granularity Behind everything simple is a huge tail of complicated

Iwona DUDEK , CNRS, France UMR 3495 CNRS/MCC MAP

[in] K Lippincott, The story of time , Larousse, 2000 . . re re , s. 13, s. , Time Larousse, 2000 Larousse, , K. Lippincott, Lippincott, K. , U. Eco, U. The storyof time [in] [in]

tguarantee that weare to able understandtguarantee its thatnatu weare to able understand its natu ’ ’

but it doesn but it doesn Introduction UMR CNRS / MCC 3495 MAP - Marseille - F Larousse, 2000, Fig. 158 Fig. 2000, Larousse, [in] K Lippincott, KLippincott, [in] L’histoire du TempsduL’histoire , Complicated Complicated Simple Simple Final conclusionsFinal Examples conclusionsInitial historical 25 of Comparison with multiple granularities (two case studies) (two multiple granularities with Final conclusionsFinal Examples conclusionsInitial calendars historical 25 of Comparison

with multiple granularities (two case studies) (two multiple granularities with

simple idea simplesolution> problemsimple objective simple simple idea simplesolution> problemsimple objective simple Behind everything huge a is tail simple of complica visualisation of data data of visualisation visualisation of data data of visualisation

Time granularity ted Time granularity Behind everything simple is a huge tail of complicated

Scientific background architect of architecture and urbanism evolution of architectural artefacts

studying sources : artefact itself (states, transformations …) Simple UMR- MAP MCC / CNRS 3495 Marseille- F Time granularity Behind everything simple is a huge tail of complicated

My scientific background architect history of architecture and urbanism evolution of architectural artefacts

studying sources : artefact itself (states, transformations …) context ( urban, historical, geographical, …) Simple UMR- MAP MCC / CNRS 3495 Marseille- F Time granularity Behind everything simple is a huge tail of complicated

Nature of historical data sets

heterogeneity XIII th c incompleteness Mai 1450 imprecision lineage 15 th July 1346 etc.

summer night 1702

every morning XV th c

temporal indications are often inconsistent in terms of granularity Simple UMR- MAP MCC / CNRS 3495 Marseille- F Time granularity Behind everything simple is a huge tail of complicated

Nature of historical data sets

summer night 1702 Objective : store and query without any additional approximations

Problem : define (the smallest temporal unit) …, , , … and granules (temporal aggregate, e.g. n )

Idea : start from how time is handled in general (through calendars) Simple UMR- MAP MCC / CNRS 3495 Marseille- F Complicated UMR CNRS / MCC 3495 MAP - Marseille - F Continental Celtic ( Calendar Celtic Continental Attic stateAttic calendar calendar Tibetancalendar Julian ( calendar Japanese Coptic calendar Babylonian aí calendarBadí’ ( Muslimcalendar aieePwkncalendarPawukon Balinese (solar) Incascalendar ( calendar Pre- Hebrew (republican) calendar Roman calendar Gregorian Incas calendar (lunar) Incascalendar calendar Symmetry454 Inuitcalendar calendar republican French Maya and Aztec calendars ( calendars Aztec and Maya Byzantinecalendar Hijri Taiintaiyoreki Dżahilijja ) Xiuhpohualli, Tonalpohualli) Xiuhpohualli, als oin calendar Coligny Gaulish ) ) ) ) Comparisonof 25 alternative calendars Comparisonof 25 alternative calendars cultures or civilisationsor cultures and periods historic of range a wide covering

eleven key aspects of calendars: of aspects key eleven Behind everything huge a is tail simple of complica

Time granularity ted Comparison of 25 alternative calendars UMR CNRS / MCC 3495 MAP - Marseille - F 60 ua oa uioa agricultural lunisolar solar lunar inyears 604 intercalation rhythm intercalation beginning of a a of beginning number of seasonsof number beginning of a a of beginning 002000 1000 14.IX cyclesnatureof midday 1872-73 midnight 0–1 – 10 j indays types of a month (duration) month a of types year leap a an common a in of number number of days in a week ina days of number 5 days day 1 days 5 Comparisonof 25 alternative calendars Comparisonof 25 alternative calendars 23h cultures or civilisationsor cultures and periods historic of range a wide covering eleven key aspects of calendars: of aspects key eleven sunset

year discretisation of cyclestype and presence of usage zone and period

type Behind everything huge a is tail simple of complica sunrise ? nodata number of days in a common ina days of number 354 387 number of days in a leap ina days of number

Time granularity ted Time granularity Behind everything simple is a huge tail of complicated

Gregorian calendar

3000 2000 1000 1 1000 2000

1582

01.I 365 366 x x + x 4 100 400

Pope Gregory XIII (Luigi Lilio), 24 February 1582 (a papal bull, )

spring 11 March instead of 21 March (a drift of 10 days since Roman ) Time granularity Behind everything simple is a huge tail of complicated

The reformed calendar was adopted later that year by a handful of countries, with other countries adopting it over the following centuries.

3000 2000 1000 1 1000 2000

1582

01.I 365 366 x x + x 4 100 400 Anno Diocletiani

Julian calendar Nostri Iesu Christi

3000 2000 1000 754 1 284 1000 2000

46 +80 days

01.I ? 365

366

3000 2000? 1000 1000 2000

1800 500 new spring equinox

354 ~21.III

/ 383/384 (7 x 19)

19

Hebrew calendar

3761 3000 2000 1000 1000 2000

359

354/355/356 III-IV 383 / 384 385

19 Maya and Aztec calendars

3114 3000 2000 1000 1000 2000

650 1521

VII Xiuhpohualli (haab) 52/104/520 365 377/378/379 52

? 13

? Tonalpohualli (Tzolk'in) 72 260 272/273/274

Egyptian calendar

3000 2000? 1000 1000 2000

238

solicit of

365 [ 21.VI ] [ 19.VII ]

1460 French republican calendar

3000 2000 1000 10001792 2000

1793 1805 autumnal equinox

365 22-23.IX

Inuit calendar

3000 2000 1000 1000 2000

1800-1830 midnight 365 Japanese calendar (Taiintaiyoreki)

3000 2000 1000 1000? 2000

[645 ] [879 ] 1872-73 winter

354 ~20.II / 383/385

60

19

Chinese calendar (Taichu)

3000 2000 1000 1000 2000

~2637 1929

new moon 354 (I,II,IV)

21.I -20.II 384 (III,V) / (7 x 19) 60

19 PreIslamic calendar (Dżahilijja)

3000 2000? 1000 1000 2000

632 new moon autumnal equinox

354 22/23. IX 359/360

Muslim calendar (hijri)

3000 2000 1000 622 1000 2000

632

22-23.IX 354/355

19 30 Burmese calendar

3000 2000 1000 638 1000 2000

354

~17 IV / (7 x 19) 384/385

19 354 384/385

Attic state calendar

3000 2000 1000 ? 1000 2000

[508 ][407 ] 322

354 ~22.VI ± 15

384 Balinese Pawukon calendar

3000 2000 1000 1000 2000

~1500

? ? 210

10 – 1 j

Incas calendar 3000 2000 1000 1000 2000

1532 [] 700 [~ VI ] [~22.XII ] 365 ?

[ ] [ ]

? Pleiades rise 328

09/08.VI ~354 ~365 / Japanese calendar ( Taiintaiyoreki ) 19 60 60 /

/ Babylonian calendar 19 (7 x 19) / Burmese calendar 19 (7 x 19) Chinese calendar 19 60 /

/ 19 Pre-Islamic calendar ( Dżahilijja )

Symmetry454 calendar 1117 293 ? [ , ] [ , ] Incas calendar (solar) French republican calendar

Egyptian calendar 1460 Soviet calendar

Coptic calendar

Julian calendar 28 Gregorian calendar 400 100 /+400 28 8 j Roman calendar (republican)

Inuit calendar [ , ] 5 30 Continental (Gaulish Coligny calendar) [ , ] ? 19 50 Muslim calendar ( Hijri ) 19 30 Attic state calendar

Xiuhpohualli 52 52/104/520 ? Maya and Aztec calendars ? Tonalpohualli 13 ? Badí’ calendar 19 361 ? Incas calendar (lunar) ? 10 – 1 j Balinese Pawukon calendar Time granularity Behind everything simple is a huge tail of complicated

Comparison of 25 alternative calendars

What we noticed : • each historical calendar has its own specific granularity • similar mechanisms of time discretisation year, month, week, day … • different quantification different number of days in month, week, year • historical calendars are subject to change over time including in terms of granularity • importance of cultural aspect and way of life • presence of cycles natural or calendar based Complicated UMR- MAP MCC / CNRS 3495 Marseille- F Time granularity Behind everything simple is a huge tail of complicated

Comparison of 25 alternative calendars

What we noticed : • each historical calendar has its own specific granularity • similar mechanisms of time discretisation year, month, week, day … • different quantification different number of days in month, week, year • historical calendars are subject to change over time including in terms of granularity • importance of cultural aspect and way of life • presence of cycles natural or calendar based • independence of cycles of nature

• recurrent phenomenon – discontinuity of time in calendars due to human manipulation Example: Complicated UMR- MAP MCC / CNRS 3495 Marseille- F 80 additional days in year 46 BC, 11 days less in 1582 AD (in , Fréjus … but not Strasbourg or London …) Time granularity Behind everything simple is a huge tail of complicated

Case studies

• succession of calendars for a given place

• underline presence of cycles

• show temporal indications with their own, imperfect granularity Complicated UMR- MAP MCC / CNRS 3495 Marseille- F Case studies UMR CNRS / MCC 3495 MAP - Marseille - F withmultiple granularities Genericframework for visualisingtime withmultiple granularities Genericframework for visualisingtime two case studiestwo •

chapel of St Anne in Southern Alps (2400 m(2400 Alps in Southern Anne St of chapel Behind everything huge a is tail simple of complica Time granularity France France

AMSL ted ) Case studies UMR CNRS / MCC 3495 MAP - Marseille - F withmultiple granularities Genericframework for visualisingtime withmultiple granularities Genericframework for visualisingtime two case studiestwo •

belfry of an ancient town hall in Kraków, in Kraków, hall town ancient an of belfry Behind everything huge a is tail simple of complica Time granularity

Poland ted Case studies UMR CNRS / MCC 3495 MAP - Marseille - F chapelof St Anne in Southern Alps chapelof St Anne in Southern Alps • • • • colours types of events/processesof types colours visualisation

Gregorian calendar period calendar Gregorian overall lifetime of the chapel chapel the of lifetime overall Behind everything huge a is tail simple of complica

Time granularity ted Time granularity Behind everything simple is a huge tail of complicated

chapel of St Anne in Southern Alps

• cyclic events are represented in a –like manner 26 VIII • meteorological do not coincide with astronomical seasons winter is the longest season (average season length fuzzy cyclic behaviour)

• annual pilgrimage to the chapel Case studies Case UMR- MAP MCC / CNRS 3495 Marseille- F Case studies UMR CNRS / MCC 3495 MAP - Marseille - F 26 VIII 26 16 VII 1699 VII 16 aDu cause de la La Doux à procession au lac de "sommes allés en sècheresse ..." beginning of of beginning VII 1909 VII chapelof St Anne in Southern Alps chapelof St Anne in Southern Alps au commencement de

réparations juillet des Behind everything huge a is tail simple of complica 1751 lac et la chapelle sont fête de sainte Anne, le connus sous le nom de première fois de la mention pour la Time granularity

La Doux ted Time granularity Behind everything simple is a huge tail of complicated

chapel of St Anne in Southern Alps

16 VII 1699 07 VII 1729 18 VII 1743

16 VII 1699

07 VII 1729

18 VII 1743

1751 1751 24 XII 1753 1776 24 XII 1753

1776

beginning of VII 1831

beginning of VII 1909 beginning of VII 1831 beginning of VII 1909 winter 1918-1919 winter 1918-1919

summer 1920

26 VII 1921

summer 1920 26 VII 1921 Case studies UMR CNRS / MCC 3495 MAP - Marseille - F artefact's lifetime artefact's 26VIII

chapelof St Anne in Southern Alps chapelof St Anne in Southern Alps Behind everything huge a is tail simple of complica collecting money collecting avalanche

Time granularity ted Time granularity Behind everything simple is a huge tail of complicated

tower of an ancient town hall in Krak ów

• fires of Cracow’s town hall tower Case studies Case UMR- MAP MCC / CNRS 3495 Marseille- F Case studies UMR CNRS / MCC 3495 MAP - Marseille - F towerof anancient town hall in towerof anancient town hall in • • • • the astronomical seasons astronomical the meteorological seasons do not coincide with with coincide not do seasons meteorological this artefactfor cyclic annual any lifetime of this artefact traverses two calendars two traversesartefact this of lifetime seasons moving moving seasons Visualising time with multiple granularities: (a rough approximation) a generica framework Krak Krak ó ó w w Case studies UMR CNRS / MCC 3495 MAP - Marseille - F towerof anancient town hall in towerof anancient town hall in • • any cyclic event for this artefact this for event cyclic any rhythm of transformations/reparationsof rhythm Visualising time with multiple granularities: a generica framework Krak Krak ó ó w w Case studies UMR CNRS / MCC 3495 MAP - Marseille - F oldest historical sources are less less are sources historical oldest a fire of an artefact is generally short event (in event (in short is generally artefact an a fire of towerof anancient town hall in towerof anancient town hall in precise Visualising time with multiple granularities: in terms terms of temporal granularityin a scale of year) of a scale a generica framework Krak Krak ó ó w w Visualising time with multiple granularities: a generic framework

buildings that furnished the Main Market Square in Cracow • fires at the Market Square Case studies Case UMR- MAP MCC / CNRS 3495 Marseille- F

oldest historical sources are less precise terms of temporal granularity Visualising time with multiple granularities: a generic framework

buildings that furnished the Main Market Square in Cracow

oldest historical sources are less precise terms of temporal granularity Visualising time with multiple granularities: a generic framework

Conclusions • each historical calendar has its own specific granularity – one model ? • depending on where changes over time occur, the analysis may require different visual instruments ‘tailored’ to the local conditions (in particular to the succession of calendars with various sometimes local time discontinuities, cycles of seasons, time granulation, etc.) • study of cyclic and fuzzy periodic behaviour may help in better understanding data sets we handle in the context of historical sciences • the day/night notion could appear as the smallest common time interval (‘universal chronon’) within reach when wanting to compare calendars – however exceptions here

Conclusions exist (e.g. in Inuit’s calendar) UMR- MAP MCC / CNRS 3495 Marseille- F

[dans] K Lippincott, L’histoire du Temps , Larousse, 2000 Visualising time with multiple granularities: a generic framework

If we deal with the notion of the time in our research

it is worth to take some time to think about ‘‘ time’’ . Conclusions UMR- MAP MCC / CNRS 3495 Marseille- F

[dans] K Lippincott, L’histoire du Temps , Larousse, 2000