4 ms·
One memorable example of this was a book which said you could tell the temperature of a star by the wavelength of the light it emitted. It then asked you to cal
by AndrewOMartin 5y ago
One memorable example of this was a book which said you could tell the temperature of a star by the wavelength of the light it emitted. It then asked you to calculate the temperature of stars in a depicted galaxy. I'm sure there are some subtleties that are not exactly perfect but good enough for a school textbook.
The part that made Feynman erupt in anger was the follow up question, "what is the total temperature of the galaxy".
- pharmakom 5y agoCan you explain this?
- DuskStar 5y agoThe problem is incredibly ill defined. Do they want the sum of the temperatures calculated above? (Nonsensical) The temperature that the galaxy would have if you mixed everything together? (Insufficient information on star size and material composition) The average of the stars temperatures? (ALSO nonsensical!)
- mattkrause 5y agoWhat's wrong with the average temperature over many stars? It gives you the best possible estimate (in a MSE sense) for the temperature of a new star for which you know nothing about. It may not be a great estimate (e.g, the distribution is multimodal because stars come in various types), but it doesn't seem obviously nonsensical.
- jmount 5y agoI haven't seen the source. But I am guessing the anger is temperature is a number that doesn't make since to blindly add. Example: 2 boiling pots are not 200 degrees C. Or more technically temperature is the mean molecular kinetic energy, an average not a total.
- mattkrause 5y agoThe really frustrating part is that a trivial edit--ask for the average temperature instead--could make it into a sensible question.
- vlovich123 5y agoAn average of an average does not yield any number that has any useful definition.
- mattkrause 5y agoCould you elaborate? The average (over 24 hours) temperature yesterday was 25˚C. You could certainly ask how that compares to other August 29ths in different years. This even has a name ("grand mean"), so I'm surprised that someone thinks it's never useful.
- vlovich123 5y agoI may have overstated slightly. The mean of means is equivalent to the overall mean iff > the subsamples have the same number of data points It's unlikely to be useful in any other situation. Certainly not for averaging the temperature of a galaxy.
- mattkrause 5y agoYes, that's obviously how the math works out. Both the overall mean and mean-of-means have sensible interpretations though. Suppose you observe a random sample of stars and find their temperatures to be 6000, 6250, 6750, and 7000C. The best possible guess[0] for the temperature of a new star drawn from that population is 6500C. The average temperature of all the starstuff may be different if one star is larger than another, but that's an answer to a slightly different question. In fact, I would argue that the mean-of-means is often a more appropriate summary statistic than the overall mean of the observations when there are repeated measurements. [0] Under L2 loss, with no prior, etc etc
- RichardCA 5y agoIt's an easy mistake to make, to have incorrect pedagogy around the concept of temperature, and Feynman was fanatical about correct pedagogy. This is always good: https://youtu.be/Q1lL-hXO27Q https://youtu.be/Q1lL-hXO27Q
- bmn__ 5y agoThe story is in the page linked above. ctrl+f temperature
- dekhn 5y agototal... or mean? it's an intensive property (something that was "taught" to me many years ago, in school).