"Mathematical logic is the science of algorithm evaluating algorithms." Do you think that this is an overly generalizing, far fetched proposition or an almost trivial statement? Wait, don't cast your vote before the end of this short essay! It is hard to dispute that logic is the science of drawing...
The quantum Russian roulette is a game where 16 people participate. Each of them gets a unique four digit binary code assigned and deposits $50000. They are put to deep sleep using some drug. The organizer flips a quantum coin four times. Unlike in Russian roulette, here only the participant...
The overall message is not really new technically, but its philosophical implications are somewhat surprising even for mathematicians. In general, looking at the same thing from different angles to helps to get acquire more thorough understanding even if it does not necessarily provide a clear short term benefit.
A few years ago, I chatted with a few very good mathematicians who were not aware (relatively straightforward) equivalence between the theorems of Turing and Goedel, but could see it within a few minutes and had no problem grasping the the inherent, natural connection between logical systems and program evaluating algorithms.
I think, that there is quite a bit of mysticism and misconception regarding mathematical... (read more)
I expected the reaction with the countably infinite models, but I did not expect it to be the first. ;)
I wanted to get into that in the write up, but I had to stop at some point. The argument is that in order to have scientific theories, we need to have falsifiability, which means that this always necessarily deals with a discrete projection of the physical world. On the other hand so far every discrete manifestation of physical systems seemed to be able to be modelled by Turing machines. (This assumption is called the Church thesis.) If you add these two, then you arrive by the above conclusion.
Another reason for it not... (read more)
"Mathematical logic is the science of algorithm evaluating algorithms."
Do you think that this is an overly generalizing, far fetched proposition or an almost trivial statement? Wait, don't cast your vote before the end of this short essay!
It is hard to dispute that logic is the science of drawing correct conclusions. It studies theoretically falsifiable rules the lead to derivations which are verifiable in a finite amount of mechanical steps, even by machines.
Let's dig a bit deeper by starting to focusing on the "drawing correct conclusions" part, first. It implies the logic deals both with abstract rules: "drawing" and their meaning: "conclusions".
Logic is not just about mindless following of certain rules (that's... (read 1596 more words →)
The object of life is not to be on the side of the majority, but to escape finding oneself in the ranks of the insane.
Marcus Aurelius
I agree with you. I also think that there are several reasons for that:
First that competitive games are (intellectual or physical sports) easier to select and train for, since the objective function is much clearer.
The other reason is more cultural: if you train your child for something more useful like science or mathematics, then people will say: "Poor kid, do you try to make a freak out of him? Why can't he have a childhood like anyone else?" Traditionally, there is much less opposition against music, art or sport training. Perhaps they are viewed as "fun activities."
Thirdly, it also seems that academic success is the function of more variables: communication skills, motivation, perspective, taste, wisdom, luck etc. So early training will result in much less head start than in a more constrained area like sports or music, where it is almost mandatory for success (age of 10 (even 6) are almost too late in some of those areas to begin seriously)
I found the most condensed essence (also parody) of religious arguments for fatalism in Greg Egan's Permutation City:
Even though I know God makes no difference. And if God is the reason for everything, then God includes the urge to use the word God. So whenever I gain some strength, or comfort, or meaning, from that urge, then God is the source of that strength, that comfort, that meaning. And if God - while making no difference - helps me to accept what's going to happen to me, why should that make you sad?
Logically irrefutable, but utterly vacuous...
You should not take the statement too literally: Look it in a historical context. Probably the biggest problems at Russel's time were wars caused by nationalism and unfair resource allocation due to bad (idealistic/traditionalist) policies.. Average life expectancy was around 40-50 years. I don't think anyone considered e.g. a mortality a problem that can or should be solved. (Neither does over 95% of the people today). Population was much smaller. Earth was also in a much more pristine state than today.
Times have changed. We have more technical issues today, since we can address more issues with technology, plus we are on a general trajectory today, which is ecologically unsustainable if we don't... (read more)
I just find it a bit circular that you want evidences for the assertion saying that assertions need evidences.
I'd prefer Sunday or Saturday (9/5 would work for me.)
Why? Do you agree with him? :)
The quantum Russian roulette is a game where 16 people participate. Each of them gets a unique four digit binary code assigned and deposits $50000. They are put to deep sleep using some drug. The organizer flips a quantum coin four times. Unlike in Russian roulette, here only the participant survives whose code was flipped. The others are executed in a completely painless manner. The survivor takes all the money.
Let us assume that none of them have families or very good friends. Then the only result of the game is that the guy who wins will enjoy a much better quality of life. The others die in his Everett branch, but they... (read 279 more words →)
First: sorry for the bad grammar! Let me start with rephrasing the first sentence a bit more clearly:
"In order to define semantics, we need to define a map between the logic to the model ...."
It is correct that this description constrains semantics to maps between symbolically checkable systems. Physicists may not agree with this view and could say: "For me, semantics is a mapping from a formal system to a physical system that could be continuous or to which the Church thesis does not hold."
Model theoreticians, however, define their notion... (read more)