Jak na mě vyskočila matematika

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Jak na mě vyskočila MATEMATIKA David Majda Praha, 6.5.2015

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INTRO

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{ time: "2015-05-03T09:29:15.000Z" space: "default", source_type: "metric", name: "response_time", value: 134.675 }

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read … | ( batch :5 seconds: | reduce max('value') by host | @timechart; keep time, value | @logger )

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read … | ( batch :5 seconds: | reduce max('value') by host | @timechart; keep time, value | @logger ) read @timechart batch reduce keep @logger

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DEMO

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LOGIKA ALGEBRA I ALGEBRA II ALGEBRA III ANALÝZA TEORIE RELATIVITY

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LOGIKA

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read status = 500

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read status = 500 or (status = 404 and url !~ …)

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read status = 500 or (status = 404 and url !~ …)

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Konjunktivní normální forma

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(a 1,1 ∨ … ∨ a 1,m(1) ) ∧ … ∧ (a n,1 ∨ … ∨ a n,m(n) )

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read status = 500 or (status = 404 and url !~ …)

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read (status = 500 or status = 404) and (status = 500 or url !~ …)

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read (status = 500 or status = 404) and (status = 500 or url !~ …)

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ALGEBRA I

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read … | reduce c = count(x) s = sum(x) m = max(x)

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{ c: 3, s: 6, m: 3 } read … | reduce c = count(x) s = sum(x) m = max(x) { x: 1 } { x: 2 } { x: 3 }

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{ c: 2, s: 3, m: 2 } read … | reduce c = count(x) s = sum(x) m = max(x) { x: 1 } { x: 2 }

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{ c: 1, s: 1, m: 1 } read … | reduce c = count(x) s = sum(x) m = max(x) { x: 1 }

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{ c: ?, s: ?, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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{ c: 0, s: ?, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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{ c: 0, s: ?, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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{ c: 0, s: 0, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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{ c: 0, s: 0, m: ? } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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{ c: 0, s: 0, m: undefined } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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{ c: 0, s: 0, m: undefined } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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Neutrální prvek

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e: ∀a(e ⊕ a = a ⊕ e = a)

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{ c: 0, s: 0, m: -Infinity } read … | reduce c = count(x) s = sum(x) m = max(x) (nic)

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ALGEBRA II

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read … value > 0.95 | reduce c = count()

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Elasticsearch Cassandra read … value > 0.95 | reduce c = count()

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Elasticsearch Cassandra read … value > 0.95 | reduce c = count()

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Asociativita

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(a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)

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count count_unique sum avg min max first last pluck percentile sigma

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count count_unique sum avg min max first last pluck percentile sigma

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Monoid

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Množina S, operace ⊕ : S ⨉ S → S ⊕ je asociativní na prvcích S V S existuje neutrální prvek vůči ⊕

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ALGEBRA III

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read time < :2015-04-01:

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Moment Duration :2015-04-01T20:05:27.034: :now: :3 weeks and 1 day ago: :20:05:27.034: :3s: :1 hour and 23 minutes:

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read time < :2015-04-01: - :1 day:

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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Afinní prostor

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m 1 m 2 m 2 t d 1 d 2

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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Dimenzionální analýza

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v = s / t η = P výst / P vst

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D N / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D D / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D D / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D D / D → N D / N → D D % N → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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N * D → D D * N → D D / D → N D / N → D D % D → D M + D → M D + M → M D + D → D M - M → D M - D → M D - D → D

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ANALÝZA

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emit -from 0 | batch 2 | reduce count() | batch 4 | reduce count()

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emit … | batch 2 | reduce count() | batch 4 | reduce count() { time: 0 } { time: 1 } { time: 2 } { time: 3 } { time: 4 } { time: 5 } { time: 6 } { time: 7 } { time: 8 } { time: 2, count: 2 } { time: 4, count: 2 } { time: 6, count: 2 } { time: 8, count: 2 } { time: 4, count: 2 } { time: 8, count: 2 }

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Infinitezimály

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ε > 0 ∀x ∈ R, x > 0: ε < x

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emit … | batch 2 | reduce count() | batch 4 | reduce count() { time: 0 } { time: 1 } { time: 2 } { time: 3 } { time: 4 } { time: 5 } { time: 6 } { time: 7 } { time: 8 } { time: 2 - ε, count: 2 } { time: 4 - ε, count: 2 } { time: 6 - ε, count: 2 } { time: 8 - ε, count: 2 } { time: 4 - ε, count: 2 } { time: 8 - ε, count: 2 } < 2 < 2 < 2 < 2 < 4 < 4

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TEORIE RELATIVITY

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Minkowského metrika

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ds2 = c2dt2 - dx2 - dy2 - dz2

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ds2 = c2dt2 - dx2 - dy2 - dz2

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ZÁVĚR

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OTÁZKY?

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KAM DÁL? http://en.wikipedia.org/wiki/Conjunctive_normal_form http://en.wikipedia.org/wiki/Disjunctive_normal_form http://en.wikipedia.org/wiki/Identity_element http://en.wikipedia.org/wiki/Associative_property http://en.wikipedia.org/wiki/Monoid http://en.wikipedia.org/wiki/Affine_space http://en.wikipedia.org/wiki/Dimensional_analysis http://en.wikipedia.org/wiki/Infinitesimal http://en.wikipedia.org/wiki/Minkowski_space

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POUŽITÉ OBRÁZKY http://commons.wikimedia.org/wiki/File:Torus.png http://commons.wikimedia.org/wiki/File:World_line.svg