soreff comments on Rationality Quotes May 2013 - Less Wrong

6 Post author: katydee 03 May 2013 08:02PM

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Comment author: [deleted] 02 May 2013 03:48:24AM *  112 points [-]

"The spatial anomaly has interacted with the tachyonic radiation in the nebula, it's interfering with our sensors. It's impossible to get a reading."

"There's no time - we'll have to take the ship straight through it!"

"Captain, I advise against this course of action. I have calculated the odds against our surviving such an action at three thousand, seven hundred and forty-five to one."

"Damn the odds, we've got to try... wait a second. Where, exactly, did you get that number from?"

"I hardly think this is the time for-"

"No. No, fuck you, this is exactly the time. The fate of the galaxy is at stake. Trillions of lives are hanging in the balance. You just pulled four significant digits out of your ass, I want to see you show your goddamn work."

"Well, I used the actuarial data from the past fifty years, relating to known cases of ships passing through nebulae that are interacting with spatial anomalies. There have been approximately two million such incidents reported, with only five hundred and forty-two incidents in which the ship in question survived intact."

"And did you at all take into account that ship building technology has improved over the past fifty years, and that ours is not necessarily an average ship?"

"Indeed I did, Captain. I weighted the cases differently based on how recent they were, and how close the ship in question was in build to our own. For example, one of the incidents with a happy ending was forty-seven years ago, but their ship was a model roughly five times our size. As such, I counted the incident as having twenty-four percent of the relevance of a standard case."

"But what of our ship's moxie? Can you take determination and drive and the human spirit into account?"

"As a matter of fact I can, Captain. In our three-year history together, I have observed that both you and this ship manage to beat the odds with a measurable regularity. To be exact, we tend to succeed twenty-four point five percent more often than the statistics would otherwise indicate - and, in fact, that number jumps to twenty-nine point two percent specifically in cases where I state the odds against our success to three significant digits or greater. I have already taken that supposedly 'unknowable' factor into account with my calculations."

"And you expect me to believe that you've memorized all these case studies and performed this ridiculously complicated calculation in your head within the course of a normal conversation?"

"Yes. With all due respect to your species, I am not human. While I freely admit that you do have greater insight into fields such as emotion, interpersonal relations, and spirituality than I do, in the fields of memory and calculation, I am capable of feats that would be quite simply impossible for you. Furthermore, if I may be perfectly frank, the entire purpose of my presence on the bridge is to provide insights such as these to help facilitate your command decisions. If you're not going to heed my advice, why am I even here?"

"Mm. And we're still sitting at three thousand seven hundred to one against?"

"Three thousand, seven hundred and forty five to one."

"Well, shit. Well, let's go around, then."

The Vulcan your Vulcan could sound like if he wasn't made of straw, I guess? Link

Comment author: soreff 05 May 2013 04:59:52PM -1 points [-]

And with 542 survivals, assuming Poisson statistics, the one-sigma bounds are around +-4% of that. I'll believe Spock most significant figure, but not the other three. :-)

Comment author: Kindly 05 May 2013 07:17:24PM 4 points [-]

To summarize the important bits of the "Do steel-Vulcans provide excessive significant digits?" discussion:

Suppose that the one-sigma range tells us that where the quote has 3745, some reasonable error analysis says 3745 plus or minus 173. Then the steel-Vulcan would still say 3745 and not, e.g., 3700 or 4000, for the following reasons:

  1. 3745 is still the midpoint of the range of reasonable values, and thus the closest single value to "the truth".

  2. Taking meta-uncertainty into account, you still should assign some probability to how likely you are to survive, which is going to be some probably-not-round number like 1 in 3745.

This sort of accuracy is probably not very helpful to humans: I don't have a cognitive algorithm that lets me distinguish between 1 in 3745 odds and 1 in 3812 odds, so saying "about 1 in 4000" provides all the information I'll actually use. Presumably a species that can come up with this kind of answer in the first place feels differently about this; in fact, there's probably some strong cultural taboo against rounding.