Originally posted by royalchickeni find it interesting that you would consider the examples i gave to be mathematics simply because they involve deductive reasoning. it suggests that though the mathematics is not presently available to handle these ideas quantitatively, it may be at some future time. reminds me of asimov's foundation series in which they used psychomathematics (i think that's what it was called) to predict future events. it's a neat idea! more on this later perhaps ...
Very good post, first. I think both of those things you mentioned are mathematics, but I'd like to compromise. Clearly, for practical purposes my definition is too broad. So we can also stipulate that the arbitrary axioms must have ...[text shortened]... science in which a statement being 'true' has any real meaning.
by your definition, i see no purpose in discussing whether physics came first in a temporal sense since people (never mind non-people) were engaged in physics long before this sort of math came about.
however, since you have stated that math is a branch of deductive reasoning (and not the other way around), it might be interesting to look at the search for truth through mathematics vs physics. i agree that 'truth' is less arbitrary in math that other sciences, but i still have some questions on that for you as well as the notion that there is no empirical observation.
or if you want we could talk about paul erdos. that was one neat guy for sure!
or if you like we could play chess ...
How about we play chess and talk Erdos and physics.. I'm actually working on one of his famous problems at the moment. I'll send you a game when I finish a few (I'm playing a few too many at the moment). Ask away, though.
I never really disputed that physics was phirst in a temporal sense, but rather in the sense of its 'importance'. Basically, I was thinking that you wqere asking whether physics has the phinal say.
Originally posted by royalchickensounds good to me! that's a great 'definition' of senility by erdos!! what is the problem you are working on? is it one of those that he offered a monetary reward for? i'll wait till you are ready and then we can play.
How about we play chess and talk Erdos and physics.. I'm actually working on one of his famous problems at the moment. I'll send you a game when I finish a few (I'm playing a few too many at the moment). Ask away, though.
I ne ...[text shortened]... hinking that you wqere asking whether physics has the phinal say.
i don't think physics has the final say (though it really does have the phinal say since a mainal say is quite meaningless), but that's only because a final say doesn't seem to exist. all that could be done is to construct models (often mathematical) and you can't ever quite get it right, but you can get it 'good enough' to be useful (until the next better one comes along).
in math though very often you can have a final say because you essentially create your own universe - so mathematical truth is achievable to some extent. though even in one's own self-consistent universe there are things that don't aways seem to be crystal clear (i remember an engineer friend of mine at looniversity wistfully saying to me "do you remember those days when there was a right answer in math?"😉
what do you say about this though: mathematics is still observationally based since
1. all axioms have some observational point of reference (albeit not in the natural world)
2. any derivation of consequences from axioms (or consequences) still has to be validated and this requires experimentation and observation (again not through our 5 natural senses)
First, I am working on the conjecture: "If S is some set of natural numbers such that the sum of the reciprocals of the elements of S diverges, then S contains arbitrarily long arithmetic progressions". I actually came up with this conjecture myself following on something Acolyte put in the Posers and Puzzles forum a while back. It was in an email discussion that someone told me it was an Erdos problem, and, upon further investigation, it seems to be the potentially most lucrative one. And rightly so....😕.
Anyway, observation is certainly a key feature in the actual doing of mathematics. Enormous amounts of time are spent looking at various structures and patterns, and trying to impose some semblance of order before actually whipping out the deductive axe and going to work. However, the actual product is not based on observation, whereas data is an integral part of sciencetific knowledge. That was a beautiful comment you made, about inventing one's own universe in maths.
Originally posted by royalchickenwell, mathematics is beautiful - pity that it is so often depicted otherwise in school.
First, I am working on the conjecture: "If S is some set of natural numbers such that the sum of the reciprocals of the elements of S diverges, then S contains arbitrarily long arithmetic progressions". I actually came up with this ...[text shortened]... ul comment you made, about inventing one's own universe in maths.
that is a $3000 erdos problem - at least it was in 1979, may be more nowadays with inflation 😀
he stated it would imply that the primes contain arbitrarily long arithmetic progressions and that would be really very nice.
however, he also said he didn't think he would have to ever pay that money, but that he should
"leave some money for it in case I leave. (There I mean leave on the trip for which one doesn't need a passport.)"
so good luck to you and may you find your success!