I'll start.
>What is the probability that given a certain level of facial symmetry (represented as a number in (0, 1), 1 being perfectly symmetrical) you are the most attractive person in a given population?
Some assumptions:
1. Facial symmetry is the only criteria we consider for attractiveness
2. Facial symmetry scores are approximately normal but the variance and mean are unknown
>If you do an experiment in a space ship traveling near the speed of light (say 99.99%) will the results of that experiment be the same if you did it on Earth?
>Irrational numbers can be represented algebraically, transcendentals cannot. Does this mean you get an irrational number from the product or quotient of two irrational numbers? What about for transcendentals?
>What is the likelihood of developing lung cancer for any given cigarette smoked? What does the probablity density function look like as a function of cigarettes smoked? Linear? Exponential? Logarithmic?
Some assumptions:
1. Everyone has the same genes
2. Every cigarette is the same
>>8349730
>99.99% speed of light
The results of the experiment won't be the same as if you did it on Earth because the Earth's not really an inertial reference frame. But the results will be the same as a spaceship travelling at any constant speed (assuming no gravity).
What will the world look like a thousand years from now?
>>8349738
>constant speed
So it would have to be a body not experiencing any force?
Are there any pairs of infinite fields where the additive group of one is the multiplicative subgroup of the other? (finite case: Z3 and Z2).
>>8349744
Basically yeah. Though technically objects in free-fall (under gravity) can be considered as inertial reference frames locally, however this concept cannot be expanded to form a global inertial reference frame in free fall.
>>8349730
The product/quotient of two irrational numbers is not necessarily irrational; simplest examples would be the product of a square root with itself, or the quotient of any number with itself.
100% parents if you have superior genetics, 0% otherwise
>>8349820
This is pretty much speculation on my part. But if a frame matches the acceleration and higher derivatives at each instant in time of the rocket then you should get the same results probably. Would like a proper physicist to confirm.
>>8349848
By time I meant proper time (time as measured in the rocket and the similarly accelerating reference frame).
>>8349848
Yes. This is pretty much what the equivalence principle comes down to. Given no tidal forces one can't distinguish between uniform acceleration and gravity.
>>8349857
But doesn't that mean that the laws of physics are different for people in different reference frames? Given that the results of their experiments are different?
Of course the question is then 'how are they different?', what if it's just a difference in the numbers (i.e different constant values) but the equations and functions are the same shape?