Thought experiments
Posted by ardianto86 at 01:23 AM on July 7, 2007.
Lately i've been thinking about proofs.. I was curious about induction. Firstly, i noticed the method of induction used in 'mathematical induction' is actually quite different from the induction used in sciences. In mathematical induction, it gives an exhaustive proof, as it is generalized by the terms n, n+1, etc. In science however, induction goes like.. if A behaves this way, so will B. Or, if A behaves one way today, it will behave the same way tomorrow. The method of induction used in science often goes unproven, but we knew it works! The sun will rise in the east again tomorrow as it does today! But what's the real basis of that claim?
One day i was thinking about Newton's Law, F=ma. The question goes like this : if the experiment applies to one object, why would it apply for every other objects? How many objects should we test in order to prove that the equation F=ma is valid? And if we assume that it applies for everything, is it by induction? But we know that induction in science is not soundly grounded. One solution to solve this, is by thought experiment. Let's say there's a cube. It is tested and it obeys the law F=ma. Now we cut the cube in half. On what basis you would say that the right cut would obey and the left cut wouldn't obey? What if we mould the cube into other object's shapes? Yes... perhaps by asking a question like these, we would then come to a conclusion that it is indeed logical to apply induction so that the equation applies to all matters. The proof to justify the induction used is by thought experiment! Thought experiments can help in explaining induction in sciences, but not all! For example, we can't prove that the sun will rise in the east again tomorrow. It is because it talks about the future, which is always uncertain, and there's no way asking questions can convince us about something that happens tomorrow. Perhaps at best, we can question 'why would tomorrow be different?', which is un-answerable. We must apply induction blindly in this case.
I just realised that thought experiments can prove a lot of things indeed! It can proof that science is limited! How so? Imagine we run a machine that types random letters in papers, suppose we limit the letters such that it fits a number of A4 papers. All permutations, it will then produce enormous amount! It will include all parts of novels, scientific journals from all times! The number of works printed would be enormous! But it is limited. Therefore, since every scienctific work can be written on words which are limited, it is thus limited. There is an end to science! But of course we wouldn't know when would that be. Popper mentioned that scientific theories couldn't be verified, it can just be falsified. Therefore, the symptom when we've reached the end of science, is that, people will still seek for verifications, people will still be experimenting, hoping to come up with new theories. They will search for infinity, but they couldn't falsify the final theory till eternity. Now, perhaps some of you might question.. can the 'final science' then, explain everything? To answer this, let's go a bit further. Perhaps we're all familiar with the notion that reality/truth exists somewhere out there, and it is quite different from our false interpretations / deductions. But we're all convinced that reality exist! It is there! And if someone have caught a glimpse of that reality, trying to formulate it in words, fit in the size of the number of A4 papers, his account would surely be found within the chunk! Therefore this further proves that the final understanding of truth can be obtained! The matter is, we don't really know whether the truth is coherent, i believe it is. Or maybe, is it really attainable? Arguing so far, it is attainable, but what if let's say, it is too complicated till it require infinite amount of A4 paper to explain in full detail? And would that be possible? Or would there be a case where the limitation is in our language to express that reality? Who knows?.. but the main point is this.. thought experiments are useful.. perhaps we can prove something crucial, hehe.. 
