Ouch, this hurts to read. It's not novel and lacks a very basic understanding of math.
The graph of y/(x^2+y^2)=(x+1)/(x^2+y^2) by definition contains the points that satisfy this equation. This is exactly the set of points for which y = x + 1.
The "fuzzy" graph is just coloring the difference between the left hand side and right hand side. This is very basic, not new, and it's definitely not "the graph of y/(x^2+y^2)=(x+1)/(x^2+y^2)".
Why would you say it's not a graph of y/(x^2+y^2)=(x+1)/(x^2+y^2)? I would argue that a conventional/binary graph is also not a "pure" representation of the equation, but rather one possible representation - one that runs it through a "left_side == right_side?" boolean filter. In fact, there is no way to visualize an equation with doing something to it.
There's an equal sign in the equation. That means it is true when y = x + 1. There's no filter we're applying, that's literally what the equation says. What you plot is f(x,y) = (y-x-1)/(x^2+y^2). The line plot is when that equals zero, the fuzzinss of it is when it doesnt. But notice that f(x,y)=0 is exactly equivalent to y=x+1. They're exactly the same. Thus, when you're plotting the fuzzy graph it is definitively _not_ a plot of y=x+1, it's a plot of z=(y-x-1)/(x^2+y^2) and those are not the same thing.
We'd only need to "apply a filter" to get the line graph if we started with z(x,y), but that's not what you wrote
I think the parent basically sensed that you're not a trained mathematician and is trying to throw their middle-school math textbook at you.
The simplest definition of a "graph of a function" is that it's a representation of the points satisfying some underlying equality. Your plot isn't that. A more conventional name would be a heatmap: a plot of a function that takes two parameters - x and y coordinates - and then assigns a third value (color) to each.
I don't think the distinction is all that interesting. They're both function plots.
The "graph" of a function is formally defined as exactly those points that make the equation true. https://en.wikipedia.org/wiki/Graph_of_a_function Granted, the graph is only one visualization of a function, and not the only valuable one.
Of course we also have to remember that functions are not the same as equations, and a given function, or more generally relation, can be represented by multiple different equations. For a trivial example, multiply both sides of your slashdot equation by a constant, or add x*y.
Maybe your dentist just needs more business? Im half kidding but i once had a dentist that told me I had 4 cavities that needed to be fixed, but when I to a 2nd dentist, she spotted zero cavities
Some dentists are way too aggressive about fillings. My dentist keeps a watch on smaller cavities and if they aren't progressing terribly they hold off.
IIRC there were studies saying that flossing isn't as great as people suppose it is.
My completely uneducated guess is that it's marginally useful for people with good teeth (shape, spacing) because debris doesn't accumulate as easily, and brushes are effective.
For my case (crooked teeth, very narrow gaps) it's a great helper to get out the debris, morsels of food etc. that the brush can't get out.
I shared this with HN on many occasions. My wife has crowded teeth, doesn't floss, barely touches her waterpik, doesn't use any proper brushing technique. She probably had a couple of fillings done since I met her 20 years ago. In the meantime I have cavities almost every year, one root canal and a dental implant on a previosly failed root canal. I flossed since university and use mouth rinses and electric toothbrushes and so on. Except for genetics, there are a few differences in our habits throughout the years. I would always brush in the evenings but I was neglecting mornings (somehow I internalized something that a teacher once said that brushing in the morning is silly because you haven't eaten anything). I also drink way too much coffee which is acidic, she doesn't drink any. And lastly, I would at times avoid dentist appointments for years, which probably didn't help.
Edit: I forgot to mention, when I was younger, I used to snore and breathe through my mouth a lot. I think this has also negatively affected my teeth.
You started out good with what seemed like an easy comparison, she doesn't floss, you do, she still has better teeth. But then you go on to show all the other differences, especially not always brushing twice a day, different diet, avoiding dentist, and its hard to understand the point of your post.
My wife and I have an almost identical routine and diet, we use the same brand electric brushes, always twice a day, and usually have coffee together. However, she's not had many dental problems, but I've had to go to the dentist tons this year. Oh, incidentally I also knocked my front teeth out in a cycling accident.
You're right, I lost the plot. I still think it's mostly genetics, just because her hygiene and frequency of dentist visits are comparable to mine. I wish I was keeping record though, because little things can add up. I obviously placed low priority on morning brushing but on the other hand she never flosses, and here we're discussing the minute details of flossing technique.
I read an article a few years ago about what brushing actually does for your teeth and why it works. The premise was that brushing applies fluoride and removes the bacterial film that eventually turns into plaque - and that about 2 minutes of brushing a day would be sufficient if we were perfect at brushing. Doing it twice a day ensures that you get good coverage. It also went into the best brushing technique etc.
Since reading that I've not stressed about missing the odd brush here and there. I've also been more conscious how I brush. I stopped flossing because my gums seem quite sensitive to it and it doesn't have great evidence of effectiveness. I use a inter-denture pick/brush occasionally when needed. This all seems to have improved things for my teeth considerably, my dentist now saying they're really clean - and ironically stopped suggesting I floss more.
I wasn't joking in my previous post about the cycling accident that destroyed my front teeth, except that it happened 20 years ago. This year the crowns I had fitted failed so I've had those removed and implants installed. It's been very painful, I left replacing them probably 10 years longer than I should have. Yesterday I got a temporary bridge on the implants, which I can't use for biting. Still 2-3 months away from having the permanent new crowns fitted.
I've recently realized how much technique matters, I was advised to use the modified bass technique (and also an inter-dental brush around the implant). My aggressive brushing used to cause my gums to recede, even with expensive soft toothbrushes, but I think it's improving since adopting the new technique.
Sorry to hear about your painful experience. I do a lot of cycling and my greatest fear is falling and hurting my teeth. Actually, my implant is a result of me not taking out a molar that had a root canal a decade ago and was getting inflamed a lot. Should've extracted it much earlier, because the recurring inflammation ate away the bone. I was lucky they had enough bone to work with, needed to wait half a year for it to heal and grow after extraction (there is still a visible depression in the gumline). I do floss, but one minor annoyance is that it catches on these ridges where my filling are, I even managed to break a piece once, so I'm a bit more hesitant about scraping with the floss.
This is plausible. My dentist says I should use toothpicks, but they are not useful for me as they don't really fit between my teeth. I do the most problematic of my tooth with an "extra small" pick now, and I can usually get those four gaps done before the pick breaks.
If you floss too hard or aggressively then that can be bad for your teeth/gums. If you floss only rarely causing your gums to bleed when you do and you don't wash or brush away the dried blood, that can also be bad. But I don't believe that any dentist in good faith would advise not to floss, if done properly.
there are studies that show that flossing with the wrong technique doesn't do much. and it's meh on cavity prevention. what it does do is prevent gingival inflammation, which can be good for gum health, especially if you're prone to getting food caught in there.
I am not talking about usability or accessibility but rather just a nice feeling of using the UI. Of course that is subjective but if I click and it appears as close to zero time perception then to me that is much better than lag and/or animation.
That would indeed be pointless because I was originally replying to a single UI interaction, where it doesn't really make a huge impact whether it happened in 2 or 5 frames.
You're trying to bring in continuous changing of frames here which is obviously perceived differently.
No, it's sometimes just extremely easy to recognize people who have no idea what they're talking about when they make certain claims.
Just like I can recognize a clueless frontend developer when they say "React is basically just a newer jquery". Recognizing clueless engineers when they talk about AI can be pretty easy.
It's a sector that is both old and new: AI has been around forever, but even people who worked in the sector years ago are taken aback by what is suddenly possible, the workflows that are happening... hell, I've even seen cases where it's the very people who have been following GenAI forever that have a bias towards believing it's incapable of what it can do.
For context, I lead an AI R&D lab in Europe (https://ingram.tech/). I've seen some shit.
Define "not trivial". Obviously, experience helps, as with any tool. But it's hardly rocket science.
It seems to me the biggest barrier is that the person driving the tool needs to be experienced enough to recognize and assist when it runs into issues. But that's little different from any sophisticated tool.
It seems to me a lot of the criticism comes from placing completely unrealistic expectations on an LLM. "It's not perfect, therefore it sucks."
As of about three months ago, one of the most important skills in effective LLM coding is coding agent environment design.
If you want to use a tool like Claude Code (or Gemini CLI or Cursor agent mode or Code CLI or Qwen Code) to solve complex problems you need to give them an environment they can operate in where they can solve that problem without causing too much damage if something goes wrong.
You need to think about sandboxing, and what tools to expose to them, and what secrets (if any) they should have access to, and how to control the risk of prompt injection if they might be exposed to potentially malicious sources of tokens.
The other week I wanted to experiment with some optimizations of configurations on my Fly.io hosted containers. I used Claude Code for this by:
- Creating a new Fly organization which I called Scratchpad
- Assigning that a spending limit (in case my coding agent went rogue or made dumb expensive mistakes)
- Creating a Fly API token that could only manipulate that organization - so I could be sure my coding agent couldn't touch any of my production deployments
- Putting together some examples of how to use the Fly CLI tool to deploy an app with a configuration change - just enough information that Claude Code could start running its own deploys
- Running Claude Code such that it had access to the relevant Fly command authenticated with my new Scratchpad API token
With all of the above in place I could run Claude in --dangerously-skip-permissions mode and know that the absolute worse that could happen is it might burn through the spending limit I had set.
This took a while to figure out! But now... any time I want to experiment with new Fly configuration patterns I can outsource much of that work safely to Claude.
The statement I responded to was, "creating an effective workflow is not trivial".
There are plenty of useful LLM workflows that are possible to create pretty trivially.
The example you gave is not hardly the first thing a beginning LLM user would need. Yes, more sophisticated uses of an advanced tool require more experience. There's nothing different from any other tool here. You can find similar debates about programming languages.
Again, what I said in my original comment applies: people place unrealistic expectations on LLMs.
I suspect that this is at least partly is a psychological game people unconsciously play to try to minimize the competence of LLMs, to reduce the level of threat they feel. A sort of variation of terror management theory.
For one - I’d say scoped API tokens that prevent messing with resources across logical domains (eg prod vs nonprod, distinct github repos, etc) is best practice in general. Blowing up a resource with a broadly scoped token isn’t a failure mode unique to LLMs.
edit: I don’t have personal experience around spending limits but I vaguely recall them being useful for folks who want to set up AWS resources and swing for the fences, in startups without thinking too deeply about the infra. Again this isn’t a failure mode unique to LLMs although I can appreciate it not mapping perfectly to your scenario above
edit #2: fwict the LLM specific context of your scenario above is: providing examples, setting up API access somehow (eg maybe invoking a CLI?). The rest to me seems like good old software engineering
I don’t really see how it’s different than how you’d setup someone really junior to have a playground of sorts.
It’s not exactly a groundbreaking line of reasoning that leads one to the conclusion of “I shouldn’t let this non-deterministic system access production servers.”
Now, setting up an LLM so that they can iterate without a human in the loop is a learned skill, but not a huge one.
I don’t think anyone expects perfection. Programs crash, drives die, and computers can break anytime. But we expect our tools to be reliable and not fight with it everyday to get it to work.
I don’t have to debug Emacs every day to write code. My CI workflow just runs every time a PR is created. When I type ‘make tests’, I get a report back. None of those things are perfect, but they are reliable.
I'm not a native speaker, but to me that quote doesn't necessarily imply an inability of OP to get up the curve. Maybe they just mean that the curve can look flat at the start?
I remember the time they were cracking down because I had entered 90%+ of the tickets into the ticket system (the product manager didn't write tickets) and told me that "every ticket has to explain why it is good for the end user".
I put it in a ticket to speed up the 40 minutes build and was asked "How does this benefit the end user?" and I said "The end user would have had the product six months ago if the build was faster."
The graph of y/(x^2+y^2)=(x+1)/(x^2+y^2) by definition contains the points that satisfy this equation. This is exactly the set of points for which y = x + 1.
The "fuzzy" graph is just coloring the difference between the left hand side and right hand side. This is very basic, not new, and it's definitely not "the graph of y/(x^2+y^2)=(x+1)/(x^2+y^2)".