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Intuition tells me no, but, using the jury system by example, is it not true that the jury system over the course of history has a 0% probability of never convicting a person falsely? Thanks!

I do hope that we keep a little bit of skepticism towards this proposal, as much as I strongly dislike everything the GOP and the president has done thus far, I would not want this bill to turn into anti-corruption against the GOP, and ignore a Democrat. I realize far fewer Democrats are as corrupt as the Republicans, but there will always be bad eggs, and we must always seek to protect our institutions.

It is the people like Balewa that show us humanity. We can be furious over politics, human rights violations, abuse, injustice, and any number of things in this world, but knowing there are people like this man in the world keeps a lot of us going. Thank you for sharing.

All cells in multi-cellular organisms that divide when they are not supposed to, are cancer cells. The cancer cells can be otherwise healthy. All cells originate from the inherent genetic ability to divide, it is only deactivated in most cells in our body. All it takes is a molecule interacting with the wrong part inside the cell, and then the lever for cell division is activated. Cancer is inevitable as long as we leave the ability to divide endlessly in place (The hTERT gene and ALT mechanism). Hence cancer is an aging process, and the only aging process where every disease caused by it, is called the same name regardless of where it happens in the body. Whereas diseases caused by for example loss of cells is called Parkinson's when it happen in the brain, and heart-disease when it happens in the heart.

Here are some interesting papers if you are into such things, first the proposed cure for cancer involving removing all cells' ability to divide endlessly: http://www.sens.org/files/pdf/WILT-FBS.pdf

Next a paper about what causes cancer, and its 6% genetic, 29% lifestyle, 65% chance, or time for the wrong molecule to bump into the wrong part inside a cell which starts its cell division even though there is no need for additional cells. http://science.sciencemag.org/content/355/6331/1266

I'm not trying to be pedantic, I'm just curious, is it or is it not technically more accurate to say it is not down to chance, but rather the process by which someone gets cancer is extremely, extremely chaotic? Like two perfectly identical twins who have done everything the EXACT same their entire lives for each and every second would get cancer at the same time if their genetics was predisposed to it, right? Or is it truly random, like what cells do is not causal in any way to getting cancer? Thanks!

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I don't remember too much about the minigames besides them being really fun, enjoyable, and not providing something unwanted or antithetical to the game. I see no reason for it not being in osrs besides it being in rs3, but maybe I'm missing something?

It was already mentioned on a Q&A that the volatile tool would not be brought in game due to it giving bonus exp. That is one of the major points that players would want from stealing creation, so it's an iffy chance it would pass a poll.

Yea I didn’t care much for the rewards, I liked to stop the grind and have a purely fun part of the game that wasn’t efficiency based you know?

S

All mass has an energy equivalence.

But are they two different things or is it all just energy?

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The title may be confusing, so let me give an example.

If you have a large number of water droplets hanging from a bar of arbitrary length lying horizontally above a surface, you can model the time it takes for a randomly selected droplet to **hit the surface** as a probability distribution, most likely resembling a bell curve.

Then, if the bar is attached to a pivot in the middle and rotates by an angle theta, then the droplets closer to the surface have an increased chance to hit the surface first over the droplets that are on the other end of the bar.

My question is: is there a current well-defined formalism that describes how much the distribution skews as a function of the angle? (You can increase the dependent variables by also changing the surface angle, or making it change at a constant rate, etc) Thank you!

Not being much for statistics, I'm not completely understanding /why/ you would want to do this. The original distribution seems to address "how long before a drop falls," whereas if the second distribution maintained resolution about the location of drops, I'm not sure if you would be answering the same question.

All I can offer is an example similar to what you're describing that I've seen in practice. Consider the Weibull distribution, and the parameter which changes its shape.

If I was modelling some kind of system (my inclination is, a bunch of eggs that may or may not survive), I could assume that the parameter which determines system behavior (survival) is drawn from the Weibull distribution.

By observing my system over many reproductive cycles, I could estimate this survival many times and eventually determine the shape of the Weibull distribution from which it came. This would necessarily mean I found out the shape parameter for the distribution, which is determined by my system.

In my example, the connection is phenomenological (the shape parameter is not defined by my biology) and I'm not sure when/why you would work in the opposite direction.

But afaik: yes. If you wanted to define a probability distribution in terms of a quantity of interest in your system, you could do this. Probability distributions are already defined by parameters. As far as analysing the effect of this, I think it largely depends on the distribution you use and the assumptions you make.

Apologies if I've misunderstood your goal here!

That was helpful, thank you! I did not word my post very well, but I’ll attempt to clarify a bit more. Say we know each drop will start falling in between t=0 and t=5, where t=2.5 being the “expectation value” and all other times falling on a bell curve. Then, you can apply that same curve to the system I described above, as it will describe the probability to fall for all drops on the bar. If the bar is laying horizontally, the time for any drop to hit the surface should fall exactly in line with the curve + the time needed to fall and hit the surface.

However, if you rotate the bar, this does not change the distribution of the time to start falling, but it does change the distribution of time to hit the surface, as drops that fall in the expected value of t=2.5 but are closer to the surface than a drop that falls at t=1.5 could hit the surface at the same time depending on the height.

Hopefully this clarifies rather than confuses, thank you.

Hi,

I didn't understand your original post, but this part makes more sense. Actually, I now don't understand what you mean by saying "...start falling in-between t=0 and t=5, where t=2.5 being the 'expectation value' and all other times falling on a bell curve." For one thing, you seem to be talking about a distribution that takes a value of zero for t<0 or t>5, but the Gaussian function never takes any value of zero. For another thing, here you are talking about the time a drop of water starts falling, but then later on you are talking about the duration of the fall.

It might help to set up mentally a particular experiment, with devices to measure whatever number you're talking about.

Anyway, let's consider what you sort-of seem to be talking about in the second paragraph. We imagine a function f(t) where t represents a duration for a water drop falling, and such that if we choose an interval such as [a,b] which is the set of numbers between a and b, the probability that a single water drop's duration is in the interval [a,b] is given by the integral from a to b of f(t)dt.

Next, you might want to take a variable like y to represent positions on the rod, and if the rod is parametrized by numbers in some other interval [c,d] you might have another function g(y) such that the probability of a random drop originating from a sub-interval [f,h] is the integral of g(y)dy on the interval [f,h].

If things are uniform, then g(y) is just the constant 1/(d-c).

If the rod is tilted in the way you say, you might be interested in another function k(y) which is the duration of falling that a drop at position y would have.

Now, these functions are related to each other. A drop has duration of falling in an interval [v,w] if and only if k(y)\in[v,w] where y is the point of origin of the drop. That is to say, y is in the inverse image of [v,w] under the function k. If we simplify things and assume that k is monatonically increasing, this is the interval [k^{-1} v, k^{-1} w]. The probability that this is so is then the integral of g(y)dy over this interval, and according to the choice of g where it was just uniform, this is (k^{-1} w - k^{-1} v)/(d-c).

But we also knew that this same number is the integral of f(t)dt from v to w. Differentiating, we find that our function f(t) is just 1/(d-c)k^{-1} .

Without the assumption that g is constant or k is monatonic a similar calculation is possible. Note also that I have done nothing but define various functions and relate them, according to my attempt to interpret how you were wanting to set up your experiment. I didn't really use any theorems of math or statistics.

By the way, you also know k(y) = (2ah(y))^{1/2} where a is the acceleration due to gravity and h(y) is the height of point y above the surface. So k(y)^{2} /(2a) = h(y) and y=h^{-1} (k(y)^{2} )/(2a) so the inverse function of k is the inverse function of h composed with squaring and dividing by 2a. In your example h is just a linear function of slope the cosine of theta and its inverse is a linear function with slope secant(theta). If you know the height of the midpoint of the rod over the surface you can make this all completely explicit and write down a formula for the function f.

That really helps, thank you for such an informative post.

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But how does this explain when very light objects are thrown across “new” ice at very low temperatures and still slide around just the same? You can see this with a hockey puck for example.

What do you mean by "account for"?

Sorry I should have clarified. By “account” I mean in measurement, subjects/professions where moment to moment precision is required, etc. For example, if I was an SR-71 Blackbird pilot, maybe that delay could be significant. I’m sure there are some consequences of doing everything with a slight delay to time

Our bodies incorporate this delay: we are able to catch balls or time out movments to other kinds of stimuli in the outside world fairly accurately.

Right, I do understand that the brain sort of has V-Sync, where what we’re seeing is times with our movements, but then there’s still a delay as to what is actually happening in the real world. Does this delay have significant consequences?

I think what you are looking for here is a better label than "simplest" - what this really is Fermat's Principle of least time. Consider a ray of light travelling from A to B - it will go quickest in a straight line, right? That's the shortest path. Consider now a ray going from A to B, but we force it to bounce off a mirror along the way.... what angle of reflection now would give the quickest path from A to B?

- It turns out that the law of reflection (incident angle = the reflected angle) also minimises this time taken.

The photon travelling along this path can indeed also have other photons travelling nearby along other paths, but something slightly different happens - because of the slightly different path lengths, parts of the photons will constructively or destructively interfere with each other on the screen or whatever it is they land on. The end result is, if you see a specularly reflected spot, it is precisely because it came from a path that allowed constructive interference to occur.

Not sure I 100% follow here. How does the incident angle minimizes time? And how can we talk about a photon going from A to B, when B isn’t known to the photon? How could the photon “know” that it wants to go to a certain point in space, does it not just have a direction?

Yes, it would have to be exactly perfect. It’s an unstable equilibrium, so any nonzero perturbation would destroy the equilibrium. You’d never be able to make the particle stay at the center in practice.

It’s the same with a sphere instead of a circle, just in 3D rather than 2D.

Interesting, I’m guessing this is equivalent to a perfect sphere resting atop a point on a hill yes? And is it actually non-zero or just close? Like if the distance to one of the points were like half the length of a nucleus, would it still destroy the equilibrium? Thanks!

Interesting, I’m guessing this is equivalent to a perfect sphere resting atop a point on a hill yes?

Yes, exactly. That's another unstable equilibrium.

And is it actually non-zero or just close?

If everything about the situation is exactly perfect, the equilibrium has a "size" of exactly one point in space. The charge must exist exactly at the center, or it's not at the unstable equilibrium.

Right, but are we sure that if the difference was extremely extremely small (maybe a plank length?) then it would still destabilize? I feel like it wouldn’t, but at what point would the discrepancy be enough?

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