Heavily inspired by a conversation with Keshav Srinivasan and Richard Ngo during MATS 10.0.
The week ahead of you is packed. This isn't your usual brand of busy—you're phoneless, so you can't check the details, but (as far as you can remember) every hour of every day is spoken for. Tonight will be particularly hectic…
You're mid-conversation when Someone Important walks by. They pause, turn around, and ask: "Hey, when are you going to finish That Thing you said you'd do?"
Level 0 procrastination: "I'll finish it by tonight!" Problem: you're busy tonight.
Level 1: "I'll finish it by tomorrow!" Problem: one day is obviously not enough to finish That Thing. And besides, you might be really busy tomorrow!
Level 5: "I'll finish it within 5 days!" Problem: this is starting to feel hopeless—you don't have your calendar on you right now, and you barely even have an order-of-magnitude estimate for how long doing That Thing will take you! Would even 100 days be enough?
…
Eureka!
Level procrastination: "By tonight, I'll let you know when I will finish That Thing by!" If we had said "I'll finish it within days" for any finite , we would have only days in which to complete That Thing; by choosing level instead, we have attained the freedom to mull things over tonight (with our calendar!), decree "I'll finish it within days" then, and subsequently enjoy the extra day of free working time! The symbol refers to the smallest transfinite ordinal, heuristically defined to be a new symbol such that for every finite ordinal (a.k.a. natural number) . This very clever move buys you strictly more leeway than any finite level of the procrastination hierarchy—we have ascended to transfinite procrastination. (Another way to understand level is as "by tonight, I will pick a finite level of the procrastination hierarchy to commit to."[1])
…
Problem: you're really busy tonight.
…
Level [2] procrastination: "By tomorrow, I'll let you know when I will finish That Thing by!" Problem: …you don't even know how long it's going to take you to figure out how long doing That Thing will take you! And what if you're busy tomorrow???
Level procrastination: "By one week from tomorrow, I'll let you know when I will finish That Thing by!" Problem: this is starting to feel unprincipled. Who's to say if 8 will be enough? It'd be much easier to choose if only you had your calendar. So what if you just…
Level procrastination: "By tonight, I will let you know a date by which I will let you know when I will finish That Thing by!" Naturally, is also known as [3], and it satisfies for any finite . We can understand this level as "by tonight, I will let you know a date by which I will do level ," or more generally as "by tonight, I will pick some ordinal , and I will commit to that level of the transfinite procrastination hierarchy."[4]
…
Problem: you're really, really busy tonight.
Level : "By tomorrow, I will let you know a date by which I will let you know a date by which I will finish That Thing!" Problem: you're starting to get curious how far you can go!
Level : "By tonight, I will let you know a date by which I will [let you know a date by which I will [let you know a date by which I will finish That Thing!]]" This is "by tonight, I will let you know a date by which I will do level ." Is this really the whole story? Do we just keep going to , , etc. forever…?
Problem: you now have new tools by which to handle "forever".
Level : "By tonight, I will either let you know a date by which I will finish That Thing, OR I will let you know a date by which I will [let you know a date by which I will finish That Thing], OR I will let you know a date by which I will [let you know a date by which I will [let you know a date by which I will finish That Thing]], etc. etc." That sure is a mouthful, but since (a.k.a. ) satisfies for any finite ordinal , we can more simply say "by tonight, I will pick a level of the transfinite procrastination hierarchy to commit to," or (oversimplifying a little, a la the previous footnote) "by tonight, I will pick some and do level ."
Level : "By overmorrow, I will pick a date by which I will do level ." We can also say this as "by overmorrow, I will do level ."
Level : "By tonight, I will pick some and do level ."
Level : "By tonight, I will pick some and do level ."
Level : "By tonight, I will pick some and do level ."
Level : "By tonight, I will pick some and do level ."
Level : "By tonight, I will pick some and do level ."
Level : "By tonight, I will pick some and do level ."
Keen procrastinators will be pleased to hear that there is no end to this madness. What we have discovered here is the hierarchy of transfinite ordinals, which has numerous non-procrastinatory applications including enabling the unworried slaying of mathematical hydras.[5]
Thankfully, the theory of transfinite ordinals assures us that any strictly decreasing sequence of ordinals must eventually terminate. This means that diligently[6] partaking in transfinite procrastination guarantees that we will finish That Thing in finite time! You can decide to postpone the task, or decide to postpone deciding how to postpone the task, or decide to postpone thinking about how many levels of postponing you want, and so on… but as long as each decision moves you to a strictly lower ordinal this process will eventually terminate!
For example, let's imagine that I decide to work at level : "by tomorrow, I will send you the date by which I will [send you a date by which I'll finish That Thing]." One day passes, so it's tomorrow and we're at level —I need to pick a date by which I'll send you a date. I think about it, and I say, "okay, by 50 days from now I will tell you the date by which I will finish That Thing." In making that decision, I've jumped from level down to level ! Now 50 more days pass, so we're at level —I need to pick a date by which I'll finish That Thing. I think about it, and I think about it, and I say, "by 100 days from now, I'll finish That Thing." Here I've jumped from level down to level 100… which means that within 100 days I must be done! In this scenario, I finish That Thing within 151 days; no matter how many days I chose at each step, the total time to completion would still be finite.
Hopefully the utility of transfinite procrastination is now clear: not only can you delay your responsibilities arbitrarily far in the future, but you can also delay thinking about your responsibilities, and thinking about thinking about them, and so forth… And yet, unlike less sophisticated forms of procrastination such as "I'll do it later", a transfinite procrastinator who sticks to their word must finish their duties in finite time!
Unfortunately, transfinite procrastination comes with two significant downsides which one must not forget.
The first downside of transfinite procrastination is its insidious cost. It's easy to forget, but when I say "in 5 days I will decide on the deadline," I now have two tasks to do: deciding on my deadline, and doing That Thing. If I say "tomorrow I'll decide on the deadline by which I'll decide on the deadline," I now have three tasks. Those additional administrative tasks didn't need to exist! With each new "" you generate additional work, and if you do enough transfinite procrastination then you will have spent more brainpower on that self-inflicted deadline-deciding work than you ultimately spend on the actual fucking task!
The second downside of transfinite procrastination is that, although it guarantees you will finish That Thing in finite time, it makes no guarantees about whether you finish it before the Singularity.
More generally, for any ordinal , we execute level procrastination by "pick some number , then do instances of level chained back to back." In our case, we have , which means "pick some number of tomorrows"!
Not ; ordinal addition is noncommutative, and . For the purposes of our procrastination you can imagine these ordinals being consumed from right to left; is "wait one day, then choose a date," while is "choose a date, then add one day to it." In the latter case, you may as well just choose the one-day-later date in your step anyway! So gives us no more procrastination power than plain , illustrating that !
Not , as ordinal multiplication is also noncommutative: means " copies of ". The analogy is less straightforward than for addition, but we can say that with we get two deadline choice opportunities (pick a number of days by which you pick a number of days), whereas with we get a single choice of how many s we'll use (pick a number , then finish within pairs of days, i.e. within days). Since "pick a finite even number of days" is no more powerful than plain 's "pick a finite number of days", we can see that .
Technically, "I will tell you my next " is not quite the same thing as "I'll tell you by when I will tell you by when I will finish"—in particular, the former allows us to say "I'll finish it tomorrow" tonight, while the latter as stated does not—but in practice they are the same: for example, tonight, we can say "I have decided that the date by which I will give you my deadline is today… so now I will give you my deadline: I will finish by tomorrow!"
To be clear, "diligently" refers to keeping your promises! If you say "by tomorrow, I'll send you a date by which I will finish That Thing" and then tomorrow comes and goes and you haven't sent said date, you've defeated the whole purpose of transfinite procrastination and none of this applies.
I've also seen some people use non-well-founded procrastination: "I'll give you an update tomorrow", where an "update" can be just another message of the same type.
Heavily inspired by a conversation with Keshav Srinivasan and Richard Ngo during MATS 10.0.
The week ahead of you is packed. This isn't your usual brand of busy—you're phoneless, so you can't check the details, but (as far as you can remember) every hour of every day is spoken for. Tonight will be particularly hectic…
You're mid-conversation when Someone Important walks by. They pause, turn around, and ask: "Hey, when are you going to finish That Thing you said you'd do?"
Level 0 procrastination: "I'll finish it by tonight!"
Problem: you're busy tonight.
Level 1: "I'll finish it by tomorrow!"
Problem: one day is obviously not enough to finish That Thing. And besides, you might be really busy tomorrow!
Level 5: "I'll finish it within 5 days!"
Problem: this is starting to feel hopeless—you don't have your calendar on you right now, and you barely even have an order-of-magnitude estimate for how long doing That Thing will take you! Would even 100 days be enough?
…
Eureka!
Level
If we had said "I'll finish it within
freeworking time!The symbol
…
Problem: you're really busy tonight.
…
Level
Problem: …you don't even know how long it's going to take you to figure out how long doing That Thing will take you! And what if you're busy tomorrow???
Level
Problem: this is starting to feel unprincipled. Who's to say if 8 will be enough? It'd be much easier to choose if only you had your calendar. So what if you just…
Level
Naturally,
…
Problem: you're really, really busy tonight.
Level
Problem: you're starting to get curious how far you can go!
Level
This is "by tonight, I will let you know a date by which I will do level
Problem: you now have new tools by which to handle "forever".
Level
That sure is a mouthful, but since
Level
We can also say this as "by overmorrow, I will do level
Level
Level
Level
Level
Level
Level
Keen procrastinators will be pleased to hear that there is no end to this madness. What we have discovered here is the hierarchy of transfinite ordinals, which has numerous non-procrastinatory applications including enabling the unworried slaying of mathematical hydras.[5]
Thankfully, the theory of transfinite ordinals assures us that any strictly decreasing sequence of ordinals must eventually terminate. This means that diligently[6] partaking in transfinite procrastination guarantees that we will finish That Thing in finite time! You can decide to postpone the task, or decide to postpone deciding how to postpone the task, or decide to postpone thinking about how many levels of postponing you want, and so on… but as long as each decision moves you to a strictly lower ordinal this process will eventually terminate!
For example, let's imagine that I decide to work at level
One day passes, so it's tomorrow and we're at level
Now 50 more days pass, so we're at level
Hopefully the utility of transfinite procrastination is now clear: not only can you delay your responsibilities arbitrarily far in the future, but you can also delay thinking about your responsibilities, and thinking about thinking about them, and so forth… And yet, unlike less sophisticated forms of procrastination such as "I'll do it later", a transfinite procrastinator who sticks to their word must finish their duties in finite time!
Unfortunately, transfinite procrastination comes with two significant downsides which one must not forget.
The first downside of transfinite procrastination is its insidious cost. It's easy to forget, but when I say "in 5 days I will decide on the deadline," I now have two tasks to do: deciding on my deadline, and doing That Thing. If I say "tomorrow I'll decide on the deadline by which I'll decide on the deadline," I now have three tasks. Those additional administrative tasks didn't need to exist! With each new "
The second downside of transfinite procrastination is that, although it guarantees you will finish That Thing in finite time, it makes no guarantees about whether you finish it before the Singularity.
More generally, for any ordinal
Not
Not
Technically, "I will tell you my next
This video illustrates the hydra-slaying process particularly well.
To be clear, "diligently" refers to keeping your promises! If you say "by tomorrow, I'll send you a date by which I will finish That Thing" and then tomorrow comes and goes and you haven't sent said date, you've defeated the whole purpose of transfinite procrastination and none of this applies.