Paradoxes and theorems every developer should know

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@jaytaph 1 Joshua Thijssen jaytaph Paradoxes and theorems every developer should know

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@jaytaph Disclaimer: I'm not a (mad) scientist nor a mathematician. 2

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@jaytaph German Tank Problem 3

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@jaytaph 4 15

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@jaytaph 5

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@jaytaph 5 53 72 8 15

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@jaytaph 6 k = number of elements m = largest number

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@jaytaph 72 + (72 / 4) - 1 = 89 7

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@jaytaph 8 Intelligence Statistics Actual June 1940 1000 169 June 1941 1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem

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@jaytaph 8 Intelligence Statistics Actual June 1940 1000 169 June 1941 1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem 122

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@jaytaph 8 Intelligence Statistics Actual June 1940 1000 169 June 1941 1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem 122 271

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@jaytaph 8 Intelligence Statistics Actual June 1940 1000 169 June 1941 1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem 122 271 342

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@jaytaph 9

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@jaytaph 9 ➡ Data leakage.

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@jaytaph 9 ➡ Data leakage. ➡ User-id's, invoice-id's, etc

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@jaytaph 9 ➡ Data leakage. ➡ User-id's, invoice-id's, etc ➡ Used to approximate the number of iPhones sold in 2008.

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@jaytaph 10 Monthly Invoice IDs Monthly Invoice IDs Monthly Invoice IDs Monthly Invoice IDs Jan 2476 2303 Feb 10718 14891 Mar 19413 27858 Apr 28833 41458 May 38644 55429 Jun 48633 55429 Jul 102606 59027 84961 Aug 109331 69715 100308 Sep 116388 80684 116020 Oct 123721 91935 132004 Nov 131241 103455 148341 Dec 139236 115276 164976

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@jaytaph 11 Monthly Invoice IDs Monthly Invoice IDs Monthly Invoice IDs Monthly Invoice IDs Jan 2476 2303 Feb 10718 14891 Mar 19413 27858 Apr 28833 41458 May 38644 55429 Jun 48633 55429 Jul 102606 59027 84961 Aug 109331 69715 100308 Sep 116388 80684 116020 Oct 123721 91935 132004 Nov 131241 103455 148341 Dec 139236 115276 164976 Estimated subscriptions Estimated subscriptions Estimated subscriptions Estimated subscriptions Jan Feb 8242 12588 Mar 8695 12967 Apr 9420 13600 May 9811 13971 Jun 9989 14525 Jul 10394 15007 Aug 6725 10688 15347 Sep 7057 10969 15712 Oct 7333 11251 15984 Nov 7520 11520 16337 Dec 7995 11821 16635

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@jaytaph 12 Monthly Invoice IDs Monthly Invoice IDs Monthly Invoice IDs Monthly Invoice IDs Jan 2476 2303 Feb 10718 14891 Mar 19413 27858 Apr 28833 41458 May 38644 55429 Jun 48633 55429 Jul 102606 59027 84961 Aug 109331 69715 100308 Sep 116388 80684 116020 Oct 123721 91935 132004 Nov 131241 103455 148341 Dec 139236 115276 164976 Estimated growth / size Estimated growth / size Estimated growth / size Estimated growth / size Jan Feb Mar 105% 103% Apr 108% 105% May 104% 103% Jun 102% 104% Jul 104% 103% Aug 103% 102% Sep 105% 103% 102% Oct 104% 103% 102% Nov 103% 102% 102% Dec 106% 103% 102%

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@jaytaph ➡ Avoid (semi) sequential data to be leaked. ➡ Adding randomness and offsets will NOT solve the issue. ➡ Use UUIDs (better: timebased short IDs, you don't need UUIDs) 13

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@jaytaph Confirmation Bias 14

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@jaytaph 15 Hypothesis....

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@jaytaph 16 Evidence!

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@jaytaph 17 Hypothesis conﬁrmed!

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@jaytaph 18

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@jaytaph 2 4 6 19 Z={…,−2,−1,0,1,2,…}

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@jaytaph 21% 20

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@jaytaph 21 5 8 ? ? If a card shows an even number on one face, then its opposite face must be blue.

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@jaytaph < 10% 22

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@jaytaph 23 coke beer 35 17 If you drink beer then you must be 18 yrs or older.

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@jaytaph 23 coke beer 35 17 If you drink beer then you must be 18 yrs or older.

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@jaytaph 23 coke beer 35 17 If you drink beer then you must be 18 yrs or older.

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@jaytaph Cognitive Adaption for social exchange 24

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@jaytaph hint: Try and place your "technical problem" in a more social context. 25

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@jaytaph 26 5 8 ? ? If a card shows an even number on one face, then its opposite face must be blue.

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@jaytaph 26 5 8 ? ? If a card shows an even number on one face, then its opposite face must be blue.

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@jaytaph 26 5 8 ? ? If a card shows an even number on one face, then its opposite face must be blue.

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@jaytaph Birthday paradox 27

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@jaytaph Question: 28 > 50% chance 4 march 18 september 5 december 25 juli 2 februari 9 october

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@jaytaph 23 people 29

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@jaytaph 366* persons = 100% 30

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@jaytaph Collisions occur more often than you realize 31

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@jaytaph Hash collisions 32

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@jaytaph 16 bit value 300 elements 33

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@jaytaph rand(1,100000) 117 elements 34

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@jaytaph Watch out for: 35 ➡ Too small hashes. ➡ Unique data. ➡ Your data might be less "protected" as you might think.

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@jaytaph Heisenberg uncertainty principle 36

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@jaytaph 37

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@jaytaph 38

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@jaytaph 39 x position p momentum (mass x velocity) ħ 0.0000000000000000000000000000000001054571800 (1.054571800E-34)

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@jaytaph The more precise you know one property, the less you know the other. 40

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@jaytaph This is NOT about observing! 41

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@jaytaph Observer effect 42 heisenbug

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@jaytaph It's about trade-offs 43

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@jaytaph Benford's law 44

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@jaytaph Numbers beginning with 1 are more common than numbers beginning with 9. 45

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@jaytaph Default behavior for natural numbers. 46

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@jaytaph 47

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@jaytaph find . -name \*.php -exec wc -l {} \; | sort | cut -b 1 | uniq -c 48

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@jaytaph find . -name \*.php -exec wc -l {} \; | sort | cut -b 1 | uniq -c 48 1073 1 886 2 636 3 372 4 352 5 350 6 307 7 247 8 222 9

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@jaytaph 49

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@jaytaph Bayesian filtering 50

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@jaytaph What's the probability of an event, based on conditions that might be related to the event. 51

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@jaytaph What is the chance that a message is spam when it contains certain words? 52

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@jaytaph 53 P(A|B) P(A) P(B) P(B|A) Probability event A, if event B (conditional) Probability event A Probability event B Probability event B, if event A

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@jaytaph 54 ➡ Figure out the probability a {mail, tweet, comment, review} is {spam, negative} etc.

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@jaytaph ➡ 10 out of 50 comments are "negative". ➡ 25 out of 50 comments uses the word "horrible". ➡ 8 comments with the word "horrible" are marked as "negative". 55

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@jaytaph 56

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@jaytaph 57

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@jaytaph 58 "Your product is horrible and does not work properly. Also, you suck." "I had a horrible experience with another product. But yours really worked well. Thank you!" Negative: Positive:

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@jaytaph 59

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@jaytaph 60 Find me on twitter: @jaytaph Find me for development and training: www.noxlogic.nl / www.techademy.nl Find me on email: [email protected] Find me for blogs: www.adayinthelifeof.nl