EqD Article: www.equestriadaily.com/2012/04…
Digibrony's Q&A: www.youtube.com/watch?v=5mg-UN…
MLP Conspiracies: www.youtube.com/watch?v=-Sym1h…
Thoroughly analyzing "A friend in deed": www.youtube.com/watch?v=aoJUVU…
Everything wrong with "Dragonshy": www.youtube.com/watch?v=paSJ-y…
EDIT 7th April, 2012: Corrected a large error in mug's size I found.
Time taken: 10 - 16 hours.
The small apparent errors in multiplication are not mistakes; they include multiplied fractions that were not shown earlier due to rounding.
Assuming a population of 3,650, if you walked around Ponyville and managed to meet 100 ponies every day, then after a week you would have a 68.4% chance of meeting at least one of the Mane 6.
You would have to meet at least 1,400 ponies if you wanted for that probability to be bigger than 90%.
S1 - S3 screentime analysis: fav.me/d5kzo28
Pony size and mass estimation: fav.me/d5qzfa2
Life, death, sex, pregnancy and birth: fav.me/d5fd4rz
"20% cooler, 10 seconds flat" meme's thermodynamics calculaton: fav.me/d6abphp
Screentime analysis paper fallout: fav.me/d5q9oyx
Binary Mane 6 Picture: fav.me/d5s0lzj
I see that college has been useful to someone...
On another note, can you count the population of Canterlot next? Maybe the whole of Equestria? Or the Changelings?
Maybe you can ask several of the developers of Hearts of Iron 4's : Equestria at War where did they get the figures for the populations they use?
In any case, really nice maths you got there.
Oh, calculating Canterlot's population would be time-consuming, and I don't have enough energy for such things recently. I mostly now write comics (though they sometimes feature my nerdy math calculations about statistical trivias too, but they are not nearly as big projects as this one.)
To answer your questions, I say that this presentation was quite glear to me. Also those little jokes (such as "thanks Twi") were freshing and helped me to keep the focus on the math. (I'm not a math-person myself, I only have a small capability to understand it in some low level.) You asked was there any flaws/good things in you presentation's texts and as an amateur writer (I have been writing actively for 3-4 years now) I can say this:
There was enough text to understand and it was short enough so that I didn't get bored. It was interesting and (as I said before) clear and understandable. The only tip that I could give to you, is to avoid too long senceteces. Short sentences make it easier to read. This wasn't really a proplem but I'm still saying it so you don't fall on that trap so to speak. I am very aware that in mathematical explanation it is really hard. (And as you can see, I tend to write long sencetensies myself.) So more like, you would try to make sure that there isn't too many long sentences after another. Overall, it was very good.
Actually it would be 100%, because Pinkie Pie would greet you ASAP.
This was a good read though! Probably slightly outdated by statistical info from newer seasons, but still!
And that math was not advanced. It was just easy, but time consuming.
If I tried to do advanced math, I would give up soon after I began.
And of course, most, if not all, of them would show up at the Welcome To Ponyville Pinkie Pie Party you'd get when you arrive, so...
The one mug per pony is certainly not a hard and fast rule, so for all we know the average could be 3 mugs of cider per pony or even more.
Measuring by pixels doesn't work well when objects are different distances from the camera. The mug is at least 1 1/2 feet closer to the camera than Applebloom's head, and the barrels are several feet behind Mac in the other shot.
The other method seemed to be very slightly more sound, but given the incredible variance between your estimated population sizes, it seems ultimately to produce no reliable data either.
I appreciate what you tried to do here, but in the end I'm afraid the result is so imprecise and varying that no usable data can pulled from this study.
And about the shrinkage-of-objects-due-to-distance, yeah, I know.
It can be anyways slightly corrected by using 1.1 or 0.9 multipliers on various values calculated in sub-steps, or by less half-assed distance shrinkage calculations.
Also I could've used calculus for estimating volumes better, and created better models which take customer imigration into account (and various other stuff people suggested to me), but after some point the slight increase in accuracy is no longer worth the time spent improving the analysis... plus it stops being fun, and fun was the sole reason why I did the analysis.
Btw.: If you plan to use the perspective in whatever future analyses you will be doing, know that the animators screwed up the size shrinkage for bigger distances - I checked the math. Short distance shrinkage is probably fine though.