Delta1212

I made a couple of notes on the train yesterday and also thought that something looked a bit wonky, but didn't want to comment yet because I hadn't done anything more than back of the envelope math without an envelope and so didn't feel robustly confident in that conclusion. For the 96 draws on record, this was the number of times each number was drawn in first position: 0 - 11 1 - 13 2 - 12 3 - 9 4 - 11 5 - 11 6 - 7 7 - 5 8 - 6 9 - 11 And the number of times that each number was drawn in the second position: 0 - 10 1 - 9 2 - 14 3 - 6 4 - 11 5 - 8 6 - 5 7 - 11 8 - 10 9 - 12 And the total number each was drawn all together: 0 - 21 1 - 22 2 - 26 3 - 15 4 - 22 5 - 19 6 - 13 7 - 16 8 - 16 9 - 23 Additionally, there were 22 numbers that were drawn twice, 5 numbers drawn three times and the number 22 was drawn four times. This leaves 33 numbers that were drawn a single time and 39 numbers that were never drawn. Was going to look into how many repeats you would expect with 96 draws out of a sample of 100 with replacement but forgot by the time I got home.

The problem, of course, is that often with jackpots that large, you get multiple winners and wind up having to split the pot, and that can very easily take it from profit to major loss unless the jackpot is worth the ticket value several times over.

Following up on Strange's comment: If expansion were caused by gravity from some mass beyond the observable universe, that mass must completely surround our universe as, as Strange said, expansion is isotopic. However, if the universe were uniformly surrounded by mass in this way, you run into the problem described by She'll theorem, where the gravity from the mass on one side of our universe winds up canceling out the gravity from the mass on the other side. So, you wind up with two possible scenarios: An even distribution of mass outside of our universe, in which case the gravity cancels out and it cannot be the cause of expansion. Or an uneven distribution, in which case it can exert a gravitational pull on matter within our observable universe, but biased in a particular direction, in which case it cannot be responsible for the isotopic expansion we observe in our universe.

The odds of rolling 3 then 3 then 3 are exactly the same as the odds of rolling 3 then 3 then 2. So even though rolling two 3s and a 2 in some combination is more likely at the beginning than rolling three 3s, once you start rolling and excluding possibilities, the odds change. If you roll a 2 on your first throw, you don't maintain the original odds of getting three 3s (which drop to 0) and neither do you retain the original odds of rolling three 3s if you at first roll a 3. Once you get to the final draw, the odds of getting the exact pattern of previous numbers that you got is exactly the same for all numbers. You have exactly the same chances of rolling 33333333 as rolling 45826478. Which means that, once you've rolled up to that point, your odds of getting 333333333 and 458264783 are exactly the same. Also, keep in mind the Birthday Paradox, when talking about numbers repeating. Despite there being 365 possible birthdays, you only need 23 people in a room to get a 50% of at least two people in the group sharing a birthday, and the odds increase to over 99% chance of someone charging a birthday at only 70 people. With 100 possible number instead of 365, a series of 22 draws gives you a 92% chance that at least one number will repeat even if there is no bias. There may very well be bias in this lottery, but you still need to learn to distinguish what is and is not an actual sign of bias. We as humans have a tendency to see patterns that aren't there because we improperly weight the importance of certain things when it comes to calculating probabilities and it can make it look like there are patterns or expected results that are not actually present. Something that seems like a very strong indication of a pattern can easily just be noise or even precosely the expected outcome of a random system, so it's important to learn how to distinguish between real signs of a pattern and ghosts cooked up in the wiring of your brain. Otherwise you may stumble across a situation where there really is a pattern and go chasing it down the wrong rabbit hole because you don't know what the actual pattern you're exploiting really is.

How many numbers are there available to be picked, and how many numbers per ticket?

I genuinely have no idea why that was so entertaining.

Specifically in lions, I believe it induces the mother to become fertile again, so male lions will kill the cubs of vanquished rivals in order to replace them with their own. In that respect, infanticidal behavior certainly provides a reproductive advantage.

You think people living in non-industrial societies have less complex minds?

Just look for the suicide stele.

Yes, I should clarify that I was noting that in opposition to a freelancer or contractor who works in the office, as that is the area where things get fuzzier in casual speech. An employee can obviously work somewhere other than the office (I'm working from home tomorrow, myself), but someone who is paid on a freelance or contracted basis and does not work at the same location as the full employees is the situation where they are most obviously not an employee. It may be a bit fuzzier for companies that have no office space at all and where everyone who works for the company works off-site full time, but those situations are comparatively rarer still. And while, yes, "contractor" is more commonly used to mean someone doing construction, in the context of employment there is no ambiguity and nobody is going to be confused by it. Just like how "car" is most commonly used to refer to an automobile but if you're on a train you can still tell someone which car you are in without worrying that they are going to think you drove your vehicle onto the train or something equally silly. Also, I'd say I associate "freelancer" with someone who does work usually on a project basis, and the work tends to be fairly solitary. As in, they will do the whole project, or a fairly self-contained portion of a larger project, themselves. A contractor, by contrast, would be used to do normal office work or work in a more collaborative or team-based environment, potentially working with full employees doing the same or similar work. The work that most commonly fits the bill for freelancer in that case would be artists or newspaper writers, but there are other jobs where you could do it. Really any kind of writing at all, programming, web design, video work, private investigator or really any of a number of semi-solitary professions. If you can work for a different company from one project to the next, doing pretty much the same work and without considering it to be a change of jobs, I would consider that a freelancer. A contractor would be more strongly associated with a specific organization for the job they are doing in my mind.

I agree up to a point, but casually "employee" is often used to refer to anyone employed by a company, which may include some people who are technically contractors. If it's someone who is working off-site the distinction is a little clearer and I wouldn't ever refer to those people as employees, but there are situations where the distinction is mostly down to how they are paid, what benefits they are so and the expectations of long-term employment, whereas their day to day duties are not any different from a regular employee's. I've known people who switched between contractor and employee with no difference being made to their work other than how their paychecks were processed, and it's entirely possible to work with someone in a company and not know whether they are technically a contractor or full employee. It's the existence of this group of contractors that I think makes the term "employee" a little fuzzier than it otherwise would be, and I'm not sure that it makes as strong of a distinction with contractor in such a situation as it would for someone who, for instance, is doing work for multiple companies at a time or comes and goes on a purely project oriented basis.

There may be other forms of matter, but there are not other elements. Elements are specific things. They are atoms with specific proton counts. By definition, you cannot fit any more elements between the ones we already know about.

Right, but there is a difference between "being on a space ship" and "being on a spaceship with a prop acceleration away from the black hole", the latter of which, as swansont pointed out, was not stipulated until your last post.

"Permanent employee" might even be better for making the contrast. I would probably phrase your statement as something more like "I want to work for you and would be happy to do so as either a full employee or as a contractor on a freelance basis." Emphasizing the dichotomy really requires additional words beyond just "employee."

Only if the ship is accelerating away from the gravitating body with the equivalent of 200g. And in an 800g gravitational field, that requires... a 1000g acceleration.

Yes, but would not the resistance depend on the thrust of the ship, in which case you'd get the same pancaking effect regardless of whether there is a black hole involved or not?

But the tax break he arranged for the company is still there, right? So it's not a total loss!

In which case, yes, all directions lead to the singularity, so if you speed up, no matter what direction you accelerate in, you are accelerating towards the singularity and will reach it sooner.

On which side of the event horizon?

Well, the range of vocal sounds humans can make would not have been any different at the point in time that the wheel was invented than it is now, and considering the number of physical adaptations that we have to allow precise and varied vocal control, plus the propensity to build a working language out of the merest scraps even as children, I'd say that it's probable that language has evolved well passed the stage of stereotypical caveman grunts by the time Anatomically Modern Humans appeared on the scene, which was well before the appearance of the wheel.

Why do you think people didn't have any language when they invented the wheel?

Yes, you're right. Not sure what it was exactly that I was thinking when I read that now.

Don't you have that backwards?

Yes, by now everyone knows what happens when you invite the strippers, JFK and Stalin, but it is far less often mentioned what happens when you invite the stripper, JFK, and Stalin.

It's not a matter of whether or not it is correct. There is no standardized system of comma usage in the English language but rather multiple competing style guides. Some use the comma, some do not. The debate is over whether it is clearer, and therefore better, to use the comma or whether it is unnecessary.