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> Where am I going wrong?

In short, infinities are complicated and intuition doesn't work well.

In slightly longer, you're talking about the difference of the rate of growth of two functions rather than actually about the cardinalities of the sets.

We define two sets as having the same cardinality when we can create a bijection between them. We can list the primes in order from smallest to largest and number them with the natural numbers. So we'll have 2 match up with 0, 3 with 1, 5 with 2, 7 with 3, etc. Every single prime number will correspond with a natural number AND every single natural number will correspond with a prime number, no exceptions. So they must be the same size. They are also the same size as the integers and the rational numbers but the set of real numbers is a bigger infinity.


In the case where you're using a fingerprint unlock for your own phone, you are both Henchman #752 and the boss.

Hmmmm, you make a valid point.

> Would you design mathematical notations based on the opinion of 5th graders?

It's not their opinions. It's about how they naturally think.

And, yes, if I could change mathematical notation in a manner that made it easier to learn without introducing a more significant disadvantage, I would do it in a heartbeat.

Things are the way they are for a reason but that reason isn't necessarily that the way things are is the best.

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It's not just about non-programmers being insufficiently precise. It's also about the different ways they express precision compared to how you have to do it for existing programming languages. For example, the paper talked about how the participants tended to talk about doing something to everything in a set in vectorised terms whereas scalar languages tend to be more common outside of scientific settings.

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> The list of things they taught kids for the PacMan study also seemed very... well, technical.

What list? Perhaps I'm just missing it or there's another link I haven't seen but they don't seem to mention having taught the kids anything--especially anything technical--before the Pac-Man study.

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My mistake, that list was something the researchers before the task was conducted, not part of it.

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I've heard a few before: "hypothesis contrary to fact", "what if" fallacy, and "counterfactual fallacy". None of the names are really great and none of them seem to be particularly common but I've never seen any better names for it or any used more commonly.

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You're the first one to say "only waiters"; savanaly certainly didn't. Their statement was clearly in the abstract and not an endorsement of the current tipping status quo.

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I know. I just brought his point to a logical conclusion. We should tip everybody that provides a good service. Including 10% for the surgeon that just did your knee replacement for $15786 :-)

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To an extent, at least, it's not so ridiculous as your "logical conclusion", at least not based on current US tipping etiquette.

For one, 10% on $15786 is a little silly, sure. But current etiquette already recommends flat rates for certain types of services so this could logically be extended to certain other cases.

And secondly, even brought to the logical conclusion, extending tipping would only make sense where it could reinforce proper incentives and would be actively bad where it reinforces perverse incentives. A legal avenue for bribing cops is certainly problematic in a way that bribing waiters for better service isn't, for example.

That's not to say I'm arguing in favour of tipping but I don't think it's as clearly unreasonably as your example would suggest.

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In what way is a waiter's service different from a supermarket cashier's service or your dentist's service? All I am saying it's totally arbitrary that among many service professions only for waiters tipping is an essential part of their income. Sure you can tip your plumber but even without tip he will earn good money.

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Where did I--or anyone--say it was different? Again, we're talking abstract, not current status quo.

That said, there are key differences between a dentist or plumber and a waiter or cashier. The obvious one is a private-practice dentist or self-employed plumber where they're setting their own fee and getting directly paid. In such cases there's no problem for tipping to solve. The other big one regardless of public or private is that there's a major power imbalance where the dentist or plumber is effectively acting as the agent of the patient or customer. Check-ups, routine cleanings, and such aren't an issue but when it comes to things that need fixing it's the dentist or plumber telling the customer "this is the service you require" and selling them that service. This is a principal-agent problem itself and tipping only exacerbates the issue rather than solving it.

Like I said previously, the logic of where tipping could or could not make sense is based on what sort of incentives it reinforces, if any. And, also like I said previously, I am not arguing in favour of tipping, either, and I'm especially not arguing in favour of tipping making up an essential part of one's income.

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A few explanations you can add for more-falsehoods.rst:

> 15. Unix time is the number of seconds since Jan 1st 1970.

The section you quote from Wikipedia shows why this one is false: leap seconds. Similar to how the number of hours between 00:00 and 3:00 in most of the United States depends on whether the timezone remains constant, springs forward, or falls back, the number of seconds between two Unix timestamps depends on how many leap seconds were inserted or deleted in that time frame.

> 16. The day before Saturday is always Friday.

This one is true only within the assumption but I'm not sure if the falsehood is literally false. When Alaska did the calendar change it had two consecutive Fridays (October 6th & 18th, 1867). This gives us the day after Friday not being Saturday but technically not the day before Saturday not being Friday. The falsehood still holds in spirit (outside of the assumption), of course, and it's possible somewhere else had it be true in practice as well.

> 27. The weekend consists of Saturday and Sunday.

The weekend differs across the world. Friday and Saturday is another popular one but Brunei gets a special shout out for having a Friday and Sunday "weekend" with Saturday being a working day.

> 59. DST is always an advancement by 1 hour

As far as I know, this is currently true if you aren't dealing with historical datetimes but Singapore will mess you up with historical data. They had a really odd case[1] where they went on DST by advancing 20 minutes and then ended DST without changing the clock at all.

[1] http://www.timeanddate.com/time/zone/singapore/singapore?sye...

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Wikipedia suggests that there's an Australian island that still uses a half-hour DST.

https://en.wikipedia.org/wiki/Daylight_saving_time#Procedure

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I do. I don't like small coins.

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> It is disingenuous and/or ignorant to suggest that temporarily loading an email into memory for the purpose of displaying it on the users screen [...]

I may be wrong, but I think they were referring to things like spam detection, malware detection, possibly search indexing, and such rather than just "temporarily loading an into memory for the purpose of displaying it."

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