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).
Lucas chess is chess GUI, not an engine, but it comes with many different engines, some even tuned to different grandmasters styles. I am not sure what you meant by "learning how you play", but you can indeed adapt their strength and "personality" to always match more or less equal opponent. You can also have another engine watching the game giving you hints. I am sure having a personal trainer is better, but more expensive and time consuming and you would need practice as well. There is also a nice feature to play with a strong engine trying to survive as long as possible (i.e. the game stops if the evaluation drops below set threshold), it's nice for opening training.
I've found this program a few months ago when I was looking for non-web free chess software for windows. There are surprisingly few options, mostly outdated and with unpleasant interface. Lucas chess is an exception. Interface looks nice, although it takes some time to get used to it, and there are many interesting options to analyse your games, play with many different engines an study (various problems, endings, openings). The source is open (python!) and there are quite frequent updates. I am a happy user and I recommend it to all chess enthusiasts, it's worth to try it.
Yes, of course he knew that all occurrences are equally probable, but he took into consideration what other people bet. Anyway as I remember when asked about that strategy few years later he said he changed the sequence (to 2,3,4,5,6,7 or something similar) to avoid potential prize sharing with people who followed his advice.
I read once about a famous mathematician who claimed that whenever he plays lottery he chooses the sequence 1,2,3,4,5,6 because nobody else would. Also it seems strange that so many people would choose a sequence that most people would call "not random" and suspicious (hence the article). Maybe those people follow the advice of this famous mathematician. Authorities should check the occurrence of this series in the previous games to see if that many people really like this sequence or if it was a one time event. Thinking about this, it would be interesting to see what numbers people choose, if there are some outliers preferred by many. I wonder if there are lotteries that publish such data?
Indeed, very interesting. Imagine the (not so distant) future web populated with ai generated gibberish that would be indistinguishable form the real thing. It could make English unusable for online knowledge sharing and could cause the switch to another language (and another, and another...). The threat is very real. There should be a scifi novel based on that (probably already is, hopefully not generated by gtp3)
For each human being having GI there are many tasks that person won't be able to perform. For example proving math theorems, doing research in physics, writing a poem, etc. Specyfic AGI could have its limitations as well.
Thanks, it's a bit unexpected. How good is Power Point for math intensive animations? I am not sure I could easily (or at all) recreate most of the demos from mainm repo, but maybe I am missing something. I will have a look, I am intrigued.
Sorry, I did not mean to be toxic. But I really believe that anyone complaining about math notation should try to propose something and show us a page or two to judge. I would also appreciate some examples showing possible improvements in notation. I don't understand what's wrong with Sigma, I find this notation beautiful, as well as integration sign.
Math is still taught at the blackboard and the notation works fine there. See for example https://www.youtube.com/c/FredericSchuller - he is very careful to explain all notation he uses and he is writting down more text than the usual professor. In my opinion it shows that math notation is fine and the problem is that ideas behind are complex and hard to grasp.