5 ms·

> incorrect and unintuitive The thing that you might be missing is that "incorrect" is (usually) objective, but "unintuitive" isn't necessarily so. I can see h

by gs17 5y ago

> incorrect and unintuitive The thing that you might be missing is that "incorrect" is (usually) objective, but "unintuitive" isn't necessarily so. I can see how someone else would think additive opacity is intuitive, even if it's very easy to show that it isn't correct.

marcosdumay 5y ago
Every one of those things limited to [0; 1] combine multiplicativelly. (Mostly because they are some kind of probability or vectorial projection - what are the same thing, by the way.) You are right that "intuitive" is a subjective property. But I'm completely lost trying to imagine what kind of life experiences can lead on to expect them to be additive.
- nerdponx 5y ago
  I also thought that opacity was additive and clamped to 0,1 until right now. Seem intuitive to me. Half + half = whole. When I make a chart in R and set the color to alpha 0.5, the result looks more or less like an opaque point if I plot 2 of them on top of each other. Apparently that's wrong, but it's consistent with my not-very-precise observations, and I have never had a need or desire to learn more about how opacity works. One cannot be an expert in all things. What intuition should a layperson have to suggest that obviously opacity/transmissivity is multiplicative? I don't see the value in deriding the incorrect intuition of uneducated people. In statistics at least we accept that statistics is hard specifically because it can be unintuitive.
  - marcosdumay 5y ago
    Out of curiosity, did you have any rationalization for why clamping it made sense, or you just didn't think about it?
    - nerdponx 5y ago
      "How can something be more opaque than fully opaque?" was my intuition (and probably many other people's). Also RGBA numbers are generally clamped to 0,255.
      - marcosdumay 5y ago
        Ok, I guess the repulsiveness of a clamping operation is something we learn. If one doesn't learn to fear it, it's an operation like any other. Should have been obvious, but I never thought about it.
        Agentlien 5y ago
        Why do you call it repulsive? It's a very common operation in graphics. Even so that certain graphics processors have a flag for floating point operations which allow the results to be saturated (clamped to [0,1]) at no extra cost. I know I prefer to avoid it and design equations so it isn't necessary. That often helps make the math cleaner and more well behaved. But repulsion sounds stronger than what I feel. I would say there are plenty of cases where things do act additively yet we wish to clamp their values to a specific range (often valid colours).
        marcosdumay 5y ago
        It does appear when you are trying to optimize graphical operations and change the real physical models with approximate ones. It's also a signal that your approximate model won't behave well on repeated application, what is normally not a problem in graphics display, but a red flag on general purpose image processing. On a physical model, it is a very strong signal that you messed something up and your model is wrong. Sometimes you get something that looks like a sigmoid but has the exponential parts very short, so it looks like a clamped linear function, but you normally need some kind of mechanism limiting the output on the linear region. Simple phenomena do not have clamping, it is a very complex operation.
        Agentlien 5y ago
    - jrochkind1 5y ago
      The naive model: Eventually you've blocked all the light, and adding more semi-transparent things on top can't block any more light.
  - riversflow 5y ago
    > What intuition should a layperson have to suggest that obviously opacity/transmissivity is multiplicative? My intuition is that if I put on dark sunglasses I can still see through other dark things (like a CD or welders glass) if I look at something bright enough (like the sun). If opacity/transmissivity is modeled like it works in real life, given this example, it follows that it wouldn't be additive.
    - nerdponx 5y ago
      That's a great point, and it illustrates the problem with the mental models of uneducated people. It's difficult to know what information should and shouldn't be part of the model! I figured it just didn't work like real life, because RGBA numbers are clamped.
  - teawrecks 5y ago
    > What intuition should a layperson have to suggest that obviously opacity/transmissivity is multiplicative? Tinted windows and sunglasses come to mind. Intuitively, if you put translucent things back to back, you expect light to still pass through, albeit less of it, but always some. A noteworthy exception is when using polarized filters, which can unintuitively block out 100% of light depending on the angle between the filters.
  - wruza 5y ago
    It’s just bad intuition, sorry :) E.g. when you mix two grays (#80808000) in RGBA space you probably don’t expect white. None of R, G, B, A are additive in a sense of color/transparency mixing. They are only additive component-wise regarding the resulting color, i.e. R+G+B is a color, but two reds aren’t 2R.
- coldtea 5y ago
  >But I'm completely lost trying to imagine what kind of life experiences can lead on to expect them to be additive. I, on the other hand, am completely lost trying to imagine what kind of life experiences can lead one to believe the OP error requires some "unique/rare" life experience. How about the very common life experience of (a) not being good at math but still being a programmmer and having eventually to deal with something math-y? or (b) the life experience of someone who might now enough math to get this, but didn't give it alpha opacity much thought before, and the simple addition model was good enough for them (as they never had to do anything special with it)?

by gs17 5y ago

marcosdumay 5y ago

Every one of those things limited to [0; 1] combine multiplicativelly. (Mostly because they are some kind of probability or vectorial projection - what are the same thing, by the way.) You are right that "intuitive" is a subjective property. But I'm completely lost trying to imagine what kind of life experiences can lead on to expect them to be additive.

nerdponx 5y ago
I also thought that opacity was additive and clamped to 0,1 until right now. Seem intuitive to me. Half + half = whole. When I make a chart in R and set the color to alpha 0.5, the result looks more or less like an opaque point if I plot 2 of them on top of each other. Apparently that's wrong, but it's consistent with my not-very-precise observations, and I have never had a need or desire to learn more about how opacity works. One cannot be an expert in all things. What intuition should a layperson have to suggest that obviously opacity/transmissivity is multiplicative? I don't see the value in deriding the incorrect intuition of uneducated people. In statistics at least we accept that statistics is hard specifically because it can be unintuitive.
- marcosdumay 5y ago
  Out of curiosity, did you have any rationalization for why clamping it made sense, or you just didn't think about it?
  - nerdponx 5y ago
    "How can something be more opaque than fully opaque?" was my intuition (and probably many other people's). Also RGBA numbers are generally clamped to 0,255.
    - marcosdumay 5y ago
      Ok, I guess the repulsiveness of a clamping operation is something we learn. If one doesn't learn to fear it, it's an operation like any other. Should have been obvious, but I never thought about it.
      - Agentlien 5y ago
        Why do you call it repulsive? It's a very common operation in graphics. Even so that certain graphics processors have a flag for floating point operations which allow the results to be saturated (clamped to [0,1]) at no extra cost. I know I prefer to avoid it and design equations so it isn't necessary. That often helps make the math cleaner and more well behaved. But repulsion sounds stronger than what I feel. I would say there are plenty of cases where things do act additively yet we wish to clamp their values to a specific range (often valid colours).
        marcosdumay 5y ago
        It does appear when you are trying to optimize graphical operations and change the real physical models with approximate ones. It's also a signal that your approximate model won't behave well on repeated application, what is normally not a problem in graphics display, but a red flag on general purpose image processing. On a physical model, it is a very strong signal that you messed something up and your model is wrong. Sometimes you get something that looks like a sigmoid but has the exponential parts very short, so it looks like a clamped linear function, but you normally need some kind of mechanism limiting the output on the linear region. Simple phenomena do not have clamping, it is a very complex operation.
        Agentlien 5y ago
  - jrochkind1 5y ago
    The naive model: Eventually you've blocked all the light, and adding more semi-transparent things on top can't block any more light.
- riversflow 5y ago
  > What intuition should a layperson have to suggest that obviously opacity/transmissivity is multiplicative? My intuition is that if I put on dark sunglasses I can still see through other dark things (like a CD or welders glass) if I look at something bright enough (like the sun). If opacity/transmissivity is modeled like it works in real life, given this example, it follows that it wouldn't be additive.
  - nerdponx 5y ago
    That's a great point, and it illustrates the problem with the mental models of uneducated people. It's difficult to know what information should and shouldn't be part of the model! I figured it just didn't work like real life, because RGBA numbers are clamped.
- teawrecks 5y ago
  > What intuition should a layperson have to suggest that obviously opacity/transmissivity is multiplicative? Tinted windows and sunglasses come to mind. Intuitively, if you put translucent things back to back, you expect light to still pass through, albeit less of it, but always some. A noteworthy exception is when using polarized filters, which can unintuitively block out 100% of light depending on the angle between the filters.
- wruza 5y ago
  It’s just bad intuition, sorry :) E.g. when you mix two grays (#80808000) in RGBA space you probably don’t expect white. None of R, G, B, A are additive in a sense of color/transparency mixing. They are only additive component-wise regarding the resulting color, i.e. R+G+B is a color, but two reds aren’t 2R.
coldtea 5y ago
>But I'm completely lost trying to imagine what kind of life experiences can lead on to expect them to be additive. I, on the other hand, am completely lost trying to imagine what kind of life experiences can lead one to believe the OP error requires some "unique/rare" life experience. How about the very common life experience of (a) not being good at math but still being a programmmer and having eventually to deal with something math-y? or (b) the life experience of someone who might now enough math to get this, but didn't give it alpha opacity much thought before, and the simple addition model was good enough for them (as they never had to do anything special with it)?