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"The one on the left, with the clumps, strands, voids, and filaments is the array that was plotted at random, like stars." Are stars really plotted at random?
Up to the largest scales the universe is randomly clumped/stringed/voided.
Were the bombs actually mostly random?
Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…
This is actually an important lesson for game designers. Real randomness is very frustrating for players! Games should be designed to not be random. For example, there's an expansion to The Settlers of Catan that lets you use cards instead of dice to ensure a nice smooth distribution of resources... I think it's a lot more fun!
I was bit by another random quirk in World of Warcraft. There was a long-running achievement called "What a Strange Long Journey it has Been", which took at least a year in real-time to complete, and you had to actively play during each of the ten or so in-game festivals and holidays, and do some quests and tasks during each. If you missed a festival, you had to wait another year to do it again, so if you were aiming for the achievement, you really wanted to do it in one go.
During their version of Valentine's, each player got a bag of heart-shaped candy, and the task you had to complete was to pull out at least one each of the eight different heart candies. But you could only pull a piece of candy once every hour or so, each time you pulled a piece you had a 1/8 chance to get a certain piece, but the holiday was time-limited, so you had about two weeks to complete it.
Sounds easy and fair, right? 1/8 chance, get all eight pieces, two whole weeks, easy! Except that there was one piece that I just never got. The piece that said "I LOVE YOU!". And as the time went by, I got more and more frantic, logged in more often so as not to miss any opportunity to pull a piece of candy, but no luck.
So, I did a quick bit of math. You can pull one piece every hour for two weeks, but sleeping, not playing, missing days etc, meant that I effectively pulled ~100 pieces. The chance of missing a certain piece is 7/8, so missing a certain piece 100 times in a row is (7/8)^100, which is roughly a little bit more than one in a million.
With ten million players all doing the same thing, there's going to be a number of them that will hit that "one in a million" chance, which means that whoever designed that part of the achievement didn't do their homework, didn't do the math. Because intuition tells you that 1/8 chance is plenty! Hundreds of tries, of course everyone will get all pieces! Except proper math tells you otherwise, and I was one of the "lucky" outliers.
(Later, they apologized and retroactively removed that part of the achievement, so I got my purple nether-drake mount without having to wait a year extra.)
Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…
if (item == tier2.druid.pants)
return (item = plate-wearer-loot());
Were the bombs actually mostly random?
Meanwhile German agents in England were also observing the success or failure of the V2s, and in particular where they'd landed.
However, in an effort to deceive the Germans, the British started reporting the correct time of successful attacks, while mentioning an incorrect location.
Moreover, a double agent called Eddie Chapman also fed false information back to the Germans.
As a result, the aimers never really got a grip on ranging accurately. The bombs started landing to the south east of London.
There's considerably more detail about this in Most Secret War by R V Jones, who was involved in all sorts of ruses to confuse the enemy. Well worth a read.
Eddie Chapman (Agent ZigZag) was played by Christopher Plummer in the film Triple Cross. It seems to be on YouTube.
"The one on the left, with the clumps, strands, voids, and filaments is the array that was plotted at random, like stars." Are stars really plotted at random?
That's a good question. There's obviously more stars in the directions of the galactic plane (what we observe as the Milky Way), but the individual stars that we see in the night sky tend to only be the ones that are really close to us (relatively speaking). So it's a question of which effect dominates the other. I think it'd be interesting to see how well the distribution of stars fits a Poisson distribution.
With that it gets hard to truely say what is random or what is a as yet unknown pattern. This is why many have taken the approach of not having a single source of random numbers but use many and average out from there. There again is that random as the chances with such an approach of getting a high or low value would be biased out.
So with that I postulate one mans random string is another mans non-random string. So with that I define randomness as a yet undertermind sequence or a data. So the included Dilbert post is with that extreemly clever and totaly true.
Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…
A market would also fix this, in effect averaging over the entire population. Given players' anger at pieces not dropping as often as they "should", the market would converge approximate the true ratio between drop frequencies of different pieces.