From my recent experience I believe you can train your mental vision, at least to some extent. I play chess and the ability to imagine a position and moves in your head is quite common among chess players, but I was always struggling with it. I could not see the board clearly in my mind and when I was doing exercises on telling the color of a given square I was checking coordinates parity, as I could not see it in my mind. Only recently I tried to train chess vision starting with 3x3 board, than extending to 4x4 and finally glueing 8x8 with 4 4x4 boards. To my surprise after a while I started seeing the board more clearly and I could memorize some simple positions. I've noticed that my general mental vision improved significantly at the same time. If you don't play chess you can start with playing tic tac toe in your head, focusing on seeing the board and marks. I think such exercise is better than imaging an apple, because you can objectively check if what you see is correct. Any board game would do, but start with a small board, and extend only when you feel comfortable. Imagining horse moves on a 4x4 board, focusing on seeing square colors helped me a lot.
I've been using this app and its Android version for years (there is also one for iOS) and I've never found anything close. Too bad that the project seems to be abandoned. It's a pity, and a great loss that it was not open sourced. The app is still usable though, and I encourage you to try. Please let me know if you know anything similar. I am aware of desmos and geogebra, but I think this one is superior. Especially the graphics, 2d, 3d, vector fields and many more. Super fast, interactive, I really like the asthenic.
Delta is a pretty special magazine about math, physics, and astronomy that’s been around for over 50 years. What makes it cool is that even though it’s meant for high schoolers, the content is actually quite advanced — even math grads might find it interesting. It’s kind of like the Russian Kvant. I’ve always thought it should be available in English, and now it is! Hopefully this won’t be a one-off. Definitely worth checking out.
Even though I code for a living and mostly enjoy the process, I’ve spent the last few nights with Cursor, migrating my old C# project to Python. I decided to do it without providing my old code to the tool and without coding at all. Surprisingly, it was amazing—just like having a super-efficient, eager programmer at your service. In just a few sessions, I managed not only to rebuild my old app but also to add many new features that would have taken me days to develop. (I decided to use PyQt6 for the GUI, despite having zero experience with it.)
So, if you know how to run code and understand the absolute basics, just start with Cursor. The free version should be good for a start, and then it’s just $20 per month. You can learn in the meantime by asking questions, etc. However, I would focus on understanding high-level concepts because mundane coding seems to be a solved problem now.
It’s a bit sad from a coding enthusiast’s perspective, but on the other hand, it makes you super productive when you have an idea for an app.
I recommend goQuest (mobile app), and playing 9x9 go. I used to play on KGS, but it is less crowded now (the problem is that there are too many servers: OGS, IGS, Tygem, Wbadul, etc
and no one dominates, therefore you wait for the game, you need a rating, etc. Most are not very modern, mobile unfriendly, etc.). Also 19x19 takes too much time for me when comparing to chess, 9x9 is perfect, and goQuest has many active players, after a few seconds you get a match (they offer 13x13 and 19x19, but those are less active I suppose).
The problem is that we want names with distinct first letter for the simple chess notation and "horse" and "queen" conflict with "king" and each other.
"I mean, in your example, how can the first "infinite bus" ever empty in the first place to fill up the infinite hotel?"
This is easy, you need to shout at the people so each person leaves the bus twice as fast as the previous one. For example the frst person needs 1 minute to leave the bus, the second 0.5 minute, etc. In 2 minutes the bus is empty :)
Can you give some examples of this "ample historical evidence"? I saw quite convincing video recently where a guy goes through all, known to him, sources and debunks them (https://m.youtube.com/watch?v=WI72JNz0IC8 - warning: might be offensive for a diehard believer).
The list starts with things that may well have considerable historical evidence, but ends by proposing an argument that would not even be logically valid: one could rationally hold that the material world is not all that exists, without accepting that Christ’s resurrection occurred.
As for calling materialism an a priori leap of faith, well, that hardly distinguishes it from the alternatives, though maybe that’s the point.
Yeah, just as an example religious Jews and Muslims do not subscribe to “material world is all that exists” but nevertheless does not belive in the ressurrection of Jesus.
