Leaderboard

Hello Francis and welcome. The short answer is no Godel is not about statements we can prove, like yours, but statements we will miss out because we cannot derive them from our axioms. There is a really good introductory book by Raymond Smullyan about this called Forever Undecided Which is fun to read. I think a pdf may be available. Meanwhile here, what do you know about axiomatic structures in Mathematics?

That’s not how clocks work. That’s not even how these measurements work - we don’t care about this “rectangular pulse” We just count the decays. Discrete values. We have a radioactive sample. We measure 1000 dps at the reference system. Now we move the clock up such that the frequency changes, according to your theory, to 998 dps. GR predicts 1001 dps. Let the system sit there for an hour. Then we compare to the reference. From what you’ve said, your prediction is 120 decays fewer, what GR predicts is 60 more.

You seem to have some idea about axioms and seem to understand that axioms are what you start with (accept as true without question). Using these axioms you can then develop theorems (= very important results) (such as Pythagoras) and lemmas (less important results) What is not often said is that the axioms must be about something. These 'somethings' are given in definitions, which usually outnumber the axioms themselves. In your example (Pythagoras) in Euclidian Geometry there are 5 axioms and 23 definitions. The axioms you need for ordinary arithmetic are known as Peano's axioms https://mathworld.wolfram.com/PeanosAxioms.html https://en.wikipedia.org/wiki/Peano_axioms

Good question. +1 1+1=2 is a definition. The axioms only require the existence of 0 and 1. Were it not for the definitions (symbols, substituters) 2, 3, 4, etc., we would have to write 7 as, 1+1+1+1+1+1+1 If the axioms (associative law for sum) didn't allow for the proof that (1+1)+1=1+(1+1), etc. we would have to distinguish between "these 2 kinds of three": One for the left sum and another for the right. This actually happens in more general algebraic systems, like groups, octonions, etc. I hope that helps.

Thanks for your quick responses. I don't much about axiomatic structures in Mathematics. Only things I know is what I read on Wikipedia. Just out of curiosity, is it PROVED in mathematics (like proving the Pythagoras theorem) that 2 + 2 = 4?? I.e. 0 + 0 = 0. 0 + 1 = 1, 1 + 1 = 2. Are these Axioms in mathematics??? Or is there a proof??? What is it called?

Some true statements can’t be proven, but AFAIK the incompleteness theorem doesn’t say which statements.

If you allow me a to maintain my analogy a little longer; if the tumor is not malignant, it may just result in giving you an awesome tattoo that distinguishes you from the boring un-tattooed atheists. You are not enslaved and you keep your cool religious gear. What's not to like? I don't see mindfulness or the like as a variation; rather, as a much healthier substitute. But that's just how I view it.

The earth isn't a perfect sphere and there are other perturbations, such as the moon. LEO satellites have atmospheric drag (more than higher orbits). Even sunlight affects satellites, making them spin But the first pass here should be a search, because this is explained in some detail on multiple sites. e.g. https://www.sciencedirect.com/science/article/pii/B9781483227160500232

"The saddest aspect of life right now is that science gathers knowledge faster than society gathers wisdom" Isaac Asimov