The Fourth Dimension vs Black Hole Vision

The Fourth Dimension is a 30-page interactive book that explains a single mathematical idea in language that anyone can understand. Instead of static images or canned videos, this app employs a unique 3D touch interface that lets you literally grasp the concept of the fourth dimension with your own hands. “Not only can you blow your own mind over and over again, you can also enjoy watching your friends’ minds being blown in front of you.” — Cult of Mac “One of the coolest apps I've ever used... The Fourth Dimension is to boring learning apps what Carl Sagan's Cosmos was to staid science documentaries.” — BuzzFeed “The app is very cool, and it's unlike pretty much anything we've seen in the App Store.” — The Verge “This is one of my most favorite iOS apps ever.” — George Musser, contributing editor for Scientific American and author of The Complete Idiot's Guide to String Theory (App Store user reviews follow.) “Blew my mind. I generally don't use 'learning' apps as they're mostly gimmicks. This one, though, truly made me think. I hope this developer comes out with more outstanding apps such as this one. Bravo!” — Iceitic “Astounding. That some people care passionately enough about tesseracts to go create a fantastic app for others to understand them is incredible. The app is extremely well designed, wittily written, and executed with love. That alone is worth buying it, besides the fact that I learned what the hell a tesseract was.” — Duncan MacMichael “Fantastic! This is what someone really smart, and who really knows how to teach well, can do with a tablet. And the authors are funny, too, which is a neat bonus.” — DNY “Fantastic app. I work at a leading UK university. If only all our material was this well written and presented. Definitely worth buying and then spending a bit of time with over a day or two to get your head around the fourth dimension. Great app!” — JulesFM “Great job! This app does the best job explaining the 4th dimension. Why learn it in some boring classroom when here you can have an interactive and visual explanation.” — Aco Strklalj Over 250,000 people have blown their minds with this app.

What would the world around you look like if you were staring at a black hole? This application places a black hole in the field of view of your iPhone’s camera and gravitationally "lenses" the resulting live video feeds just as a black hole would warp the light from surrounding stars. The resulting "Black Hole Vision" reveals interesting features of black hole lensing, including a "photon ring" of strongly lensed images around the black hole. The measurement of this photon ring will be the target of future astronomical observations from space with the Black Hole Explorer: an orbit satellite that will take the sharpest images in the history of astronomy! To learn more about BHEX, head over to https://www.blackholeexplorer.org/. The code is open source and freely available on GitHub at https://github.com/graveltr/BlackHoleVision, along with documentation that explains the underlying black hole lensing equations and how they are implemented in Black Hole Vision. The code was written at Vanderbilt University by Trevor Gravely with input from Dr. Roman Berens and Prof. Alex Lupsasca. We also acknowledge Dominic Chang for useful input and comments. This project was supported by CAREER award PHY-2340457 and grant AST-2307888 from the National Science Foundation. The lensed image of the spiral galaxy Messier 101 was generated using material produced by NASA and STScI and can be found here: https://hubblesite.org/contents/media/images/2006/10/1865-Image.html?news=true. License: This app includes a port of the GNU Scientific Library's (GSL) implementation of Jacobi elliptic functions and the elliptic integrals to Metal. It is licensed under the GNU General Public License v3.0 (GPL-3.0). You can view the full license and obtain a copy of the source code at: https://github.com/graveltr/BlackHoleVision.