I have some intermittent ability to lucid dream. I have noticed that if I am acting as a "passenger", the imagery is vivid and I will be able to recall everything. Sometimes something in the dream will prompt me to think. It might be entering a phone number, or reading text. As soon as I engage the process of thinking, the imagery goes away. Long lucid dreams for me rely on me being able to remain in the passenger seat.
In my waking life I consider my aphantasia similarly - I can imagine things and get the briefest of a "snapshot" of an image, but any attempt to hold onto it means it vanishes - I don't know how that's related but I suspect that it is.
I know this is different to how I am wired for sound, because I have inner music, inner voices, etc. I can replay music at will, change voices, investigate and modify them, all with perfect quality of audio recall. Earworms can be really annoying ;)
FWIW I’m exactly like you. My ability to replay music sometimes surprises me.
Sometimes I’ll hear a song on the radio I haven’t heard in decades and be able to anticipate tiny details precisely (like, “here’s where the harmonica comes in in Karma Chameleon” or “here’s where the fretless bass is gonna bend a note”. You?
Just as sound, not language. When hearing sing in my head I’ll hear the little details. When listening to song on radio I’ll know when those details are coming, even if I haven’t heard the song in ages.
What is the thing with Komodo having exclusivity for Valve hardware in Japan by the way ? We wanted to buy a SteamDeck OLED in Japan last year and it all the big department stores in Akiba it was sold out - kinda indicating Komodo is not really handling this very well if they have no stock.
I'm not species-ist. If a digital sentient being has something to say and they can express it through music, I'm more than willing to listen.
But listening to these samples, it's obvious that, while technically proficient, they have no voice. Funnily enough, neither does most of the human produced music slop that existed before gen AI.
All it exposes is that most people have no taste. This is as good as shuffling through popular songs on Spotify.
Am I as good as Claudio PRC, Donato Dozzy, Ken Ishii or Takkyu Ishino? Not even close. But wanting to make more is reward enough for me to keep trying.
it's not. We were able to get rid of 6 fingered hands by getting very specific, and fine tuning models with lots of hand and finger training data.
But that approach doesn't work with code, or with reasoning in general, because you would need to exponentially fine tune everything in the universe. The illusion that the AI "understands" what it is doing is lost.
I am a new initiate into the world of 3d printing for minis. I decided a resin printer does not suit my small apartment lifestyle, and got an Elegoo Centauri Carbon FDM printer. It's pretty plug-and-play, there was very little setup required.
www.reddit.com/r/FDMminiatures/ will give you an idea of the level of quality you can reach. With the smallest 0.2mm nozzle, will it reach resin levels? Close but not really. Is it good enough for me to screw around with, improve my painting skills, and play casual games? Certainly.
Also I subbed to the OnePageRules patreon, they offer alternative minis and rulebooks that are very similar to GW, with an alternate for fantasy and 40K, as well as fleet battles and other stuff.
> Here we report “3D necroprinting,” a biohybrid manufacturing technique that repurposes female mosquito proboscides as high-resolution 3D printing nozzles. The mosquito proboscis, with its unique geometry, structure, and mechanics, enables printed line widths as fine as 20 μm ...
My theory is that people who like math have a reward system that responds well to gaining an understanding on empirical concepts. I have that, and it does drive me to keep studying math. Not that I find it easy though, I don't think I'm able to skip steps, and I often have to repeat things I've already done before they sink in. The difference is that I find this process enjoyable, so I don't mind spending the time.
If I can compare to another activity, I've always wanted to be an artist as well, and have spend quite a bit of time trying to build up the skills. The problem is that, if I'm honest with myself, is I just don't enjoy the process of creative expression, it doesn't trigger any reward system that means anything for me. I wish it did but there's just nothing there. It was a hard pill to swallow, but I realized I like the idea of being an artist, but I don't enjoy the process. Hence my ultimately crummy artwork!
Sorry, I realized I'm talking about myself more than you, but I hope it's some help. The point I hope it makes is that everyone has a different personality, and from that different reward systems. It sounds to me like yours doesn't align with math, and that's fine. I wouldn't try to force yourself to study something which you don't love, at least if it's optional self study. Find subjects that you love learning, and the results will come naturally.
> The difference is that I find this process enjoyable, so I don't mind spending the time.
This is definitely the difference for at least some of the people out there, however...
Imagine however that you do enjoy it at the start so you move on from topic Y to topic Y+1, then to to Y+2. However you find that you no longer understand Y and you need Y when you are doing trying to learn Y+3 so you study Y+3 and Y, now your progress in Y+3 has been slowed down.
Really your goal was to get o Y+7 though that is where you can start breaking new ground and contributing but as you try Y+4 and Y+5 the gains stop and maybe even reverse. You are now on a learning treadmill(perhaps sometimes falling off and having to restart too) redoing Y-1,2,3,4,5 not moving forward. Often it is possible to find a trick/skill/simplification/etc to continue moving forward to get to Y+6,7.
How long would you find the process fun on that treadmill though? I think it is common to not find covering the same ground over and over fun or never being able to make it to the point where you are part of peer group where you can contribute. An understandable result is when those people invest elsewhere, where they see better returns.
I've been doing similar for about a year. My target is to learn the math needed to make 3d games, so basically algebra, geometry, calculus and linear algebra.
I started with brilliant.org, and while I liked the level of polish in the interactive lessons, I found the lesson structure to be out of sequence, often referring to things that haven't been covered yet. They didn't seem to have put as much thought into pedagogy as Math Academy as described in TFA.
So I gave up on that and instead have been shipping several kilograms of dead tree across the pacific in the form of The Art Of Problem Solving series of textbooks. They are great, the lesson structure and building up of complex ideas from first principles is outstanding. They will humble you though, as the exercises are tough. They're also quite expensive but IMHO worth it.
Math Academy does look interesting, If I was not halfway through my series I would probably take a look. But I do enjoy having reference books on hand. Many times I've jumped back to brush up on a topic that has slipped from memory.
I solve my exercises with the most low tech solution possible, but I like the freedom it gives me to try new approaches, and nothing beats the latency between idea to ink on paper.
edit: also wanted to add that I've enrolled Chat GPT4 as my tutor. Contrary to many other's experiences that I've read, I find it to generally be very good at reasoning in this level of mathematics. It's helped me many times when I've gotten stuck. And on the occasions where it bullshitted its way to an incorrect answer, I always challenge it if I don't understand, and we ultimately find out if it hallucinated something (rare, can usually be fixed by restating the problem), or I gave it the wrong input to start with (unfortunately more common than I'd like)
I'm in that camp and can suggest a few recommendations in order of:
https://d3dcoder.net/ -- The DX12 book is the latest edition. The books have several chapters at the beginning covering 3d transformations.
https://foundationsofgameenginedev.com/ -- The first installation, Mathematics. This will cover a lot more ground and derive things from first principles while not being overly formal.
Are you using any of the stuff you're learning for whatever practical 3d game-making things you're working on? Just curious how it's working out, you've picked a pretty broad foundation as a starting point.
I took a brief detour late last year to study "Linear Algebra: Theory, Intuition, Code", and to my surprise it stuck pretty well. The author said the pre-reqs were just "basic high school math", but I'm glad I had recently done lots of algebra and geometry, as the difference between that and some vague memories of stuff I did 30 years ago in school is pretty wide.
I haven't started any 3d game projects yet. For that, my plan is to do the webgpufundamentals.org course first. Scanning the TOC, I think I would be able to attempt it from what I learned from the linear algebra book.
That said, I'm doing AOPS Intermediate Algebra at the moment, and the Precalc text covers more advanced trig and matrix stuff, so I'm thinking it would be good to finish at least to there before starting to apply the knowledge.
Yeah, it sounds like you're not far from the point where you can start jumping ahead and working backwards to fill in the bits that you're missing - that's what many people naturally and instinctively try and it can work but can also be frustrating if one misjudges one's degree of proficiency. You don't often see 'I'm just going to give myself a full secondary school maths refresher' which is more demanding on time and self-discipline but at least we know it's pretty reliable given those things.
Ah, okay. I actually took calculus in 8th grade. I studied another two years past that, dropped out, and then later did a complete 180 and graduated with a literature degree.
I'm now over 40 and interested in relearning the math I learned long ago and pushing a bit further than I had before.
There’s also an intermediate number theory class that’s basically at the level of a college elementary NT course (one that does not assume abstract algebra), an Olympiad geometry class, and a group theory class. The first two do not have a text, the third has a text but you can’t get it without enrolling.
I bought the whole set for my kid. He's also doing Brilliant.
It starts at somewhere that the kids are at the end of primary school (at least in the UK) and ends somewhere in high school. My kid could already do all the pre-algebra stuff, so that book went fast. The way I see it, the kids waste a lot of time in the middle years when they already know the arithmetic and pre-algebra, but might as well be doing a bunch of more interesting things.
I think it's a weird way to learn math, and I learned it this way in school. Most of these courses just teach information memorization and recall. sin(x)^2 + cos(x)^2 = 1, etc.
I would start with something like Elementary Analysis: The Theory of Calculus, and work from there. You'll eventually arrive at the same place -- Calculus but from a much stronger mathematical foundation.
You learned using the AOPS books? Don't be fooled by the titles, these books exclusively use a proof-based approach to construct a pretty wide foundation around these topics.
AoPS are among my favorite math books, but they're definitely not proof-based or particularly rigorous in terms of formalism.
They do focus on complex problem solving, which is equally important. The key value-add of AoPS are interesting, often beautiful examples and problems.
However, they don't do proofs or formalism much. They don't do applications or show what math is useful for. And they completely, totally, and universally screw up units (you'll have problems trying to equate a length with an area and similar; that's true of their classes as well, and RSM is similar).
I don't think there's a one-stop-shop for math, though, which does everything right. AoPS is at the peak of their particular game (which is right in the name: problem-solving).
That's best complemented by:
- Something which does data, applications, visualizations, and storytelling well.
- Something which does early exposure / surface learning well
- Something which is more formal and rigorous in terms of proofs and derivations
- Something which touches on a broad set of interesting topics (graph theory, oddball parts of geometry, etc.)
- In 2024, I would add something which does computational mathematics well
Nothing I know of does all those well in a one-stop-shop.
I have not found that to be the case, the books I have read have gone into deep foundational detail to build up knowledge. Perhaps you're referring to Vol 1 & 2 of "The Art Of Problem Solving"? I haven't read them but from what I know they are a distillation of core concepts for students looking to do competitive maths.
It's confusing because that title is also the name of the publisher / website of the series of the books I'm reading.
Are you doing the online classes or only the books? I wanted to register for the online classes but they seem to be heavily oriented towards interactive learning.
Just self study with the (physical) books. I did also try the ebook combo for the Prealgebra book, but I found typing latex in the answers to the exercises was cumbersome.
I think the online classes with interactive lessons is a separate thing, but I don't have any experience with that.
The ones that have “instructors” and class times have chat-based sessions that you can skip if you prefer. Part of the homework is based on an adaptive problem system (Alcumus, which you can actually use for free) and part is weekly problem sets mostly based on the textbook. Writing (proof) problems are graded by a human so it is a useful way to get feedback on your proof-writing skills (if you know you are worse at it than a college math major).
Math as prep for 3d game programming. I've been out of school a long time, and when I was there I didn't even get to the pre-calculus level.
This year I've churned through all the introductory level texts from Art Of Problem Solving. Yes, they're written for high schoolers and you need to have some humility to admit you might be missing or have forgotten some fundamentals, but the lesson strucutre really appeals to me. It's the only series I've found that respects the learner and really builds up knowledge one piece at a time.
Before I start the intermediate texts and the calculus book, I've taken a detour to "Linear Algebra: Theory, Intuition, Code" and it's sticking a lot better now than previous attempts on the subject. So that gives me some confidence.
This is awesome to hear. I took trigonometry and business calculus 1 & 2 in college, but that's a far cry from what I'd need to do anything interesting with ML which I'm interested in trying.
I've bought a few textbooks for statistics, math, and data engineering - I'm in the middle of getting my life together in terms of habits and time management so hopefully I'll be right there with you doing what is essentially remedial math for someone in their 30s, lol. I know it will be exciting once I make space for it and get into a rhythm. Cheers!
The Art of Problem Solving books are not for regular high schoolers. I'd say they're more geared towards gifted high schoolers (which may eventually go on to compete on contests such as the USAMO or the IMO). So definitely no shame in learning from them.
I am currently reading the introductory books of AOPS as I did not do well in high school math. I did not find the way my teacher taught math interesting because it didn't connect with real-world applications. The hardest thing I face as a 21-year-old going through the middle and high school math books is accepting that I lack the foundational knowledge and setting my ego aside. My plan is to learn calculus and linear algebra as a follow-up.
I was at Charles Sturt University in 95, and have fond memories of starting up Trumpet Winsock on the computer lab's Windows machines and telnetting into a chat mud called Forest (Forrest?), which I'm pretty sure was hosted at UTS. Or was it one of the other Sydney unis?
Anyway, it was insane that you could text chat with these other users in the ether, disconnected from physical reality but still able to message in real time. Certainly shaped my experiences of the early Internet.
I have some intermittent ability to lucid dream. I have noticed that if I am acting as a "passenger", the imagery is vivid and I will be able to recall everything. Sometimes something in the dream will prompt me to think. It might be entering a phone number, or reading text. As soon as I engage the process of thinking, the imagery goes away. Long lucid dreams for me rely on me being able to remain in the passenger seat.
In my waking life I consider my aphantasia similarly - I can imagine things and get the briefest of a "snapshot" of an image, but any attempt to hold onto it means it vanishes - I don't know how that's related but I suspect that it is.
I know this is different to how I am wired for sound, because I have inner music, inner voices, etc. I can replay music at will, change voices, investigate and modify them, all with perfect quality of audio recall. Earworms can be really annoying ;)
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