[HN Gopher] How was the size of Earth first measured? (2015)
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How was the size of Earth first measured? (2015)
Author : redbell
Score : 78 points
Date : 2023-08-24 11:08 UTC (2 days ago)
(HTM) web link (stardate.org)
(TXT) w3m dump (stardate.org)
| willis936 wrote:
| "First" is awfully confident assertion about an event thousands
| of years ago. "Earliest known" is more accurate.
| crazygringo wrote:
| Doesn't "earliest" already imply "earliest known"? Since
| obviously we can't assert anything _not_ known.
| willis936 wrote:
| It 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 wrote:
| Of 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.
| [deleted]
| ghaff wrote:
| A 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/
| zaps wrote:
| [flagged]
| mcdonje wrote:
| Classic Carl Sagan clip relaying this story:
| https://m.youtube.com/watch?v=8hZl3arO7SY
| [deleted]
| extragood wrote:
| This 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.
| crazygringo wrote:
| > _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._
|
| It seems like it very recently had been:
|
| https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Ar.
| ..
|
| There are some Stack Exchange questions that give more
| background:
|
| https://astronomy.stackexchange.com/questions/38892/how-
| did-...
|
| https://hsm.stackexchange.com/questions/14722/how-did-
| eratos...
|
| Pretty clever to use the illumination of the moon to figure
| it out!
| extragood wrote:
| That is clever! Thanks for sharing these. It's endlessly
| fascinating to read about how such accurate conclusions
| were made via simple observation and deduction.
| andrewmutz wrote:
| Another way to word it would be "the shortest shadow of the
| entire day"
| extragood wrote:
| I 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) 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 wrote:
| Eratosthenes was (IMO) pretty amazing in the range of interests
| and accomplishments: 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
| [deleted]
| politelemon wrote:
| I 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.
| xattt wrote:
| Given the large distance between the cities, how did they
| communicate to confirm that the sun was indeed overhead at
| particular time and date?
| Sharlin wrote:
| Well, 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.
| gshubert17 wrote:
| The key is that this phenomenon was well known and predictable.
| First get the date right, then wait until local noon for the
| sun to be at its maximum altitude. The Egyptians had long had
| excellent calendars, so they could use past records to predict
| the date.
| mytailorisrich wrote:
| They measured something at solar noon. This can be
| independently measured without communication and only requires
| to agree on the date.
|
| The key, really, was to be able to pick 2 locations on the same
| longitude and to have enough math/trigo to perform the
| calculation.
| tzs wrote:
| Note that they don't actually need to be on the same
| longitude. It just makes measuring the north/south distance
| between them a lot easier.
|
| The angle between the sun and the zenith at local solar noon
| will be the same everywhere at a given latitude so that part
| doesn't care if the cities are on the same longitude..
|
| You do need to know the north/south distance between the
| latitudes of the two cities, and picking two cities on the
| same longitude makes that easier to measure: just go straight
| from one to the other and note how far you traveled.
|
| If the longitude was substantially different you'd have to
| use spherical trigonometry to figure out the north/south
| distance from the distance and bearing of the straight route
| between the cities, and for that you need to know the size of
| the sphere you are on.
|
| Instead you'd have to do something like travel north from the
| southern city until you are at the same latitude as the other
| city (probably determined by observing the altitude of the
| North star), note how far you've traveled, then travel east
| or west along a line of constant latitude to try to reach the
| other city. If you miss the other city because you didn't get
| the latitude quite right, you'd have to move north or south,
| updating your north/south distance estimate, and try again,
| repeating until you actually hit the other city.
| vermooten wrote:
| Thank you! I've wondered that, can't wait to see what he answer
| is.
| NeoTar wrote:
| I 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.
| kwhitefoot wrote:
| You don't need to communicate in real time. You just need to
| agree on which date to do the measurement and that is
| determined by reference to the stars. Priests had been
| maintaining the calendar already for quite some time. Then you
| just wait for the sun to reach the zenith, noon. Now you can
| measure the angle of the sun from the vertical then it's
| relatively simple trigonometry to calculate the circumference.
|
| See https://en.wikipedia.org/wiki/Earth%27s_circumference
| MilStdJunkie wrote:
| The 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.
| bryan0 wrote:
| Terrence 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...
| 082349872349872 wrote:
| Wow, TIL the reason Aristarchus' contemporaries didn't accept
| his heliocentric model...
| nico wrote:
| pages 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 wrote:
| http://homework.uoregon.edu/pub/emj/121/lectures/tycho121.h
| t...
|
| > 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.
| DoughnutHole wrote:
| > 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.
| BreadPants wrote:
| Technically 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 wrote:
| Why are Pyramids the first evidence of Earth's measurements?
| ahazred8ta wrote:
| There 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-h...
| divbzero wrote:
| 5% 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?
| Simon_O_Rourke wrote:
| [flagged]
| mturmon wrote:
| Downvoted, 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?
| helsinkiandrew wrote:
| Reminds 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
| bedobi wrote:
| I 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 wrote:
| I 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.
| dylan604 wrote:
| When I was in school everyone _hated_ word problems, but to me,
| they were the most clear examples of the answer to "when will
| I ever use this". Sure, maybe you don't care that a train
| leaving New York traveling at 55mph while a car leaving Philly
| traveling at 35mph did any thing, but they were definitely real
| world examples.
|
| I had a physics teacher that had a unique way of providing
| examples that always revolved around a little monkey that he
| liked to draw on the overhead. The monkey was usually
| on/in/near a tree, and we had to use those dreaded equations to
| figure out whatever was being asked. As dorky as it was, it
| definitely helped illustrate in way it sounds you never got. I
| always enjoyed his class, and he is definitely one of the three
| teachers I had that was on a different level from the rest.
| Each of those three teachers set me on a path of where I am now
| that none of the others did.
| sgtnoodle wrote:
| I had a calculus professor that asked a physics problem on a
| quiz, and all the students that understood physics got the
| problem "wrong". It was something dumb about pulling a
| wheeled suitcase up an incline at a constant speed, and
| wanted to know the total torque on the wheels...
| mhuffman wrote:
| Which video?
| bedobi wrote:
| Harder to find than it should be due to YouTube
| enshittification of their search but
|
| https://youtu.be/ohdysfFWO4w?si=iEz-HcFabRFc1kID
| opportune wrote:
| You may be interested in an Astrophysics course. I took one in
| college taught by an Astronomy professor and was surprised most
| of the content was focused on what we could determine about
| stars, galaxies and such based on what we could measure from
| them. In retrospect that seems obvious but I guess I had
| assumed the content would be like really heavy theories of
| stellar formation or gravity or something.
|
| In my course we basically progressed from the traditional OG
| methods of measurement to increasingly sophisticated methods.
| It's amazing how much you can learn about stars and galaxies
| just from combining models of black body radiation, spectral
| lines, and red shift with the wavelengths of the light they
| emit.
| [deleted]
| jasonwatkinspdx wrote:
| Yeah, a lot of schools do a poor job of tying math to practical
| applications. And no those absurd word problems in elementary
| algebra are not what I mean. Calculus, for example, makes _way_
| more sense if it 's presented alongside physics.
| politelemon wrote:
| I 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.
| tiffanyg wrote:
| This is an unfortunately very uniform problem with "school",
| I'd say (in the US system / nomenclature) from about post-
| elementary up to "undergrad". Too much of the junior high
| school and high school classes end up as "piles of facts". The
| vast majority of attempts to improve education* never deal with
| this underlying issue, and, thus tend to just make the problem
| even worse. (Most likely, for various reasons including
| 'difficulty', attempts are made to avoid this issue.)
|
| You can impose any standards you want - if all you're training
| on and testing for is ~regurgitation of facts, that's what's
| going to be optimized for - all of the forces at play will push
| even the best of teachers (those who might try to provide
| something other than the driest most immediate-term "goal-
| oriented" course / experience) towards this terrible (minimum)
| "standard".
|
| At this point, I highly doubt this will ever be fixed - and
| certainly, can't see that happening in my lifetime. In the past
| few decades, hostility, and outright MARKETING of hostility,
| towards education has increased dramatically. Education is
| perennially underfunded and massively inequitable from locality
| to locality (and at even "finer grained" levels). Most of the
| fights around education these days are so far removed from
| questions of SERVICE and ARE WE DOING THE BEST WE CAN FOR
| FUTURE GENERATIONS? that there's just no way to imagine any
| serious or appropriate attempt can be made to address the real
| inadequacies of our recent & current system.
|
| It's truly a shame. We'd all be far better off if there was
| more investment in, respect for, etc. education, teachers,
| STUDENTS (our kids), etc. Partly, this is a generational issue
| that even gets at the voting power of generations ... It is
| possible that Gen X, in part by being a smaller "generation"
| and in part because of their own experiences of being
| comparatively ignored and pushed to the side by the priorities
| of other generations [particularly, the older generations]
| across their own "lifecycles", will actually help swing things
| back a little towards student-oriented service (so-to-speak).
| But, I'm not 'optimistic' either regarding intention or, even
| more so, actual action.
|
| It's a kind of tragedy, blasting people IN THEIR FORMATIVE
| YEARS with piles of facts in such a way as to kill off INTEREST
| and the possibility of real UNDERSTANDING, guaranteeing we end
| up with a far less informed, engaged, and healthy COMMUNITY and
| PEOPLE than we might otherwise have.
|
| * Most, seemingly, quite ill-advised, unfortunately. Ill-
| advised based on research and the experiences of people who
| have spent years studying (sometimes, even, with a methodical
| empiricism!) "pedagogy" and "child psychology", and those who
| have worked on and refined models that tend to have real
| advantages (e.g., "Montessori" comes to mind - the data is
| mixed but generally supportive of the benefits of this
| comparatively grounded in science method, see, e.g.,
| https://www.nature.com/articles/s41539-017-0012-7). Part of
| this is because of various "stakeholders" engaging in the usual
| tug-of-war BS where only lip-service is paid to the actual
| target population this essential SERVICE is supposed to be
| CENTERED ON...
| dataflow wrote:
| > 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?
| Zetice wrote:
| We 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.
| postmodest wrote:
| Land 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/eratosthen...
| pomian wrote:
| Staking 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 wrote:
| Imagine what it took to make the highly accurate topo maps
| they relied on.
| ralferoo wrote:
| A very long piece of string.
| gtfoutttt wrote:
| That was for putting back the farm claims along the Nile.
| Professional rope stretchers did that.
|
| This was paced.
| xorbax wrote:
| And well enough that they ended up only a couple percent off
| [deleted]
| kemotep wrote:
| I 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
| irrational wrote:
| I 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 wrote:
| I'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 wrote:
| This is in every encyclopedia ever... I'm amazed when people
| don't know this (!)
|
| Next we will hear about Ptolemy... then Galileo :)
| simonh wrote:
| You need to read this. https://xkcd.com/1053
| [deleted]
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