Alan Forrester wrote in a discussion of multiple universe quantum physics and David Deutsch's books:

The stuff [in the multiverse] doesn’t come from anywhere. There is a continuous infinity of fungible frogs, like the real number line. That continuous infinity of fungible frogs differentiates over time. The number of instances of frogs doesn’t increase or decrease as a result of the differentiation. You’re just taking the set that already exists and dividing it up. The same amount of stuff exists before and after a division.

And Justin Mallone asked:

I've found stuff involving infinity really difficult to wrap my brain around in a way I felt like I could understand and explain and apply. This post reminded me of that fact.

And I don't have trouble understanding complex concepts generally, so I assume I have some systematic mistake or set of mistakes I'm making in my thinking about infinity in particular, but I don't know what it is.

I can easily conceive of some actual set number of universes differentiating many times. Like you have 1024 universes, and they differentiate in some way where something happens in half the universes and something doesn't happen in half the universes (lets call the thing Event A or something). And then you look at the 512 Event A universes and something happens in 3/4 of them (Event B) and so you have 384 Event A + B Universes, 128 Event A Only Universes, and 512 No Event Universes. And on and on.

But the endless differentiation of infinities of universes seems weird to me. I guess cuz one of the things about the sort of differentiation I was just describing is that you can easily assess the ratios of stuff happening in them. You can think of stuff in terms of probability of happening across the set of universes you're considering -- like above you could say it's equally likely that neither Event occurs and that at least 1 Event occurs.

But doing that with infinity seems harder. If you differentiate an infinite set of universes in some way, you still have an infinity after the differentiation, although both are smaller (?!) than the infinity that you had before the differentiation. What??? 樂

To compare sizes of sets you need ways to measure the sets.

For finite sets a standard measure is the integer number of elements.

It's not the only measure people care about. Another thing you can do is weight the elements of the set and then measure the total weights of the sets and compare that. This kind of comparison can be more useful. E.g. you could look at the total weight of the set if you were looking at carrying sets of tools in a backpack. In that case, volume would be an issue too. And you could come up with measures of the utility of each tool and add up the total utility of each set.

Real scenarios are often more complicated than easy-to-calculate measures. Just because your tools have X total volume, and your backpack has X+1 total volume doesn't mean they will fit. One could be too long, or there could be no way to pack them together without empty space in gaps between some tools. And the utility of a set of tools isn't just the sum of the utilities of the individual tools. If a screwdriver is 4 utility, that doesn't mean 2 of that screwdriver is 8 utility. And nails have more utility if you also have a hammer.

The utility of a set of tools is too complex an issue for people to define a measurement function that's very accurate, so they do critical thinking instead (which may involve some utility measures as loose approximations). The weight and volume issues are both simple enough someone could do a good job defining it and inputting their measurement function into a computer which would accurately calculate it. This isn't trivial but it's doable today and people could get good, useful results with it. Companies like FedEx have computer programs that worry about packing objects into spaces and considering weight and volume. FedEx cares especially about putting boxes into cargo holds of trucks and planes. And there are mathematicians who like to calculate how to tightly pack spheres and other shapes into spaces with the least wasted volume, and they know some stuff about how to do that.

So some facts:

• You can define dozens (or trillions) of different measures on one set. You can measure the same set multiple ways.

• Some measures are more useful to human concerns than others. Some are harder to measure than others.

• There is no canonical single measure for sets provided by the universe's instruction manual. There isn't like the one objective measure. There are often a variety of worthwhile measures for a set, and also many, many more arbitrary and dumb measures.

• Some measures help address many different human problems, as well as more important problems. Their reach is a sign of their objective value.

• Inches and meters are measures created by humans to help solve human problems. They are relatively useful and objectively valuable compared to many other measures.

• Quantity is a more complex measure than people take for granted, and it's not really a singular measure across all types of sets. In order to measure quantity of iPhones you need a definition of what sets of molecules constitute one iPhone. Then if you want to measure quantity of hammers, you need a totally different definition of what is one hammer. Quantity is only measurable with a supplemental function defining what is "one" of something, and that supplemental function varies for different objects. This complexity is something humans take for granted as common sense

OK now let's talk about numbers.

Different infinite sets can be measured and get different results.

You can look at infinite sets and measure them as "Is it finite or infinite?" and come to the conclusion "infinite" for all of them, and think they're the same.

But there are other measures. The set of all real numbers has more stuff in it than the set of all integers, even though they're both infinite. This fact is then actually used for measuring other infinite sets -- is it the same size as all integers, or all reals, or something else?

The way to compare infinite sets is to consider whether there is a mapping that puts the sets in one-to-one correspondence.

I will show you a mapping from the set of all integers to the set of all odd integers. This shows they are the same size! (Same size according to the normal, useful way mathematicians measure infinite sets.)

The mapping function is: n*2-1

You take an integer, n, and you double it and subtract 1. Now you have an odd number, m.

This is a one-to-one correspondence. No m repeats and no m is left out. You can pick any odd number m and find that there is exactly one integer n which corresponds to it via this mapping function.

The function is also reversible and the reverse gets you a one-to-one complete correspondence from odd integers to integers. You just take an odd integer, add 1 and halve it and boom you've got an integer. And you can get any integer by doing this.

BTW you only need to find one mapping function to make your point. There are other mapping functions which work just as well. Such as n*2-27. That also maps integers to odd integers with complete one-to-one correspondence.

This set mapping stuff is counter-intuitive because people initially feel like there are twice as many integers as odd integers, so the measure should say it's twice as big. But this measure says they are the same size! Yet this is the measure that's actually useful, has reach, has lots of objective value, is used in math a bunch. You could define some measures which assign an integer size to infinite sets and assigns twice as large an integer to the integers as the odds, but that's either not useful or sufficiently obscure/niche that I'm not familiar with it.

And people feel like you would run out of odd integers when trying to have one odd integer for every integer. And you would with finite sets. There are twice as many integers from 1-100 as odd integers in that range. And the same goes for 1 to a trillion.

But you don't run out of numbers with infinite sets. That you're mapping 101 to 50 and 10001 to 5000 is not a problem. You can just keep going up and never run out of odd integers to map to all the integers. I think the best way to look at this is just that you can pick any integer and clearly see there is exactly one odd integer it corresponds to with our mapping.

A complete one-to-one correspondence means sets are the same size in some meaningful sense. It's like putting one set on the left, one on the right, and drawing a line between every element on the left to every element on the right. And every single element in each set has exactly one line connecting it to the other set. Just like if I have 4 goats and you have 4 cows and we drew 4 lines and saw our sets of animals were the same size. But if you had 5 cows then we couldn't draw lines in this way, you'd have an extra cow with no line touching it, or else i'd have a goat with 2 lines touching it.

There is no one-to-one correspondence from the integers to the reals, which is why the reals are considered a bigger set. That thing you can do to correspond odds to integers is not possible with integers to reals. That makes reals a bigger set than integers in a way which integers aren't bigger than odds. And this particular way of measuring set size turns out to be valuable, useful, helpful -- it's a good way to think about things for many purposes.

You're having trouble because you're using your intuitions about quantity measures of finite sets, including I presume that there's only one way to measure a set.

Physicists have a measure of infinite sets of universes. The results are fractions like 0.2 or 0.01. And it means what you would expect: e.g. you measure the universes where event A happens, get 0.5, and that means it happened in 50% of universes.

You could measure as a fraction of the whole multiverse but you normally don't want to. You can also measure as a fraction of a region of the multiverse, like the ones where you exist and are doing this experiment at this time and everything else is the same too. Then of those initially identical universes, you end up with 3 sets of universes and one has a measure of .5 and one has a measure of .375 and one has .125 (these are the numbers from Justin's example quoted above for No Event, A Event Only and A+B Events.)

How can an infinite set get a finite measure? Well it's just like if there were hypothetically infinite points in an inch, it could still be measured as one inch. And another distance could be two inches, and they both have infinite points but there's still this useful measure in which one is twice as long as the other. Current physics doesn't say an inch of space is infinitely divisible into infinite points, but that is a familiar classical physics scenario which people's intuitions don't struggle with so much.

Anyway this stuff is really confusing without the right background knowledge: having some general understanding of sets, measures, mappings, infinite sets, etc. So this should help give you some leads to think about and lead to some followup questions.

BTW I don't even know where this stuff is taught or good books explain it. I learned most of this from David Deutsch personally.

PS I am not an expert on math or physics terminology and may have used a technical term a little bit wrong or omitted a technical term that is normally used. I've tried to focus on clearly and understandably presenting useful, important concepts.

Most people don't like being told "no".

It's common that people ignore a request instead of refusing. They say nothing instead of "no". Especially online. In person sometimes it's hard to say nothing so they change the topic, or some something unclaer, or say "maybe" (then don't do it), rather than clearly saying "no".

In Overwatch, people commonly ask you to switch to a different hero. If you reply, "no" you're giving them useful information. You aren't going to change, so maybe someone else should consider changing. Knowing what you're going to do lets people synergize with it better. But people get angry if you say "no" and take it better if you silently ignore them. If you refuse them they feel challenged and confronted and try to fight with you. But if you're silent then you haven't challenged their right to order you around, and haven't confronted them socially, and they don't have anything to fight over. You appear the coward. And what happened is ambiguous. Maybe you're having problems with your headphones and didn't even hear them.

I prefer the type of people who say "no" instead of being silent. But most people are the silent coward types, and most people dislike it if you say "no" as if you have a right to say it and it's a valid, reasonable decision. People want conflict to be hidden in general. If I say "no" it's obvious we disagree, you want me to do X and I refuse. Silence hides the conflict better.

Passivity is immoral but normal. Asserting yourself stands out more. Communicating provides useful information, and silence is ambiguous – but people don't care much about that, they care about social status and interaction.

People are frequently silent because it's easier. Why go to the trouble of saying "no" – even if it's useful information – when people will hassle you for it? This is unfortunate. It'd be better if people communicated more honestly and weren't punished for it.

I've been playing Overwatch, a team-based (6 vs 6) first person shooter game. This raises a variety of interesting problems.

There are 23 heroes. To learn best, do you specialize in one or two heroes? Or do you play a wide variety and try to pick whatever is the optimal hero at any time? (You can switch heroes mid game to handle different situations. Hero switching is part of the game.)

Do you practice by playing the game, or do you do something else to practice like target practice shooting or 1v1ing a friend? Do you play more or do you read guides and watch gameplay footage from top players or tournaments? Do you spend time on test experiments to learn details about the game physics?

Do you do your best to try to win every game, or do you sometimes do something for learning purposes which you think can help you win future games?

How much attention do you spend on your mouse settings, your mouse pad, your hardware and frame rate, etc? Or just don't worry about it and play a lot?

Voice chat is integrated into the game and very important for coordinating better teamwork. How do you deal with mean people who insult you? People on your team who get angry and try to lose on purpose for revenge? People who are passive, quiet, and non-communicative? People who don't listen and don't follow team strategies? People who disagree about strategy?

Some of my answers:

Don't get into arguments with your team. Ignore assholes and mute them if they're persistent. (Sometimes I ask people to stop flaming and just focus on playing the game. Sometimes this works but sometimes they just keep at it and respond to the request with more flaming. If I ask someone to stop and they continue then I definitely mute them.) And if you really want to win, it's better not to trigger these people since they're really common. If I play Ana (healer) then basically no one gets mad at me ever, but if I play Widowmaker (sniper) then I get complaints in the majority of games (often there are complaints in the setup phase before the game even starts, so it's not even based on my quality of play). So it's easier to win games with Ana just because my team is happier.

Focus on one hero at a time until you're comfortable with them. It's really hard to learn much if you play a hero for one or two games then switch. It really helps to play at least 100 games in a row with one hero (play them at least 90% of the time, you can't realistically use them 100%), and more is better. (Games take like 10-15 minutes typically.) Once you get a good handle on one hero, then you can learn a second hero. Then a third. And keep going back to the heroes you're good with regularly to stay fresh with them. You learn more by understanding several heroes to see the game from multiple perspectives, but focused practice on one hero at a time is really valuable to learn them initially. Playing all the heroes is a bad idea which will spread you too thin, but playing several is a good goal to work towards. (It's a good idea try all the heroes a little bit at first to see which you want to learn and to learn the very basics of what they do.)

Don't just play the game. Watch a few tournaments to see what good, organized teams do. That's worth being familiar with to get a better idea of optimal play. Watch some pro streams who play heroes you play to see gameplay from the perspective of one really good individual. Try to find streamers who explain what they are doing and talk a lot so you can learn more. Make sure the streamer is a very good and serious player, not a casual "fun" streamer, but it's fine if they are like #1000 in the world, not #5, that's plenty good enough. Read and watch some guides until they get repetitive. Each different information source offers some value and you should try them all, each has its own strengths.

Playing to learn is good (like playing a hero you're less good at but want to practice). But try your best to win sometimes too. Do both. I bought a second account so I can practice on one and try my best on the other.

Playing a lot is important but it's also good to practice specific stuff like aim and 1v1s at least a little bit. It's another information source with its own strengths, so try it a bit. I do recommend focusing on playing the most, but try everything else a bit and see what value it offers.

Focusing on playing and not setup is important, especially when you're new. But mouse settings are legitimately a big deal. Many new players have their mouse move way too fast. Not like 20% too fast. Like 10 times too fast or more. I started out that way because it works fine in other types of games and for regular computer use. I lowered my mouse speed many times. Over time I improved other aspects of my setup, but the rest weren't urgent and could be done gradually so it's never very much of the time spent on Overwatch. (Like play for 20 hours, than spend half an hour improving your setup. Repeat. That's a reasonable ratio. It's worth optimizing stuff if you play a lot, but you don't want to get distracted from actually playing.)

Play the heroes you want to play as long as they are reasonably good. Which heroes are really good changes over time as the game gets new patches. Don't chase what's currently considered the very best heroes. As long as your hero choices that you like are pretty good, just stick with them. And don't play a hero you're bad at just because it's the right hero pick in the situation. You can do that to practice, but don't do it to win. A lot of players pick heroes they suck at in an attempt to win the game because they think the hero is needed in the situation. But having that player on a hero they are good at is way more important than having the optimal heroes.

If people don't communicate and don't do teamwork, you have to try to work with them. Watch what they do and help them with it. It's better that the whole team follows him and does an inferior plan than he just does something alone and dies. It's possible to win if you work together even if it's not the strategy you would choose. But if people are doing different things separately against a full enemy team, you'll basically never win. It's very hard to win any fights against a full team of 6 players without also having your own 6 players all fighting. So if someone attacks at the wrong time, go attack with him too. If you die, so what, you'll just respawn at the same time as him, so it doesn't really matter. (What else are you going to do, stay alive and wait for him to respawn? That will take the same amount of time. You might as well go try since everyone has equal respawn times, there's often no harm in dying at the same time your ally dies. If you lose a fight you lose the fight, it doesn't matter that much if you wait for one guy to respawn or everyone.)

Discuss!

meta discussion isn't a problem. DD was wrong.

the actual problem is parochial content that isn't of general interest. that includes stuff about specific people, events, times, places, activities (including conversations) that lack objective importance and value.

say a confused idiot is arguing boring, wrong details about a sub-point of a sub-point of a sub-point, and every single sub-point is totally misconceived and he's gone way down the rabbit hole.

it's equally boring if you then reply with parochial meta ("here is where your discussion methodology went wrong when going from sub-point 2 to 3, you should have...") or parochial non-meta (specific, detailed arguments about sub-point 3 that no one cares about because no one else has the same idea you're criticizing because they don't make that exact sequence of errors to get to that bad idea).

you want to say something interesting and important that a third party who doesn't know anyone involved in the conversation could care about. it doesn't matter if this is meta (great tips on writing, on communication, on how to discuss like Paths Forward stuff, thinking methodology content, talking about methodological errors people make, talking about error-correcting methods) or non-meta (talking about parenting, dating, politics, economics, art, programming, gaming). what matters is if it's general-interest or parochial. being about one specific person or conversation is a way to make things parochial, whether it's meta (discussing the conversation directly) or not (the detailed sub-points themselves of the parochial conversation that no one cares about).

another aspect of meta discussion is it's frequently off topic. suppose originally the conversation was about schools, and now it's about discussion methods. that's a topic change. topic changes aren't a bad thing in general. conversations shouldn't be limited to the original topic. tangents should be allowed. however, topic changes can be problematic when people are disorganized which is common. disorganized people can't deal with a branching, unbounded conversation that covers many issues and deals with sub-issues, connections to other fields, etc. the problem here isn't really meta discussion, it's some people lacking the skills to deal with multi-topic conversations at all, whether the second topic is a meta-topic or not. (they'd have equal trouble talking about both school and liberalism at once, because they'd lose track of the big picture and how the two topics are connected.)

do not consider "is what i'm about to write meta discussion?"

consider "is what I'm about to write parochial? is what I'm about to write of general, objective interest to strangers?" also if you're changing the topic or adding an additional topic to the conversation, consider if you and others involved have the organizational skill to deal with it.

People often think something they do is bad and then try to stop right away. Like smoking or spending lots of time on Facebook.

Often they don't do anything at all about it for a long time. Then they abruptly try to quit their "habit". (Peeing isn't call a "habit". People usually only call something a "habit" if they think it's bad.)

First they didn't judge their activity. They weren't thoughtful. Then they get super judgey. They think of a reason it's bad and now view it as totally unacceptable.

If something is a significant part of your life, or you otherwise find it difficult to stop, then don't try to quit abruptly.

Pay attention to what you do. Pay attention to how you feel about it. Try to understand why you do it. Try to learn more things about it, both good and bad. Write down factual notes about what you do including thoughts and feelings you have as part of the activity. Think of it as an information-gathering phase.

Don't threaten the activity. Then that part of you will get defensive. Do introspection. Be more thoughtful, present and mindful about it. That isn't an attack. Don't attack that part of yourself.

Once you understand yourself better (gather information for longer than you think is enough) then you can calmly analyze what you learned and consider if you'd like to make any changes and what problems you could run into.

What's good about the activity that maybe you don't want to give up? Maybe you can find another way to get it, and get that working first, and then after that's already successful then you could quit the original activity since you don't need it anymore.

When you quit it should be easy. If you have a good solution then you won't have much temptation, relapses, mixed feelings, etc. If you're running into those kinds of issues then stop trying to quit and go back to the learning-but-not-changing phase.

This all fits with the general pattern I advocate of powering up first (especially by learning) and then doing things when they're easy. Trying to do things when they're hard is inefficient and you'd be better off learning more instead of putting so much effort into doing this one thing early.