Especially liked the quote "logloglog x goes to infinity with great dignity.", I should have a t-shirt printed with that!
Two ideas come to mind:
* Do you believe that the difference between what we believe and can prove (in science, of course) will eventually go to zero (barring a small number of topics)? I am of this opinion. I also take the strong position that this expansion of science will eat away at other topics such as philosophy and religion, so as much as their dominion will be insignificant. Of course, I cannot prove this belief.
* This post shows the difference between, say, a theoretical mathematician and an engineer (or a person from any of the other disciplined who work on applied fields) so well. "Both his statements are technically false, but both have a grain of truth to them...", I find that most of the time this is adequate, if the idea works. Think of Heaviside using what would later be called the Dirac delta function, with a lack of rigor that made mathematicians shudder. But it worked.
"Believe" doesn't seem to be used in the sense of arbitrary belief here; it's used more in the sense in which something is expected to be the case with less than conclusive proof, such as how I believe that the weather is pretty much the same as last time I looked out the window.
With that in mind, I would actually expect the opposite trend: for belief to grow at a faster rate than proof. Historically, answers have normally led to more questions.
Do you believe that the difference between what we believe and can prove (in science, of course) will eventually go to zero (barring a small number of topics)?
Perhaps not. Philosophically, much of what people believe is unprovable insomuch as it would require proving a negative...which isn't strictly possible if I'm to believe my courses in logic and mathematics.
(I suppose you could prove a negative assertion positively through an exhaustive proof, but that's unfeasible for most cases since it would require observing and documenting everything possible. e.g. You cannot prove there is no God, only that God has not been observed.)
What do you mean by "will eventually go to zero"? Decrease monotonously? That seems kind of obvious: knowledge expands and rarely shrinks (barring WW3).
In layman's terms here's what I was trying to say: think of the set of (scientific, which could be a muddy distinction) questions to which currently there's no clear explanation, e.g. do magnetic monopoles exist, what is the nature of dark matter, etc. The question is whether eventually this set will be getting smaller (or even zero, because there might a finite number of things to know in the universe, and once we explain everything, that's it)
I think the answer to this is clearly no. Answers tend to spawn more questions not fewer.
More formally, if you are considering mathematics to fit with your idea of science, then Godel's Incompleteness Theorem shows that there is an infinite amount to learn and an infinite amount that can never be proven and yet is true. Even without appealing to Incompleteness, just look at the fact that Mathematics is spawn new subdisciplines at a regular rate and will always be able to do so.
The article is nothing like the conversation I had in my head when I read the title. I think I have been spending way too much time with conspiracy theory promulgators...
I find that when I start debating current issues in politics, religion, weather, etc. I pull from a gestalt I have built with little ability to prove individual facts.
Two ideas come to mind:
* Do you believe that the difference between what we believe and can prove (in science, of course) will eventually go to zero (barring a small number of topics)? I am of this opinion. I also take the strong position that this expansion of science will eat away at other topics such as philosophy and religion, so as much as their dominion will be insignificant. Of course, I cannot prove this belief.
* This post shows the difference between, say, a theoretical mathematician and an engineer (or a person from any of the other disciplined who work on applied fields) so well. "Both his statements are technically false, but both have a grain of truth to them...", I find that most of the time this is adequate, if the idea works. Think of Heaviside using what would later be called the Dirac delta function, with a lack of rigor that made mathematicians shudder. But it worked.