Philosophy of Everything

Reality is pretty complex, alright... Normally we expect reality to be far more complex than we can comprehend in a limited human mind. Each time we look to one object, many other objects go outside our perception field, even if the eye can still see them. And this is OK, because we have only a limited processing brain power for perceiving the reality. It's not only the limit of perceiving reality, there is also a limit in our capacity of "knowing" about reality. If we think about it, it is very intuitive: the physical mind is far smaller than the reality we want to know about. In order to know about reality, we need to have a model about reality stored inside our minds.

I want to give you an intuition about  Kolmogorov complexity , without being very formal. Basically, Kolmogorov complexity defines a measure of how small can you compress a certain string of characters. You can think about it like measuring how small can you make a file (string of characters) by compressing it with ZIP or similar. A file storing a very redundant information (like "aaaaaaaaaaaaaaaa....") can be compressed in a much smaller size compared with a random one. For calculating the "Kolmogorov complexity", the "compressed" form is considered to be something like a self-extract archive: the shortest program that can output the initial string of characters (the "file/string to be compressed"). The Kolmogorov complexity is more general and includes classical compressing algorithms. For example a Huffman code is not very powerful in compressing a string like "123456789101112131415161718192021222324..." (concatenated consecut...

" P equals NP? "  is a million dollars unsolved problem . Introduction " P" is the class of problems where we have algorithms that solves the problem in polynomial time. " NP"  is the class of problems having solutions that can be proven in polynomial time once you "guess" the solution. This is analogous with the sorting problem: it's easier to check the correct sorting of a list than to actually sort a list. Of course, if you can fully solve the problem in polynomial time, you can also prove it in polynomial time, so P is included in NP. However, NP seems to contain some very hard problems that cannot be currently solved in polynomial time. It is believed that NP contains some problems that can never be possibly solved in P. I will not do a formal proof, more like an argument or a sketch. You might have more patience and skills to develop some of these ideas even if they might have flaws in the current form. You can take it a...

"It's more moral for a doctor to kill a germ than to allow the germ to kill his patient. The germ wants to live. The patient wants to live. But the patient has moral precedence because he's at a higher level of evolution" In "Lila, an Inquiry into Morals", Robert M. Pirsig brings intriguing reflections about the philosophy of moral using as pretext a river journey he had on a boat. Here I will bring my insights based on this book. Many of this reflections will be my own re-interpretations that were inspired by the book. Even my understanding on Pirsig's views might not fully correspond to the original author's intention.

A virtual machine is a common example of simulation. It can take the description of a (virtual) "computer" state and continue the execution from that point on. You can simulate a huge computer given a computer with more memory than the virtual machine, although it might be way slower. However, such virtual machine does not answer the problem because it normally simulates a computer with less memory. The question is, can a computer to simulate a virtual computer that has the same capabilities as itself? Before answering this, let's exclude some trivial (forbidden) cases of "simulations": A calculator will always do exactly what it does, it will be identical with itself, we will not call this a simulation of itself. Copying the exact state of another identical computer in a "twin brother" will not be considered simulation. Starting 2 identical computers with the same input will not be considered like one is simulating the other.

"Believe" is often associated with religion. However, even for using the " scientific method ", we are forced to assume certain qualities of the Universe that we cannot prove nor fully verify. The most basic assumption is that there are common laws that are universal and they function the same across the whole Universe. This is a leap of faith that we have to take if we believe that the Universe can be understood at all by humans.

We have this requirement: "Create the smallest program that will print the full text of the play Othello by William Shakespeare". I should warn you that the requirement hides a trick and you will hate the solution. The program does not need to run efficiently. Actually, it does not need to run in reasonable time. It just has to be very short. And to be proven to answer the requirement, eventually... No external random source is allowed and no input from user.