/sci/ - Science & Math

If you put a random infinitely long line on the Cartesian plane, what is the probability that any integer coordinates are on that line? By an integer coordinate I mean any point (a, b) where "a" and "b" are integers.

If you need specification how the "random line" is drawn, let's just say you select two uniformly random points inside a unit circle centered at origin and then draw the line through those points.

You roll three dice at the same time which counts as one roll: a 10-sided dice, a 100-sided dice and a 1000-sided dice. The dice have one side colored so that rolling that side has the probability 1/10, 1/100 and 1/1000 for each dice respectively.

1) Given that you begin rolling the dice an unlimited number of times, what is the probability that the first time that a colored side occurs is when it occurs on all of the three dice in the same roll simultaneously?

2) What is the probability that you have rolled the 1/1000 change before rolling the 1/100 even once?

>>15554670
Hmmmm. Kinda makes sense I guess.

>>15485612
Any number in the form 0.000 ... 0001 added to the number in the form 9.999 ... 999 is equal to 1 if the number of zeros and nines are the same. For example, 0.9999999 (seven nines) + 0.0000001 (seven zeros) = 1.

But because 0.999... has infinite nines, any arbitrarily small number added to it will not make it equal to one. Instead the result will be greater than one.

>>15411420
Perhaps speed of light is the 'speed of sound' of spacetime

>>15299444
I'd assume that there has been a fitness benefit for the ability to contemplate. Ability to contemplate stuff is to humans what the ability to fly has been to birds. If there is some benefit in being able to fly, it does not imply that there is any benefit in the ability to fly into windows.

I asked this to myself also and almost made a thread about it. But I think I figured it out.

Take a car as the example. By doing some math we know that going from 100 to 101 mph takes 201 times the amount of energy that it takes to go from 0 to 1 mph despite the fact that you are pushing the car the same amount of time and the difference in speed is exactly one unit.

Now, the thing is this. In the high speed scenario, the pistons of the engine go up and down a lot more times compared to the low speed scenario. The pistons are exerting the same amount of force but since they go up and down a lot more times, it requires a lot more energy; particularly 201 times more in this example. Each time the piston goes around one cycle, it needs a constant amount of fuel to exert the same force. But because the engine is running faster, the pistons make more cycles, so they need more fuel which means the engine uses more energy. I know a car doesn't exactly work this way but the principle is the same. No matter which gear ratio it uses, no matter how the engine is designed, something in the engine is spinning faster or taking more energy when you accelerate from high speed compared to low speed.

Even simpler example I came up with is skii'ing on snow. Imagine that you are sliding on snow with skis on your feet. In one scenario, you are going really fast and decelerate one unit of time. In a second scenario you decelerate the same amount of time as last time but you had just the right speed to decelerate to full stop. In the first case, the marks that you made on the snow are much longer compared to the other one so you had to use more energy to make them (despite the fact that you were slowing down the same amount of time with the same amount of force).

>>14731585
>>14731543
>>14731589
Is there even any valid moral arguments to be made about making female clones of yourself to serve in your harem? I mean, as long as you pay for the serivices needed to bring the girls forth so to speak, genetic engineering, surrogacy and so on.

Your DNA is after all your property and should you by all rights, have the right to do whatever you want with what's yours?