Alex Strinka

One source of interpersonal misunderstanding and conflict is the difference between Ask Culture and Guess Culture.

In Ask Culture, you're allowed to ask for just about anything, and you also have to accept that your request might be denied. In Guess Culture, you can only ask for something that you're confident the person you're asking will be willing to provide. When people from Ask Culture and Guess Culture interact with each other, it's easy for both sides to the see the other as rude.

Although the difference is framed in terms of making requests, I think it has more to do with whether or not you're allowed to deny a request.

In Ask Culture, you're allowed to deny a request for any reason. But in Guess Culture, denying a request is considered impolite, unless you've got a really good reason. If someone makes a request that you just don't want to accept, you're forced to either do the thing even though you don't want to, or be impolite by refusing. Which is where the implicit rules about what you can request come from, because you don't want to put someone else in that situation, or for someone else to put you in that situation.

Furthermore, it's not a simple dichotomy. What counts as a really good reason to deny a request will vary from culture to culture, and some cultures will have more or fewer than others.

A related topic is making offers. In some cultures (at least, so I've read) you're expected to turn down an offer. The first offer is only made to be polite. If they really want you to have it, they'll offer it again. It's considered rude to accept the first offer.

This feels to me like a continuation of Guess Culture. Not only are you not allowed to deny a request, you're required to preempt the request by making the offer first. But because you still might not want to actually fulfill the offer, the recipient is expected to turn it down.

Of the cultures I described, I think Ask Culture is the best. And I say that even though I'm more naturally inclined to Guess Culture. But, explicit communication is less prone to misunderstanding than implicit communication. Guessing what another person wants or is willing to do is generally less reliable than asking them.

While I do think we should strive to Ask more, we should also recognize that different people have different expectations and different preferences, and we should strive to be more accepting of those differences.

Five years ago, I started tracking my weight and steps per day. I've also tracked things like how many calories I consumed, how much caffeine I consumed, whether I ate animal products that day and what I did that day. Some of those things I stopped tracking after a while, or didn't start until more recently.

I started doing it as part of a New Year's resolution to lose weight and be more productive. I read about the idea on Reddit, and it seemed like a good idea, so decided to give it a try. It's been pretty effective, at least for the things that are straightforward to measure.

Weight and steps are in that straightforward category. Weight is just a matter of stepping on a bathroom scale, and I have a pedometer app on my phone that detects my steps. But other things are much harder to handle. I tried a few different ways of measuring my productive activity. How many to-do list items did I check off? How many minutes did I spend doing various kinds of activity? None of them really worked for me. I think the problem is that the numbers don't capture what I mean by productivity, and I haven't been able to figure out how to define what that in terms of anything objectively measureable.

Doing the tracking is relatively easy. It only takes a few minutes a day. The hardest part is just remembering to do it, which I've done by making it part of my bedtime routine. Though gathering the data can be difficult too, depending on what you're measuring. Counting calories is a pain, but absolutely worth it if you're trying to lose weight.

I've found it to be very motivating to be able to look back and clearly see the progress I've made. And it lets you notice if you're backsliding sooner.

Something I've found is that the very act of tracking changes my behavior. I didn't have any particular goal in regard to the number of steps, but by recording that number, I pay more attention to it, and I end up walking more as a result. Simply being mindful of something can change how you act, and tracking is a regular reminder to be mindful.

It's also pretty easy to set up if you want to do something similar yourself. I use a Google docs form and spreadsheet. You can see an example form here. You can copy that and link the form to a spreadsheet so it adds the data to the spreadsheet automatically when you submit the form.

I've added a new program to my programs page: HexBoggle!

It's basically Boggle, but with a hexagonal grid, instead of a square one. Right now it's just single-player, but I intend to add multiplayer eventually.

Try it out, and let me know what you think! What other features should I add to it? Leave a comment here, or send me an email!

In the field of linguistics, there are the concepts of descriptivism and prescriptivism. Descriptivism is about describing how language is used. In contrast, prescriptivism is about prescribing how language should be used.

Linguistics, as a science, must necessarily be descriptivist. You don't learn about something by telling it how you think it should work. To learn about the world, you need to observe the world without judgement.

But that doesn't mean there's no place for prescriptivism. In fact, I would argue that prescriptivism is unavoidable, to a degree. When you speak or write, you have to choose what you're going to say. Many of those decisions happen unconsciously, without deliberate intent, but not all of them. Descriptivism alone can't tell you what words to use.

Where prescriptivism goes wrong is in saying that you should speak a certain way because it is the right way. The problem is that there is no single right way of speaking.

Consider, are people who speak a different language wrong? That seems patently absurd to me, and I think most people would agree. But if using different vocabulary and different grammer isn't wrong when you're speaking a different language, why should it be wrong if you're speaking a different dialect?

Furthermore, there's no clear line between a separate language, and a dialect. Typically, two different ways of speaking would be called separate languages if they're not mutually intelligible and dialects if they are. But consider a case where group A can communicate with group B, group B can communicate with group C, but group A can't communicate with group C. This is called a dialect continuum, and is actually fairly common. Do groups A and C speak different languages, or dialects?

And how do you determine which way of speaking is the correct one, anyway? Historically, it was just whichever dialect the monarch or nobility spoke, but why should their opinion matter more than anyone else's today?

Instead of trying to speak correctly, you should try to speak in a way that maximizes your audience's understanding. (At least if you're trying to communicate, which is usually the came when you speak.)

When I was in elementary school, I had a teacher who told us there were fewer even numbers than whole numbers, because half of all whole numbers are even, and the other half are odd. I argued that there must be same amount because there an inifinite amount of whole numbers and an infinite amount of even number, and infinity equals infinity.

Well, it turns out, my conclusion was correct, but my reasoning wasn't.

That probably seems really strange. Surely, if you take the set of all even numbers, and then you add all the odd numbers, it would end up bigger than it started, right?

To answer that, we need to talk about what it means for two sets to be the same size. For finite sets, it's simple; just count how many elements there are. But you can't count to infinity, so that doesn't work for infinite sets.

You can say that if set A contains all the elements of B, but set B doesn't contain all the elements of set A, then set B must be smaller, but that won't work for every pair of sets.

So, mathematicians came up with the concept of cardinality, which works for every set. The way it works is that two sets have the same size if you can come up with a mapping between the two sets, such that every element in each set is associated with exactly one element in the other set.

Here's an example. Let's say you have the two sets {Red, Green, Blue} and {Circle, Square, Triangle}. We can make this mapping:
Red ⇔ Circle
Green ⇔ Square
Blue ⇔ Triangle

Every element in the first set is associated with exaclty one in the second set, and every element in the second set is associated with exactly one in the first, so those two sets have the same cardinality. And, because they're finite, we can also just count them and that works too.

In fact, you could even say that this is actually the same process as counting. You're making a mapping between the set you're counting and the set {1, 2, 3...n}.

And this same concept can be applied to infinite sets. Here's a mapping between all integers and all even integers: For every integer N, N ⇔ 2N

This mapping associated every single integer with exactly one even integer and every single even integer with exactly one integer. Therefore, the two sets have the same cardinality.

You can even make such a mapping between all integers and all positive integers, or between all integers and all rationals, so all of those different sets have the same cardinality too.

Does that mean every infinite set is the same size as every other infinite set?

No!

It turns out that the set of all real numbers is bigger than the set of all integers.

Here's how can show that. First, assume that there is such a mapping, so you can associate every real number with exactly one integer. That means you can put those real numbers in an ordered list, so you can talk about the first number in the list, the second one, and so on.

But there's a real number that's nowhere on the list. To find it, we need to build it, digit by digit, based on the numbers in the list. Here's an example list:
#1: 0.40396...
#2: 0.09714...
#3: 0.73175...
#4: 0.90453...
#5: 0.97491...
⋮

I've bolded some digits, because those are the ones we're looking at. The first digit of the first number, the second digit of the second number, and so on, along the diagonal.

For each digit, we'll add one to it (Or if it's nine, subtract one. What matters is that we get a different number than what's already there.)

By doing that, we'll get a number that starts 0.58262...

This number can't be equal to the first number, because the first digit is different. It can't be equal to the second number, because the second digit is different. And so on, for every single number in the list. And notice that this works for every possible list of real numbers, not just this example.

Since there's a real number that's not in the list, the mapping must not include every single real number, and therefore the sets don't have the same cardinality. This is called Cantor's diagonal argument

So just because two sets are infinite doesn't mean they have the same size.