In principle you can stack arbitrarily many levels of meta, but I’m reminded of Eliezer’s ultrafinitist principle that you never need more than two. The more levels you stack up, the wobblier the stack gets because the possibilities at each level multiply, and sometimes the right thing to do is to just drop the Jenga tower on the floor.
Here is an extract from the 1954 film, “The Maggie”. Link goes to the relevant timestamp. I’ve provided the words below but it’s more entertaining to watch.
An American businessman has chartered a plane to chase “The Maggie” (a Clyde puffer) somewhere in the Inner Hebrides. At last he catches sight of the boat. The following conversations ensue.
On the plane:
The Businessman: Where do you figure they’re heading for?
The Pilot: It looks like they’re putting into Inverkerran for the night.
The Businessman: But tell me, if they thought I thought they were going to Inverkerran, where do you think they’d head for then?
The Pilot: Strathkathick, maybe.
The Businessman: I know this sounds silly, but if they thought I’d think they were going to Strathkathick because it looks as if they’re going to Inverkerran, where would they head for then?
The Pilot: My guess would be Pennymaddy.
The Businessman: Well, if there’s such a thing as a triple bluff, I’ll bet Mactaggart invented it. Ok, Pennymaddy.
On the boat:
Mactaggart (the captain): Aye, he’ll have guessed we’re making for Inverkerran.
The Steersman: Will he not go there himself then?
Mactaggart: Och no, he’ll know we know he’s seen us, so he’ll be expecting us to make for Strathkathick instead.
The Steersman: Well then, shall I set her for Pennymaddy?
Mactaggart: No, because if it should occur to him that it’s occurred to us that he’d be expecting us to make for Strathkathick, then he’d think we’d be making for Pennymaddy.
The Steersman: Well then shall I set her for Penwhinnoy?
Mactaggart: Och, no. We’ll make for Inverkerran, just as we planned. It’s the last thing he’s likely to think of.
Another issue with stacking is that your measurement and prediction error stacks, so at a certain depth you have basically no certainty about any conclusions at that depth.
In principle you can stack arbitrarily many levels of meta, but I’m reminded of Eliezer’s ultrafinitist principle that you never need more than two. The more levels you stack up, the wobblier the stack gets because the possibilities at each level multiply, and sometimes the right thing to do is to just drop the Jenga tower on the floor.
Here is an extract from the 1954 film, “The Maggie”. Link goes to the relevant timestamp. I’ve provided the words below but it’s more entertaining to watch.
An American businessman has chartered a plane to chase “The Maggie” (a Clyde puffer) somewhere in the Inner Hebrides. At last he catches sight of the boat. The following conversations ensue.
On the plane:
The Businessman: Where do you figure they’re heading for?
The Pilot: It looks like they’re putting into Inverkerran for the night.
The Businessman: But tell me, if they thought I thought they were going to Inverkerran, where do you think they’d head for then?
The Pilot: Strathkathick, maybe.
The Businessman: I know this sounds silly, but if they thought I’d think they were going to Strathkathick because it looks as if they’re going to Inverkerran, where would they head for then?
The Pilot: My guess would be Pennymaddy.
The Businessman: Well, if there’s such a thing as a triple bluff, I’ll bet Mactaggart invented it. Ok, Pennymaddy.
On the boat:
Mactaggart (the captain): Aye, he’ll have guessed we’re making for Inverkerran.
The Steersman: Will he not go there himself then?
Mactaggart: Och no, he’ll know we know he’s seen us, so he’ll be expecting us to make for Strathkathick instead.
The Steersman: Well then, shall I set her for Pennymaddy?
Mactaggart: No, because if it should occur to him that it’s occurred to us that he’d be expecting us to make for Strathkathick, then he’d think we’d be making for Pennymaddy.
The Steersman: Well then shall I set her for Penwhinnoy?
Mactaggart: Och, no. We’ll make for Inverkerran, just as we planned. It’s the last thing he’s likely to think of.
Another issue with stacking is that your measurement and prediction error stacks, so at a certain depth you have basically no certainty about any conclusions at that depth.