Yes, "same shape" in this context means "isometric". Rotations and reflections are considered differences in the way the shape is placed into the plane, not differences in the shape itself.
The trades were not annulled, because NYSE ruled them not "clearly erroneous". Which is why it is was an existential mistake, not just an embarrassing one.
I had the same question while reading. It's probably obvious to the startup crowd, which is why it wasn't made explicit, but I think the trick is this: a company which will never make a profit is (should be) worth zero, but a company that has the ability to make a profit in the future is valuable, even if current profits are zero. So rather than making a profit and paying it to yourself, it's better to make the company as valuable as possible to other people by reinvesting everything, and then sell stock or borrow against it for your own consumption. That definitely seems true for the most prominent outliers, but no idea whether it's actually true for the average or median owner / founder.
I guess this why EBITDA is important: if you have positive EBITDA and stop growing the business, you can pay off your loans, finish depreciating your existing equipment, and with I=D=0 you have real profits.
This is true of almost everything in math. You learn some definitions and techniques in one class, and it doesn't all become clear what's going on until you've used those to as the base layer for solving some other problems in the next class. Part of it is just that it's hard to teach you need the first concept in order to understand the second, but you need the second to understand why you should care about the first, so it's all a bit circular.
> Headlines about Supreme Court cases are almost uniformly misleading, because they suggest the Court is making decisions on policy issues rather than legal issues.
I agree with this completely, but it doesn't help when justices begin their opinion / concurrence / dissent with a long policy discussion before talking about the legal questions. That's been the case in several of the recent decisions.
That's not it at all. All parties agreed that Congress passed a law allowing the EPA to regular carbon emissions by setting emission limits on different types of power plants based on the best current technology available for emission reduction. The disagreement is whether that allows the EPA to set emission limits which are impossible to achieve, with the goal of forcing fossil fuel plants to shut down or subsidize renewable sources.
If you're talking about the FDIC, that protects you only in the case that the bank fails. It doesn't have anything to do with fraud against you in particular.
That's exactly what they did. The article says $172m disgorgement (how much the CFTC thinks they profited from this), $311m restitution (the amount the CFTC thinks JPM harmed others but didn't capture), and $436m civil penalty ("naughty boy" fine).
Another insane fact: in the US, circumcisions are usually done by obstetricians. Doctors who are trained on and work on exclusively women, except for a single surgical procedure on newborn male babies.
Medallion distributes their earnings and stays a fixed size rather than compounding, so it's a category error to compare their returns to most hedge funds. (At 66% return for 30 years, they'd own everything in the world otherwise). They're more like an internal prop-trading firm, which makes their returns good but not insane.
Pandas is still numpy under the hood, but you can create a numpy array that points to memory that was allocated elsewhere, so conversion to pandas can be done without copies in nice cases where the data model is the same (simple data type, no nulls, etc.): https://arrow.apache.org/docs/python/pandas.html#zero-copy-s...
On Tuesday, GME traded more volume than any other stock, and that's on a day when the total market volume was much higher than usual (Wednesday is now the all-time record for share volume).
Also highly recommend his book "Topology from the Differentiable Viewpoint". Or any of his books for that matter; he's a famously good mathematical writer.