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Possibly relevant what specific grade(s) are these students from, and are they in any sort or gifted program or is it a normal middle school population.
"Green" or other color words are already in your vocabulary of trusted primitives, otherwise the question couldn't even be spoken. "Green" is (to a good enough approximation) a particular pattern of activation of cone cells in your retina, or (an approximation of an approximation, but still good enough) a point in the color space computed by a camera's CCD photoreceptors.
The query at hand is whether the same cone cells are firing (or whether the camera's CCDs return the same value) when looking straight up when out of doors on a cloudless day, as they do when looking at whatever type of object results in the color judgement "green" (for instance, grass or a tree).
That's the content of the belief. The original questions are answered from that basis.
Question 2 (of which question 1 is a special case) consists of evaluating the fit between the above and the observations we can collect. So, we point cameras (or eyes) at trees, then at the sky, and compare the results.
Question 3 entails pointing cameras at objects of different colors and picking to describe "sky" the same color word that we use to describe objects that have roughly the same values as the sky.
(Though question 3 is more complicated in its most general case - for instance to describe what happens when we start out with no color words whatsoever and learn them from experience. We're still updating on the results of a procedure that's very similar, but we do it without having yet formed the category "color word".)
Thanks for writing this explanation.
I have tested my belief using the built-in "sky-detector"(my eyes) and I can tell that it's false, for the sky is clearly blue with a tint of white. Still, there are some instances where my "sky-detector" could be faulty(e.g., eye disorders, neurological conditions), but since other people's "sky-detectors" and machines have confirmed my belief, I guess it's true.
But how true? Is there, say, an algorithm I can use to assign numerical values to the probability of my belief? Assuming that there is such an 'algorithm', how can I use it to compare my initial belief to the belief I now have(i.e., the sky is blue with a tint of white)?
In response to
Learning the basics of probability & beliefs
True beliefs reliably control anticipation. If you build a sky-detector that bases its decisions on color discrimination, you should anticipate that the detector's decisions will be appropriate to the extent that your theory of the sky's color is correct.
Let's imagine that the sky-detector's function is to orient a water spray toward the sky, so as to maximize the area sprayed. (Because "sky" is what's up when outdoors.)
Place the device on various surfaces. The color of sky is the color of whatever makes the device most confused, spraying in random directions.
While you make an interesting case for testing my belief, I do not know how to build a "sky-detector". So I still am oblivious as to whether my belief is true or not.
Right, but how do you evaluate pros and cons, and project outcomes ? Obviously you wouldn't take an action that has more cons than pros, and therefore has a poor projected outcome, but that doesn't tell me much.
For example, what made you decide to begin spending time on writing posts on Less Wrong, as opposed to spending that time on reading quantum physics books, or lifting weights, or something ?
I assign an util to each possible outcome.
what made you decide to begin spending time on writing posts on Less Wrong, as opposed to spending that time on reading quantum physics books, or lifting weights, or something ?
I do read quantum physics and lift weights and whatnot! :) As to why I decided to spend time here, see my original post.
No, I only take part in activities that have some long-term benefit.
That makes sense. What algorithm are you using to decide which activities have some long-term benefit ?
Pros&Cons and projected outcomes.
I look for background info on the piece I consider reading and read its abstract.
What about pieces that blend truth and fiction, such as historical novels or most newspaper articles ?
See the reply below. I'm not good at explaining this stuff.
Fair enough, but I'm still curious. Do you participate in any activities that you find enjoyable, but ultimately not very useful in the long term ? I'm not trying to be glib here; I genuinely want to learn about your way of thinking.
What about pieces that blend truth and fiction, such as historical novels or most newspaper articles ?
I don't usually read those kinds of pieces.
Do you participate in any activities that you find enjoyable, but ultimately not very useful in the long term ?
No, I only take part in activities that have some long-term benefit.
Nonfiction because: my faulty brain sometimes mistakes fiction for reality...
In this case, how do you know what is fiction (and therefore you shouldn't read it) and what is not (and therefore you should read it) ?
and cognitive economy - there is a finite amount of knowledge I can store, so I must be sure that it is accurate knowledge.
Can you elaborate ? I'm curious about the topic because I've heard this statement from several of my friends, but I can't quite wrap my head around it.
In the interests of full disclosure, I personally do read fiction: primarily because I find it enjoyable, but also because it sometimes enables me to communicate (and receive) ideas much more effectively than nonfiction (f.ex., HPMoR).
In this case, how do you know what is fiction (and therefore you shouldn't read it) and what is not (and therefore you should read it) ?
I look for background info on the piece I consider reading and read its abstract.
Can you elaborate ?
See the reply below. I'm not good at explaining this stuff.
Horace wrote that the purpose of literature is "to delight and instruct". It delights precisely because it's instructive and it's up to you to decide whether you only need precise information(nonfiction) or embedded information(fiction).
In response to
Deciding what to study at undergraduate level
I'll second the recommendation for bioengineering, that's exactly the field you're describing.
However, you might find at the undergraduate level that you'd be better off studying something that will get you a very solid foundation in mathematics and computer programming, which are the languages bioengineering uses to represent and model the behavior of biological systems.
Being an interdisciplinary field, it's critical to balance your time spent learning the various sciences to become an effective bioengineer. You need to have an understanding of very different areas of science such as cell biology and fluid mechanics, so you can integrate these ideas together in your research.
In my experience, students with a background in physics, mathematics, or chemistry actually do better in graduate level bioengineering courses than students whom studied bioengineering or life sciences as undergrads. The formerer were learning to solve complex problems and represent phenomena with mathematics while the bioengineers were memorizing facts and nomenclature in biology classes. Memorizing biological facts is much easier to pick up on your own when you need it, whereas math proficiency is a skill that must be developed over years of practice.
Many prominent professors of bioengineering actually have their degrees in the physical sciences, and taught themselves the relevant biology.
The most important advice I can give is to start doing research in your field of interest NOW. Even in high school, you can volunteer to work in a professors lab. Performing research is where the real education occurs, not in the classroom.
Bioengineering looks like the right choice but, unfortunately, my only available options are either General Engineering or Biomedical Science. To illustrate how these courses are organized at undergraduate level, see this for Biomedical Science and this for General Engineering.
I guess I should go with General Engineering.
I only read certain things
What kinds of things, out of curiosity, and why do you read them and not other things ?
Nonfiction because: my faulty brain sometimes mistakes fiction for reality(e.g., I used to believe that Santa is real) and cognitive economy - there is a finite amount of knowledge I can store, so I would rather make sure it's accurate, truthful, useful knowledge.
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tomme, welcome to lesswrong, gday I'm Peacewise.
re
Fair crack mate, "Santa" is a standard fiction/lie perpetrated by society and parents, hardly something to be used as evidence of a "faulty brain". In fact its more likely to be evidence that your brain was and is functioning in a developmentally normal state.
I suggest you reconsider your position on fiction, since you state
there is indeed plenty of accurate, truthful and useful knowledge within the realm of fiction. Shakespeare has plenty of accurate and useful knowledge about the human condition, just to give you one counter example. "Out damned spot, out " by lady Macbeth is an example of how murder and the guilt caused by the act of murder affects the human mind. (Macbeth, Act 5, scene 1.) Lady Macbeth cannot get the imagined blood stains off her hands after committing murder.
Humans are subjective creatures, by experimenting with fiction you'll be looking into the human condition, by avoiding fiction you are dismissing a large subset of truth - for truth is subjective as well as objective.
I now believe that fiction could be useful because it conveys experience. For example, The Walking Dead, the Tv series I am watching at the moment, has a complex interplay characters, as it shows how humans interact in a plethora of situations.
Most people don't have that in mind when they bump into fiction. But, as I said, if you don't have enough experience, and you need a quick dose, sometimes fiction can help you.