16-08-2019, 08:57 PM
1. The notion of proof is quite interesting one. There is well-known 4-color theorem for planar graphs, which was proved very roughly this way: if size of graph N > 1000000 then reduce it to smaller graph, otherwise check graph by means of computer program. So while the the theorem is definitely proved (its statement is true for all graphs), the question about "the proof" is not so clear. Are we ok with proving by machine? If not would we accept it if all N <=100000 were checked by human? Were is the red line?
In case of VMS the form of the solution can also be weird. What if we can guess meaning of each word, but are not able to translate it? What if we can translate each word, but cannot guess meaning?
2. But VMS is not mathematical problem, so one cannot require mathematically strict proof. Marking things as "improbable" is good approach.
Or maybe not? When using a word "improbable" good questions both for serious research and fat trolling can be: in which units do we measure probability? which of two is less improbable? at which mark does the improbability start?
3. The biggest advantage of the VMS is its size. Were it a page it would be just an endless holy war in internets.
Given this property a requirement is then the ability to explain the whole text without exceptions. A good theory either explains everything in text or has options to explain everything. Having unavoidable limitations is a bad sign.
In case of VMS the form of the solution can also be weird. What if we can guess meaning of each word, but are not able to translate it? What if we can translate each word, but cannot guess meaning?
2. But VMS is not mathematical problem, so one cannot require mathematically strict proof. Marking things as "improbable" is good approach.
Or maybe not? When using a word "improbable" good questions both for serious research and fat trolling can be: in which units do we measure probability? which of two is less improbable? at which mark does the improbability start?
3. The biggest advantage of the VMS is its size. Were it a page it would be just an endless holy war in internets.
Given this property a requirement is then the ability to explain the whole text without exceptions. A good theory either explains everything in text or has options to explain everything. Having unavoidable limitations is a bad sign.