Director at AI Impacts.
Richard Korzekwa
It seems like we suck at using scales “from one to ten”. Video game reviews nearly always give a 7-10 rating. Competitions with scores from judges seem to always give numbers between eight and ten, unless you crash or fall, and get a five or six. If I tell someone my mood is a 5⁄10, they seem to think I’m having a bad day. That is, we seem to compress things into the last few numbers of the scale. Does anybody know why this happens? Possible explanations that come to mind include:
People are scoring with reference to the high end, where “nothing is wrong”, and they do not want to label things as more than two or three points worse than perfect
People are thinking in terms of grades, where 75% is a C. People think most things are not worse than a C grade (or maybe this is just another example of the pattern I’m seeing)
I’m succumbing to confirmation bias and this isn’t a real pattern
- 16 Dec 2014 23:06 UTC; 16 points) 's comment on Welcome to Less Wrong! (7th thread, December 2014) by (
In medicine we try to make people rate their symptoms, like pain, from one to ten. It’s pretty much never under 5.
This is actually what initially got me thinking about this. I read a half-satire thing about people misusing pain scales. Since my only source for the claim that people do this was a somewhat satirical article, I didn’t bring it up initially.
I was surprised when I heard that people do this, because I figured most people getting asked that question aren’t in near as much pain as they could be, and they don’t have much to gain by inflating their answer. When I’ve been asked to give an answer on the pain scale, I’ve almost always felt like I’m much closer to no pain than to “the worst pain I can imagine” (which is what I was told a ten is), and I can imagine being in such awful pain that I can’t answer the question. I think I answered seven one time when I had a bone sticking through my skin (which actually hurt less than I might have thought).
Hi everyone!
My name is Rick, and I’m 29. I’ve been lurking on LW for a few years, casually at first, but now much more consistently. I did finally post a stupid question last week, and I’ve been going to the Austin Meetup for about a month, so I feel it’s time to introduce myself.
I’m a physics PhD student in Austin. I’m an experimentalist, and I work on practical-ish stuff with high-intensity lasers, so I’m not much good answering questions about string theory, cosmology, or the foundations of quantum mechanics. I will say that I think the measurement problem (as physicists usually refer to the question which “many worlds” is intended to answer) is interesting, but it’s not clear to me why it gets so much attention.
I come from a town where (it seems like) everybody’s dad has a PhD, and many people’s moms have them as well. Getting a PhD in physics or engineering just seemed like the thing to do. I remember thinking as a teenager that if you didn’t go to grad school, you were probably an uneducated yokel. More importantly, I learned very early that a person can have a PhD and still make terrible decisions or have terrible beliefs. I also formed weird beliefs like “chemistry is for girls” and “engineers ride mountain bikes; physicists ride road bikes”. I think I still associate educational attainment too strongly with status.
I’ve been involved in the atheist and secular humanism communities for close to ten years now. I gradually transitioned from viewing these communities as a source of intellectual stimulation to sources of interesting and relatable people. I’m still involved in the secular humanism club that I started a few years back at UT.
I was vaguely aware of Less Wrong for a while before my roommate showed me HPMOR. After reading through all of that (which had been released at the time), I got more into the site and quickly read all the core sequences. I found all of it to be much more intellectually satisfying than all of the atheist apologetics I’d read in college, and I realized how much better it was for actually accomplishing something other than winning an argument. Realizing how toxic most political arguments are and understanding why I could win an argument and still feel icky about it were pretty huge revelations for me. In the last six months, I’ve been able to use things that I learned here and made some seriously positive changes in my life. It’s been pretty great.
I’m also interested in backpacking, rock climbing, and competitive cycling. A bike race is a competition in which knowing what your opponent knows about you can be a decisive advantage. It’s very much a Newcomb-like problem. Maybe I’ll start a thread about that sometime.
That’s not an explanation, just a symptom of the problem.
This is what I was trying to convey when I said it might be another example of the problem.
I think it’s reasonable, in many contexts, to say that achieving 75% of the highest possible score on an exam should earn you what most people think of as a C grade (that is, good enough to proceed with the next part of your education, but not good enough to be competitive).
I would say that games are different. There is not, as far as I know, a quantitative rubric for scoring a game. A 6⁄10 rating on a game does not indicate that the game meets 60% of the requirements for a perfect game. It really just means that it’s similar in quality to other games that have received the same score, and usually a 6⁄10 game is pretty lousy. I found a histogram of scores on metacritic:
The peak of the distributions seems to be around 80%, while I’d eyeball the median to be around 70-75%. There is a long tail of bad games. You may be right that this distribution does, in some sense, reflect the actual distribution of game quality. My complaint is that this scoring system is good at resolving bad games from truly awful games from comically terrible games, but it is bad at resolving a good game from a mediocre game.
What I think it should be is a percentile-based score, like Lumifer describes:
Consider this example: I come up to you and ask “So, how was the movie?”. You answer “I give it a 6 out of 10″. Fine. I have some vague idea of what you mean. Now we wave a magic wand and bifurcate reality.
In branch 1 you then add “The distribution of my ratings follows the distribution of movie quality, savvy?” and let’s say I’m sufficiently statistically savvy to understand that. But… does it help me? I don’t know the distribution of movie quality. it’s probably bell-shaped, maybe, but not quite normal if only because it has to be bounded, I have no idea if its skewed, etc.
In branch 2 you then add “The rating of 6 means I rate the movie to be in the sixth decile”. Ah, that’s much better. I now know that out of 10 movies that you’ve seen five were probably worse and three were probably better. That, to me, is a more useful piece of information.
Then again, maybe it’s difficult to discern a difference in quality between a 60th percentile game and an 80th percentile game.
I’l follow suit with the previous spoiler warning.
SPOILER ALERT .
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I took a bit different approach from the others that have solved this, or maybe you’d just say I quit early once I thought I’d shown the thing I thought you were trying to show:
If we write entropy in terms of the number of particles, N and the fraction of them that are excited: α ≡ E/(Nε) , and take the derivative with respect to α, we get:
dS/dα = N log [(1-α)/α]
Or if that N is bothering you (since temperature is usually an intensive property), we can just write:
T = 1/(dS/dE) = E / log[(1-α)/α]
This will give us zero temperature for all excited or no excited particles (which makes sense, because you know exactly where you are in phase space), and it blows up at half particles are excited. This means that there is no reservoir hot enough to get from α < .5 to α = .5 .
your final answer isn’t right
You’re right. That should be ε, not E. I did the extra few steps to substitute α = E/(Nε) back in, and solve for E, to recover DanielFilan’s (corrected) result:
E = Nε / (exp(ε/T) + 1)
I used S = log[N choose M], where M is the number of excited particles (so M = αN). Then I used Stirling’s approximation as you suggested, and differentiated with respect to α.
Temperature is then defined as the thermodynamic quantity that is the shared by systems in equilibrium.
I think I’ve figured out what’s bothering me about this. If we think of temperature in terms of our uncertainty about where the system is in phase space, rather than how large a region of phase space fits the macroscopic state, then we gain a little in using the second law, but give up a lot everywhere else. Unless I am mistaken, we lose the following:
Heat flows from hot to cold
Momentum distribution can be predicted from temperature
Phase changes can be predicted from temperature
The reading on a thermometer can be predicted from temperature
I’m sure there are others. I realize that if we know the full microscopic state of a system, then we don’t need to use temperature for these things, but then we wouldn’t need to use temperature at all.
if you know the states of all the molecules in a glass of hot water, it is cold in a genuinely thermodynamic sense: you can take electricity out of it and leave behind an ice cube.
If you’re able to do this, I don’t see why you’d be using temperature at all, unless you want to talk about how hot the water is to begin with (as you did), in which case you’re referring to the temperature that the water would be if we had no microscopic information.
We don’t lose those things.
Suppose that you boil some water in a pot. You take the pot off the stove, and then take a can of beer out of the cooler (which is filled with ice) and put it in the water. The place where you’re confusing your friends by putting cans of beer in pots of hot water is by the ocean, so when you read the thermometer that’s in the water, it reads 373 K. The can of beer, which was in equilibrium with the ice at a measured 273 K, had some bits of ice stuck to it when you put it in. They melt. Next, you pull out your fancy laser-doppler-shift-based water molecule momentum spread measurer. The result jives with 373 K liquid water. After a short time, you read the thermometer as 360 K (the control pot with no beer reads 371 K). There is no ice left in the pot. You take out the beer, open it, and measure it’s temperature to be 293 K and its momentum width to be smaller than that of the boiling water.
What we observed was:
Heat flowed from 373 K water to 273 K beer
The momentum distribution is wider for water at 373 K than at 293 K
Ice placed in 373 K water melts
Our thermometer reads 373 K for boiling water and 273 K for water-ice equilibrium
Now, suppose we do exactly the same thing, but just after putting the beer in the water, Omega tells us the state of every water molecule in the pot, but not the beer. Now we know the temperature of the water is exactly 0 K. We still anticipate the same outcome (perhaps more precisely), and observe the same outcome for all of our measurements, but we describe it differently:
Heat flowed from 0 K water to 273 K beer
The momentum distribution is wider for water at 0 K (or recently at 0 K) than at 293 K
Ice placed in 0 K water melts
Our thermometer reads 373 K for water boiling at 0 K, and 273 K for water-ice equilibrium
So the only difference is in the map, not the territory, and it seems to be only in how we’re labeling the map, since we anticipate the same outcome using the same model (assuming you didn’t use the specific molecular states in your prediction).
Remember, this isn’t my definition. This is the actual definition of temperature used by statistical physicists.
I agree that temperature should be defined so that 1/T = dS/dE . This is the definition that, as far as I can tell, all physicists use. But nearly every result that uses temperature is derived using the assumption that all microstates are equally probable (your second law example being the only exception that I am aware of). In fact, this is often given as a fundamental assumption of statistical mechanics, and I think this is what makes the “glass of water at absolute zero” comment confusing. (Moreover, many physicists, such as plasma physicists, will often say that the temperature is not well-defined unless certain statistical conditions are met, like the energy and momentum distributions having the correct form, or the system being locally in thermal equilibrium with itself.)
I’m having trouble with brevity here, but what I’m getting at is that if you want to show that we can drop the fundamental postulate of statistical mechanics, and still recover the second law of thermodynamics, then I’m, happy to call it a feature rather than a bug. But it seems like bringing in temperature confuses the issue rather than clarifying it.
The first way is that the water doesn’t flow heat into the beer, rather it does some work on it.
This actually clears things up quite a lot. I think my discomfort with this description is mainly aesthetic. Thank you for being patient.
Under the profession listings, it says 35 people and 4% for Business. 35 is 2.7% of 1500.
I remember answering the computer games question and at first feeling like I knew the answer. Then I realized the feeling I was having was that I had a better shot at the question than the average person that I knew, not that I knew the answer with high confidence. Once I mentally counted up all the games that I thought might be it, then considered all the games I probably hadn’t even thought of (of which Minecraft was one), I realized I had no idea what the right answer was and put something like 5% confidence in The Sims 3 (which at least is a top ten game). But the point is that I think I almost didn’t catch my mistake before it was too late, and this kind of error may be common.
I would expect for asexuals to be overrepresented
Why do you expect this? It seems reasonable if I think in terms of stereotypes. Also, I guess LWers might be more likely to recognize that they are asexual.
Literally every group had at least one member who supplied a P(God) of 0 and a P(God) of 100.
Okay, I’ll bite: What does someone mean when they say they are Atheist, and they think P(God) = 100% ?
I think the argument is that it is desirable for the optimal strategy for learning to be very similar to the optimal strategy for getting a good grade. Greater information about what is on the exam increases the difference between the two.
I used to teach physics to pre-med students (a nearly-identical situation to [2] in the original post). I tried to write my exams so that simply memorizing a large set of very specific algorithms for solving a problems wouldn’t work, but nobody would have to be very clever in order to get a good grade.
In addition to this, I looked at the course material and asked “Is there anything thing on here that a doctor really needs to know?”. I decided it was good for doctors to know how half-lives work, since this is important for things like drug dosing, as well as probably other things I don’t even know about (since anything who’s rate of decay is proportional to it’s value will behave the same way). So, I explained to my students that a discharging capacitor was mathematically identical to the way that some drug concentrations decrease over time, and that there absolutely, positively would be a question about it on the exam. I didn’t say anything else very specific about what would be on the rest of the exam. That exam had one question about a discharging capacitor, followed by a second question that was the same as the first, but reworked in terms of drugs. Most students got the first one right, but fewer got the second.
I think that part of my distaste, as an instructor, for students knowing a lot more about what is on the exam was that I wound up talking a lot more about the same things, and it got boring.
Delayed response is also great to cool off heated discussions.
I’ve had this experience as well. Usually a five to ten minute wait is long enough for me to chill out and say something less inflammatory when things start getting bad.
I am taking a graduate course called “Vision Systems”. This course “presents an introduction to the physiology, psychophysics, and computational aspects of vision”. The professor teaching the course recommended that those of us that have not taken at least an undergraduate course in perception get an introductory book on the subject. The one he recommends, which is also the one he uses for his undergraduate course, is this: http://www.amazon.com/Sensation-Perception-Looseleaf-Third-Edition/dp/0878938761 Unfortunately, this book goes for $60-75 for used loose leaf, all the way up to $105 for new hardcover. I’d rather not pay that, unless I can get an independent recommendation for it, or for some other book on the subject.
Does anybody here have a recommendation? Are there good course notes available on the web somewhere?
I have this issue with motivation. I need to clean my house, but I have a difficult time getting myself to do it, unless I think I can finish it all at once. For example, based on past experience, it takes me around three hours of focused effort to get things from where they are now to satisfactory, but I only have ninety minutes. While I could get half-way there now, and finish up sometime later in the week, I imagine myself working hard for 90 minutes, and still having a messy house. Then I do something else instead, unless I’m in a state where cleaning seems less unpleasant than usual.
Does anybody have advice for combating this problem?
(edited for a typo)
Yes, I’ve read that. Thanks for the reminder.
I think I’m having trouble with the ‘expectancy’ part of the equation. That is, I know that I will fail to complete the task now. Or, maybe you would say that the immediate value is almost zero.
Many things in our best models of physics are discrete, but as far as I know, our coordinates (time, space, or four-dimensional space-time coordinates) are never discrete. Even something like quantum field theory, which treats things in a non-intuitively discrete way does not do this. For example, we might view the process of an electron scattering off another electron as an exchange of many discrete photons between the two electrons, but it is all written in terms of integrals or derivatives, rather than differences or sums.