- About Terence Tao and the Distance Ladder
I love how instead of a pi, Tao is a tau :)
I love you used Tau to represent Terrence Tao lol
the Tau creature lore drop was not one I was expecting today
Tao is Tau, nice
This 👌
I feel like explaining the “how” is what makes it memorable
- Earth
thought you were gonna say “which this margin is too narrow to contain” 😅
How ancient astronomers reasoned step by step to conclude that the Earth passed through the shadow of the Moon and not another planet in the solar system ?
Flat earthers at "Wait, that's illegal"
-
anyone else seeing the cool illusion that when you shake your phone, the dark moons in the middle seem to jiggle around?
the animation!!
“Cinema is the ultimate pervert art-form: It doesn’t give you what you desire, it teaches you how to desire.”
brown The question of in my pov is a hint at how much more knowledgeable people in the antique were. The vast distance was in some circles most likely a common place, the picture the surviving written traditions give us is necessarily very incomplete.
* How did Eratosthenes know that the Sun was so far away that its light rays were close to parallel?
I read that in cosmos by Carl sagan
at as the earth rotate we will also have a circular arc of places where the sun will be completely overhead on that day so that effect will be happening everyday what so great in tropic of cancer also at
* is it completely accurate to say that on the summer solstice, the Earth's axis of rotation is tilted "directly towards the Sun"?
Thankyou very much Grant but I still have one more doubt I am confused at what you said that when the earth's axis is in direction toward sun , then the line passing through earth center and sun will be passing through somewhere at north pole as seen in video at so if this is the case then if the earth rotates on its axis on solistic day then the line joining earth's center and sun will cross this one point I.e north pole so How is this tropic of cancer is formed ??? Shouldn't there be a single point instead of whole circle of tropic of cancer....❤btw loved the video...just beautiful
i am very confused becz how grant created that circular arc if the sun is in the same line of axis then at a single point in northen hemisphere there should be sun overhead from where does the tropic of cancer comes ??? i am very confused...
*northern hemisphere* summer solstice --> Tropic of Cancer. (for the southern hemisphere summer solstice in December it would be the Tropic of Capricorn)
* Wait, aren't there two tropics? The tropic of Cancer and the tropic of Capricorn?
* I thought the Earth wasn't a perfect sphere. Does this affect this calculation?
At you say the measurement of the circumference of the Earth is "pretty good with no technology", but Eratosthenes wouldn't have been able to measure the 7 degree angle without the gnomon, a piece of technology.
* Are the riverboat merchants and the "grad student" the leading theories for how Eratosthenes measured the distance from Alexandria to Syene?
The grad student joke really cracked me up XD
it's so wholesome to hear his "belly laugh"
Prof Tao's ominous laughter while joking about graduate students doing manual labor hits a little different, as a graduate student myself 💀😂
His laugh 😆🙏🏼
The Pure Laughter of Education-Ladder Humor ❤
That's exactly how I would expect a great mathematician to laugh
the nerd laughter is a mathematical proof that Terence Tao is a genius.
The most common theory today about measuring this distance is the use of Bematists, counting camels steps to measure distances. Camels are known to have a very constant step distance.
- Moon
At : the method used to measure the Moon's radius assumes that the Sun is at a much larger distance than the Moon itself, so that the Earth's shadow (umbra) doesn't converge. So the Moon radius has been estimated after the Sun distance......Very nice video!
Question at , how do we know that the size of the shadow of earth is twice the radius of the earth?Are we approximating that the sun is infinitely far away so all sunrays are parallel?
* How long is a "lunar month" in this context? Is it really 28 days?
Correct me if I am wrong but I believe the scanning animation at is actually going the wrong direction. Since the Earth rotates counter-clockwise (from "above") then we would see the "top" side of the moon first
If that is the case, is the animation from to
minutes, because the Moon rotates in the same direction as the spinning of Earth around its axis. The animation therefore is also moving in the wrong direction as well (related to this, the line of sight is covering up the Moon in the wrong direction to the Moon rising at around ).
I don't think it's right. looking down from the north pole, both earth rotation and moon revolution are counter clockwise.And it's widely know moon rises 50 minutes later each passing day, means it takes longer than 24 hours.
And shouldn't the line of sight animation at also rotate counter-clockwise?
It’s slightly more, not less. The moon rotates around Earth from west to east, same direction as our own rotation around the Axis
Correct me if I am wrong, but at , it's actually slightly *more* (not less as said by Dr. Tao)... It takes the moon 24 hours and 50 minutes between moon rise to the next moon rise.
* Is the time taken for the Moon to complete an observed rotation around the Earth slightly less than 24 hours as claimed?
Animation at seems to show the moon going in a retrograde orbit which is not how it actually orbits the earth.
correct? Because line of sight is scanning over the moon clockwise and moon is moving anti clockwise. Nevertheless, fantastic video, among the best on YT in general. .Just before posting this I noticed that Mr Tao posted a link (first comment) with Q&A with corrections and explanations where this is also clarified.
- Sun
I love how it does not just say “not to scale” but rather “not remotely to scale” even when it is more accurate than most science text books.
τ has such a concise way of speaking
This is why I Love learning new things.. was watching the background and have always wondered how people figured this out. At I yelled out "I see" when you moved the right angle.. I got it.
"as your lovely illustration will show" how nice that he has so much confidence in you!
"As your lovely illustrations will show..." One of the most awesome things you see here is just the mutual respect they have for each other, Terence and Grant. It really does show how important cooperation is in the sciences and mathematics
At wouldn't Tangent of the angle be the one to use here? Since sine of the angle equals the side opposite divided by the hypotenuse, meaning the distance between earth and moon divided by the distance between moon and sun. I thought tangent was opposite divided by adjacent, meaning distance between earth and moon divided by distance between earth and sun. If you use: tan(angle)=Dm/Ds and solve for Ds you get: Dm/tan(angle)
random trig question but, why are we able to know the theta angles are the same here?
hours - due to the motion of the Earth around the Sun (or the Sun around the Earth, in the geocentric model). [A similar correction needs to be made around , using the synodic month of 29 days and 12 hours rather than the "English lunar month" of 28 days (4 weeks).]
That value when calculated is coming about 18 minutes not 30 minutes as stated in the video
* I plugged in the modern values for the distances to the Sun and Moon and got 18 minutes for the discrepancy, instead of half an hour.
they had water clocks also
@ I'd like to here more about how the "30 minutes between (we see half) and (moon is halfway around its orbit)" was measured. In theory you can do it with a clock and a VERY precise examination of the Moon's surface, such that you know precisely what landmarks lay on its exact half, and then with a clock you know exactly where it is relative Earth. But even then, I'd imagine the terminator is not a clear line, and of course there are limits to telescopes' resolving capability. Ofc 1 arcsecond resolution isn't that hard to achieve at visible wavelengths, so maybe it's easier than I think. The error is OOM 1 part in 100 with a good telescope so nevermind I answered my own question.
- Heliocentrism in Antiquity
if complete lunar and solar eclipses didn’t exist, would it be much harder to figure out all these distances? how else would we get to the part at about the distance to the sun? (just halfway through watching gotta jot this note down)
For his time, why would he be inclined to say that a smaller object MUST orbit a larger object ?? It wouldn't be for much later when Galileo finds the moons of Jupiter, but even then: you couldn't conclude definitively that it is always the case based on such a low sample of observations. It wouldn't be until Newton that we link gravitational forces to orbits... (no?)
Ive wondered the same issue for yearsBut the graphics don't explain it tooIf we're rotating away , how our view doesn't shift?!Where are constellations located then?Thx
was honestly an incredible moment to ponder about, because it’s that counterargument against the heliocentric model that sets up just how big the universe is. Imagine being one of the first people connecting the dots that the heliocentric model is actually true, but the constellations not moving as the Earth orbits the Sun is also approximately true.
which song is playing at this point?
dude, WHERE IS THAT?!!!
* Could the parallax problem be solved by assuming that the stars are not distributed in a three-dimensional space, but instead on a celestial sphere?
@ could it not also have been true that the constellations were in a single, uniform layer? Almost like a very slow moving cloud that is just moving too slowly for us notice, or a feature of a boundary that we only see parts of
This actually shows how the often quoted "extraordinary claims require extraordinary proof" doesn't necessarily invalidate a claim. And also serves to show nescience doesn't stem from ignorance but can very well come from a place of logic
"it shows you that even when you get the maths right, you don't necessarily get to the truth...." — Terry Tao
- Kepler’s genius
This was not made so clear in our discussions or in the video (other than a brief glimpse of the timeline at ), but Eratosthenes's work actually came after Aristarchus, so it is very likely that Eratosthenes was aware of Aristarchus's conclusions about how distant the Sun was from the Earth. Even if Aristarchus's heliocentric model was disputed by the other Greeks, at least some of his other conclusions appear to have attracted some support. Also, after Eratosthenes's time, there was further work by Greek, Indian, and Islamic astronomers (such as Hipparchus, Ptolemy, Aryabhata, and Al-Battani) to measure the same distances that Aristarchus did, although these subsequent measurements also were somewhat far from modern accepted values.
it amazes me how whatever documentary, paper or history books, they love to "jump ahead" from about 0 BCE to 1600.. Isn't it wonderful how every genius and wonderful guy suddenly pops after the 15th century ? weird that from 500bce to 1500 it was the golden age of the most valuable civilzation that world has seen, the Islamic golden age. but no, newton suddenly found everything, and kepler as well
* Did nothing of note happen in astronomy between Eratosthenes and Kepler?
"Each time you take that next step, it's always heroic"Incredible quote.
Why are you using a portrait of Kepler that's been known to be a fake for years? 😒
days" for the earth to go . Isn't it like 365.25 since we have to add a a day every 4 years unless the year is divisible by 100? I think there's even another rule that comes after that but point being it's not exactly 365, it's *about* 365 :P
* Isn't it tautological to say that the Earth takes one year to perform a full orbit around the Sun?
* How did Copernicus figure out the crucial fact that Mars takes 687 days to go around the Sun? Was it directly drawn from Babylonian data?
- One small correction, the majority of Copernicus’s data was from Islamic (Arab/Persian) astronomy, not Babylonian.
you know how many times I have studied this Keppler thing but couldn't get it into my thick head, and now with this animation I finally got it??? My eyes welled up with tears. Thank you thank you thank you THANK YOU!!!
every time i hear about this theory i wonder and ask if anyone knows why 'that' order of platonic solids for the ratios? why not most faces to fewest, or vice-versa?
* What is that funny loop in the orbit of Mars?
* Can you elaborate on how we know that the planets all move on a plane?
Technically, these are two times when the technique of triangulation fails to be accurate; and also in the former case it is extremely difficult to observe Mars due to the proximity to the Sun. But again, following the Universal Problem Solving Tip from , one should initially ignore these difficulties to locate a viable method, and correct for these issues later.
* Can one work out the position of Earth from fixed locations of the Sun and Mars when the Sun and Mars are in conjunction (the same location in the sky) or opposition (opposite locations in the sky)?
h () to complete the full circle. However Moon is also moving in the same direction around Earth and during that 24 h it moves 1/27,3 of full circle. So the Earth has additional 24 h/27,3 to move to catch up or cca 50 minutes.
As a modern astrophysics PhD student I really shouted 'omg' and had goosebumps when I see at how the ellipse orbit of the earth was derived....
Damn! That was so genius! What a madlad!
From childhood, I have always curious in how astronomer use star's position to calc things out, as they are circled around earth, they do not stay in a flat coordinate system in my poor imagined space, when we are in earth, they stay at our front and back, left and right, it also hard to image how to solid record those things down. I never really dig into it, even though, every time I read some articles about solar system, black hole in central of galaxy, it make me feel ill to imagine how to record those things down, and how to calc some position out by those records. I really want to support this video in some worshipful ways, just for this 's "This is a genius thing". To know that this is a genius thing to figure out how to use those wired records, make me feel so comfortable and release, that make my stupid be acceptable!
How did they know about the 687 days of Mars' orbital period?
* So Kepler used Copernicus's calculation of 687 days for the period of Mars. But didn't Kepler discard Copernicus's theory of circular orbits?
* Did Brahe have exactly 10 years of data on Mars's positions?
years, but with many gaps, due both to inclement weather, as well as Brahe turning his attention to other astronomical objects than Mars in some years; also, in times of conjunction, Mars might only be visible in the daytime sky instead of the night sky, again complicating measurements. So the "jigsaw puzzle pieces" in are in fact more complicated than always just five locations equally spaced in time; there are gaps and also observational errors to grapple with. But to understand the method one should ignore these complications; again, see "Universal Problem Solving Tip #1". Even with his "idea of true genius" (which, incidentally one can find in Einstein's introduction to Carola Baumgardt's "Life of Kepler"), it took many years of further painstaking calculation for Kepler to tease out his laws of planetary motion from Brahe's messy and incomplete observational data.
The animation from to
: the points on earth's orbit seem to cluster closer together near the perihelion and spread out at the aphelion, isn't it meant to be the other way round to conserve Copernicus' rule on equal area for equal time intervals?
We can hardly imagine the immense effort and brilliance it must have taken for them to collect, store, share, and analyze such vast amounts of data. The mathematics we take for granted today looked entirely different back then, and they lacked the standardized units, precise tools, and advanced technology that we now rely on. Despite these challenges, their determination, intellectual drive, and hunger for knowledge must have been extraordinary.
- Where this leaves us
The sad part is here
