Alex Strinka

This video shows some good examples of a dolly zoom.

So, how does this work?

Imagine you're standing in one spot, and a person is 10 feet in front of you, a house is visible behind the person 100 feet in front of you, and a mountain is visible behind the house miles away from you.

Now consider what happens if you move 10 feet backwards. The person is now 20 feet away from you, so the distance to the person has doubled. But the distance to the house has only increased by 10%. And the distance to the mountain is negligbly larger than it was before.

That means that, from your point of view, the person now appears to be about half as large as they did before, while the house will only be about 10% smaller, and the mountain will have barely changed at all.

Now, imagine you look at the person through a camera, and you zoom in, so they look twice as large. The zoom affects everything equally, so everything gets twice as large. Now the person looks as large as they did before, but the house looks significantly larger than it did before, and the mountain looks almost twice as large.

Here's an interactive demo of that. There's a small red sphere close to the camera, a larger blue cube farther from the camera, and a very large green triangle very far away from the camera. The top half is a side view, showing the camera and its field of view. (The green triangle isn't visible, because it's ten times farther away from the camera than the blue cube.) The bottom half shows what the camera sees.

The sliders let you adjust the camera's position and zoom. You can see that when you adjust the zoom, the camera's field of view changes, and from the camera's point of view, the sphere, cube and triangle all grow and shrink proportionally. But when you move the camera, the apparent size of the sphere changes much more than the cube, and the triangle barely changes at all.

When you select a focus and move the distance slider, the zoom slider changes simultaneously, to keep the focused object the same size, creating a dolly zoom effect. Notice how, at the position of the focused object, the field of view has the same size, while at points closer and farther away, the field of view gets bigger and smaller.

This is actually closely related to parallax. That post shows what parallax looks like when you move left and right. This is what parallax looks like when you move forward and backward.

Here's a quick experiment you can do right now. Look at something that's at least a few meters away from you. For the sake of a concrete example, I'll say a lightswitch that's on the far side of the room, but it could be anything. Now, close one eye and hold up your thumb so it covers the thing you're looking at. Then, close your open eye and open your closed eye.

Suddenly, the lightswitch (or whatever) is no longer covered by your thumb! Why?

Your thumb is directly between your first eye and the lightswitch, thus blocking its view of the lightswitch. But your second eye is in a slightly different place, and the line that goes from it to the lightswitch is not blocked by your thumb, so it can see the lightswitch.

This is an example of a phenomenon called parallax. It shows up in many situations and has practical applications too, so let's look into it in more depth.

Let's start with the basics. You know how when an object is close to you, it looks bigger than when it's far away? That's because we don't directly perceive an object's size or distance. We can perceive the direction to an object and the difference between different directions. Here, I'll show you what that means.

The dot on the left represents your eye, and the circle on the right is an object. The marked angle is the subtended angle, or the angular size of the object. The direction from the eye to the top of the circle is different than the direction from the eye to the bottom of the circle. The closer the circle is to the eye, the bigger that difference is, and hence the bigger the circle appears to be to the eye.

And of course, this works exactly the same when you're looking at the distance between two objects. The direction from the eye to the first object is different than the direction from the eye to the second object. The closer the two object are to the eye, the bigger that difference is, and so the apparent distance between the objects gets larger.

This is also why things that are far away appear to move more slowly. The farther away they are, the smaller the distance they move appears to be, but they still take the same amount of time to move that distance.

You can flip it around so instead of the object moving, you're the one that's moving. It's exactly the same situation, just from the opposite point of view. That's why when you're driving in a car nearby things like houses and trees go by very quickly, but distant things like mountains go by much more slowly.

Instead of one observer that's moving, you can have two observers in different places, or just two eyes. The direction from the first eye to the object is different than the direction from the second eye to the object, and that difference gets bigger the closer the object is to the eyes.

This is one of the ways you can tell how far away something is. When you look at something very far away, your eyes are nearly parallel, but when you look at something very close to you, you have to cross your eyes.

That's how stereograms work. You show one picture to one eye, and a picture that was taken from a slightly different position to the other eye. Here's an example. Cross your eyes until the two images are on top of each other. When they line up, you should be able to see the trees and houses "pop out" in front of the skyscrapers.

This is actually how astronomers can measure the distance to nearby stars. The Earth circles around the Sun, so in six months it will be about 300,000,000 km (186,000,000 miles) from where it is now. That's a very, very large distance, but even then the parallax deviation of the nearest star is less than 0.001 degrees. This was actually used as an argument in favor of geocentrism, because that was too small for anyone to measure until the 1800s. They thought it was more likely that the Earth was stationary than that the stars were millions of times farther away from the Earth than the Sun.

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!