Imagine you have a ruler. You want to cut it exactly at 10 cm mark.
Maybe you were able to cut at 10.000, but if you go more precise you'll start seeing other digits, and they will not be repeating. You just picked a real number.
Also, my intuition for why almost all numbers are irrational: if you break a ruler at any random part, and then measure it, the probability is zero that as you look at the decimal digits they are all zero or have a repeating pattern. They will basically be random digits.
> Maybe you were able to cut at 10.000, but if you go more precise you'll start seeing other digits, and they will not be repeating. You just picked a real number.
A reasonably defensible inference would be that adding a finite amount of precision adds a finite number of additional digits. That is a physically realizable operation. There's no obvious physical meaning to the idea of repeating that operation infinitely many times, so this is not clearly a meaningful way of defining or constructing real numbers. If you were trying to use this construction to convince a skeptic that irrational real numbers exist, you would fail -- they would simply retort that arbitrary finite precision exists and that you have failed to demonstrate infinite non-repeating, non-terminating precision.
I think of mafia as providing services that a government/legitimate private entities cannot provide.
Human trafficking - yup, I should have thought of that. In the counties listed in the link the governments does serve that mafia function. I was US centric in my thinking.
Prostitution - no. It can be legal, but the government does not engage in it.
Drug trafficking - I am sure some governments do it. I wouldn't put US in that list. Both the government investigations and the newspaper investigations found the allegations unsupported, according to the given link. I would say it could happen incidentally but organized crime does not need to worry about the government as a competitor in this space.
Gambling - the lottery is not illegal gambling. But you can argue that is tautologically true.
Racketeering - I don't see where in that link it says that the government engages in racketeering. Rico is a law that makes prosecuting racketeering easier.
There's some inconsistency between the pyramid graphic and the written guideline. For example whole grains are moved to the tip of the pyramid. But the written guidelines say 2-4 servings a day.
Windows 11 has transitioned from a standalone tool into a digital storefront that prioritizes recurring revenue through aggressive prompts for Microsoft 365 and OneDrive subscriptions. By mandating cloud-based Microsoft Accounts, the OS effectively anchors your identity to a marketing ID, allowing the company to track behavior and monetize your data. The interface now functions as an advertising platform, injecting "recommended" apps and sponsored content directly into the Start menu and search results. Ultimately, this shift means users are no longer just customers of a product, but recurring assets whose attention and telemetry are sold to sustain Microsoft’s ecosystem and maximize shareholder value.
20+% of adults have anxiety, which they include here. So 38% for any of the conditions they listed ("mental health conditions and learning disabilities, like anxiety, depression, and ADHD" plus everything else) doesn't seem off base.
I think it's correct. They were lost to the general public and were considered missing. When a smaller yellow diamond surfaced there was speculation that it's the Florentine diamond that was cut.
I'm not in the jewellery business but I would be very surprised if the diamond industry didn't have a pretty good idea where things lay. That kind of multi-caret stone has a premium. You need to know provenance. The risk it's a blood diamond or stolen is very high.
Lost to wider society? Yea, I can buy that but it's a stretch.
It's not "lost" the way a medieval triptych hanging in an alms house for centuries and found to be worth millions is a "lost masterpiece" or works coming out of safe deposit boxes where some GI has hoarded loot after ww2. The titular holders decided to put a time lock on their deposit box but had clear title to the assets.
Demographers can predict when people are going to die but they have no way to predict how many children they will have.
They have been getting it wrong for a long time, assuming that the gradual decrease in birthrate will stop, only to be proven wrong.
They can't just extrapolate assuming that birth rates will keep dropping since that would reduce the birthrate to 0. So they do the next best thing and assume it will stay constant.
But in reality, we just don't know which way it will go.
Imagine you have a ruler. You want to cut it exactly at 10 cm mark.
Maybe you were able to cut at 10.000, but if you go more precise you'll start seeing other digits, and they will not be repeating. You just picked a real number.
Also, my intuition for why almost all numbers are irrational: if you break a ruler at any random part, and then measure it, the probability is zero that as you look at the decimal digits they are all zero or have a repeating pattern. They will basically be random digits.
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