume this one and prove newer entities by building blocks of existing theorems.

Venkster, the devil:Exactly my point sir, but by breaking the scenario, you can break these elementary results...like I said, I can prove two plus two is not four...

Monsieur Sapota:I am not denying that, but that proof has to be satisfied with at least 3-4 method and should justify world scenario, all advance theorems represent some or other real life scenario and then they are proved using many concurrent methodologies, proving things which are absurd is also possible, but that cannot be done with existing mathematical practices. For example, if i write a new theorem on laws of motion, I must obey Laws of Netwon, i must satisfy many quantization of my results. or if i say my new law does not obey Newtonain, then i must prove that newtonian results are wrong in these sets of circumstances. And trust me if you are challenging a law existing from centuries, you better have a proof right from the basic building element, otherwise ur result is wrong.

Venkster, the devil:Nahin sir thats where you are wrong, all "proofs" of yours are built upon certain basic laws in which we believe the world to behave, but none of these laws have been proved, and hence we can always create new basic laws that run outside this world to disprove anything...

Monsieur Sapota: dood, all basic laws are proved.

Pythagorean, newtonian, la placian, de moiviers or Einstenien, all laws are proved.

there are no basic laws which don't have proofs.

Why do u think calculus or vectors were invented or for that matter all those advance transforms were derived?

if new laws are invented they are first held until they are mathematically or in some way proved. No law is approved without a proper proof and i have not seen any exception to that.

Venkster, the devil:Nahin sir all basic laws are only proved at the macro level, everything breaks down at the micro or super macro level and you know that...

Monsieur Sapota:micro level? why would i prove some laws at level where there is no requirement for them. Newtonian laws are no good at quantum level? and quantum laws are no good at macroscopic level. There is an objectivity associated with each science and the scope of proof is limited in that sphere. As i early said all basic laws are proved from practical understanding and everything else is based on those basic blocks.

Venkster, the devil:Sir but even those basic laws break down under different conditions, which brings me back to my first point, that some basic hypothesis has to be made (which cannot be proven), for example, most basic laws are based on the theory of space and time, but both of these break down at the super-macro level...

Monsieur Sapota:all laws are provided to be true under set of circumstances, even the velocity of light changes, but under severely different set of governing factors and is rarely observed(~10 raised to some mind boggling small number). All laws of time and space are not absolute, you can make hypothesis, but what are the ground works for it. I mean you just go randomly and make your hypothesis and then say i will find a proof and my proof will contain new hypothesis designed by me only? no i don't think that works fine for me. All law are primitives of some other law and the smallest of the laws are proved by observations and results and practical applications.

Venkster, the devil:Nahin sir thats what I've been trying to tell you...all laws are primitives of some other laws and the smallest of laws are something that have been assumed to be true...

Monsieur Sapota: okay, lets say for example that all basic laws are assumptive. where are those assumptions derived from?

Venkster, the devil: From some things that just cannot be proved...for example the basest of basest, gravity...

Monsieur Sapota:but gravity is not a hypothesis its a fact, and if you don't remember there has been thousands of experiment to prove its constants value and the the laws governing gravity i.e. Universal law of Gravitation has been proved by Newton in mathematical terms and results are tallied with respect to actual values.

Venkster, the devil: Sir it has been proved only through experiments, there is no effective theory as to why it exists...

Monsieur Sapota:yeah, there is no theory of its existence, but its not hypothesis either. As far as i know huge work on existence of gravitation has been done, but no concrete findings have been made. in fact all major scientist of applied mechanics and classical mechanics has devoted substantial time to the existence of gravity.

Venkster, the devil: So then since no concrete findings have been made, it still is not proof is it, but there are a million and one formulae based on gravity and its essentials...sir my point is this, that any proof works only within a given environment, it fails outside of that, therefore nothing is absolute...

Monsieur Sapota:i am not making claims to absolutism either. The reason is not found, but its existence is verified. And formulas are used for application and not for the cause. Finding reason for something is quite different from stating it exist. For example to find gravitational force between two objects a formula is derived, now the value of constant is calibrated with experiments. gravity may or may not be absolute, but exception to the newtonian gravity laws in STATIC mode is not known (atleast not until now), so in static scenario its absolute, but for dynamic it behaves differently, so all laws are subject to certain scope, where they hold true.

Venkster, the devil:So then since everything is defined only within a certain scope, is it not possible to find a scope where there may be no definition?

Monsieur Sapota:scope without definition: hmmm, that's interesting. may be some time space theory of some distant stars or blackholes or may be quasars have such set of parameters, but here on earth(since all laws are formulated here), scope is so well defined.

Venkster, the devil: You'll be surprised sir but even on earth there are conditions that have yet to be defined...for example at the deepest points of the ocean...

Monsieur Sapota: at deepest point in ocean Gravity holds true? what else does not hold true there?

Venkster, the devil: Not about gravity, was just giving you an example of places where things might not be the same as in the real world...

Monsieur Sapota:yaar, time-space law bends at places which can bend light, at sea bottoms that does not happen. The scope is not just about geographical parameter, but they varies with directions and set of parameters like heat, light and many such things. Now the real world scenario is: for a calculation of 10 raised to 10, 10 raised to -10 is minuscule and ignoring it is apt for all practical purpose, now you know that is not limitation of law, but it is limitation of masses to adhere to such complex system. Most of theories tend to make assumption in order to make calculation simpler, otherwise deriving a law to fullest is very much possible, but not feasible and fruitful for practical purpose.

Venkster, the devil:But then practicality is set by the very world we live in, so something that is practical to us may not be practical to someone under a completely different set of conditions...

Monsieur Sapota:haan, off course practicality is nothing but limiting case of theory, since theory gets derived from it. As i pointed out set of circumstances are nothing but the part of scope of theory, assumptions made, constants declared and things ignored

Venkster, the devil: Hehehe so we're agreeing that not everything can be proved completely, so some things have to be postulated??

Monsieur Sapota: we were not discussing that, we were discussing that basic laws are not just hypothesis(okay that's what i say).

Venkster, the devil:Basic laws are not just hypotheses (not hypothesis) so long as they are within a certain set of conditions, hence the statement cannot be generalized...

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