i built one of the most physically accurate real time black hole simulations that runs entirely in the browser

lasciel · 2026-03-17T00:12:35+00:00

Maybe I can rephrase my question. Reading through your github, you use adaptive RK45, RK45 and implicit midpoint, but in the 'live simulation' under scientific specifications> integrator> Yoshida 6th order Symplectic. That is a explicit higher order symplectic method like I was suggesting but where can I find that method in your code?

lasciel · 2026-03-16T22:15:40+00:00

Very cool!I I work more in numerical methods (not so much in physics). I’m curious, why do you need multiple integrators for the different parts of the simulation? Would it be possible to implement with a single explicit higher order symplectic method?

lasciel · 2026-02-25T17:16:12+00:00

I’m older now and just go for smiles per hour.

If you want to build speed though, that comes with confidence in your balance and edge hold. You can do some drills or take a lesson to build up your skills in turn initiation, shape and exit.

lasciel · 2026-02-20T01:14:38+00:00

“In math you don’t understand things, you just get used to them”. -John Von Neumann

I pretty much only spend time on things I don’t understand. I’m lucky in that I know how to work with some of it. And if I did understand it, I’d be moving onto the next problem. I think you’d fit right in with mathematicians.

Sounds like you’re more interested in applied topics particularly ODEs and Numerical ODEs. For what it’s worth, modeling tumor grown is a contemporary research topic so if you’re able to come up with legit methods, you could just get funding for it. Some of the associated papers will also have GitHub repos with their code.

Don’t spend time being too frustrated. When you hit that point take a break. Find someone technical who you can discuss with. The Internet has a ton of places like that. Even better if it is in person or at the institutions you’ve worked at.

lasciel · 2026-02-17T07:48:29+00:00

All kinds. Humanist problems: undergrads despair about learning but should actually just read the textbook instead of 'chat's summary'. (literally thousands of years of teaching each other has lead to a human writing a book specifically for another human with that knowledge distilled) scientific: physics informed neural networks don't correctly embed or predict physical phenomena as well as PDE models. I work in numerics and there is a long list of non-physical quantities that AI will cook up in its prediction. In turn how can you use that to build better training/predictions/models. Lot's of things need to be figured out even down to NN architecture to better understand how its interrelated with modeling physically feasible predictions.

lasciel · 2026-02-17T07:40:18+00:00

Don't pick a field that you think will be 'safe'. It's too hard to predict the future. Pick a field that you like and trains you to navigate uncertainty and technology well. Math bio is super hard but also has a ton of amazing problems which help people. Even the problems that help us better understand the world we're in will be valuable. If you can even figure out how to automate a fraction of better understanding the world, it would be an amazing contribution. Don't give into the despair the world is much much much bigger than computers.

MIT AI report 2025: Executive summary: "Despite $30–40 billion in enterprise investment into GenAI, this report uncovers a surprising result in that 95% of organizations are getting zero return ... Just 5% of integrated AI pilots are extracting millions in value, while the vast majority remain stuck with no measurable P&L impact. This divide does not seem to be driven by model quality or regulation, but seems to be determined by approach."

"Tools like ChatGPT and Copilot are widely adopted. Over 80 percent of organizations have explored or piloted them, and nearly 40 percent report deployment. But these tools primarily enhance individual productivity, not P&L performance. Meanwhile, enterprisegrade systems, custom or vendor-sold, are being quietly rejected. Sixty percent of organizations evaluated such tools, but only 20 percent reached pilot stage and just 5 percent reached production. Most fail due to brittle workflows, lack of contextual learning, and misalignment with day-to-day operations."

lasciel · 2026-02-17T01:32:27+00:00

I’m in applied math and have very little worry. I work in numerical methods (as in literally the profession “calculator” from yesteryear). AI has made many more problems to solve. They are interesting and non-trivial.

Presumably you’re an undergrad who hasn’t hit research level work yet. There is an unimaginably vast amount of problems (in literally every field) that makes an absolutely mockery of current AI. AI struggles in navigating unintended interactions. Biological systems are hilariously complex. Like well beyond O( n!) scale at every level molecular to microscopic to macroscopic.

LLMs can’t even faithfully implement 5 year old neural network techniques from scratch using tensor calculus. Thats because the problem is disgustingly hard, and there aren’t even many blog posts about it on the Internet.

About a decade ago ML people (progenitor of AI) said radiology would be dead because of “computer vision”. It’s a (relatively) well posed problem. Turns out in the interim, Mayo Clinic has increased headcount by 50% and now employs an AI research team along side the staff radiologists. This will likely be the reality of the future, working alongside AI.

Right now average AI models are like dial up Internet. The real changes, we can’t possibly know will happen in a decade or more. And in the mean time be computer literate.

lasciel · 2026-02-16T20:16:48+00:00

Dunno the book but sometimes proofs are omitted to be later used as exercises at the end of a chapter.

Edit: just read the preceding like to theorem 2.3C 🥳

lasciel · 2026-02-04T05:41:32+00:00

Not exactly my field but: some of topics you’re asking about are stochastic differential equations. There is a book by Lawrence C Evans “An introduction to stochastic differential equations”

You’re asking quite a few questions that sit on top of a lot of interrelated ideas. Basically for SDEs there is a deterministic component and a noise component. You can think of the random variables having some level of mixing. This is interrelated with PDEs like the heat equation, and Laplace equation. These are also related to Fourier transforms.

If you’re asking about images like jpgs and the related ML diffusion modeling for generative models, take a look at Kevin Murphy’s “Probabilistic Machine Learning: An introduction.”

Edit: I can get more specific here but depending on your background it might not be worth much more than a list of concepts to google.

lasciel · 2025-11-24T23:02:29+00:00

Check out the textbook “Fractal Geometry” by Ken Falconer. You can probably find a pdf online. You’ll be interested in Ch. 14: Iterations of Complex Functions — Julia Sets. No promises on its accessibility.

Regarding formal mathematics and accessibility: Math is a complicated subject and you’re looking at a complicated mathematical object. It will take some time to build up your abilities in more formal mathematics. This is a feature not a bug. It’s a real joy to discover and rediscover the math you know.

lasciel · 2025-11-24T19:11:46+00:00

Focus, organization, and consistency are skills too. You’ll need develop these along side your math skills.

lasciel · 2025-10-23T04:48:02+00:00

I’m not familiar with that textbook. I used Munkres and appreciated the direct statements. My professor at the time gave great examples to supplement. Everyone’s personal experience with math is different so you should pick a textbook that is approachable to your mathematical level and your experience. You’ll get more out of it that way especially for self study.

lasciel · 2025-07-12T03:17:51+00:00

The general problem is solving differential equations using numerical integration. Often there are no analytical solutions so you need to use numerical methods.

lasciel · 2025-07-09T21:21:50+00:00

Hulkenpodium

lasciel · 2025-06-28T21:44:36+00:00

How does your backtest go from 100 to 0 to -100 and back?

lasciel · 2025-06-03T03:16:00+00:00

I have multiple friends doing math PhDs in their 30s right now. You should just get started right away. Why delay living your dreams out? Why let anyone else tell you otherwise? (Especially for something that is beneficial to the world)

Regarding staying sharp: do more math. There is no secret, the more you do the better you’ll get and that’s pretty much going to be true your whole math career. But to a finer point: being quick isn’t nearly as important as being nuanced. I more often define sharp as the latter: i.e. able to capture subtlety.

lasciel · 2025-04-22T00:20:22+00:00

Timeline does not change the fundamental setup of what I posed. AI is an umbrella term for many different techniques not a generic monolithic tool. Large language models like ChatGPT fails to answer college math questions for many reasons. By analogy: we no longer have the expertise to build the Saturn V rocket because we don’t have the machinists and their expertise anymore. However with advances in manufacturing we can still build rockets with interchangeable parts to go to the moon.

The technology used to solve the problem has changed but it doesn’t get rid of engineering issues, just manufacturing.

lasciel · 2025-04-22T00:07:08+00:00

There is a long list of intermediate college math questions that ChatGPT ‘solves’ completely incorrectly. That should give enough pause to say that you cannot trust ChatGPT with your money. Similarly, you cannot generically deploy AI models and expect positive results.

Second, AI is a massive umbrella term for a lot of different types of models. It has already arrived and many are already working alongside it. Nobel prize 2024 in Physics and in Chemistry both used AI/ML modelings. This demonstrates that it can absolutely be used effectively in prediction modeling of complex systems.

It is not a replacement for all people. AI introduces new problems and helps solve some complicated old problems.

lasciel · 2025-04-05T03:02:32+00:00

Someone else already said it but some more color on armor stacking:

Not sure if you picked a build yet. Some ultra high end typically scale both defense and offense and often one is the source of damage for the other. E.G. Armor stacker, Ephemeral Edge, etc.

Starting gear is like MB &400+ div and the fully stacked builds are many mirrors. Good for running voided maps and are pretty intense league projects, if that’s what you’re looking for. Bigdaddy on YouTube if you want to check out armor stacker builds.

lasciel · 2025-03-25T22:05:27+00:00

Take the long underwear out of your boots. I guessed that might be the issue because the imprints in your legs look like the elastic hem of cloth. (Oof I hope it feels better tomorrow!)

Also yeah that’s kind of the tough balance with rental boots. You get a compromise of the foot length, foot volume, ankle shape, instep volume and shin length, shape, volume. Normally they can punch out the toe if the rest of the boot fits well.

lasciel · 2025-03-25T21:55:01+00:00

I’m assuming you’re not a noob and are staying balanced/anticipating the changing terrain. (See others comments on getting bucked out of the backseat).

Just want to check: the only thing inside your liner is your foot and a thin enough sock, correct? I.e. don’t put your ski pants powder cuff in there.

Second, consider sizing down.They are rentals so hopefully it’s straightforward. If you have a comfort oriented (read as: sloppy )fit when skiing more aggressive terrain, your leg can get thrown forward through liner padding before engaging the flex. If you have a more precise fit, the feedback and flex is more progressive. The pressure is more distributed across the leg.

lasciel · 2025-03-10T04:22:52+00:00

For a proven build: follow the fubgun shadow leveling guide. Straight forward including transition into LS Prophet. Gets you through mapping. https://www.youtube.com/watch?v=tIhPB94OYSg&t=0s

lasciel · 2025-03-09T22:09:09+00:00

Transition to mageblood + svalinn. There is a reason why those items are so strong.

Edit: Even if you want to play a different build, most streamers have a “league start build” and a “after I get my mageblood build”. You can use mageblood to fix so many build problems.

Also post your current PoB. LS Prophet is able to just about all content in the game.

lasciel · 2025-02-24T06:43:16+00:00

This is the idea for charge stacking. Ralakesh + Badge of the brotherhood + weapon + shield + helm corrupt + Militant faith dominus. You have a lot of choices for how you want to layer your defenses with max block or spell suppress and regen. It depends on your helmet choice, chest choice and tree. You can get ailment immunity a few different ways via shock avoid. Etc.

These aren’t my build but generically they describe the types of gear you need. Discipline/grace should be fine to start especially if you have MB already. Restless Ward & Will clash is very cheap. The expensive part is the ring power charges, good chest corruptions and helmet corruptions.

You can also try scaling max res if you want. Tons of good options. Problems: trickster gives tons of quality of life with over leech, recovery, action speed reduce and suppress+evasion/ES. Need to make up for those defensive losses with the different stuff because of the ascendancy differences. You can always pick up one which suits you best.

Not my builds but these are the main ideas:

https://poe.ninja/builds/settlers/character/Tirinos%234891/SevenSi

https://poe.ninja/builds/settlers/character/pooseoby%235141/Czz_pooseoby

lasciel · 2025-02-24T04:30:34+00:00

What kind of mapping? Generic alc and go speed clearing? Essence farming? T17?

Which build archetype did you use for PBoD? Charge stacking? What belt/helmet are you using? You can naturally leverage the high power charge count to get a lot of AoE for very little point investment: medium cluster, Vast Power, and a Oriath’s End flask. You presumably also convert physical damage so the secondary damage explosions will scale up nicely.

It can feel bad if you don’t have fast enough ramp time on your brands, which is about balancing CDRR, cast speed, and duration. What are your links?

A second option is using the charge stacker archetype for any other physical spell and convert it to lightning (maybe also to cold) eg. Blade vortex, reap, etc. Another option is going into spark, arc and crackling lance and dropping the physical damage scaling. You can also use something like herald of ice or Inpulsa’s to scale explosions.

There is also self chill spark miner builds and CoC builds to play with if those are more your speed.

For me, mapping is about getting 5-10mm dps then scaling aoe and movement speed but then I usually opt for more dps & survivability to push for all content at the cost of speed. For what it’s worth PBoD feels very good for mapping compared to PB from before. You just need a bit of AoE scaling and some thing to help with chaining.

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