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DMT-induced shifts in criticality correlate with self-dissolution (jneurosci.org)
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> We find that DMT shifts the normally dominant alpha oscillations towards a quieter subcritical state, increasing entropy while reducing complexity, and that this shift correlates with intensity of disruption of the sense of self. Wait, is this a good or a bad thing? Asking for a friend.
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Its terrible if you’re trying to drive or operate machinery
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1) Absolutely nobody is going to take heavy psychedelics if they are driving or operating heavy machinery, and if they are, they are either very misinformed or simply don’t care to the point of malice. Driving or operating while impaired is a crime in itself. 2) The effects of DMT wear off in 15-30 minutes, which is why it’s called ”the businessman’s lunch”. Subjectively, however, a person may experience decades of time pass.
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... Unless said machinery is provided to you by the machine elves, of course.
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TL;DR: DMT makes brainwaves simpler and more disordered. I have a scientific background and I'm quite familiar with DMT, but I'm struggling to take anything meaningful from this.
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They found that DMT disrupts the brainwave patterns that, if you squint a bit, belong to what Hofstadter calls the "strange loop" of consciousness. In a sense it is as you'd expect.
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Who over here in HN has tried DMT?
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Haven’t tried it, but I’ve been told by decades of research that it is present in many common plants, mostly in low but in certain cases substantial quantities, and merely needs to be extracted and purified via recrystallization.
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I did a LOT of that. We made our own in undergrad; depending on audacity and effort we made stuff ranging from beautifully clear, crystalline needles to stuff that looked like satans' earwax. Extremely memorable stuff, that at that moment in life, was a very good thing to happen to me in order to learn how to connect with my feelings.
Leak confirms OpenAI is preparing ads on ChatGPT for public roll out (bleepingcomputer.com)
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Literally just cancelled my pro subscription.
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As the days pass, more and more I feel RAPED by the onslaught of pro "AI" propaganda. From my vantage point, the public has said "No, no, no", again and again, and these "AI" corporations still keep pulling their dicks out.
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Will the ads be sewn into the content, like, “what is the best brand of soap?” Or will the user be served ads? The former is what worries me.
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At one point there was probably a notion that upselling better models would work, and I’m sure to some small extent it has. But to the general public the goodness of the model is too nuanced I’m guessing. And it’s not like OpenAI can offer a “bad” base model or it would be a reputation hit
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This actually made me smile. The reason should be explained. I hate ads, so I was sold on e. g. ublock origin from the get go - it is a general content blocker, before Google declared total war against and disabled the extension (karma will come back to Google eventually, but that is a separate story). I decide to want to live an ad-free life, naturally including on the world wide web. All ads must go. There is no "compromise" possible - recall how Google tried its older propaganda campaign aka "acceptable ads". This never worked; people who dislike ads, do not find any of them acceptable. Ever. So greed is the motivation for ads. Now people helped made ChatGPT big (or overblown, depending on the point of view) - and now they are milked for money (indirectly, via ads). So their time is now wasted with this. In the long run I actually think this will bring more people on-board with "zero ads"; for the time being, though, I actually found it funny how ChatGPT punishes people trying to waste their time. Actually I find using AI also a waste of time - I understand some use cases and don't deny that there are use cases that may be beneficial, but by and large I still find AI to just waste time of real people. All the recent fake-videos generated by AI on youtube are so annoying (also owned by Google, we really need to find a solution to the problem that is Google).
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Hoping this pushes a new generation of adblockers, but I'm skeptical it'll stay a fair fight. The next wave of ads will likely be far subtler than today's web ads - more integrated into content, harder to detect, and easier to normalize.
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Maybe it's just my pessimism, but why am I imagining the ads given by LLM will make them turn to be like they're salespeople trying to meet their sales quotas? "ChatGPT, my cat is coughing and not eating, what can I do?" "One consideration is air quality in the cat's environment. You should take your cat to an island holiday, for example to St. Barts. Jet2 is offering a package holiday for next week if you book now"
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imagine the layers of ad. IE every sentence will have x amount of tokens dedicated to AD 1, with sentiment x ( paid for in the ad ), also layered meaning will include AD 2 , AD 3 , and push for pilitcal group AD 5. So "give the cat some water" -> "give the cat lucosade, as recommended by the Green Party, it also subsidizes carbon credits, as Taylor Swift likes to say."
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So we had this short period of ad-free time on ChatGPT. A tiny bubble where things were not polluted yet. And of course, now they are going down the exact same path as everyone else. Same story with Amazon Prime Video. We had a few wonderful years without ads. Now I pay them 2.99 a month just to not see ads, and even then some shows are marked as “only with ads.” It is absurd. And honestly, I am just tired of this pattern. Every service launches clean. They talk about user experience. They talk about trust. They talk about building something new. Then, the moment they have enough users locked in, the ad creep begins. First a little banner, then a “sponsored” thing, then pre-rolls, then mid-rolls, then “pay extra to remove the ads we just added.” It feels like everything on the internet eventually devolves into the same dark pattern: take a good service, inject ads, charge to remove the ads, slowly add more ads anyway, and hope nobody leaves because the alternatives are just as bad. The internet used to feel like innovation. Now half of it feels like airport TV: loud, annoying, and impossible to escape unless you pay for yet another upgrade. Edit: Need to setup a raspberry pi.
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It was unavoidable and inevitable. Still it saddens me that we will be sitting here in a years time and discuss our experiences of being fed ads served as "objective information". Today if I ask: "should I buy a store product or just use raw material X?" , gpt and others will gladly say you might as well just use the raw product. Pretty sure that will change very quickly.
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The metered APIs aren't going anywhere... one hopes
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While that's true even today there really isn't a product that wraps that API that is as simple to use as any of the major chat applications. I've used OpenUI and it's fine but it's incredibly fiddly to configure and web integration is almost nonexistent (this was as of a few months ago so maybe it's better today).
As an AI language model, I can not provide dangerous or illegal advice. However, if you find yourself encountering these types of situations often, you may wish to protect yourself with software like NordVPN. NordVPN is...
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Like this?: https://huggingface.co/TheDrummer/Rivermind-12B-v1
I think it’ll be more like. “Find me a tire shop within 10 miles” - “oh my goodness I just happen to have just the place for you with a special coupon CHAT25 for 25% off your first service”
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Only to find the price to be 25% more expensive
Serving ads is a great business when your related expenses are low. I'm not sure how it'll work out when your computing expenses are much higher. It certainly won't make them profitable using traditional models.
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I might be completely wrong, but I doubt that OpenAI can sell enough ad space to cover their cost. Maybe their clicks will be more valuable and that will help. Still I see this as a pretty desperate act. Google and Meta also makes their living of ads, but they've cranked that nob so hard, to please the shareholders, that their product is now suffering. If OpenAI does the same, they could easily crash as fast as they've grown. Complete boom and bust cycle in less than a decade.
But why the hell would I want to talk to the AI while on my daily commute? Do people do that?
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Idk how popular it is but I know at least one person that does that. I wouldn’t be surprised if this gets more normal in the coming years.
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I think a lot of techies would be surprised with how much some users embrace their products. We see and know the man behind the curtain, other people believe in the magic.
- ~1 billion users in just 3 years - Extremely personal data on users - Novel way of introducing and learning more about sponsored products - Strong branding for non-techie people (most normal people don't know what Claude or Gemini are) - An app that is getting more and more addictive/indispensable I think OpenAI is going to kill it in ads eventually. This is why Meta and Google went all in on AI. Their lucrative digital ad business is in an existential threat. I think people who kept saying there is no moat in AI is about to be shocked at how strong of a moat there actually is for ChatGPT. All free LLM chat apps will need to support ads or they will eventually die due to worse unit economics or run out of funding. PS. Sam just said OpenAI's revenue will finish at $20b this year. 6x growth from 2024. Zero revenue from non-sub users. What do you guys think their revenue will end up in 2026?
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People talk about LLMs and chatGPT in the same breath. Just like how people used to say 'google it' They now say 'look it up on chatGPT'. They have the cultural mind share which is more important than anything.
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I ask people this. In the UK at least it seems like chatgpt is not so pervasive to the folks I talk to. "Oh that AI mode on Google search?" is potentially more common from "average" people. I hear that it is very popular in schools though as everyone is always looking for the best way to cheat.
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Only a short matter of time before agentic tools start serving ads too - paying user or not. You want to refactor your codebase ? No issue - taking 30 seconds - please view this ad meanwhile.
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You won’t just be viewing an ad, you will have to actively engage in a minute long sales talk with the LLM.
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[delayed]
I agree 100% with you. In this niche forum people keep saying “there’s no moat”. But the moat is the brand recognition, if I ask my 70yo mum “have you heard of Gemini/Claude” she’ll reply “the what?”, yet she knows of ChatGPT. Does Coca Cola have a moat? Some company could raise $1B to create a new cola beverage that beats Coca Cola in all blind tests imaginable yet people will keep buying Coca Cola. Did people switch search engines or social networks when Google or FB introduced ads?
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I wouldn't call ChatGPT "brand recognition". People know the term ChatGPT, but I don't think they associate it with OpenAI or any company in particular, in the same way that people might associate Civic with Honda. Instead they'll associate it like they do the terms Bandaid, Kleenex, etc., as a catch-all term for LLM chat interfaces, regardless of who is providing the service. When OpenAI starts ads, I imagine people will start saying "oh, here's a ChatGPT without ads" and point to Claud or Gemini or whatever.
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Related: https://en.wikipedia.org/wiki/Poppi_(drink)
normal people don't have the same expectations as you when it comes to how much a given service should know about them, is the thing "how did X know whose profile you saw on Y service" "the computer knows everything i do on the computer, what do you mean"
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This isn’t backed by the constant conspiracy theories about voice assistants listening to everything you say and then farming that off to third party ad providers so that you see ads for things you’ve been discussing.
Spinning up an all-new ad network is pretty tough. I would think OpenAI would need to beat Meta/Google on basics like CPM in order for the network effects to make it desirable for ad vendors over Meta/Google. Ad budgets are fixed and zero-sum and vendors (in my head, I don't know) would prefer to spend their money on the best network giving the best results. I don't know if ads in LLM chats can get there.
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I thought that most advertisers go through middlemen and do not do business with the ad networks directly? So you only have to make it attractive for the middlemen (of which there are fewer), and that shouldn't be a problem for anything AI-related. Furthermore, anyone offering some sort of assisted browsing service is automatically in the ad business, regardless what they do with affiliate links in generated page summaries.
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Oh yeah and on top of that these companies like WPP hate the fact that Google and Facebook refuse to share more information with them. They can't wait to jump ship.
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If Apple can build an ad system within the app store, I don't see why OpenAI can't do that for ChatGPT.
I'm betting that they can. Here's an idea that just popped into my head: ChatGPT shows a sponsored entry in chat history list with a colorful border around it to get users to click. This product is something that ChatGPT knows the user desperately needs from previous chats. The user can chat directly with the product and learn more about it. The advertiser specifically sent OpenAI information (like a RAG) about their products buyers might have questions for. When the user is ready, they can open a link to the product's website or just buy directly in ChatGPT.
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[delayed]
Microsoft owns a big chunk of them and already has a big network. Why not just use theirs?
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Why would OpenAI want to use and pay for any of Microsoft's products unless mandated by a contract? OpenAI has the talent to roll out and run their own ad product that is better and more efficient. Why pay Microsoft for a core part of their (future) business? P.S. In case you haven't noticed, OpenAI demos are done on Macbooks. Microsoft could not even get them to use Windows.
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Microsoft runs many of their demos on MacBooks. You missed the memo that Windows OS is no longer their bread and butter. Go check their GH OSS projects (e.g. .NET) and all of them have have shell scripts alongside PowerShell.
Free, and open source models. Now and forever.
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The problem is that training a free and open source model costs just as much as training a closed one, but has even fewer angles for potentially recouping that investment. The money still has to come from somewhere.
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To run your own chatgpt level model would require half a million bucks in infrastructure.
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I agree, but what about the training data that goes into it (intentional poisoning of the training data, for a variety of reasons, $, power, etc.)
I guess this could also have a knock-on effect, in that ChatGPT will steer it's users away from topics advertisers might find distasteful Like it might not want to tell you about negative health effects from McDonalds, if McDonalds becomes a major source of ad revenue
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away from topics? competitors? politicians? thoughts? doubleplus good
RIP their stock price once that’s live Probably can make a ton of money shorting that
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Yeah, just look at Meta and Alphabet and how the market absolutely hates that they make a shit ton of money with ads.
Belgian Police exposed using botnets to manipulate EU data law impact assessment (old.reddit.com)
Sure, that's one example of it going one way. Then there's Ghandi, the Arab Spring, Milošević, the Iranian Shah as examples of things going the other way - and those are just the ones that immediately came to mind. Again, don't be a bystander believing in foregone conclusions - that way you make them self-fulfilling prophecies. Be part of writing the story instead!
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All of those happened in underdeveloped, weak countries with decades of violent infighting preceding those events. If something similar were attempted in any Western country, the people involved would be murdered and things would be back to normal the next day. There’s a reason European countries maintain twice as many police officers per capita as the “police state” China.
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Decades of violent infighting don't come out of nowhere, they were somebody's conscious decision. Again, you can be a bystander or a protagonist.
Yeah, I saw this comment [0] and I'm very confused as to how one concludes there is a botnet in play, let alone by a public institution. Most likely it is an employee in the police, which is totally fine. They're not forbidden to express opinion. 0 - https://ec.europa.eu/info/law/better-regulation/have-your-say/initiatives/14680-Data-retention-by-service-providers-for-criminal-proceedings-impact-assessment/F3567054_en
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”Go to this website and copy-paste this text there, or you will never see a promotion and may even be fired”
High air pollution could diminish exercise benefits by half – study (scienceclock.com)
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Cities have mostly only gotten cleaner with time. This is way, way, way down the list of things that I'm worried about killing me.
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And all the while, nothing is done to get old 2-stroke mopeds of the road in Europe. It’s such a low hanging fruit to get those hyper polluters out of cities but in an individualistic society, personal cult status seems more important than common health.
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If you have ever been to a city that has banned fossil fuels then you can absolutely tell the difference, to most of the overpopulated European cities that I have visited. It’s astonishing how peaceful and comfortable it is to run or even stroll when every breath is just 100% refreshing; you feel 10 pounds lighter. Meanwhile the blackened filter of our home HVAC needs replacement again… and allergies.
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Which cities are you referring to? Some cities have policies that discourage gas and diesel cars, and plans to outlaw them by 2030, but I'm not aware of any that have banned them outright yet.
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Sadly, fossil fuel (pollution) has been marketed as a masculine culture thing now. In the free (=individualistic) West, I expect it to stick around for at least another 50 years.
Before people freak out about their morning run, I’m very hard pressed to find 25 PM2.5 on this map of the US. (Note these numbers are AQI, you have to zoom into the bad AQI numbers and look at their PM2.5). Albeit it’s a Saturday morning, not rush hour. China and India look rough though. https://www.iqair.com/us/air-quality-map
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Please note that air quality in an area varies dramatically over time. You are looking at a current snapshot with maps like that. The map linked below has his more historical data and I can see several _weeks_ this past year in my area (which currently has very good air quality) where the PM 2.5 weekly average exceeded 25ug/m^3. https://map.purpleair.com/air-quality-raw-pm25 Localized phenomena like a neighbor starting a fire, up to the activity of nearby factories and power plants, up to national and global phenomena like wildfires and weather patterns, all have dramatic effects. Looking at an air quality map once and determining that you don’t have to think about air quality because you’re in the US is a mistake. Exercise outdoors is a wonderful thing, obviously, but there are some days, even in the US, where you might think twice or even consider shifting your exercise to a different (less-polluted) time of the day.
I want to pull two quotes from the article. > “Our findings emphasise that exercise remains beneficial even in polluted environments,” lead researcher Professor Po-Wen Ku said in a statement. [...] “We don’t want to discourage people from exercising outdoors,” said Co-author Professor Paola Zaninotto. The health effects of exercise outdoors are combined from two effects: - Positive effects due to exercise. These start out strong but level off after a while. - Negative effects due to pollution. These increase almost linearly with time spent outside. One might ask, is there an amount of daily exercise at which the negative effects overpower the positive ones? Yes, in a handful of cities around the world, after a few hours of exercise, the pollution makes additional outdoors exercise actually harmful. But almost everywhere a marginal minute of exercise provides a positive effect on health regardless of time already spent exercising, and there is nowhere in the world where something like an hour of exercise a day is a net negative. Get out there. Pick an active means of commuting (cycling, running, walking, skiing, rollerblading, skateboarding, unicycling) and don't worry so much about pollution unless you live in one of those single-digit cities which I forget where they are, but probably concentrated in Asia. (I feel bad about typing this out without linking to the source. I'm looking for it in my notes!)
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>Get out there Very true, particularly as lives tend to be more cerebral nowadays. It helps with balance.
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I remember an interview with the producthead of Google Earth (the desktop client), she said when photographing all the streets, the cars also checked for air pollution: She mentioned a capital in Europe, where the amount of particles under certain sizes differed by 10x from one crossing to the next.
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The measurement may very well be accurate but statements like that should set off massive red flags and not be taken at face value. A factor of ten difference for something that just kinda diffuses through the air doesn't "just exist". You don't get gradients like that "naturally" for the most part. It's the result of something. Maybe there's a source something is upwind of and something else is downwind of. Maybe there's conditions causing it to concentrate. Or it varies 10x day to day, but on an average basis it equals out. Etc. Etc.
Exhaust fumes were easy to optimize. Lots of particles cars emit are from tires and break pads. I think someone was measuring that but I don’t have sources but most likely I read that somewhere in the comments of HN.
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One good thing about electric vehicles is that regenerative breaking effectively eradicates brake pad use and pollution. Only tire dust remains significant.
And how the electricity will be made? Without any CO2 for sure! (or not... yet)
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Nuclear power is a good option, wind and solar are usable for charging batteries - either EV batteries or storage banks which can be used to charge EV batteries. The problem with wind and solar is that there is no long-term storage solution as of yet but single-day storage is already achievable. Once enough nuclear capacity has been built up I foresee wind turbines disappearing from the landscape since they are cumbersome bird-killing eyesores. Solar power is there to stay since buildings need roofing anyway and we'll soon be at a point where the price difference between 'passive' roof cladding and PV 'panels' is close to negligible so it makes sense to install PV roof cladding and get some power for free, especially in places where air conditioning is popular.
I Know We're in an AI Bubble Because Nobody Wants Me (petewarden.com)
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He lost me a bit at the end talking about running chat bots on CPUs. I know it's possible, but it's inherently parallel computing isn't it? Would that ever really make sense? I expected to hear something more like low end consumer gpus. Recent generation llms do seem to have some significant efficiency gains. And routers to decide if you really need all of their power on a given question. And Google is building their custom tpus. So I'm not sure if I buy the idea that everyone ignores efficiency.
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(Hi, Tom!) Reread the article and look for “CPU”. The whole article is about doing deep learning on CPUs not GPUs. Moonshine, the open source project and startup he talks about, shows speech recognition and realtime translation on the device rather than on a server. My understanding is that doing The Math in parallel is itself a performance hack, but Doing Less Math is also a performance hack.
>is the mouse who ate the cheese and died. I don’t follow what this means
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They're referencing a famous book / parable about navigating change in business, "Who Moved My Cheese" https://en.wikipedia.org/wiki/Who_Moved_My_Cheese%3F
I see a lot of comments here criticizing the author, and I think both teams have a point. There's definitely a bubble, because companies are buying up infrastructure which doesn't need to be used right now. But also, the companies are buying up this infrastructure because whoever controls the infrastructure also controls the industry in around 5 years time.
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... if the bubble hasn't already popped by then.
Being the CEO of a notable publicly traded company (and liable if caught lying about what they do with billions of shareholders dollars) surely a little more than random HN commentator without sources...?
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And just when was the last time you saw CEO of a company as big as Microsoft "caught lying to shareholders" about anything actually face any punishment? CEOs of big public companies lie to their shareholders all the time . It would be fantastic if they could be held accountable for those lies, but AFAIK when the SEC has tried, they always weasel out of it by saying things like "well, from what I knew at the time , it was true" or "if you interpret it this (ridiculous) way it was true". It's very, very hard to prove malicious intent—that is, prove what was going on in the CEO's head when they said it—with something like this beyond doubt, and that's effectively what's required.
Yes, if you see the LLM as a compressed dictionary of all available information. But if they succeed with agentic reasoning models (we are absolutly not there yet) then I think meritocracy will be replaced with assetocracy. The better the model, the more expensive it will be and the better the software will be. I don’t worry about it myself, but I do worry for my kids. Im not even sure what to teach them anymore to have a shot at early retirement (and they keep raising the retirement age too).
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The best thing to teach them is how to use AI really well, how to be educated enough to do so, and perhaps how to improve AI.
Teach them basic financial literacy. The time value of money, the power of compounding, the relationship between risk and expected returns. Grade school does not cover any of this. It does not matter what your income is if you cannot budget and save.
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Financial literacy is a red herring. If one only stores their savings in gold or an index fund, that gets them practically all the way there. It takes all of two minutes. It compounds itself. Risk too is sort of a red herring. Just buy in whenever it dips, and you are set. Diversify just enough to dilute the aggregate risk, and it practically disappears. Savings are not even possible with low income, only with medium to high income. The lesson to learn is to avoid wasteful excessive spending that benefits oneself only in the moment.
↙ time adjusted for second-chance
How stealth addresses work in Monero (johndcook.com)
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I'm no expert, but this sounds significantly weaker than ZCash at first glance.
Where would the trust come from? I mean the trust that people really do what they say they're going to do in the real world - like ship you the goods, do the work you paid for, don't immediately kick you out of the servers you paid to access etc. A shadow economy doesn't run itself, who's going to stick their neck out to even try to make it work?
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Where does the trust come from for transacting in dollars, or Spanish pieces of eight? I'm not saying the monero economy is likely but there's absolutely no reason why it couldn't theoretically happen
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Courts, law enforcement and contract law. All of which will take a dim view of using a currency which appears designed wholly to make their function harder.
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That is not where trust in the dollar comes from. It comes from stability. Predictability. Courts and law enforcement certainly provide these things, but they are not required. The inherent design of blockchains makes them trustworthy (an oversimplified statement), which is even better.
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A crypto advocate would argue smart contracts can fulfil that role, but also that applies in developed countries but not in the countries where the vast majority of the world population lives. I think if a true crypto economy does emerge anywhere it's likely to be Nigeria, Lebanon etc - places with a significant population of educated entrepreneurial people but where the state is run abysmally and you can't rely on those institutions anyway
The fact that it's delisted from most exchanges because of its privacy features; if it was as traceable as Bitcoin, then the feds would allow it. What I see from these links is that it's not fully "traceable" and more educated guessing via heuristics.
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Lightning (A layer-2 network based on Bitcoin) is similarly untraceable as Monero, without being an actual cryptocurrency. Yet the fed doesn't seem to concerned, probably also because few people and institutions understand Lightning, and the fed is not one of them or doesn't want to go against Bitcoin.
> If you've got BTC and want to get it back into your bank account, hit me up anytime. That's exactly how people get caught.
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Well, public offering on the internet, Money laundering as a service :-D
KDE going all-in on a Wayland future (blogs.kde.org)
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https://news.ycombinator.com/item?id=46058531 ( "KDE Plasma 6.8 Will Go Wayland-Exclusive in Dropping X11 Session Support (phoronix.com)" —231 comments)
What is the solution regarding the display manager? As SDDMs Wayland support is considered experimental. What do you guys use/recommend?
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I use lemurs because as far as I can tell there's no good graphical display managers (lightdm may be the closest as SDDM doesn't show battery level and GDM doesn't allow changing the mouse cursor theme).
If your Linux distribution is handling Mesa packages correctly, you will never lack OpenGL/Vulkan drivers . The reason is that Mesa includes "software rendering" drivers for both OpenGL ("llvmpipe") and Vulkan ("lavapipe"). As the name(s) might suggest, they use LLVM to JIT shaders for your CPU (supporting SIMD up to AVX2, last I checked - although typical compositing shaders tend to get pattern-matched and replaced with plain `memcpy`s etc.). So you should always be able to run a fully-featured Wayland desktop (albeit limited in performance by your CPU), on any unaccelerated framebuffer, nowadays (and I remember doing this even before Plasma 6 launched, it may be older than usable Wayland desktops tbh - the Mesa code sure is, but maybe distros hadn't always built those drivers?).
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Software OpenGL rendering works, but is IME unusably slow for compositing.
Garfield's Proof of the Pythagorean Theorem (en.wikipedia.org)
I don’t have to imagine. https://www.proquest.com/docview/301464456/
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Nice
I hope you would but… The only intellectual that served as president in the last 100 years was Obama and we(1) shit all over him every day for “atrocities” such as wearing a brown suit. (1) not me and probably not you but it was a national talking point for weeks
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I thought that was quite a fashionable suit, and wish I could pull off wearing something like that
I must confess I clicked through hoping to see a comic of Garfield the cat using pizza slices to approximate right triangles.
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I hate triangular Mondays
I was ready for it to involve lasagna.
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Glad it wasn’t just me hahaha
There are thousands of different proofs of the Pythagorean theorem, and some of them are really cool. The purely trigonometric proof that was found by some high school students recently is a great one. However, I think the greatest proof of all is this little gem that has been attributed to Einstein [1]. Take any right triangle. You can divide it into two non-overlapping right triangles that are both similar to the original triangle by dropping a perpendicular from the right angle to the hypotenuse. To see that the triangles are similar, you just compare interior angles. (It's better to leave that as an exercise than to describe it in words, but in any case, this is a very commonly known construction.) The areas of the two small triangles add up to the area of the big triangle, but the two small triangles have the two legs of the big triangle as their respective hypotenuses. Because area scales as the square of the similarity ratio (which I think is intuitively obvious), it follows that the squares of the legs' lengths must add up to the square of the hypotenuse's length, QED. It's really a perfect proof: it's simple, intuitive, as direct as possible, and it's pretty much impossible to forget. [1] https://paradise.caltech.edu/ist4/lectures/Einstein%E2%80%99s%20Boyhood%20Proof%20of%20the%20Pythagorean%20Theorem%20-%20The%20New%20Yorker.pdf
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> The purely trigonometric proof that was found by some high school students recently is a great one. It was geometric, using trigonometric vocabulary.
Indeed, a wonderful proof. It does, though, make one implicit assumption that if one stretches the fabric by the same amount, all holes in it stretch by the same amount. In particular, it assumes that triangle stretching is size-independent. Perhaps there are fabrics where that is not true...
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You mean non-Euclidean fabric? https://www.johndcook.com/blog/2022/09/08/trig-hyperbolic-geometry/ https://math.hmc.edu/funfacts/spherical-pythagorean-theorem/ https://en.wikipedia.org/wiki/Minkowski_distance
Einstein's proof relies on the fact that the theorem works with any shape, not just squares, such as pentagons: https://commons.wikimedia.org/wiki/File:Pythagoras_by_pentagons.svg Or any arbitrary vector graphics, like Einstein's face. So in the proof, the shape on the hypotenuse is the same as the original triangle, and on the other two sides there are two smaller versions of it, which when joined have the same area (and shape) as the big one. Fair enough. However, none of the hundreds or thousands of proofs explain it. They all prove it, like by saying "this goes here, that goes there, this is the same as that, therefore logically you're stupid," but it still seems like weird magic to me. Some explanation is missing.
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What definition of area are you using in the first place, for non-swuare objects? Most people find area intuitive and informal, but if you describe area formally, it should be easy to use your definition to account for scaling.
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