If genunie Bayesians will always agree with each other once they've exchanged probability estimates, shouldn't we Bayesian wannabes do the same?

An example I read comes to mind (it's in dialogue form): "This is a very common error that's found throughout the world's teachings and religions," I continue. "They're often one hundred and eighty degrees removed from the truth. It's the belief that if you want to be Christ-like, then you should act more like Christ—as if the way to become something is by imitating it."

It comes with a fun example, portraying the absurdity and the potential dangers of the behavior: "Say I'm well fed and you're starving. You come to me and ask how you can be well fed. Well, I've noticed that every time I eat a good meal, I belch, so I tell you to belch because that means you're well fed. Totally backward, right? You're still starving, and now you're also off-gassing like a pig. And the worst part of the whole deal—pay attention to this trick—the worst part is that you've stopped looking for food. Your starvation is now assured."

This threshold thing is interesting. Just to make the idea itself solid, imagine this. You have a type of iron bar that can bend completely elastically (no deformation) if forces less than 100N is applied to it. Say they are more valuable if they have no such deformations. Would you apply 90N to 5 billion bars or 110N to one bar?

With this thought experiment, I reckon the idea is solidified and obvious, yes? The question that still remains, then, is whether dust specks in eyes is or is not affected by some threshold.

Though I suppose the issue could actually be dropped completely, if we now agree that the idea of threshold is real. If there is a threshold and something is below that threshold, then the utility of doing it is indeed zero, regardless of how many times you do it. If something is above the threshold, shut up (or don't) and multiply.

I hate to break it to you, but if setting two things beside two other things didn't yield four things, then number theory would never have contrived to say so.

Numbers were invented to count things, that is their purpose. The first numbers were simple scratches used as tally marks circa 35,000 BC. The way the counts add up was derived from the way physical objects add up when grouped together. The only way to change the way numbers work is to change the way physical objects work when grouped together. Physical reality is the basis for numbers, so to change number theory you must first show that it is inconsistent with reality.

Thus numbers have a definite relation to the physical world. Number theory grew out of this, and if putting two objects next to two other objects only yielded three objects when numbers were invented over forty thousand years ago, then number theory must reflect that fact or it would never have been used. Consequently, suggesting 2+2=4 would be completely absurd, and number theorists would laugh in your face at the suggestion. There would, in fact, be a logical proof that 2+2=3 (much like there is a logical proof that 2+2=4 in number theory now).

All of mathematics are, in reality, nothing more than extremely advanced counting. If it is not related to the physical world, then there is no reason for it to exist. It follows rules first derived from the physical world, even if the current principles of mathematics have been extrapolated far beyond the bounds of the strictly physical. I think people lose sight of this far too easily (or worse, never recognize it in the first place).

Mathematics are so firmly grounded in the physical reality that when observations don't line up with what our math tells us, we must change our understanding of reality, not of math. This is because math is inextricably tied to reality, not because it is separate from it.

It's a bit unfortunate that these articles are so old; or rather that people aren't as active presently. I'd have enjoyed some discussion on a few thoughts. Take for instance #5, I shall paste it for convenience:

If the last 11 egg-shaped objects drawn have been blue, and the last 8 cubes drawn have been red, it is a matter of induction to say this rule will hold in the future. But if you call the blue eggs "bleggs" and the red cubes "rubes", you may reach into the barrel, feel an egg shape, and think "Oh, a blegg."

It struck me that this is very deeply embedded in us, or at least in me. I read this and noticed that my thought was along the lines of "yes, how silly, it could be a non-colored egg." What's wrong with this? What's felt is an egg shape, not an egg. Might as well be something else entirely.

So how deep does this one go; and how deep should we unravel it? I guess "all the way down" is the only viable answer. I can assign a high probability that it is an egg, I simply shouldn't conclude anything just yet. When is it safe to conclude something? I take it the only accurate answer would be "never." So we end up with something that I believe most of us holds as true already: Nothing is certain.

It is of course a rather subtle distinction going from 'certain' to 'least uncertain under currently assessed information'. Whenever I speak about physics or other theoretical subjects, I'm always in the mindset that what I'm discussing is on the basis of "as is currently understood," so in that area it feels rather natural. I suppose it's just a bit startling to find that the chocolate I just ate is only chocolate as a best candidate rather than as a true description of reality; that biases can be found in such "personal" places.

I have a question related to the initial question about the lone traveler. When is it okay to initiate force against any individual who has not initiated force against anyone?

Bonus: Here's a (very anal) cop out you could use against the least convenient possible world suggestion: Such a world—as seen from the perspective of someone seeking a rational answer—has no rational answer for the question posed.

Or a slightly different flavor for those who are more concerned with being rational than with rationality: In such a world, I—who value rational answers above all other answers—will inevitably answer the question irrationally. :þ