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Paradoxes and theorems every developer should know
Joshua Thijssen
June 21, 2016
Technology
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Paradoxes and theorems every developer should know
Joshua Thijssen
June 21, 2016
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Transcript
1 Joshua Thijssen jaytaph <?php namespace
2 Joshua Thijssen Consultant and trainer @ NoxLogic Founder of
TechAnalyze.io Symfony Rainbow Books author Mastering the SPL author Blog: http://adayinthelifeof.nl Email: jthijssen@noxlogic.nl Twitter: @jaytaph Tech nalyze WWW.TECHANALYZE.IO
3 https://dutchtechrecruitment.nl/ Text
Disclaimer: I'm not a (mad) scientist nor a mathematician. 4
German Tank Problem 5
6
6 15
7
7 53 72 8 15
8 k = number of elements m = largest number
72 + (72 / 4) - 1 = 89 9
10 Intelligence Statistics Actual June 1940 1000 169 June 1941
1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem
10 Intelligence Statistics Actual June 1940 1000 169 June 1941
1550 244 August 1942 1550 327 https://en.wikipedia.org/wiki/German_tank_problem 122
10 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
10 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
11
11 ➡ Data leakage.
11 ➡ Data leakage. ➡ User-id's, invoice-id's, etc
11 ➡ Data leakage. ➡ User-id's, invoice-id's, etc ➡ Used
to approximate the number of iPhones sold in 2008.
11 ➡ Data leakage. ➡ User-id's, invoice-id's, etc ➡ Used
to approximate the number of iPhones sold in 2008. ➡ Calculate approximations of datasets with (incomplete) information.
12
➡ 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
14 Collecting (big) data is easy Analyzing big data is
the hard part.
Confirmation Bias 15
2 4 6 16 Z={…,−2,−1,0,1,2,…}
21% 17
18 5 8 ? ? If a card shows an
even number on one face, then its opposite face is blue.
< 10% 19
20 coke beer 35 17 If you drink beer then
you must be 18 yrs or older.
20 coke beer 35 17 If you drink beer then
you must be 18 yrs or older.
20 coke beer 35 17 If you drink beer then
you must be 18 yrs or older.
Cognitive Adaption for social exchange 21
hint: Try and place your "technical problem" in a more
social context. 22
BDD 23
24 5 8 ? ? If a card shows an
even number on one face, then its opposite face is blue.
24 5 8 ? ? If a card shows an
even number on one face, then its opposite face is blue.
24 5 8 ? ? If a card shows an
even number on one face, then its opposite face is blue.
TESTING 25
26 ➡ Step 1: Write code ➡ Step 2: Write
tests ➡ Step 3: Proﬁt
public function isLeapYeap($year) { return ($year % 4 == 0);
} 27 https://www.sundoginteractive.com/blog/confirmation-bias-in-unit-testing testIs1996ALeapYeap(); testIs2000ALeapYeap(); testIs2004ALeapYeap(); testIs2008ALeapYeap(); testIs2012ALeapYeap(); testIs1997NotALeapYear(); testIs1998NotALeapYear(); testIs2001NotALeapYear(); testIs2013NotALeapYear();
public function isLeapYeap($year) { return ($year % 4 == 0);
} 27 https://www.sundoginteractive.com/blog/confirmation-bias-in-unit-testing testIs1996ALeapYeap(); testIs2000ALeapYeap(); testIs2004ALeapYeap(); testIs2008ALeapYeap(); testIs2012ALeapYeap(); testIs1997NotALeapYear(); testIs1998NotALeapYear(); testIs2001NotALeapYear(); testIs2013NotALeapYear();
public function isLeapYeap($year) { return ($year % 4 == 0);
} 28 https://www.sundoginteractive.com/blog/confirmation-bias-in-unit-testing
29 ➡ Tests where written based on actual code. ➡
Tests where written to CONFIRM actual code, not to DISPROVE actual code!
30 TDD
31 ➡ Step 1: Write tests ➡ Step 2: Write
code ➡ Step 3: Proﬁt, as less prone to conﬁrmation bias (as there is nothing to bias!)
Birthday paradox 32
Question: 33 > 50% chance 4 march 18 september 5
december 25 juli 2 februari 9 october
23 people 34
366 persons = 100% 35
Collisions occur more often than you realize 36
Hash collisions 37
16 bits means 300 values before >50% collision probability 38
Watch out for: 39 ➡ Too small hashes. ➡ Unique
data. ➡ Your data might be less "protected" as you might think.
Heisenberg uncertainty principle 40
It's not about star trek (heisenberg compensators) 41
nor crystal meth 42
43 x position p momentum (mass x velocity) ħ 0.0000000000000000000000000000000001054571800
(1.054571800E-34)
The more precise you know one property, the less you
know the other. 44
This is NOT about observing! 45
Observer effect 46 heisenbug
It's about trade-offs 47
Benford's law 48
Numbers beginning with 1 are more common than numbers beginning
with 9. 49
Default behavior for natural numbers. 50
51
find . -name \*.php -exec wc -l {} \; |
sort | cut -b 1 | uniq -c 52
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
53
Bayesian filtering 54
What's the probability of an event, based on conditions that
might be related to the event. 55
What is the chance that a message is spam when
it contains certain words? 56
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
58 ➡ Figure out the probability a {mail, tweet, comment,
review} is {spam, negative} etc.
➡ 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
60 negative "horrible" 10 comments 25 comments 8 comments
61
62 ➡ More words? ➡ Complex algorithm, ➡ but, we
can assume that words are not independent from eachother ➡ Naive Bayes approach
63
64 We must know beforehand which comments are negative?
TRAINING SET 65
66 "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:
67 ➡ 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.
➡ Collaborative ﬁltering (mahout): ➡ If user likes product A,
B and C, what is the chance that they like product D? 68
69 Mess up your (training) data, and nothing can save
you (except a training set reboot)
70 ➡ 30% change of acceptance for CFP ➡ 5
CFP's Binomial probability
70 ➡ 30% change of acceptance for CFP ➡ 5
CFP's 1 - (0.7 * 0.7 * 0.7 * 0.7 * 0.7) = 1 - 0.168 = 0.832 83% on getting selected at least once! Binomial probability
http://farm1.static.ﬂickr.com/73/163450213_18478d3aa6_d.jpg 71
72 Find me on twitter: @jaytaph Find me for development
and training: www.noxlogic.nl / www.techademy.nl Find me on email: jthijssen@noxlogic.nl Find me for blogs: www.adayinthelifeof.nl