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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.
Help me teach Bayes'
Next Monday I am supposed to introduce a bunch of middle school students to Bayes' theorem.
I've scoured the Internet for basic examples where Bayes' theorem is applied. Alas, all explanations I've come cross are, I believe, difficult to grasp for the average middle school student.
So what I am looking for is a straightforward explanation of Bayes' theorem that uses the least amount of Mathematics and words possible. (Also, my presentation has to be under 3 minutes.)
I think that it would be efficient in terms of learning for me to use coins or cards, something tangible to illustrate what I'm talking about.
What do you think? How should I teach 'em Bayes' ways?
PS: I myself am new to Bayesian probability.
"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.
Learning the basics of probability & beliefs
Let's say that I believe that the sky is green.
1) How can I know whether this belief is true?
2) How can I assign a probability to it to test its degree of truthfulness?
3) How can I update this belief?
Thank you.
Best shot at immortality?
What looks, at the moment, as the most feasible technology that can grant us immortality (e.g., mind uploading, cryonics)?
I posed this question to a fellow transhumanist and he argued that cryonics is the answer, but I failed to grasp his explanation. Besides, I am still struggling to learn the basics of science and transhumanism, so it would be great if you could shed some light on my question.
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.
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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.