Time 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 but it doesn ’t guarantee that we are able to understand its nature . U. Eco, Time , s. 13, [in] The story of time , K. Lippincott, Larousse, 2000 Time granularity Behind everything simple is a huge tail of complicated Simple simple objective simple problem simple idea > solution Complicated Comparison of 25 historical calendars Initial conclusions Examples - visualisation of data with multiple granularities (two case studies) Final conclusions [in] K Lippincott, L’histoire du Temps , Introduction UMR- MAP MCC / CNRS 3495 Marseille- F Larousse, 2000, Fig. 158 Time granularity Behind everything simple is a huge tail of complicated Scientific background architect history 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 second Saturday 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 chronon (the smallest temporal unit) …, week, month season, … and granules (temporal aggregate, e.g. n chronons) Idea : start from how time is handled in general (through calendars) Simple UMR- MAP MCC / CNRS 3495 Marseille- F Japanese calendar ( Taiintaiyoreki ) Time granularity Tibetan calendar Behind everything simple is a huge tail of complicated Babylonian calendar Burmese calendar Chinese calendar Comparison of 25 alternative calendars Hebrew calendar covering a wide range of historic periods and Pre-Islamic calendar ( Dżahilijja ) cultures or civilisations Symmetry454 calendar Incas calendar (solar) eleven key aspects of calendars: French republican calendar Egyptian calendar Soviet calendar Coptic calendar Julian calendar Gregorian calendar Byzantine calendar Roman calendar (republican) Inuit calendar Continental Celtic Calendar ( Gaulish Coligny calendar ) Muslim calendar ( Hijri ) Attic state calendar Complicated UMR- MAP MCC / CNRS 3495 Marseille- F Maya and Aztec calendars ( Xiuhpohualli, Tonalpohualli) Badí’ calendar Incas calendar (lunar) Balinese Pawukon calendar Time granularity Behind everything simple is a huge tail of complicated lunar solar lunisolar agricultural 1000 2000 Comparison of 25 alternative calendars covering a wide range of historic periods and 604 1872-73 cultures or civilisations eleven key aspects of calendars: type in years cycles of nature in days period and zone of usage 60 presence and type of cycles 10 – 1 j year discretisation 5 days 1 day number of seasons number of days in a week number of days in a common year beginning of a year 14.IX 354 387 number of days in a leap year intercalation rhythm number of months in a common an a leap year types of a month (duration) Comparison of 25 alternative calendars alternative 25 of Comparison UMR- MAP MCC / CNRS 3495 Marseille- F beginning of a day midday midnight 23h sunset sunrise ? no data 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, Inter gravissimas ) spring equinox - 11 March instead of 21 March (a drift of 10 days since Roman times) 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. <http://en.wikipedia.org/wiki/Gregorian_calendar > Gregorian calendar 3000 2000 1000 1 1000 2000 1582 01.I 365 366 x - x + x 4 100 400 Anno Domini ab Urbe condita Anno Diocletiani Julian calendar Nostri Iesu Christi 3000 2000 1000 754 1 284 1000 2000 46 +80 days 01.I ? 365 366 Babylonian calendar 3000 2000? 1000 1000 2000 1800 500 new moon 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 Sirius 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 sun 365 Japanese calendar (Taiintaiyoreki) 3000 2000 1000 1000? 2000 [645 ] [879 ] 1872-73 new moon winter solstice 354 ~20.II / 383/385 60 19 Chinese calendar (Taichu) 3000 2000 1000 1000 2000 ~2637 1929 new moon winter solstice 354 (I,II,IV) 21.I -20.II 384 (III,V) / (7 x 19) 60 19 Pre-Islamic 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 summer solstice 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 / Tibetan calendar / Babylonian calendar 19 (7 x 19) / Burmese calendar 19 (7 x 19) Chinese calendar 19 60 / / Hebrew calendar 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 Byzantine calendar 28 8 j Roman calendar (republican) Inuit calendar [ , ] 5 30 Continental Celtic Calendar (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 Rome, 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 Time granularity Behind everything simple is a huge tail of complicated Generic framework for visualising time with multiple granularities two case studies • chapel of St Anne in Southern Alps (2400 m AMSL ) France Case studies Case UMR- MAP MCC / CNRS 3495 Marseille- F Time granularity Behind everything simple is a huge tail of complicated Generic framework for visualising time with multiple granularities two case studies • belfry of an ancient town hall in Kraków, Poland Case studies Case UMR- MAP MCC / CNRS 3495 Marseille- F Time granularity Behind everything simple is a huge tail of complicated chapel of St Anne in Southern Alps • timeline visualisation • colours - types of events/processes • overall lifetime of the chapel • Gregorian calendar period Case studies Case UMR- MAP MCC / CNRS 3495 Marseille- F Time granularity Behind everything simple is a huge tail of complicated chapel of St Anne in Southern Alps • cyclic events are represented in a clock–like manner 26 VIII • meteorological seasons do not coincide with