3 ms·
The Shadows Lurking in the Equations – Underwater Islands
- 0xdeadbeefbabe 18d agoSeems similar to fractals.
- pfortuny 18d agoThat has another name but I forget. Essentially contour plotting in high res.
- simojo 18d agoThese visualizations are cool, but I feel only a little misleading. Any 2D relation can be plotted in 3D, and setting z=0 shows the original line in 2D. The whole notion of fuzzy is really just saying "let's make a heat map of how far z is from 0". That said, I can see how for some people, thinking about the roots of a function in 3D this way _could_ help unlock deeper understanding of where your roots are at than just staring at 3D graph.
- rcxdude 18d agoAlso, the visualisations are to some extent an artifact of how you arrange the equation: rearranging terms between the left and right side won't change the line but it will change these visualisations. The first example illustrates it nicely: the 'hole' only exists because of a redundant division by (x^2 + y^2) on either side of the equation.
- Jaxan 18d agoI agree. But it’s cool to explore these things and if it’s the first time someone sees it, that’s nice!
- MarkLowenstein 18d agoMy gut tells me that exploring mathematics in this way has very high potential for bringing on future advancements. (1) Simple elements that (2) reveal coherent structures, and were (3) hidden to historic geniuses due to requiring exhaustive computation.
- Enginerrrd 18d agoIt’s not so interesting I think. They’re basically just taking equations of the form f(x,y)=k where k=0, and asking “ah but what about when k!=0”? Indeed, looking at the constant as a variable by looking at the equation f(x,y)=z IS quite useful. (I’m reminded of Feynman favorite trick for solving integrals). That generalization trick is actually useful in MANY contexts. But there’s nothing novel here.
- aeve890 18d agoThe same trick is used in f(R) theories, where the Ricci scalar in General Relativity is replaced with a linear function. https://en.wikipedia.org/wiki/F(R)_gravity https://en.wikipedia.org/wiki/F(R)_gravity Reminds me of TRIZ methods too, trying to find assumptions or constraints and playing with variations of them. So yeah, nothing novel here.
- fhdkweig 18d agoearlier discussion here: 89 comments, 11 months ago. https://news.ycombinator.com/item?id=45823141 https://news.ycombinator.com/item?id=45823141
- wrs 18d agoIsn’t the “error in the equation x = 0” just…x?
- calebm 18d agoYes.