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sorry if I went a little overboard. I didn't mean it to sound confrontational.
You didn't. I appreciated your response. Gave me a lot to think about.
I still think there is some value to my strategy, especially if you don't want to (or it would be unfeasible) to give full probability distribution for related events (ex: all the possible outcomes of an election).
Thank you for your response.
Could you comment about how my strategy outlined above would not give useful information?
The method described in my post handles this situation perfectly well. All of your 50% predictions will (necessarily) come true 50% of the time, but you rack up a good calibration score if you do well on the rest of the predictions.
Seems like you're giving up trying to get useful information about yourself from the 50% confidence predictions. Do you agree?
For the problem of how to phrase the 50% confidence predictions, it might be useful to use the more specific proposition (or one that has the smaller uninformative prior probability). For instance, if you have a race between 10 candidates, and you think candidate X has a 50% chance to win, you should phrase your prediction as "Candidate X will win the election" rather than "Candidate X will not win the election".
If you consistently phrase your 50% confidence predictions this way, then your prediction results tell you something useful. If your 50% confidence predictions come true only 10% of the time, then maybe your problem is overconfidence in your reasons to deviate from uninformed priors or overconfidence in concocting reasons to believe a certain hypothesis in the vast hypothesis space.
edit: The biggest weakness of this approach is what do you do when you're choosing between something like "this coin flip will come up heads" and "this coin flip will come up tails"? Or when it is unclear what an uninformed prior would even be.
What do you think of watching car crash compilations to counteract the Peltzman effect?
Risk compensation is one potential problem with wearing a helmet... I imagine seat belts have a similar effect, as might drivers wearing helmets. Based on this idea backwards, I've read a proposal to add a spike to steering wheels to reduce dangerous driving.
I recommend watching car crash compilations. They definitely help you feel the risk of driving on an emotional level. I feel I've learned some things that improve my driving safety, but probably the biggest safety gain is I just tend to drive more cautiously due to car collisions being very present in my mind.
Only if you decide you're defining a sensation and not some physical phenomenon...That, to me, makes defining color through qualia a definition that isn't useful all that often.
That's the definition used in the overwhelming majority of cases. Careful, technical texts often make it clear that color is a sensation. Even Isaac Newton stressed that "the rays [of light] are not colored".
Even wikipedia goes with the sensation definition of color: "Color...is the visual perceptual property corresponding in humans to the categories called red, blue, yellow, etc...The color of an object depends on both the physics of the object in its environment and the characteristics of the perceiving eye and brain."
In everyday use, when a person says things like "hand me the blue towel", that person usually does not care, know, or even think about reflectance profiles and spectral power distributions. Usually all that person cares about is that the towel "looks blue" to him and the person he's talking to. He'll say "that towel is blue" just like he'll say "that chocolate is bitter".
It's very useful to have definitions that depend on human sensations. You and I are both humans, and we often have conversations with other humans.
it's not hard to make pretty rigorous (as Lumifer suggested, with the radiation frequency, and some outside conditions added to it).
Taking "outside conditions" into account to produce an objective definition of color that does a good job of corresponding to human color sensations is actually extremely complex and a very difficult task. Human color sensations are the result of extremely complex and highly contextual processing. I have studied color vision a great deal, and it is very, very common for people to underestimate the complexity and contextual nature of color perception.
Also, you're already conceding that color is not a property of a single object, which would make color a poor example of a property of an object.
Anyway, I'll take your response as a sign that you are comfortable with the problematic nature of your example, and the more pressing concern is playing nice with philosophical tradition/convention. So, I consider the issue closed.
You are now dealing in circular logic. If you criterion for "red" is a "color sensation in humans", you have already defined red. That's it, we're done.
We would run into the same problem for any description of a quale/sensation. For example, we would describe/identify nausea, bitterness, and redness in similar ways - it's hard to directly describe sensations, so we often indirectly identify sensations by pointing to conditions that lead to humans experiencing the sensation, or pointing to how the sensation relates to other sensations. That's the unfortunate business of qualia/sensations.
So, the criterion isn't circular, it's just unsatisfying in that we basically end up saying, "in situation X, you will probably feel the sensation I'm talking about, and we've labeled that sensation 'red'".
Definitions should be judged by their usefulness.
Agree 100%. Sometimes you can pretend that color is a simple objective creature and it turn out okay, just like we can use Newtonian physics when relativistic effects are small enough for our purpose.
just define it [color] a particular mixture of wavelengths of visible light
As I said before, you CAN come up with a simple objective definition of color, but it will do a "very poor job of corresponding to human color sensations".
A particular spectral power distribution can lead to many different color sensation depending on visual context, and even the expectation and memory of the human experiencing the color sensation. This fact makes that sort of definition unfit for a lot of purposes.
Look at these two scenes. The left-hand scene contains "blue" pixels that use the same RGB value (0x6e6f73) as the right-hand scene's "yellow" pixels. And in the context of the legend at top, that RGB value produces a third color sensation: gray.
So, any definition of color that only depends on spectral power distributions will not correspond very well with actual human color sensations. The linked picture demonstrates that "the light mixture your monitor produces for an RGB value of 0x6e6f73" is nowhere near enough information to predict what color sensation a human will experience from viewing pixels with that RGB value, even within the limited range of conditions of looking at something on a monitor.
Also, the two-scene picture is not an unusual case. The highly contextual nature of color perception is ubiquitous. Human color processing is always making contextual adjustments from scene illumination. The picture of a fruit basket in this section does a good job of showing how contextual adjustments are the norm. The overwhelming importance of context in color perception massively shrinks the situations where simple objective definitions of color are useful. Treating color as a simple objective creature gets you into trouble fairly quickly.
To produce a workable definition of subjective color is much harder -- this is a practical matter in photography and graphics and whole books are written on the subject.
Yep, which is why I urged the author of the post to choose something other than color as an example of a simple/natural category.
Also, don't you mean objective? The color model work you're talking about is an effort to come up with objective mathematical models that exist outside of human minds (thus considered objective) that give outputs that correspond to sensations that exist inside human minds (those sensations being subjective). I don't want us to get hung up on what "objective" and "subjective" means, but if this conversation continues much more, it might be good to spend a bit of time making sure we understand each other when we use those words.
Neat, I recognize your username. I always liked your choice of username, and I've often enjoyed your comments. Thanks.
you could mean it as shorthand for "that object emits or reflects electromagnetic radiation with a pronounced peak around 700nm wavelength".
Except that is not sufficient nor necessary to ensure that the object would typically generate a red color sensation in humans, even in "neutral or typical conditions". So, I would not mean it as shorthand for that. Color sensations can not be boiled down to or predicted by spectral power distributions and reflectance profiles only.
I'm thinking your comment perhaps was a gentle nudge to say, "it's not too hard to make color an objective creature". Well, you can come up with some objective definition of whether some object has the property of redness, but you'd have to basically reimplement the human visual system and assume a huge amount about the object's current surroundings (or you could not go to that effort and end up with something that does a very poor job of corresponding to human color sensations). It would be similar to converting bitterness of food or soothingness of music into objective properties. Or maybe your comment was a gentle nudge in a completely different direction.
I'm going to raise an issue, and it could be fair to consider it a nitpick, but considering that you're trying to be rigorous, perhaps it is okay to be unusually technical.
Blue and green are not natural categories, or at least they are as natural as "sour tasting" or "stinky". To quote Bruce MacEvoy, "color is a complex judgment experienced as a sensation"; color is not an objective property of things in the world. When a human gazes at something, the color sensation they experience is highly dependent on all sorts of visual factors in the scene, and even depends on the memory and expectation of the human.
When I say, "that object is red", I mean it as shorthand for "that object has a reflectance, transmittance, and emittance profile that usually leads humans to experience a red color sensation when viewing the object in neutral-ish conditions". And let it be known that "red color sensation" and "neutral-ish conditions" are still massive shorthand. So really, "that object is red" is a statement concerning 1) the object 2) the human visual system 3) qualia 4) common viewing environments for humans.
I point this out because it seems wrong to try to do a bunch of rigorous thinking founded upon an extremely flawed example (flawed in the example is supposed to be about objective things, but is actually about subjective things). We even have Eliezer Yudkowsky talking about the nature of truth and using statements like "snow is white if and only if snow is white". It might sound like he's talking about facts, but imagine the analogous sentence "skunks are stinky if and only if skunks are stinky" or "chess is interesting if and only if chess is interesting". Now it is more clear the statement is about subjective experiences and actually fails to have a definite truth value.
Would you be comfortable if your natural category example was whether some music was soothing, or whether some object was bitter? If you would not be comfortable with using those subjective examples, you should not be comfortable using color as an example. If you are comfortable with those examples, you can disregard the issue I raise.
I think a lot of your points still stand, but you're taking unnecessary risks by using a flawed example.
Took the survey. I loved the calibration questions; it takes ~20 times more effort to come up with the confidence level than the answer, and I always feel I learn about myself. I've messed with some calibration question games before and was downright astonished at how well calibrated I was (the irony is not lost on me); but the questions were all in A-vs-B format rather than free form. The A-vs-B format is much easier to appear to be well calibrated.
The wolfram alpha links in the article and previous comments seem to be broken in that the parentheses in the mathematical expression are missing, meaning that the links present readers with the wrong answer. It was rather confusing for me for a bit. You might want to update the links to something like this:
S pdf: http://www.wolframalpha.com/input/?i=integrate+3%2F2+*+%281+-+2*x+%2B+2*x^2%29+++from+0+to+1
D pdf: http://www.wolframalpha.com/input/?i=integrate+6+*+%28x+-+x^2%29+++from+0+to+1