Primes and Squares

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Nathan Merrill

02:52

ok, lets say you wanted to measure whether weather prediction was accurate. Each day they said what the %chance of rain was, and you wrote down the probability of whatever happened.

so, if the weatherman said 80% chance of rain, and it didn't rain, you'd write down .2

or, if he said 66% chance of rain, and it did, you'd write down .66

given a list of these probabilities, how do you measure how accurate the weatherman is?

PhiNotPi

03:37

@NathanMerrill Are you viewing accuracy in terms of "first order"(?) where you're just measuring accuracy as a percentage (either he predicted rain or he didn't, and he was either right or wrong), or higher order, where you want to know how close the percentage he says is to the real percentage?

(The second problem being more interesting IMO)

I think it would be better if you also kept track of whether it rained or didn't, in addition to just the probability itself. There could be certain types of asymmetrical errors (constantly over/underestimating) that you could more easily see.

If you forget whether or not it rained, then over and underestimating would "look the same."

1 hour later…

Nathan Merrill

04:48

@PhiNotPi the second problem

@PhiNotPi this is true

so, given a list of (probability, boolean) pairs, calculate how accurate his percentages are

PhiNotPi

@NathanMerrill In some ways this is similar to fitting a curve to a scatterplot. x-axis = predicted probability, y-axis = actual probability.

And the scatterplot data points all have y-values of either 0 or 1.

And so we could start by deciding what type of curve we think we should use. One reasonable assumption is that the curve is non-decreasing (a higher predicted chance never means a lower actual chance).

9 hours later…

Nathan Merrill

13:38

@PhiNotPi and a "perfect" curve would be a straight line from 0,0 to 1,1?

PhiNotPi

@NathanMerrill yes

Nathan Merrill

yeah. You'd never actually get that unless you have two points at 0% and 100%

but with more data, you'd get closer

IIRC, Battle for Wesnoth has a similar thing

in essence, they have a score that indicates the "likelyhood" of your game

based on how many times a roll favors you

(which in my mind, is like a score that detects reload cheating)

Nathan Merrill

14:12

totally different topic:

for all of those people that say "There's no such thing as cold", you could easily say the opposite

right?

like, one is simply defined by the other

Martin Ender

context?

Nathan Merrill

we define heat as "high energy level"

and cold as "low energy level"

Martin Ender

well, there's an absolute zero, but no absolute max, so defining it as a positive quantity (or absence thereof) makes more sense than the other way round, doesn't it?

Nathan Merrill

is there no max?

Martin Ender

no? it's just energy. there's no hard maximum to the energy something can have.

Nathan Merrill

14:15

like, there's got to be some maximum amount of energy you can fit in a given area

yeah, I dunno

Martin Ender

no, just accelerate your particle further and its kinetic energy will increase

Nathan Merrill

Hagedorn temperature

The Hagedorn temperature is the temperature in theoretical physics where hadronic matter (i.e. ordinary matter) is no longer stable, and must either "evaporate" or convert into quark matter; as such, it can be thought of as the "boiling point" of hadronic matter. The Hagedorn temperature exists because the amount of energy available is high enough that matter particle (quark-antiquark) pairs can be spontaneously pulled from vacuum. Thus, naively considered, a system at Hagedorn temperature can accommodate as much energy as one can put in, because the formed quarks provide new degrees of freedom...

oh, it's called absolute hot

Absolute hot

Absolute hot is a concept of temperature that postulates the existence of a highest attainable temperature of matter. The concept has been popularized by the television series Nova. In this presentation, absolute hot is assumed to be the high end of a temperature scale starting at absolute zero, which is the temperature at which entropy is minimal and classical thermal energy is zero. Contemporary models of physical cosmology postulate that the highest possible temperature is the Planck temperature, which has the value 1.416785(71)×1032 kelvins, or 142 quintillion kelvins (142 nonillion on the...

and its mostly theoretical, so basing your temperatures off of it is rather silly

bah, I should really read before I speak. There is a temperature scale based off of it

Planck temperature

Planck temperature, denoted by TP, is the unit of temperature in the system of natural units known as Planck units. It serves as the defining unit of the Planck temperature scale. In this scale the magnitude of the Planck temperature is equal to 1, while that of absolute zero is 0. Other temperatures can be converted to Planck temperature units. For example, 0 °C = 273.15 K = 1.9279 × 10−30TP. In SI units, the Planck temperature is about 1.417×1032 kelvin (equivalently, degrees Celsius, since the difference is trivially small at this scale), or 2.55×1032 degrees Fahrenheit or Rankine. == ...

Martin Ender

right, but Planck quantities are (to my understanding) just the points where our theories break down, not some necessary fundamental/cosmological limit

Nathan Merrill

"As for most of the Planck units, a Planck temperature of 1 (unity) is a fundamental limit of quantum theory, in combination with gravitation, as presently understood."

so, yes?

so, it's all based on whether quantum theory is accurate at that point

Martin Ender

I understand that sentence as saying that's the limit for where the theory works, not that the theory postulates that quantities beyond that limit don't exist

3 hours later…