TheMakeAon Hacker News • Recommends
On “Fourier Toy”
These guys are one of the reasons I love mathematics. Check this out too: link to this video Edit: Didn't realize that this was also linked to in another thread on the front page as well.
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#fourierseries#epicycles#ptolemy
Ptolemy and Homer (Simpson)
Santiago Ginnobili
3.9K subscribers • 1 video on Hallway
- Recommended by 3 people: 3 on Hacker News.
Beginner. No background in the topic needed.
379K views18 years ago3 recommendations
Computer scienceGraphics and audioMath for programmersData visualizationRendering
A short animation demonstrating how a series of epicycles can reconstruct any complex shape, illustrating the concept of Fourier series.
Reconstruction of a planet's bizarre orbit with Ptolemy's system of epicycles and deferents.Why it's here
3 people recommend thisWhat people say. Recommended as a classic and highly intuitive visualization of how Fourier series and epicycles can approximate any continuous curve.
JadeNBon Hacker News • Recommends
On “Fourier visualised”
I'm only seeing an image, with no explanation, and it took me a while to realise what it was showing; so, in case anyone else is puzzled by it, each image is the sum of the previous one with a new factor (indicated by the "wheels upon wheels"). I think that the reconstruction of Homer Simpson's face (which I think I originally saw thanks to OP ColinWright!) may be a more convincing demonstration of the power of Fourier transforms: link to this video . There's a Nautilus article about it, too: link (EDIT: and an HN post discussing that: link ).
jordighon Hacker News • Recommends
On “Opposition to Galileo was scientific, not just religious”
I tl;dr'ed the article (sorry), but I wanted to say one thing about epicycles. They are not wrong and certainly can be used to explain motion, but the problem with them is that you can keep adding epicycles to fit any continuous orbit at all (this actually is because a Fourier series can converge to any continuous periodic function). This is my favourite visualisation of this fact: link to this video
jordighon Hacker News • Mentions
On “Fourier series”
Huh, so I never though about it this way. The reason you can use epicycles to draw anything is because the trig functions form a complete orthonormal system. Because you can write a Fourier series for any piecewise continuous function, you can also draw Homer Simpson: link to this video
jerfon Hacker News • Mentions
On “Why not string theory? Because enough is enough”
…which are fixed with another epicycle. Another more subtle aspect of epicycles, real ones this time, is that they are too powerful and can be used to prove anything. You can predict the motion of the planets with epicycles, it's just that the required series is very long or infinite. And with very long series of cycles, you can "predict" anything: link to this video Thus, one of the problems with epicycles both real and metaphorical is that they are indeed not refutable. Because epicycles can predict anything, they aren't that useful; they exclude far less than meets the eye at first. It isn't hard to see that characterist showing up in string theory. The theory has for a very long time had problems wi…
mannykannoton Hacker News • Mentions
On “Opposition to Galileo was scientific, not just religious”
I cannot edit my post any more , but I can still reply to it, and it seems the answer is yes: link to this video - but you need eccentricity to get the speeds right: link (10 minutes in.) Furthermore, the result is not equivalent to the heliocentric model because it has many more parameters.
witherkon Hacker News • Mentions
On “Intriguing new result from the LHCb experiment at CERN”
If your model has a lot of wiggle room it can be consistent with anything. Maybe the solar system really does move in epicycles link to this video
whatshisfaceon Hacker News • Mentions
On “Is the great neutrino puzzle pointing to multiple missing particles?”
This isn't an elephant but it demonstrates the principle: link to this video Epicycles were originally considered a good idea because it takes exactly two circles to make an ellipse, and Kepler's laws were satisfied by such an ellipse. They were "falsified,", in the two-cycle form, when closer observations revealed that Kepler's laws were not obeyed exactly. At that point, the choice was to either add more epicycles (working your way up to an elephant), or for Newton to discover universal gravitation.
codethiefon Hacker News • Mentions
On “The best proof that the Earth spins”
…at you're referring to as "proof" is no proof at all, consider that Ptolemy's epicycles (i.e. the elaborate version of the crystal spheres) are just a Fourier series and can therefore be used to describe any periodic movement across the sky. (Without you having to know anything about whether Earth rotates or not.) For a very impressive example see link to this video .…