link to the book in the website takes you here https://lacathospital.com/ ?
Visual explanations of mathematics (2020)
11–20 of 28 posts
Re: Visual explanations of mathematics (2020)
#12> We have lots of tools to write better mathematics: LaTeX, markdown, Jupyter Notebooks, and so on. But it feels like nothing has really converged yet. Technology that seamlessly mixes symbolic equations, illustrative-and-explicative annotation, and runnable code is, I am sure, not far off. [2020; emphasis added] Back in the 1990's, we had lots of tools to write better mathematics: LaTeX, HTML, Mathematica notebooks,…
Do you believe that existing open source symbolic kernels are the limitation here, given that we can now easily (for some value of n) render the notation and the notes/annotations?
I mean, there are a ton of math libraries available for most programming languages, but symbolic solving is pretty important here, because presumably people would want to (for example) show the integral or summation symbols and use algebraic notation rather than, say, Mathematica functions.
Re: Visual explanations of mathematics (2020)
#13Want to see a thousand more? Copy-paste the example image (not the URL)
https://images.squarespace-cdn.com/content/v1/549dcda5e4b0a4...
into https://yandex.com/images/
Or, the URL into https://www.bing.com/images -> "[o] Search using an Image"
Unfortunately, Google Images is too smart. Even, search by image or image URL yields results about the Fourier transform :P
Re: Visual explanations of mathematics (2020)
#14link to the book in the website takes you here https://lacathospital.com/ ?
I thought "huh, some hospital link," but it appears to be a scam site, so be wary of clicking. (Good advice anyway, but I naively thought I could trust a link on HN.)
Which link did you follow, by the way? I clicked a few, and the link to https://www.edwardtufte.com/tufte/books_visex is broken, but none took me to your link.
Re: Visual explanations of mathematics (2020)
#15I am teaching intro stats and would love to have a textbook that introduces equations in this manner. I have been trying to incorporate this style into my slides but it is not as easy as it looks. (Same issue with syntax highlighting in PowerPoint/Google Slides.)
Re: Visual explanations of mathematics (2020)
#16There is also Joyce's Java Version of Euclid's Elements: https://mathcs.clarku.edu/~djoyce/java/elements/elements.htm... and I'm still impressed by the custom Unity tools which Freya Holmér uses for her videos: https://www.youtube.com/watch?v=jvPPXbo87ds Wish Geogebra was both more capable and widely used: https://www.geogebra.org/ That said, these days if I need to plot out something I just use OpenSCAD: https://ope…
> and I'm still impressed by the custom Unity tools which Freya Holmér uses for her videos
Speaking of Unity... What blew my mind making a 3D interactive system using it was Quaternions[0]. It makes sense to me now, but that's after many discussions with a coworker having a PhD in mathematics.
Re: Visual explanations of mathematics (2020)
#17> We have lots of tools to write better mathematics: LaTeX, markdown, Jupyter Notebooks, and so on. But it feels like nothing has really converged yet. Technology that seamlessly mixes symbolic equations, illustrative-and-explicative annotation, and runnable code is, I am sure, not far off. [2020; emphasis added] Back in the 1990's, we had lots of tools to write better mathematics: LaTeX, HTML, Mathematica notebooks,…
The visual explanation is helpful to build intuition the first time you learn the concept, but noise every other time. Do you want to see a grid of rows and columns instead of the symbol '*'?
Notation is a concise format optimized for reading by a familiar audience. It's especially helpful when notation starts to be composed.
Re: Visual explanations of mathematics (2020)
#18If you are the owner of the website, could you please add a page where I can browse all the articles easily without scrolling 10 kms on every single page. It is a very interesting blog with a tonne of seismic machine learning articles that I would like to read but I have to keep hitting next and next browsing through every page. Can I just see an index or all the titles somewhere?
Re: Visual explanations of mathematics (2020)
#19I am teaching intro stats and would love to have a textbook that introduces equations in this manner. I have been trying to incorporate this style into my slides but it is not as easy as it looks. (Same issue with syntax highlighting in PowerPoint/Google Slides.)
I have had some success with PowerPoint animations. Put up the equation, and for each mouse click surround the symbol(s) you want to explain in a red box or something and have a infobox show up (which can also contain images, such as plots - very helpful). As you transition to the next symbol(s), fade away the previous infobox and surrounding box.
Re: Visual explanations of mathematics (2020)
#20I use this "annotated equation" technique in my own notes when I am working through mathematics. It's honestly kind of crazy to me that it isn't already standard practice in mathematics texts. I can see how mathematicians might feel that it is inelegant, but it certainly helps with establishing an understanding.