Let me hold you by the hand and give you a childish example: An equation may have a solution, which you may prove must exist, but that does not mean you possess the solution. Is that a bit complicated? — tom

But you were saying something about reality itself being comprehensible. We might certainly be inclined towards such an ontological belief given a supporting epistemic framework of theory and measurement. However you seem fixated on a naive Platonism when it comes to this issue. For you, the deductive truths of mathematics appear to bypass any need to demonstrate that the world is as the models say, rather than those models merely placing strong notional constraints on our speculations.

Even mathematics has had to accept that it starts its modelling with the "good guess" of an axiom. The point of Godel was to show that axioms are modelling hypotheses, not self-formalising truths. They become secured over time due to the fact they deliver - in terms of our also rather human purposes.

But all this is Epistemology 101. Curious.

Six beers, three beers, maybe you are on a different intellectual plane? Hard to tell. — tom

Well, remind me not to buy you any beers.

Sadly, there are an infinite number of wavefunction world branches in which that is guaranteed to be the case. The equation has no other solution but to say yes to the reality of every outcome, no matter how improbable.. ;)

Well, if it means Infinite Free Beers it can't be all bad. ;-)

Thank you for pointing that out. My problem is I thought about these things too long by myself, and it is not always obvious to me what other people know about facts that are transparently obvious to me. As your observe, it is transparently obvious that an axiomatic system cannot be complete and coherent simultaneously.

It is also transparently obvious to me how the Vedic thought I mentioned before is the same as quantum theory. This is because it is obvious to me that it is impossible to know the position and velocity of a subatomic particle simultaneously. Further it is obvious to me that a temperature of absolute zero is only hypothetical, hence that all objects are continually in randomized motion, even if quantized. And thus it is obvious to me that it is impossible to know where a subatomic particle is at any one point in time. It is only possible to know where it was, or how fast it is moving. Thus the Vedic philosophers were correct in thinking that matter is actually made of tiny compartments of space, inside any of which there may or may not be solidity, but it is impossible to know. What they did was anticipate, by pure thought, the results of experiments producing paradoxes which are now quaintly referred to as Schrodinger's cat and Maxwell's demon. And so I cited this as an example of how our own limited understanding shapes the limit of what we can know.

Similarly one can consider the rather jaded question of whether light is an energy wave or a particle. In some cases light behaves with quantum behavior, so it must be a particle, they say. But if you shine a light source with total emission energy of less than one photon through two close yet parallel slits, it still draws an extremely faint diffraction pattern, again with a total energy of less than one photon. How can that be, they ponder?

But it is because in our perception of gross matter, it has to be either a wave or particle. We can't natively conceive of something which is partly both, but the experiments say that the nature of photons is partly like a wave, and partly like a particle. So we have to try and imagine something that we cannot physically perceive. We have to make a cognitive leap and say there exists something which is 'in between' a wave and particle, or 'changes state between' the two.

But in reality, it is neither. It is light, that is how light is, and our attempts to define it as either a wave or a particle are introducing the paradox, generated by own limited comprehension of reality.

I wrote quite a lot today, excuse me I am going to have to rest quite a long time now.

it is transparently obvious that an axiomatic system cannot be complete and coherent simultaneously. — ernestm

Only since Gödel's theorem.

We have to make a cognitive leap and say there exists something which is in between a wave and particle, or changes state between the two. But in reality, it is neither. — ernestm

Neils Bohr dealt with that in his 'principle of complementarity'. It was so important to him that he included the Tao symbol in his family Coat of Arms:


Neils Bohr Coat of Arms

Well that is interesting. I should say it is obvious *to me* because I learned Gödel's theories when I was 15. What I am discovering as an adult is that most people were not granted such a good education.

Well that is interesting. I should say it is obvious *to me* because I learned Gödel's theories when I was 15. What I am discovering as an adult is that most people were not granted such a good education.

Trying to parse this. You were taught 'Godel's theories' at 15 in formal education setting? (what else would it mean to be 'granted' an 'good education' that included those theories?) But, though you learned those easily enough, it never struck you that others might not have been learning them in a similar manner? Like, you assumed 'Godel's Theories' were part of a universal high school sophomore curriculum? and only in adulthood were you disabused of that notion?

No, I was interested in the theory, so I read this book by Hofstadter. It wasn't very difficult so I kind of assumed no one else had a problem understanding it.

https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

But what I have since realized is that H. is a very good author, but it does take some time to read, far more than most people read books at all these days, so maybe its not so surprising the topic remains so obscure to so many.If you do like to read, well it is very easy to read, and well illustrated too, and although some of the ideas are a bit off the wall, everyone who does read it finds there are parts of it that do make a rather lasting impression. It's true not everyone can read it. At first there was quite a bit of controversy about it, and it wasn't published in the USA for quite a while. This was to the amusement of my family who thought it insane, but when it was published, it was an instant bestseller.

Also, on the topic of quantum theory, I read the following in the same year:

https://www.amazon.com/Mr-Tompkins-Paperback-Canto-Classics/dp/1107604680

Its very entertaining and I would recommend it to anyone genuinely interested in the topic.

Funnily enough, I read GEB in high school too (tho I was 17.) I liked it but I thought it was hard at that time. I guess I'm confused though, you said you didn't realize til you were an adult that most people didn't know Godel. But now you're saying you found the book on your own and you didn't imagine others would have trouble understanding it. So do you think more or less everyone finds GEB on their own, but that you are only realizing now that not everyone understands it?

I just find it very idiosyncratic to find a book at 15, learn it, and then assume everyone else knows whats in it, until realizing much later thats not the case.

No, whaty I was trying to say, it just seemed so straightforward to me, I didn't think anyone would have trouble understanding it, but what I have since learned is that it was just because H is a good author, and I had read the book. Similarly with Gamow on Quantum theory.

Ok, it may be envy, but It's just very surreal how many hard-won concepts are transparently obvious to you. Godel's theorems, Heisenbergian uncertainty etc etc. What do you think of Einstein's general relativity? Cantor's kind of a no-brainer?

Another good one, more recently, is 'brief history of time' by hawking. Maybe it is because I liked science fiction as a child, so I never thought the unintuitive could not be real, and had no trouble accepting the concepts.

Cantor I didn't discover until a few years ago, and I do have to admit it all seemed trite to me. It's difficult for me to understand how other people find it confusing.

Have you ever encountered a thought or theory that didnt seem either stupid or else trite and obvious?

Hume, Kant, Frege, Hegel, Heidegger, and a number of modern epistemologists like Kripke

I've always thought most of Hegel's pretty obvious once you get used to his prose. surprised to see him on your list - what seemed new to you? I think most people on this board agree he essentially rehearses a familiar set of gnostic/mystic principles (you know which ones I mean)

I find Kant much simpler than Hegel.

As your observe, it is transparently obvious that an axiomatic system cannot be complete and coherent simultaneously. — ernestm

Did it ever occur to you that perhaps the reason you find these things "transparently obvious" is because your understanding of them is very superficial, to the point of being nonexistent?

All the time. I keep trying to find people who can prove my worries right, but it's been a frustrating search in the USA. Mostly people here either just ape the same insulting profanities that were showered on them in their childhood, or repeat the verbal equivalent of kitsch, or make snide remarks as if even pretending to be friendly, like you, eventually followed by a vast outburst of misdirected rage. They invariably think they are being original, even though much of the same remarks have been repeatedly made for thousands of years by far less fortunate people, mostly with much less formal education yet far better grammatical skills, Outside teachers and doctors, they moreover almost invariably exhibit less manners than a dog. The rare exception is first-generation immigrants, who more native Americans frequently despise, not even overtly. Fortunately, they have other qualities that they themselves boast as virtues in their favor, especially selfishness, greed, disrespect for life other than their own, lack of empathy, infidelity in marriage, unsuccessfully repressed aggression, scorn for the industry of knowledge, and abuse of authority, that in total enable them to survive. Thank you for the conversation.