Posted: Apr 01, 2016 3:21 pm
by Thommo
blue triangle wrote:
Thommo wrote:
blue triangle wrote:
Shrunk wrote:

If I understand correctly, among the many errors BT makes is concluding from the (correct) premise that you are more likely to pick the one red ball out of nine in ten tries than in one, that it is less probable for the first ball you pull out to be red than for the tenth one. In each case the odds are 1/9.
I agree. What the fuck are you guys trying to pin on me now?


:scratch:

blue triangle wrote:I said that if you run a large number of trials with different texts, you would expect a clustering of hits at around verse 90000.

blue triangle wrote:As for your second assertion, using the binomial formula, I reckon the following odds for hitting 31415 in 20000 verses, 40000 verses, 60000 verses, etc, up to 200000 verses

p (20000) = 0.176
p (40000) = 0.283
p (60000) = 0.341
p (80000) = 0.365
p (100000) = 0.366
p (120000) = 0.353
p (140000) = 0.330
p (160000) = 0.303
p (180000) = 0.273
p (200000) = 0.244

The maximum probability is at just over 90000 verses in. In other words there is a gentle distribution curve with the peak there (and a positive skew, as expected when the minimum is zero and the maximum infinity). So I have to insist you're wrong there. In other words, if you tested text after text you would see that there would indeed be a clustering of hits at around 90000 words (assuming you had texts that long). It's more gentle than I expected, mind you.


I don't see what's to pin. He accurately described a mistake that's been made, repeated and elaborated upon.

I'm *hoping* that one of your later posts was an acknowledgement that this mistake had been identified.


We'll get to that.

But first, have you admitted to your arithmetical error yet?


I didn't make one (Not that it would matter one iota if I had). I've explained this a whole bunch of times. But here, again, you wrote:
blue triangle wrote:
Onyx8 wrote:How do the errors cancel?


One is an underestimate by 0.0012%. The other is an overestimate by 0.0011%. If we sum these then our estimate of pi + e (pie if you like :grin: ) is underestimated by 0.0001%. The actual error of the summed numbers from the true sum is about 1 in 820000. That's one thin slice of pie.

To which I replied:
Thommo wrote:It's not, but why let that bother you eh?

pi+e = 5.859874482; pi-approx+e-approx = 5.859867321

Difference = 0.00000716 or about 1 in 140,000

This further convoluted and arbitrary operation doesn't even generate a single extra correct digit.


So let's work your post through:
-One is an underestimate by 0.0012%. The other is an overestimate by 0.0011%.
This refers to two numbers, which are the relative errors in the so-called estimate of pi quotiented with pi and the estimate of e quotiented with e. That is (1-(3.141554509/3.141592654)) and (1-(2.718312812/2.718281828)).

-If we sum these then our estimate of pi + e (pie if you like :grin: ) is underestimated by 0.0001%.
"these" refers to the two numbers in the previous sentences and this number is a completely meaningless composite.

-The actual error of the summed numbers from the true sum is about 1 in 820000. That's one thin slice of pie.
This does not refer to the previous sentences in any discernible way. If one takes that just derived meaningless composite as a ratio it's 1 in 1,344,822 not 1 in 820,000. Having discarded that meaning I took it at face value and posted the "actual error" expressed as a ratio. You can see this calculation in the post of mine I've just quoted. I have accepted that in fact you did not mean this, what you meant, rather than what you said is that the relative error of the sum of pi(est)+e(est) taken as a quotient over pi+e is about 818,298 which you rounded off to 820,000.

As I've now had to explain ad nauseum this miscommunication was cleared up many posts ago and there's no accidental division or multiplication on my part. I calculated the figure you referred to accurately (and my working is still there for you to double check), but you had a different figure in mind.