The History of Time

Gabrielle Birchak/ September 2, 2025/ Ancient History, Archive, Enlightenment, Future History, Modern History, Post Classical, Protohistory

It’s time! Yes, today is about time. It’s about how humans began mea­sur­ing it, how we came to live our lives by it, and why it’s struc­tured the way it is in our cur­rent time. Wel­come to Math! Sci­ence! His­to­ry! I’m Gabrielle Bir­chak, and I have a back­ground in math, sci­ence, and jour­nal­ism. And today we’re going to take the time to learn about time! 

What time is it? Sim­ple ques­tion, right? You prob­a­bly glanced at your phone or your kitchen microwave. But what if I told you that the way we tell time, the tick­ing sec­onds, the 60-minute hours, the 24-hour day, the 7‑day week, isn’t nat­ur­al at all. In fact, it’s a patch­work of ancient cus­toms, astron­o­my, pol­i­tics, and religion.

Sun­di­al with a gno­mon — By John Carmichael — Own work, Pub­lic Domain, https://commons.wikimedia.org/w/index.php?curid=6748555

THE FIRST TIMEKEEPERS

Long before clocks or cal­en­dars, humans observed the nat­ur­al world. They fol­lowed the sun, the moon, and the sea­sons. These celes­tial cycles shaped their days, rit­u­als, and migra­tions. How­ev­er, once agri­cul­ture emerged around 12,000 years ago, pre­ci­sion was no longer a lux­u­ry; it was a mat­ter of survival.

By 愛喝奶茶 — Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=130245097

The sto­ry of time­keep­ing doesn’t begin with grand tem­ples or bronze mech­a­nisms; it begins in the Fer­tile Cres­cent, where peo­ple first set­tled per­ma­nent­ly near­ly 12,000 years ago, around 10,000 BCE. In what is now called Mesopotamia, a region lat­er divid­ed among Sume­ria, Akkad, Baby­lo­nia, and Assyr­ia. Here, small farm­ing com­mu­ni­ties began to emerge along the Tigris and Euphrates Rivers. This was the Neolith­ic Rev­o­lu­tion, dur­ing which humans tran­si­tioned from hunt­ing and gath­er­ing to cul­ti­vat­ing crops, domes­ti­cat­ing ani­mals, and con­struct­ing per­ma­nent homes. To plant, har­vest, and store food suc­cess­ful­ly, these ear­ly set­tlers would have need­ed some con­struct of time. They like­ly observed the sea­son­al pat­terns of the sun and stars, mark­ing cycles to guide their sur­vival long before the advent of writ­ten history.

By Apple­juice — Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=55087081

Over thou­sands of years, these prac­ti­cal obser­va­tions became sophis­ti­cat­ed sys­tems. By the Uruk peri­od (c. 4000–3100 BCE), Mesopotami­an astronomer-priests had divid­ed the sky into twelve equal zones, map­ping the sun’s annu­al jour­ney through what we now know as the con­stel­la­tions of the zodi­ac. They also devel­oped the sex­a­ges­i­mal sys­tem, or base-60 math­e­mat­ics, which is still with us today in our 60-minute and 60-sec­ond units. These divi­sions enabled them to mea­sure not just sea­sons, but increas­ing­ly small­er incre­ments of time, blend­ing astron­o­my, math­e­mat­ics, and record-keep­ing into a struc­tured worldview.

Mean­while, to the south­west, the civ­i­liza­tion of ancient Egypt was tak­ing shape. Although Egypt’s uni­fi­ca­tion under a sin­gle ruler didn’t occur until around 3100 BCE, its meth­ods of time­keep­ing were equal­ly ingenious.

Astro­nom­i­cal ceil­ing from Senenmut’s tomb, an ancient visu­al­iza­tion of celes­tial cycles and cal­en­dar rhythms, from 200 BCE. — By Neb­Maa­tRa — Own work, GPL, https://commons.wikimedia.org/w/index.php?curid=4441794

They devel­oped a 365-day cal­en­dar, divid­ing it into twelve months of thir­ty days, plus five “epagom­e­nal” days ded­i­cat­ed to the gods.[1] Using the heli­a­cal ris­ing of Sir­ius to pre­dict the flood­ing of the Nile, they divid­ed the day with shad­ow clocks and sun­di­als. They used star ris­ings at night, sim­i­lar in spir­it to Mesopotami­an decans, to mark the pas­sage of hours. Where Mesopotamia’s genius gave us the math­e­mat­i­cal skele­ton of time, Egypt tied it to the sun’s rhythm and the heart­beat of the Nile. Togeth­er, they laid the ear­li­est foun­da­tions of the sys­tem we still live by today.

The Egyp­tians were among the first to for­mal­ize time­keep­ing. Their obser­va­tions of the star Sir­ius ris­ing just before dawn helped them pre­dict the flood­ing of the Nile, a vital agri­cul­tur­al event.[2]

Hours? For that, we owe a debt to the Babylonians.

Astro­nom­i­cal trea­tise, tablet 1 of the series Mul-Apin (“the plough star”) which includes a list of the three divi­sions of the heav­ens, the dates (in the ide­al 360-day year) of the ris­ing of prin­ci­pal stars and of those which rise and set togeth­er, and the con­stel­la­tions in the path of the moon; near­ly com­plete. — By British Muse­um — British Museumhttps://www.britishmuseum.org/collection/image/152339001, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=90184887

BASE-60 AND THE BABYLONIANS

The Greeks and Romans lat­er inher­it­ed this mod­el. By the time Hip­parchus intro­duced equinoc­tial hours —12 equal parts for day and night, regard­less of the sea­son — the ground­work for our mod­ern hour was laid.

Why are there 60 sec­onds in a minute, 60 min­utes in an hour, and 360 degrees in a cir­cle? These num­bers seem arbi­trary, but they’re not. They’re part of an ancient sys­tem called sex­a­ges­i­mal, or base-60.

The sex­a­ges­i­mal sys­tem orig­i­nat­ed in Mesopotamia and was devel­oped by the Baby­lo­ni­ans. The Baby­lo­ni­ans lived over 4,000 years ago in Mesopotamia, mod­ern-day Iraq. They inher­it­ed a pow­er­ful lega­cy from the Sume­ri­ans, and among their many achieve­ments, which includ­ed writ­ing, astron­o­my, and archi­tec­ture, was a sophis­ti­cat­ed num­ber sys­tem based on the num­ber 60.[3]

Now you might be won­der­ing: why 60? Why not some­thing sim­pler, like 10 or 100?

Well, 60 is a super com­pos­ite num­ber, mean­ing it has more divi­sors than any small­er num­ber. Six­ty can be even­ly divid­ed by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. That makes it ide­al for split­ting things into parts, espe­cial­ly when you’re try­ing to divide hours, angles, or even prop­er­ty in a way that’s fair and flexible.

Imag­ine try­ing to divide an hour into two, three, four, or even five equal parts. Six­ty can han­dle that with­out messy remainders.

But the sex­a­ges­i­mal sys­tem wasn’t just about time. The Baby­lo­ni­ans used it in astron­o­my, math­e­mat­ics, and com­merce. On their clay tablets, they record­ed mas­sive cal­cu­la­tions, star charts, and even alge­bra­ic equa­tions, all in the base-60 sys­tem.[4]

One of their most famous tablets, Plimp­ton 322, is over 3,000 years old and con­tains what we would now rec­og­nize as Pythagore­an triples, sug­gest­ing they under­stood prin­ci­ples of right-angle tri­an­gles long before Pythago­ras did.[5]

And it was all writ­ten using a mix of base-60 for frac­tions and base-10 for count­ing whole num­bers. Pic­ture a hybrid sys­tem: they used a posi­tion­al num­ber sys­tem, mean­ing the place of a dig­it affect­ed its val­ue, just like we do with tens, hun­dreds, and thou­sands. How­ev­er, theirs was far more advanced than what the Greeks and Romans had.

The Baby­lo­ni­ans devel­oped a place val­ue sys­tem more than 1,500 years before we adopt­ed it with Ara­bic numer­als. They even used a place­hold­er sym­bol that act­ed a bit like our mod­ern zero. How­ev­er, it wasn’t exact­ly zero as we know it yet.[6]

Now, here’s where things get real­ly inter­est­ing. Baby­lon­ian astronomers used base-60 math to divide the cir­cle into 360 degrees, like­ly because the cir­cle was asso­ci­at­ed with the year, and there are rough­ly 360 days in a year, if you round out the solar cycle. That divi­sion of the cir­cle into 360 degrees stuck. And we still use it today in geom­e­try, car­tog­ra­phy, and navigation.

Like­wise, the Baby­lon­ian method of divid­ing time into 12 dou­ble-hours (for a total of 24 hours), with each hour split into 60 min­utes and each minute into 60 sec­onds, laid the ground­work for what became the stan­dard in Greek, Islam­ic, and lat­er Euro­pean astro­nom­i­cal tra­di­tions.[7]

Even though we now oper­ate in a dec­i­mal-based soci­ety, our cur­ren­cy, our cal­cu­la­tors, and our com­put­ers have nev­er real­ly shak­en off our Baby­lon­ian roots. Every time you glance at your watch, spin a com­pass, or mea­sure an angle, you’re whis­per­ing a thank you to the math­e­mati­cians of ancient Mesopotamia.

So, yes, base-60 might seem odd today, espe­cial­ly if you’re used to the clean sim­plic­i­ty of dec­i­mal nota­tion. How­ev­er, when it comes to divid­ing, mea­sur­ing, and map­ping the world, it turns out that 60 is a kind of math­e­mat­i­cal mir­a­cle. The Baby­lo­ni­ans didn’t just give us a clock. They gave us a world­view, shaped by stars, log­ic, and time­less ingenuity.

Repro­duc­ción del Cal­en­dario de Anzio (Fasti Anti­ates) del 84–55 a. C., expuesto en el Museo del Teatro romano de Cae­sara­gus­ta. El orig­i­nal está en Roma, en el Museo Nacional de las Ter­mas, y es ante­ri­or a la refor­ma de Julio César. Está pin­ta­do sobre un enlu­ci­do del que se hal­laron unos 300 frag­men­tos en 1915. By Bauglir — Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=52535591

THE ROMAN CALENDAR CHAOS

The ear­ly Roman cal­en­dar had only ten months, begin­ning in March. That’s why “Sep­tem­ber” means sev­en but is our ninth month today. Their sys­tem didn’t match the solar year and required con­stant tinkering.

In 46 BCE, Julius Cae­sar enlist­ed Egypt­ian astronomers to rec­ti­fy the issue. The new cal­en­dar was pri­mar­i­ly used for pos­i­tive pro­pa­gan­da about Julius Cae­sar and to aid his mil­i­tary in sea­son­al attacks. It served as a mil­i­tary guide. Still, the results helped to adjust the cal­en­dar in a more accu­rate form. The result? The Julian cal­en­dar: 365 days with a leap year every four years. It brought much-need­ed stability. 

Still, even the Julian cal­en­dar ran about 11 min­utes longer than the solar year. After cen­turies, that added up.

As a quick side note, the Gre­go­ri­an cal­en­dar was intro­duced in 1582 CE by Pope Gre­go­ry XIII as a reform of the Julian cal­en­dar. Its pur­pose was to cor­rect the drift between the cal­en­dar year and the solar year caused by the Julian system’s slight­ly inac­cu­rate cal­cu­la­tion of the year’s length. The reform includ­ed adjust­ing the leap year rule, which states that if a year is divis­i­ble by 4, it is a leap year. But there is an excep­tion to this. If it’s also divis­i­ble by 100, it is not a leap year. And there’s an excep­tion to that excep­tion; if it’s divis­i­ble by 400, it is a leap year after all. For the year 2000, if it’s divis­i­ble by 400, it’s a leap year. For the year 1900, which is divis­i­ble by 100 but not by 400, it is not a leap year. The year 2024, since it’s divis­i­ble by 4 but not 100 it’s a leap year.

This reform also realigned the cal­en­dar with the equinox by skip­ping 10 days in Octo­ber 1582. But this real­ly only applied to coun­tries that adopt­ed it imme­di­ate­ly. And adop­tion wasn’t instant. Catholic coun­tries, such as Italy, Spain, and Por­tu­gal, switched in 1582, but Protes­tant coun­tries took decades or even cen­turies to adopt.

THE CLOCKS BEGIN TO TICK

Now let’s talk about clocks.

Before clocks, time was mea­sured by the sky. Peo­ple relied on nat­ur­al rhythms: the sun ris­ing and set­ting, the length­en­ing or short­en­ing of days with the sea­sons, and the moon cycling through its phas­es. For thou­sands of years, these celes­tial pat­terns were enough. But as soci­eties grew, rit­u­als and respon­si­bil­i­ties demand­ed some­thing more pre­cise, some­thing measurable.

The ear­li­est time­keep­ers weren’t mechan­i­cal at all. Think sun­di­als, sim­ple yet bril­liant tools that use a shad­ow cast by a stick, or gno­mon, to tell the hour based on the sun’s posi­tion in the sky.[8] The ancient Egyp­tians used sun­di­als as ear­ly as 1500 BCE, divid­ing day­light into twelve equal parts. How­ev­er, these only worked on sun­ny days and not at night.

So they built alternatives.

Cte­si­bius water clock, 3rd cen­tu­ry BC, Alexan­dria (recon­struc­tion). Thes­sa­loni­ki Tech­nol­o­gy Muse­um — By Gts-tg — Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=64833363

WATER, CANDLES, AND STARS: THE PRE-MECHANICAL AGE

Enter the water clock, or clep­sy­dra, one of humanity’s old­est time-mea­sur­ing instru­ments. The ear­li­est ver­sions date back to ancient Baby­lon, Egypt, and Chi­na.[9]  These clocks worked by let­ting water drip from one ves­sel to anoth­er at a con­sis­tent rate. As the water lev­el rose or fell, it could be cal­i­brat­ed to mea­sure time inter­vals. Water clocks enabled time to be tracked after sun­set, a sig­nif­i­cant leap.

In medieval Chi­na, Su Song’s astro­nom­i­cal clock tow­er, built in 1090 CE, com­bined water-pow­ered mech­a­nisms with gears and wheels, ear­ly evi­dence of what would become clock­work machin­ery.[10]

In Europe, monks turned to can­dle clocks and incense clocks, which burned at pre­dictable rates. These weren’t pre­cise by mod­ern stan­dards, but they were good enough for sched­ul­ing prayers. And that’s key: ear­ly time­keep­ing wasn’t for the gen­er­al pub­lic. It was for reli­gious pur­pos­es, espe­cial­ly in Chris­t­ian monas­ter­ies, where monks were required to observe the Divine Office, a dai­ly sched­ule of prayers that took place at set hours through­out the day and night. As a result, monas­ter­ies became the first offi­cial keep­ers of time.

Sal­is­bury cathe­dral clock at Sal­is­bury Cathe­dral (St. Mary’s), Sal­is­bury, UK. — By Hugh Llewe­lyn from Keyn­sham, UK — Sal­is­bury Cathe­dral (St. Mary), CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=74606805

THE BIRTH OF THE MECHANICAL CLOCK

Now comes a game-chang­er: the mechan­i­cal escapement.

Around the late thir­teenth to ear­ly four­teenth cen­tu­ry, Euro­pean inven­tors began cre­at­ing devices that used weights, gears, and escape­ments to reg­u­late move­ment.[11] The escape­ment is what gave these machines their tick-tock rhythm. It allowed ener­gy to escape in con­trolled bursts, push­ing gears for­ward at a reg­u­lar rate, essen­tial­ly “drip­ping” mechan­i­cal time instead of water.

One of the ear­li­est ful­ly mechan­i­cal clocks was installed in Sal­is­bury Cathe­dral, Eng­land, around 1386. It had no dial or hands, just a bell that rang at reg­u­lar inter­vals.5 As a result, the first pub­lic clocks didn’t show time, they sound­ed it.

This made time a com­mu­nal expe­ri­ence. Imag­ine a town square where every­one lis­tens for the bell to sig­nal the start of a prayer, a meal, or the end of the work­day. Time became a shared rhythm, no longer hid­den in the stars or inside monasteries.

Prague Astro­nom­i­cal Clock — By Andrew Shi­va / Wikipedia, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=28608413

THE RISE OF THE CLOCK FACE

But soon, we want­ed more than bells. We want­ed to see the time.

In the four­teenth and fif­teenth cen­turies, clock­mak­ers began adding faces to their machines, often with only one hand, the hour hand. That was enough for dai­ly life, which didn’t demand minute-lev­el pre­ci­sion. The minute hand came lat­er, around the six­teenth cen­tu­ry, as mech­a­nisms became more refined.[12]

One of the most famous exam­ples is the Prague Astro­nom­i­cal Clock, installed in 1410. Not only did it tell the hour, but it also showed the posi­tion of the sun and moon, the zodi­ac signs, and even includ­ed ani­mat­ed fig­ures. Time wasn’t just vis­i­ble, it was the­atri­cal.7

As cities were filled with pub­lic clocks, time became cen­tral­ized and stan­dard­ized. It shaped work, trade, gov­er­nance, and dai­ly struc­ture. No longer was time some­thing inter­nal or intu­itive; it was exter­nal­ized, mea­sured, and managed.

One of the first pen­du­lum clocks designed by Chris­ti­aan Huy­gens, and his trea­tise on the pen­du­lum, Horologium Oscil­la­to­ri­um pub­lished in 1673, on dis­play in Muse­um Boer­haave in Lei­den, Nether­lands. By Rob Koop­man (Flickr pro­file) — https://www.flickr.com/photos/koopmanrob/3775343287/sizes/o/, CC BY-SA 1.0, https://commons.wikimedia.org/w/index.php?curid=10213922

THE PERSONALIZATION OF TIME

By the sev­en­teenth cen­tu­ry, advances in met­al­lur­gy and pre­ci­sion engi­neer­ing had led to the devel­op­ment of spring-pow­ered watch­es, which replaced weights and pen­du­lums. The inven­tion of the main­spring made clocks portable and personal.

The next major leap came with Chris­ti­aan Huy­gens and the pen­du­lum clock, patent­ed in 1656. It was accu­rate to with­in fif­teen sec­onds per day, a stun­ning improve­ment at the time.[13] Then came marine chronome­ters, essen­tial for nav­i­ga­tion at sea, thanks to John Har­ri­son in the eigh­teenth cen­tu­ry. They allowed sailors to cal­cu­late lon­gi­tude with pre­ci­sion, rev­o­lu­tion­iz­ing glob­al exploration.

And just like that, time went from pub­lic tow­ers to pock­et watch­es, a sym­bol of sophis­ti­ca­tion and punctuality.

By the twen­ti­eth cen­tu­ry, wrist­watch­es became wide­spread, par­tic­u­lar­ly dur­ing World War I, when sol­diers need­ed easy access to the time with­out fum­bling for a pock­et watch. The per­son­al clock was now stan­dard. Every­one had their own lit­tle tick­ing universe.

One of the first exper­i­men­tal quartz clocks, invent­ed by physi­cist War­ren Mar­ri­son around 1927 at Bell Tele­phone Lab­o­ra­to­ries. By Unknown author — Retrieved 14 May 2024 from Elec­tron­ics mag­a­zine, McGraw-Hill Co., New York, Vol.2, No.5, May 1931, p.652 with­out attri­bu­tion. Pub­lic Domain, https://commons.wikimedia.org/w/index.php?curid=148358177

TIME BECOMES DIGITAL

And then came the dig­i­tal revolution.

In 1927, the first quartz clock was devel­oped. Quartz oscil­lates at a con­sis­tent fre­quen­cy when elec­tri­fied, allow­ing for aston­ish­ing accu­ra­cy. These clocks didn’t rely on gears or pen­du­lums; instead, they used elec­tric­i­ty and crys­tal vibrations.

By the 1970s, quartz wrist­watch­es were mass-pro­duced and afford­able. The once-elite instru­ment of kings and cler­gy has become every­day technology.

Today, we live by dig­i­tal time, from our phones and com­put­ers to our microwaves and ther­mostats. We syn­chro­nize with atom­ic clocks, which count the vibra­tions of cesium atoms to define the sec­ond with unimag­in­able pre­ci­sion. What’s most fas­ci­nat­ing about atom­ic clocks is that they are so accu­rate that they only lose about one sec­ond every 100 mil­lion years.[14]

WHEN TIME BECAME VISIBLE, AND INVISIBLE AGAIN

Iron­i­cal­ly, though, as time has become more pre­cise, it’s also become more invisible.

We don’t watch clocks any­more; we get noti­fi­ca­tions. Our devices update auto­mat­i­cal­ly. Coor­di­nat­ed Uni­ver­sal Time, or UTC, gov­erns every­thing from GPS satel­lites to stock mar­kets to your smartwatch’s alarm. The tick­ing is silent now. But the num­bers are but a glow. How­ev­er, the bells have been replaced by a down­loaded ring­tone song; specif­i­cal­ly, the best-sell­ing ring­tone is T‑Pain’s “I’m N Luv (wit a strip­per).” Okee dokee then! I’m not gonna judge. 

But behind that glow­ing screen lies the work of mil­len­nia. Every tick of your dig­i­tal watch is the echo of water flow­ing in clay jars, of monks strik­ing bells, of astronomers chart­ing the stars.

Time became vis­i­ble when we learned to mech­a­nize it, to share it, to own it. And in doing so, we trans­formed how we work, think, and live. Today, we live in a dif­fer­ent time and world. Time is no longer a local affair because now we have time zones. And although it would make sense that we have 24-hour time zones because there are 24 hours in a day, we actu­al­ly have more time zones. If you are inter­est­ed in learn­ing more about our time zones, stay tuned for this Friday’s Flash­cards episode!

Louis Essen and J. V. L. Par­ry stand­ing next to the world’s first cae­sium atom­ic clock, devel­oped at the UK Nation­al Phys­i­cal Lab­o­ra­to­ry in 1955. By Nation­al Phys­i­cal Lab­o­ra­to­ry — http://www.npl.co.uk/upload/img/essen-experiment_1.jpg, Pub­lic Domain, https://commons.wikimedia.org/w/index.php?curid=5543813

THE TICK OF THE ATOM

Fast for­ward to the twen­ti­eth cen­tu­ry: Einstein’s the­o­ry of rel­a­tiv­i­ty showed that time isn’t absolute; it changes depend­ing on speed and grav­i­ty.[15] Still, for every­day use, we need­ed con­sis­ten­cy. In 1967, sci­en­tists defined the sec­ond using the cesium-133 atom. Atom­ic clocks now mea­sure one sec­ond as 9,192,631,770 oscil­la­tions of a cesium atom. These clocks run every­thing from GPS to finan­cial markets.

What this means is that when you check your phone, you’re look­ing at atom­ic time.

WHY THIS TIME STRUCTURE?

Why do we still live by 60-minute hours, 24-hour days, and 7‑day weeks? In truth, it’s less about log­ic and more about lega­cy. Once sys­tems become embed­ded across cul­tures and con­ti­nents, they become near­ly impos­si­ble to unrav­el. Even when rev­o­lu­tions occurred oppos­ing this sys­tem, such as when the French attempt­ed to dec­i­mal­ize time with 10-hour days and 100-minute hours, they failed to uproot what tra­di­tion cements. We still wres­tle with day­light sav­ing time and leap sec­onds. Still, despite its quirks and con­tra­dic­tions, the struc­ture we’ve inher­it­ed con­tin­ues to shape our lives with remark­able endurance.

Because time, as we know it, isn’t some­thing we dis­cov­ered; it’s some­thing we cre­at­ed. From sun­di­als cast­ing shad­ows in the sand to atom­ic vibra­tions mea­sured in bil­lionths of a sec­ond, human­i­ty has spent mil­len­nia sculpt­ing mean­ing from the silent flow of exis­tence. In shap­ing time, we shaped our­selves, our rit­u­als, our civ­i­liza­tions, our sense of order. So the next time you glance at the clock, remem­ber: you’re not just read­ing num­bers. You’re touch­ing thou­sands of years of human curios­i­ty, inge­nu­ity, and tra­di­tion. You are in sync with his­to­ry, liv­ing in the same great con­tin­u­um as the count­less lives that came before you. And in that moment, the choice is yours: to let time pass or to seize it. That being said, carpe diem, my friends!


[1] Geller, Mark, and Mark Ronan. 2014. “Friberg’s Remark­able Col­lec­tion of Baby­lon­ian Math­e­mat­i­cal Texts.” Wiener Zeitschrift for Die Kunde Des Mor­gen­lan­des 104: 233–40.

[2] Rob­son, Eleanor. 2008. Math­e­mat­ics in Ancient Iraq: A Social His­to­ry. Prince­ton Uni­ver­si­ty Press. https://doi.org/10.2307/j.ctv10qqzk0.

[3] Geller, Mark, and Mark Ronan. 2014. “Friberg’s Remark­able Col­lec­tion of Baby­lon­ian Math­e­mat­i­cal Texts.” Wiener Zeitschrift for Die Kunde Des Mor­gen­lan­des 104: 233–40.

[4] Rob­son, Eleanor. 2008. Math­e­mat­ics in Ancient Iraq: A Social His­to­ry. Prince­ton Uni­ver­si­ty Press. https://doi.org/10.2307/j.ctv10qqzk0.

[5] Neuge­bauer, Otto. The Exact Sci­ences in Antiq­ui­ty. Dover Pub­li­ca­tions, 1969.

[6] Ifrah, Georges. The Uni­ver­sal His­to­ry of Num­bers: From Pre­his­to­ry to the Inven­tion of the Com­put­er. Wiley, 2000

[7] Toomer, G.J. “Hip­parchus.” In Dic­tio­nary of Sci­en­tif­ic Biog­ra­phy, edit­ed by Charles C. Gillispie. Scribner’s, 1970.

[8] Whitrow, G. J. 1989. Time in His­to­ry : Views of Time from Pre­his­to­ry to the Present Day. With Inter­net Archive. Oxford ; New York : Oxford Uni­ver­si­ty Press. http://archive.org/details/timeinhistoryvie0000whit.

[9] Aveni, Antho­ny F. 2002. Empires of Time : Cal­en­dars, Clocks, and Cul­tures. With Uni­ver­si­ty Press of Col­orado. Boul­der, Colo. : Uni­ver­si­ty Press of Col­orado. http://archive.org/details/emporesoftimecal00anth.

[10] Need­ham, Joseph. Sci­ence and Civ­i­liza­tion in Chi­na, Vol. 4: Physics and Phys­i­cal Tech­nol­o­gy. Cam­bridge Uni­ver­si­ty Press, 1965.

[11] Dohrn-van Rossum, Ger­hard. His­to­ry of the Hour: Clocks and Mod­ern Tem­po­ral Orders. Uni­ver­si­ty of Chica­go Press, 1996.

[12] Lan­des, David S. Rev­o­lu­tion in Time: Clocks and the Mak­ing of the Mod­ern World. Har­vard Uni­ver­si­ty Press, 1983.

[13] Huy­gens, Chris­ti­aan. Horologium Oscil­la­to­ri­um. Paris, 1673.

[14] Nation­al Insti­tute of Stan­dards and Tech­nol­o­gy (NIST). “How Accu­rate Are Atom­ic Clocks?” 2024.

[15] Ein­stein, Albert. Rel­a­tiv­i­ty: The Spe­cial and the Gen­er­al The­o­ry. 1916.

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