Paradoxes and theorems every developer should know

@jaytaph 1 Joshua Thijssen jaytaph Paradoxes and theorems every developer
should know <?php namespace

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

@jaytaph German Tank Problem 3

@jaytaph 4 15

@jaytaph 5

@jaytaph 5 53 72 8 15

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

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

@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

1941 1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem 122

1941 1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem 122 271

1941 1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem 122 271 342

@jaytaph 9

@jaytaph 9 ➡ Data leakage.

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

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

@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

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

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%

@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

@jaytaph Confirmation Bias 14

@jaytaph 15 Hypothesis....

@jaytaph 16 Evidence!

@jaytaph 17 Hypothesis conﬁrmed!

@jaytaph 18

@jaytaph 2 4 6 19 Z={…,−2,−1,0,1,2,…}

@jaytaph 21% 20

@jaytaph Don't try and confirm what you know. Try and
disprove instead. 21

@jaytaph Confirmation bias is everywhere! 22

@jaytaph 23 5 8 ? ? If a card shows
an even number on one face, then its opposite face must be blue.

@jaytaph < 10% 24

@jaytaph 25 coke beer 35 17 If you drink beer
then you must be 18 yrs or older.

@jaytaph Cognitive Adaption for social exchange 26

@jaytaph hint: Try and place your "technical problem" in a
more social context. 27

@jaytaph 28 5 8 ? ? If a card shows
an even number on one face, then its opposite face must be blue.

@jaytaph 29 TDD

@jaytaph Birthday paradox 30

@jaytaph Question: 31 > 50% chance 4 march 18 september
5 december 25 juli 2 februari 9 october

@jaytaph 23 people 32

@jaytaph 366* persons = 100% 33

@jaytaph Collisions occur more often than you realize 34

@jaytaph Hash collisions 35

@jaytaph 16 bit value 300 elements 36

@jaytaph random_int(1,100000) how many attempts before 50% collision chance? 37

@jaytaph random_int(1,100000) 117 elements 38

@jaytaph Watch out for: 39 ➡ Too small hashes. ➡
Unique data. ➡ Your data might be less "protected" as you might think.

@jaytaph Heisenberg uncertainty principle 40

@jaytaph 41

@jaytaph 42

@jaytaph 43 x position p momentum (mass x velocity) ħ
0.0000000000000000000000000000000001054571800 (1.054571800E-34)

@jaytaph The more precise you know one property, the less
you know the other. 44

@jaytaph It's about trade-offs 45

@jaytaph This is NOT about observing! 46

@jaytaph Observer effect 47 heisenbug

@jaytaph Benford's law 48

@jaytaph Numbers beginning with 1 are more common than numbers
beginning with 9. 49

@jaytaph Default behavior for natural numbers. 50

@jaytaph 51

@jaytaph find . -name \*.php -exec wc -l {} \;
| sort | cut -b 1 | uniq -c 52

@jaytaph find . -name \*.php -exec wc -l {} \;
| sort | cut -b 1 | uniq -c 52 1073 1 886 2 636 3 372 4 352 5 350 6 307 7 247 8 222 9

@jaytaph 53

@jaytaph Bayesian filtering 54

@jaytaph What's the probability of an event, based on conditions
that might be related to the event. 55

@jaytaph What is the chance that a message is spam
when it contains certain words? 56

@jaytaph 57 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

@jaytaph 58 ➡ Figure out the probability a {mail, tweet,
comment, review} is {spam, negative} etc.

@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". 59

@jaytaph 60 10 comments 25 comments 8 comments negative "horrible"

@jaytaph 61

@jaytaph 62

@jaytaph 63 ➡ You might want to ﬁlter stop-words ﬁrst.
➡ You might want to make sure negatives are handled property "not great" => negative. ➡ Bonus points if you can spot sarcasm.

@jaytaph ➡ Collaborative ﬁltering (mahout): ➡ If user likes product
A, B and C, what is the chance that they like product D? 64

@jaytaph 65 Mess up your (training) data, and nothing can
save you (except a training set reboot)

@jaytaph 66

@jaytaph 67 Find me on twitter: @jaytaph Find me for
development and training: www.noxlogic.nl / www.techademy.nl Find me on email: jthijssen@noxlogic.nl

Paradoxes and theorems every developer should know

Paradoxes and theorems every developer should know

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