3 ms·

That concept of surety we cannot grasp with the observation tools we have available, but it's also not necessary to grasp it; the assumption that the 1 element

That concept of surety we cannot grasp with the observation tools we have available, but it's also not necessary to grasp it; the assumption that the 1 element was changing rather than the 111 only becomes functionally "incorrect" if it contradicts some other observation we make. Beyond that, the grand truth of what's actually happening becomes a bit uselessly murky. The real function of Occam's Razor is to allow us to simplify models for our own benefit (because simpler models are easier to interpret and use), not necessarily because the simple answer is the Actual Truth(TM), which we can't know outside of observation. There's a thought experiment in college philosophy: how do you know the universe wasn't created from nothing precisely six seconds ago, with all matter and energy in the universe arranged with the precise concentrations and momenta they would need to become the present universe in precisely six seconds?

Bromskloss 9y ago
> The real function of Occam's Razor is to allow us to simplify models for our own benefit (because simpler models are easier to interpret and use), not necessarily because the simple answer is the Actual Truth(TM), which we can't know outside of observation. What about assigning greater prior probability to hypotheses that are simpler in some sense? Is there perhaps something to that too?
- lmm 9y ago
  I'd say it's legitimate, just because simpler models have turned out to be true more often in the past, as best as we can tell.
  - Bromskloss 9y ago
    Maybe even _that_ reasoning relies upon simple hypotheses being more likely. In this case, the simple, and therefore favoured, hypothesis would be that "models with a simplicity that is similar to that of other successful models are more likely to be true".
    - lmm 9y ago
      That sounds like a more complex hypothesis to me.
      - Bromskloss 9y ago
        Maybe it's simpler than "models with a simplicity that is dissimilar to that of other successful models are more likely to be true", though it's not obvious what should be considered simple and not.
        lmm 9y ago
        Kolgomorov complexity seems like the obviously correct measure, though AIUI it's only defined relative to some fixed Turing machine. I have an idea of doing a PageRank-style weighting of Turing machines, based on how simple/complex simulating one under another is. That would align with my intuition that most basic universal Turing machines are equally valid, but one that has (say) a short instruction that outputs one particular long sequence of symbols is probably not a valid machine to use.
    - balabaster 9y ago
      Assuming that other successful models are also true and not just a wolf in sheep's clothing.
      - Bromskloss 9y ago
        Let's forget that I said "true", and switch it to "successful" instead.
balabaster 9y ago
Surely this is the same paradigm that would have opined Copernicus's heliocentric incorrect and the geocentric model accepted by the masses the correct model(?) Is it not scientific method to prove correctness, not simpleness?
- fixermark 9y ago
  The geocentric model isn't simpler; that was the problem underpinning the shift to a heliocentric model. The geocentric model required the addition of several epicycle adjustments with no observable cause. Re-framing the local system with the sun at the center eliminated most of the epicycles. (... and the remaining errors in the heliocentric model relative to the observed motion led to the discovery of the moons and, eventually, Newton's gravitational theory. The driving function, overall, is simplification of the model by removing special cases and the need for acausal "I don't know why; this is what we observe" rules).

Bromskloss 9y ago

> The real function of Occam's Razor is to allow us to simplify models for our own benefit (because simpler models are easier to interpret and use), not necessarily because the simple answer is the Actual Truth(TM), which we can't know outside of observation. What about assigning greater prior probability to hypotheses that are simpler in some sense? Is there perhaps something to that too?

lmm 9y ago
I'd say it's legitimate, just because simpler models have turned out to be true more often in the past, as best as we can tell.
- Bromskloss 9y ago
  Maybe even _that_ reasoning relies upon simple hypotheses being more likely. In this case, the simple, and therefore favoured, hypothesis would be that "models with a simplicity that is similar to that of other successful models are more likely to be true".
  - lmm 9y ago
    That sounds like a more complex hypothesis to me.
    - Bromskloss 9y ago
      Maybe it's simpler than "models with a simplicity that is dissimilar to that of other successful models are more likely to be true", though it's not obvious what should be considered simple and not.
      - lmm 9y ago
        Kolgomorov complexity seems like the obviously correct measure, though AIUI it's only defined relative to some fixed Turing machine. I have an idea of doing a PageRank-style weighting of Turing machines, based on how simple/complex simulating one under another is. That would align with my intuition that most basic universal Turing machines are equally valid, but one that has (say) a short instruction that outputs one particular long sequence of symbols is probably not a valid machine to use.
  - balabaster 9y ago
    Assuming that other successful models are also true and not just a wolf in sheep's clothing.
    - Bromskloss 9y ago
      Let's forget that I said "true", and switch it to "successful" instead.

balabaster 9y ago

Surely this is the same paradigm that would have opined Copernicus's heliocentric incorrect and the geocentric model accepted by the masses the correct model(?) Is it not scientific method to prove correctness, not simpleness?

fixermark 9y ago
The geocentric model isn't simpler; that was the problem underpinning the shift to a heliocentric model. The geocentric model required the addition of several epicycle adjustments with no observable cause. Re-framing the local system with the sun at the center eliminated most of the epicycles. (... and the remaining errors in the heliocentric model relative to the observed motion led to the discovery of the moons and, eventually, Newton's gravitational theory. The driving function, overall, is simplification of the model by removing special cases and the need for acausal "I don't know why; this is what we observe" rules).