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How was the size of Earth first measured? (2015)
- dataflow 3y ago> the distance from Alexandria to Syene -- believed to have been about 515 miles Even this part sounds amazing to me. How did they measure distances this long back then?
- postmodest 3y agoLand along the Nile was heavily surveyed, yearly, to ensure its course changes were recorded in landownership. > Long distances were measured by professional distance walkers, called bematists, who walked at a very regular pace and counted each step. Shorter distances were measured with lengths of knotted rope by men called harpedonaptai, which means “rope stretchers” https://www.maa.org/press/periodicals/convergence/eratosthenes-and-the-mystery-of-the-stades-distance-from-alexandria-to-syene https://www.maa.org/press/periodicals/convergence/eratosthen...
- pomian 3y agoStaking claims, where corner posts were placed at half kilometer intervals, were usually paced on foot, estimating for canyons, stream crossings, and other diversions. Some claims were continuous up to 20km by 20 km. This was in complete wilderness, in the Yukon, British Columbia and so on. Pre GPS. Not that long ago! They used topographic maps for reference. It is amazing how accurate the claims were, when transferred to modern mapping systems.
- njarboe 3y agoImagine what it took to make the highly accurate topo maps they relied on.
- jiggawatts 3y agohttps://en.wikipedia.org/wiki/Great_Trigonometrical_Survey https://en.wikipedia.org/wiki/Great_Trigonometrical_Survey
- ralferoo 3y agoA very long piece of string.
- gtfoutttt 3y agoThat was for putting back the farm claims along the Nile. Professional rope stretchers did that. This was paced.
- xorbax 3y agoAnd well enough that they ended up only a couple percent off
- deleted 3y ago[deleted]
- kemotep 3y agoI heard it was using a military unit’s standard marching pace to calculate the distance. Here is a wonderful video of Carl Sagan explaining it[0]. [0]: https://youtu.be/G8cbIWMv0rI?si=uRdlxGqBxxDTkUj6 https://youtu.be/G8cbIWMv0rI?si=uRdlxGqBxxDTkUj6
- Zetice 3y agoWe covered this literally this week in my intro to astronomy class, my prof said he paid a guy to walk the distance and measure it out.
- mcdonje 3y agoClassic Carl Sagan clip relaying this story: https://m.youtube.com/watch?v=8hZl3arO7SY https://m.youtube.com/watch?v=8hZl3arO7SY
- deleted 3y ago[deleted]
- extragood 3y agoThis article had one detail that was not included in the video that had always bugged me. Carl says "how could it be .. that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria". That seemingly requires coordination between 2 people across a vast distance and accurate time measurement. I rationalized that it could be accomplished with people at each location, each with a sundial, making records of shadow length, and later comparing their measurements, but it still seemed like a messy explanation. The detail of no shadow at the zenith on a specific day solves that problem. That removes the complication of the coordination of 2 observers and the lighting of the well better explains why the phenomenon was noticed to begin with. The other unresolved problem for me is that it still requires the assumption that light is parallel i.e. the sun is (relatively) incomprehensibly far away, and that was not established fact at the time afaik.
- andrewmutz 3y agoAnother way to word it would be "the shortest shadow of the entire day"
- extragood 3y agoI think that approach might only work if both locations are directly north/south from each other, unless I'm thinking about this wrong. If the locations are east/west relative to each other, the shortest shadow won't occur at exactly the same moment. edit: I guess that would still be a problem if you're using the zenith to determine the time of measurement. The best map I can find of the 2 locations used is [here](https://mathigon.org/step/circles/eratosthenes https://mathigon.org/step/circles/eratosthenes) and seems to indicate that Alexandria and Swenet/the other location are relatively north/south to each other. edit 2: some more thoughts. If 2 points at the same latitude but on the opposite sides of the world were chosen, Eratosthenes method wouldn't have worked. The sun would have the same position in the sky at the zenith, but they'd be separated by thousands of miles, implying a flat world. Whether by design or luck, it seems that Eratosthenes experiment only works if the same longitude is used for each location, and otherwise he would have arrived at a very different answer for the circumference of the earth.
- kkylin 3y agoEratosthenes was (IMO) pretty amazing in the range of interests and accomplishments: https://en.wikipedia.org/wiki/Eratosthenes https://en.wikipedia.org/wiki/Eratosthenes His name came up recently on another post on a very different topic: https://news.ycombinator.com/item?id=37236099 https://news.ycombinator.com/item?id=37236099
- politelemon 3y agoI had always associated him with the earth's measurement and didn't know the others. It was great reading through all the other things this person had done in his time including mapping the known world, and the prime number sieve. A truly fascinating polymath, it must have been so satisfying to identify previously unsolved problems, and come up with a solution for them that were more or less 'good enough'. I wonder what he would have made of the way we are today, or if he were born in this era, what kinds of problems he'd have identified that needed solving.
- deleted 3y ago[deleted]
- xattt 3y agoGiven the large distance between the cities, how did they communicate to confirm that the sun was indeed overhead at particular time and date?
- vermooten 3y agoThank you! I've wondered that, can't wait to see what he answer is.
- NeoTar 3y agoI don't know whether this is true, but I think I've heard it said in connection with this story. Egypt had a solar based-calendar, so (to a decent approximation) on every named date the sun would be in the same place in the sky. So all that would be needed was for it be known that the sun shined straight down the well on (for instance) the 14th day of the 2nd Month of Growth (I had to look up the Egyptian calendar to get that date!), and Eratosthenes just needed to measure on that date.
- ithkuil 3y agoThe trickiest part was to know the effective distance component in the North/South direction. Luckily the Nile is roughly oriented that way anyway so the distance between the two cities is roughly the same as the North/South component
- soneil 3y agoThe communication requirements are minimal. The only real requirement is that we agree on which day to perform the measurement. You and I could sit at Christmas dinner, and conspire to measure the shadow of a 1metre pole at solar noon on Easter Sunday, at our respective locations. We could then compare those measurements when we meet next Christmas.
- Sharlin 3y agoWell, the time is obviously noon by definition(*), and the date would have been well known as it's entirely predictable. Syene is about a degree or so north of the Tropic of Cancer, so essentially the only date the sun is in the zenith is the summer solstice, and that’s the day they should measure shadow length in Alexandria. Had it been farther to the south, there would have been two such days, still well known and understood by the people of the time, and had been for millennia, and it wouldn’t matter which of the days you’d pick. (*) This was 2000 years before time zones became a thing and local solar times were disengaged from the wallclock time. Not that ancient Greeks had wallclocks.
- bryan0 3y agoTerrence Tao has an old excellent presentation on the “cosmic ladder” which shows how from this measurement you can build up to measure the largest distances in the visible universe: https://terrytao.files.wordpress.com/2010/10/cosmic-distance-ladder.pdf https://terrytao.files.wordpress.com/2010/10/cosmic-distance...
- 082349872349872 3y agoWow, TIL the reason Aristarchus' contemporaries didn't accept his heliocentric model...
- nico 3y agopages 156-158: “Ironically, when Aristarchus proposed the heliocentric model, his contemporaries dismissed it, on the grounds that they did not observe any parallax effects...” “ so the heliocentric model would have implied that the stars were an absurdly large distance away.” “[Which, of course, they are.]”
- StackOverlord 3y agohttp://homework.uoregon.edu/pub/emj/121/lectures/tycho121.html http://homework.uoregon.edu/pub/emj/121/lectures/tycho121.ht... > Tycho Brahe (1546-1601) proposed an experiment that would determine whether or not the earth goes around the sun. Basically, if the Earth orbits the sun, nearby stars should periodically "move" back and forth in their position with respect to more distant stars every 6 months. If the Earth was stationary (at the center of the Universe, this wouldn't occur.
- DiogenesKynikos 3y agoYes, but historically, scientists ended up accepting the heliocentric model long before the first stellar parallax was measured. The heliocentric model's parsimony (explaining many different phenomena, such as retrograde motion of the inner planets, with the fewest assumptions) and various supporting observations (such as Venus' phases, which rule out any strictly geocentric model), combined with a physical theory that grounded the model (Newton's laws) rendered any alternative implausible by the late 1600s at the latest. It would be nearly 200 years before parallax was first detected.
- helsinkiandrew 3y agoReminds me of the Cavendish experiment to measure the Earths mass in 1798 which got to within 1% if the correct value (or the currently accepted value) https://wikipedia.org/wiki/Cavendish_experiment https://wikipedia.org/wiki/Cavendish_experiment
- DoughnutHole 3y ago> He had heard that in the nearby town of Syene midday sunlight shines straight down to the bottom of deep wells “Nearby” is an interesting descriptor for a town 515 miles away. Syene was basically the town furthest up the Nile in Egypt. You literally couldn’t get any further from Alexandria and still consider it Egypt.
- Simon_O_Rourke 3y ago[flagged]
- mturmon 3y agoDownvoted, but valid. I would claim that Ugg’s effort counts as a lower bound on the size of the Earth, and is therefore a legitimate constraint on true measurement. This bound might even be sufficient for some purposes. It also seems like ancient mariners should have been able to use the visible arc of the horizon to get a rough guess, long before Eratosthenes. All we are really arguing about is, how good are the error bars?
- bedobi 3y agoI always struggled (and still struggle) with math. A couple of years ago, randomly browsing YouTube, I came across this home made video asking how they figured out the distance to the moon before modern technology. The host starts out small scale showing he can calculate the distance to things in his back yard using trigonometry and then scales it up to the moon. My mind was blown, because no one ever told me that. It was simple, anyone could understand it. When I was in school, all I was told was to memorize abstract formulae like calculating the length of sides of triangles based on angles and known length of one side. It was never contextualized to any actual, let alone interesting or fascinating, applications.
- grog454 3y agoI had a similar experience earlier in my education. "Learning" sine and cosine was nothing compared to understanding it well enough to use in a 2d game. I went from struggling with standard algebra classes to getting 5s on AP Calculus BC and Physics.
- mhuffman 3y agoWhich video?
- bedobi 3y agoHarder to find than it should be due to YouTube enshittification of their search but https://youtu.be/ohdysfFWO4w?si=iEz-HcFabRFc1kID https://youtu.be/ohdysfFWO4w?si=iEz-HcFabRFc1kID
- deleted 3y ago[deleted]
- politelemon 3y agoI think you've highlighted well an outcome of the modern drive to "learn to pass exams" in many places. The original intention to "learn" has been lost or corrupted over time in a multi-century gradual example of Goodhart's Law in action.
- jasonwatkinspdx 3y ago
- irrational 3y agoI have to wonder what he thought when he got his answer. Was it much bigger than he thought? Did he wonder what was on the other side?
- dylan604 3y agoI'm glad I'm not the only one where my mind splits from the rest of the group and goes off in tangential directions. One of the video links here explaining triangulation to calculate distances showed examples with one of the grand canyon measurements. I stopped paying attention, and started wondering what the first person to find the grand canyon thought. "shit, I guess we've got to go around THAT!?!?"
- jheriko 3y agoThis is in every encyclopedia ever... I'm amazed when people don't know this (!) Next we will hear about Ptolemy... then Galileo :)
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- simonh 3y agoYou need to read this. https://xkcd.com/1053 https://xkcd.com/1053
- willis936 3y ago"First" is awfully confident assertion about an event thousands of years ago. "Earliest known" is more accurate.
- deleted 3y ago[deleted]
- crazygringo 3y agoDoesn't "earliest" already imply "earliest known"? Since obviously we can't assert anything not known.
- willis936 3y agoIt doesn't imply it, no. There is an absolute true "first human measurement of Earth's size" and it is not fundamentally unlearnable at this point in history. It's just very difficult to prove and we are far from the due diligence necessary for such an extraordinary statement. It should be properly qualified until we piece together a pretty complete picture of lost civilizations.
- crazygringo 3y agoOf course it's fundamentally unlearnable. No matter what we do know, we can never prove there wasn't someone else who figured it out even earlier but never wrote it down, or they did but it and all references to it were lost. Most "firsts" carry an implicit asterisk that isn't worth mentioning. The first person to run a 4 minute mile did so in 1954. With the asterisk that somebody else might have already done that millennia ago but didn't have a stopwatch. And we'll never know.
- willis936 3y agoIn that case then "earliest known" is the only thing that should ever be said and there is no justification for claiming "first".
- zaps 3y ago[flagged]
- BreadPants 3y agoTechnically we don't know how it was first measured and probably never will. The earliest evidence of the Earth's measurements is the Pyramids and good luck finding out how those were built.
- YeBanKo 3y agoWhy are Pyramids the first evidence of Earth’s measurements?
- ahazred8ta 3y agoThere are crackpots who think the builders of the Great Pyramid knew the size of the Earth. https://www.hallofmaat.com/numerology/a-critique-of-graham-hancocks-forced-numerical-relationship-between-the-great-pyramid-of-giza-and-earths-dimensions-1/ https://www.hallofmaat.com/numerology/a-critique-of-graham-h...
- StackOverlord 3y agoYou can get to the absolute dimensions of the pyramid from the crackpot equations though: https://pasteboard.co/cIMzn8KktEZy.png https://pasteboard.co/cIMzn8KktEZy.png https://tobeornottobe.org/the-great-pyramid-intro/math-constants/ https://tobeornottobe.org/the-great-pyramid-intro/math-const... https://pastebin.com/TsUtcWAa https://pastebin.com/TsUtcWAa I just found a great recap on this topic that also fits nicely with the points your link brings up, shedding a better light on the number 43,200 in other cultures (the scaling factor between the pyramid and the earth dimensions for those who TL;DR). https://fossana.medium.com/the-pyramids-of-giza-have-properties-and-contain-information-that-would-have-been-beyond-the-means-f003be2c9c64 https://fossana.medium.com/the-pyramids-of-giza-have-propert... It also addresses the fact the speed of light in m/s is encoded three times in the pyramid, twice in the dimensions, in cubits and meters, and another times via the GPS coordinates (yes 3 fucking times !). But how would they know about the duration of a second ? I don't know ! What I know is that 43,200 * 2 = 84,600, the number of seconds in a day. The thing goes deeper with this man and his investigations of the first edition of Shakespeare's Sonnets. https://www.youtube.com/watch?v=0xOGeZt71sg https://www.youtube.com/watch?v=0xOGeZt71sg https://www.youtube.com/watch?v=nIS-hNrr0-c https://www.youtube.com/watch?v=nIS-hNrr0-c
- divbzero 3y ago5% error is incredible. I wonder what Eratosthenes thought of his own measurement. Did he believe it was accurate? Or questioned if unknown factors could have thrown off his calculation?
- oxygen_crisis 3y agoHe measured it in "stadia" and there was no consensus about exactly how long a stadion was. The definitions ranged widely, from ~150m to ~210m. The low error assessment comes from magnanimously (but baselessly) choosing to use the definition of a stadion which assigns Eratosthenes the lowest error. https://en.wikipedia.org/wiki/Stadion_(unit) https://en.wikipedia.org/wiki/Stadion_(unit)
- whatshisface 3y ago>An empirical determination of the length of the stadion was made by Lev Vasilevich Firsov, who compared 81 distances given by Eratosthenes and Strabo with the straight-line distances measured by modern methods, and averaged the results. He obtained a result of about 157.7 metres Sounds like there are other lengths given by Eratosthenes which could be used to tell what he meant by one stadion.
- deleted 3y ago[deleted]
- DiogenesKynikos 3y agoEven if he only measured Earth's radius with 50% accuracy, that's still pretty impressive for the 2nd Century BC.
- ghaff 3y agoA woman from my small town was one of the folks who originally explored the Cepheid variables which would end up as sort of a cosmic yardstick. I saw a couple plays about this a few years ago. https://freedomsway.org/story/henrietta-swan-leavitt/ https://freedomsway.org/story/henrietta-swan-leavitt/
- MilStdJunkie 3y agoThe Greeks (or, more precisely, the Eastern Mediterraneans, since a ton of these guys were Phoenician) were jaw-droppingly awesome at this stuff. I wish I could have seen it. It makes you wonder how much knowledge from other places - places with wetter climates, and/or further from the colonial powers of the 19th C - has been lost. One of the contributing reasons heliocentrism disappeared from view was that a large quantity of the Pythagorean and Neo-Pythagorean texts were systematically destroyed. When the texts from Umayyad Spain were translated back in Italy, there were simply very few heliocentric-themed writings among them. It's somewhat remarkable we even got mention of Anaxagoras and Aristarchos. There's a growing suspicion among some in physics, so far as I can tell from my layman's chair, that many qualities like distance (i.e., the spatial dimensions) could be emergent phenomenon, resulting from a sort of bulk degree of freedom exhibited in macro structures (aka "Space from Hilbert Space"). It's an evocative notion, along with MOND and LQC and suchlike; it sometimes does rather seem like we're looking with the wrong set of eyes, or, rather, assuming things we perhaps shouldn't assume. I wish I had a time machine to, say, 2523, to see how this all resolves. How does it interact with the measurement methods cited in this presentation? Whether the cosmos is far larger than we think, or far smaller, or - perhaps most likely - that the thought of a cosmos being "larger" or "smaller" was an absurd starting point to begin with.
- thechao 3y agoI had a history prof address these feats-of-observation of these primordial scientists: you've got a group of totally idle wealthy, with up to 16 hours of day time to fill, across millions of people and thousands of years. Eratosthenes could've thought about this problem — and nothing else — for a thousand hours in just six months, with plenty of time off to pursue other hobbies. When's the last time you dedicated 1000 hours to a single problem?
- MilStdJunkie 3y agoAbsolutely! That's absolutely a prerequisite for these periods of very sudden advancement. Look at the 19th century! Very nearly the entire world's capacity was pulled into a very small geographic area, which then made the modern world. It's a bit depressing because of the brutality that's involved, but let's not write off Europe and Greece quite so quickly. There's plenty of powers in world history that established a similar level of "excess capacity" re: labor but didn't engage in anything that could be interpreted as "societal advancement". England, during the rise of its supremacy, decided to end slavery. Yeah yeah yeah I know - there were very good realpolitik reasons for this, and England over the centuries has had some very good PR agents, but in the end, they did it. The Enlightenment was, compared to the theocratic/autocratic fusion of the early modern era, an advancement[1]. I'll die on that hill. It wasn't possible without the blood and labor of countless aboriginal peoples, who we should honor in the same proportion, of course. [1] There's some disagreement about this in the current era, which I won't express an opinion on. "Palingenesis" is an applicable cautionary term.
- fwungy 3y agoWhat is the sun was smaller and closer than we think? One could sew the same result in that instance.
- drpixie 3y agoUnless the sun was VERY close, the actual distance doesn't matter. What matters is that the sun (or a star, or whatever you use as a reference) is so far away that there is no practical difference between "far away" and "even further". For practical purposes, we treat the sun as being an infinite distance away, and the error caused by it being ONLY 93,000,000 miles away is much smaller than Eratosthenes could measure :) It's similar to drawing perspectives, you draw perspective lines to join at the distant horizon. You don't care how far to the distance horizon. (Those ancient Greeks had amazing understanding of geometry. Much better than most of us.)
- alehlopeh 3y agoGood answer but weirdly judgy last sentence. More like, a handful of ancient Greeks had a better understanding of geometry than most of us, just like a handful of us has a better understanding of geometry than most of us. And of course, a handful of us has a better understanding of geometry than most ancient Greeks.
- drpixie 3y agoDidn't mean to come across judgy :( Apparently the ancient Greeks didn't have much, if anything, in the way of symbolic algebra or calculus - what we mostly think of as "maths". Instead their normal tool for mathematical logic was geometry. An educated Greek would have used geometry much like we use algebra. For most of us, given a non-maths problem (eg physics, chemistry, almost anything in real life...) the first thing we do is express it as an algebra problem, and solve that. The ancient Greeks used geometry in a similar way.
- andrewprock 3y agoThe podcast Song of Urania does a super deep dive into the history of astronomy, including this specific measurement. One of the insights the podcast brings to light is that there were many such estimates; relative size of the Earth, Moon and Sun - distance to the Moon, etc. By reviewing the distribution of these estimates, and the methods applied, the host of the podcast suggest that Eratosthenes was lucky to get quite so close. https://songofurania.com/ https://songofurania.com/
- jan_Sate 3y agoThis estimation method would only work under the assumption that earth is a spherical. Now that we do know that it's a sphere. But how could you figure that out back in 2000 years ago?
- kemotep 3y agoThat’s the entire thing! He read an account of a city so many miles away from where he was that on a specific day of the year had no shadows at noon. On that day in his city, shadows still were cast. If there was no discrepancies in the shadows that would make sense for a flat earth. But the discrepancy made him determine it had to be sphere and then he went out and calculated the circumference.
- zeroimpl 3y agoHuh? If I put a lightbulb above something, the place it’s above won’t have shadows, but there will be shadows at places that aren’t directly underneath.
- kemotep 3y agoOnly places near the equator will be parallel with the sun. Anywhere else, because the curve of the earth, there will always be an angle, and thus even at high noon on the summer solstice, there are still shadows in Alexandria. So I don’t understand your analogy. It doesn’t apply because the earth isn’t flat.
- taneq 3y agoBecause spheres are the best Platonic solid and so Earth must be a sphere, naturally.
- HWR_14 3y agoSpheres aren't Platonic solids.
- 3y ago
- demondemidi 3y agoHow did Eratosthenese synchronize the measurements? That seems like the biggest challenge: sync'ing two clocks and transporting one to a place 500 miles away without losing time? 2000 years ago?
- metacritic12 3y agoHe timed solar noon and travelled due north / south to avoid the time zone problem.
- anvandare 3y agoThe summer solstice ("the longest day of the year") is always the same date regardless of your latitude: June 20th/21st (in the northern hemisphere). And assuming Syene is on the same longitude as Alexandria[0], Syene's noon is Alexandria's noon. Alexandria: 31°11′51″N 29°53′33″E Syene: 24°05′20″N 32°53′59″E Tropic of Cancer: 23°26′10.4″ N [0] It isn't, which contributed to the measurement error, but close enough is good enough.
- zeroimpl 3y agoSomewhat surprised the answer isn’t based on the angle to the North Star - that’s my preferred approach and it seems less explainable by a flat earth model under assumption the stars are further than the sun
- ahazred8ta 3y agoOne calculation (75 BC) used the angle of Canopus, which was conveniently near the horizon. https://en.wikipedia.org/wiki/Posidonius#Calculation_of_Earth's_circumference https://en.wikipedia.org/wiki/Posidonius#Calculation_of_Eart...
- 31carmichael 3y agoWhat?!? The earth is flat.