I feel like making a mathematical lament of sorts, and shall proceed forthwith, but I've also a second part to the post, just so I might justify my abuse of your good graces with the first part.
Parte Uno
Outliers: Imagine a carnival game where a marble descends through matrix of nail-like bumpers until it reaches the bottom, with each location a betting opportunity. If I have this set up correctly, we'd get something like a normal distribution and a pretty bell-shaped curve when working out the probabilities. At the thin extremes, the outliers. A marble at the end has experienced a sequence of events (R/L), each with the same probabilities as any other, many times, in sequence. It is the sequence itself that is the outlier, like a thousand heads in a row on a fair coin. It happens; just not a lot.
My impossible lament: Don't ask, and there will be no details of any kind, but I am an outlier with respect to those chance events that come along and destroy, oh, say, like an unplanned volcanic eruption nearby. Sure, add that panicking and running in the wrong direction compounds the evils of such events; there's that. However, the sequence is such, and the recounting of it so cumulatively wearisome, that even the best imaginable friend would be hard pressed to reach the end of my story without crying uncle. I can easily bring a therapist to his knees. Lawyers... lawyers salivate.
I am a bit tired of the situation, and so wished to register my lament by cursing carnivals, nails, and marbles. Done. Thanks.
Parte Due
When in a facetious or pugnacious mood, I've been known to play around with measure-space-talk, and have probably gotten away with more than I ever should. Time to rectify that.
To wit. How would you describe the measure space of mayfly scientists, assuming if you would that mayflies can do science? Do you think it would take mayflies many more generations to make the same observations we do, as many more events occur outside the lifetime of each generation, or even the the time transpired for all generations in the species?...
And so on, blah blah, you can see the implied swipe at the completeness of knowledge.
But that's actually wrong, isn't it? (I know it is; I just want your take on it.) That is, at some point, a sufficient range of events is observed, such that the workings of known regularities (laws) are sufficient to now predict that any remaining observations made in a given domain (say, I dunno, stellar physics, just as an example) would only be the concrete instantiation of known laws, only unique in that sense and none other, and not a new event. That is, the measure space is complete, further observation would not yield unique new events requiring new theory.
So, the question is, how should a layman properly think about measure spaces and knowledge? How and when is it appropriate to think there is a vast amount, or an exceedingly small amount, or none at all, of possible new observations in any given domain? You see, even if I've accounted nicely and squarely for all observations so far, my theories nicely complete, how do I know I am not yet a mayfly?
[Because ISF: No cracks sought for the usual suspects. I'd simply like to hear from either folks in probability, or in hard science, as to their thoughts; no agendas, no gotchas, no backdoored "aha, then this piece of woo is true, godhelpus." I just need a refresher, that's all... and an excuse for Parte Uno.]
Parte Uno
Outliers: Imagine a carnival game where a marble descends through matrix of nail-like bumpers until it reaches the bottom, with each location a betting opportunity. If I have this set up correctly, we'd get something like a normal distribution and a pretty bell-shaped curve when working out the probabilities. At the thin extremes, the outliers. A marble at the end has experienced a sequence of events (R/L), each with the same probabilities as any other, many times, in sequence. It is the sequence itself that is the outlier, like a thousand heads in a row on a fair coin. It happens; just not a lot.
My impossible lament: Don't ask, and there will be no details of any kind, but I am an outlier with respect to those chance events that come along and destroy, oh, say, like an unplanned volcanic eruption nearby. Sure, add that panicking and running in the wrong direction compounds the evils of such events; there's that. However, the sequence is such, and the recounting of it so cumulatively wearisome, that even the best imaginable friend would be hard pressed to reach the end of my story without crying uncle. I can easily bring a therapist to his knees. Lawyers... lawyers salivate.
I am a bit tired of the situation, and so wished to register my lament by cursing carnivals, nails, and marbles. Done. Thanks.
Parte Due
When in a facetious or pugnacious mood, I've been known to play around with measure-space-talk, and have probably gotten away with more than I ever should. Time to rectify that.
To wit. How would you describe the measure space of mayfly scientists, assuming if you would that mayflies can do science? Do you think it would take mayflies many more generations to make the same observations we do, as many more events occur outside the lifetime of each generation, or even the the time transpired for all generations in the species?...
And so on, blah blah, you can see the implied swipe at the completeness of knowledge.
But that's actually wrong, isn't it? (I know it is; I just want your take on it.) That is, at some point, a sufficient range of events is observed, such that the workings of known regularities (laws) are sufficient to now predict that any remaining observations made in a given domain (say, I dunno, stellar physics, just as an example) would only be the concrete instantiation of known laws, only unique in that sense and none other, and not a new event. That is, the measure space is complete, further observation would not yield unique new events requiring new theory.
So, the question is, how should a layman properly think about measure spaces and knowledge? How and when is it appropriate to think there is a vast amount, or an exceedingly small amount, or none at all, of possible new observations in any given domain? You see, even if I've accounted nicely and squarely for all observations so far, my theories nicely complete, how do I know I am not yet a mayfly?
[Because ISF: No cracks sought for the usual suspects. I'd simply like to hear from either folks in probability, or in hard science, as to their thoughts; no agendas, no gotchas, no backdoored "aha, then this piece of woo is true, godhelpus." I just need a refresher, that's all... and an excuse for Parte Uno.]
via International Skeptics Forum http://ift.tt/1oZqqTz
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