The following is a series of exercises designed to test one's understanding of "Making Beliefs Pay Rent (in Anticipated Experiences)", a post in the Mysterious Answers to Mysterious Questions sequence by Eliezer Yudkowsky.

A. Examine the following list of statements. For each statement, ask: What observations would you expect to make if this statement were true that you would not expect to make if this statement were false, or vice-versa? If no such observations exist, indicate that this is so.

  1. Bismarck is the capital of North Dakota.
  2. The universe does not exist; all existence is imaginary.
  3. The earth is flat.
  4. The comic book Queen & Country is based on the British ITV series The Sandbaggers.
  5. Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter is a good book.
  6. "A Visit from St. Nicholas" (a.k.a. "Twas the Night Before Christmas") was written by Clement Clarke Moore.
  7. Herbert Hoover was left-handed.

B. In the Dan le Sac vs. Scroobius Pip song "Thou Shalt Always Kill", one of the injunctions given to the listener is, "Thou shalt not put musicians and recording artists on ridiculous pedestals no matter how great they are or were." After this statement comes a list of such bands, beginning, "The Beatles: Were just a band. Led Zeppelin: Just a band. The Beach Boys: Just a band." Consider just this first statement, that the Beatles were just a band. What does it imply in terms of anticipated experiences?

The author's remarks on the solutions to these questions appear in this comment.

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A. What observations would you expect to make if this statement were true that you would not expect to make if this statement were false, or vice-versa?

1. Bismarck is the capital of North Dakota.

In the political structure of the United States of America, the capital city of a state is the city housing the state government. A good way of checking which city this might be is to find the state capitol building - the building where the legislative branch meets. Therefore, if the capital of North Dakota is in Bismarck, one should expect to find the state capitol there.

2. The universe does not exist; all existence is imaginary.

There appear to be no observations which would refute this statement. There is no logical reason why any given imaginary observation would be otherwise than it is, and stating that all existence is imaginary implies that there is no non-imaginary with which the universe can be compared to show a difference.

3. The earth is flat.

There are many obvious implications of this belief - facts which would be more likely not to hold if the earth were some other shape. A selection:

a. The earth would have edges. If you proceeded in a straight line for long enough, you would encounter the edge of the earth.

b. Where the horizon was not an elevated point (e.g. a mountain), the horizon would be the edge of the earth - as the entirety of any plane figure is visible from any point above that figure.

c. Gravity would be parallel at all points. If Alice through a telescope as Bob, many miles distant, dropped an object, she would see that object fall along a trajectory parallel to the trajectory through which an object dropped at her location would fall.

d. All celestial objects - the sun, the moon, the planets, the stars - would rise and set simultaneously at all locations on Earth.

4. The comic book Queen & Country is based on the British ITV series The Sandbaggers.

One identifies the inspiration one creative work takes from another by those features which are, first, common to those works but uncommon in the wider genre, and second, not likely to be created by independent development. Both Queen & Country and The Sandbaggers are spy fiction; therefore, the evidence that Queen & Country is based on The Sandbaggers would be found in those aspects of the former which are rare in spy fiction but exist in The Sandbaggers, such as the existence of a group of three special agents within British intelligence.

5. Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter is a good book.

What are the distinguishing features of a "good book"? Common usage suggests several factors which are common (although not universal) in good books:

a. A good book is readable. It should not be overly difficult to read, understand, and finish the book.

b. A good book is enjoyable. The reader should gain pleasure while reading it, and pleasure while remembering having read it.

c. A good book is informative. The reader ought to come away from the book with true knowledge they did not have before reading it.

d. A good book is well-organized. Related material should appear together, or, where it does not, references should be made to the related material.

e. A good book is original. It should provide new knowledge, new organization of knowledge, newly enjoyable presentation of knowledge, or newly clarified presentation of knowledge, or some combination of all of the above.

Criteria such as these are more likely to be met by good books than by poor books.

6. "A Visit from St. Nicholas" (a.k.a. "Twas the Night Before Christmas") was written by Clement Clarke Moore.

Determining authorship is a complicated matter, but there are several lines of evidence which could be compiled on the subject:

a. The existence of drafts. If, among an author's papers, are found numerous pre-publication versions of a work (as is the case with Lincoln's speech at Gettysburg), this renders strong evidence that the author was the proximate creator of the work.

b. If the work is written in a style which is distinctive to other works attributed to that author, this supports the conjecture that all these works were composed by the same hand. Inversely, if the work is written in a style discordant with the remainder of an author's body of work, this suggests that it was not likely to have been written by that author.

c. Attribution. Other factors being equal, if the original publications attribute the work to an author, that attribution may usually be believed.

d. Date. If a work was originally composed when the purported author was not writing (e.g. before their birth or after their death), this refutes the premise that the author created it.

e. Content. If the work contains information which the purported author did not know or did not believe, that suggests the author did not create it.

7. Herbert Hoover was left-handed.

Left-handedness manifests in several ways in the behavior of an individual - writing and drawing being the most obvious. If Herbert Hoover were left-handed, one would have a greater expectation of seeing photographs of him writing or drawing with his left hand and less with his right. One would also expect accounts (for example, in letters, diaries, etc.) wherein his handedness was mentioned to state that he was left, not right, handed.

B. In the song "Thou Shalt Always Kill", what does "The Beatles were just a band" mean?

This is a difficult one. Clearly the Beatles were a band, but to say that they were "just" a band seems to indicate an additional claim which is not well defined. While it is possible to ascribe meaning to the statement in some contexts, without evidence that it was composed with that meaning in mind, it holds no factual value. Indeed, if one considers the statement in its original context, one finds that it, like the one preceding it, serves as an reprimand against fandom rather than a statement of fact.

3a -edges. This is not such a great answer. One could have an infinite flat plane for example (thus being flat with no edges). Similarly, one could have a hemisphere (not flat but with edges).

I agree that "edges" is a weaker implication of flat-earth than the others - but I don't think it's unjustified. For one thing, the atmosphere is not purely transparent, so it should be impossible to see the sun through it if it were infinite in (horizontal) extent; for another, the sun has to come up somewhere.

These challenges could be evaded by videogame physics, for example, but such would be in conflict with human intuition.

You could add the date of creation question to A-4. If Queen and Country came out before The Sandbaggers, that would refute the assertion that Sandbaggers influenced it. Other than that, this looks really good. I'm very pleased that this project is actually underway. Upvoted (and if I could upvote more than once, I would).

Thanks - that's a second correction I will make.

A. Observations I'd anticipate if the following were true:

  1. Bismarck is the capital of North Dakota: Maps of the U.S. or of North Dakota will have Bismark marked with the symbol for "state capital." If I went to Bismark I'd find the North Dakota state government buildings there.

    1. The universe does not exist; all existence is imaginary: I'd anticipate my experiences to contradict each other and not support a coherent model; the scientific method would fail to find predictable regularities. Note this is rather a weak expectation, as if I don't exist I'm not a very trustworthy predictor.

    2. The earth is flat: videos taken from the space station would show the oceans pouring off the edge. It would be impossible to sail around the world by always going the same direction.

    3. The comic book Queen & Country is based on the British ITV series The Sandbaggers: the former would have characters with the same names and/or personalities as the latter. The former would have a blurb on it somewhere saying "based on The Sandbaggers."

    4. Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter is a good book: Reading the book would produce positive effect or practical benefit. Reading part of it would be followed by a desire to read more of it.

    5. "A Visit from St. Nicholas" (a.k.a. "Twas the Night Before Christmas") was written by Clement Clarke Moore: A copy of "A Visit from St. Nicholas" would have the phrase "by Clement Clarke Moore" under the title, or no by line. It wouldn't have "by [some other name].

    6. Herbert Hoover was left-handed: Videos of Herbert Hoover signing something, if any exist, would show him doing it with his left hand.

B. This statement would imply that the group consisting of John Lennon, Ringo Starr, Paul McCartney, and George Harrison created and performed music, but did not produce other goods or services such as automobiles or theorem-proving.

Very nice!

Without looking at any comments or other answers:

Bismarck is the capital of North Dakota.

If I went to the place identified as "Bismarck, North Dakota" on widely-used maps and looked around, I would see a building where some folks calling themselves the North Dakota legislature were prone to meet and talk in a formalized way about North Dakota law. Their deliberations would be reported on in newspapers that could be found in many towns in the area described on many widely-used maps as "North Dakota".

The universe does not exist; all existence is imaginary.

This seems to be false by definition, since "imaginary" refers to thoughts or ideations that are distinct from everyday life. The only data we have for distinguishing "the imaginary" from "the not-imaginary" are within the universe.

The earth is flat.

If I synchronize two clocks and send them to different points "around" the earth, observers will see the same angles of shadows at the same clock times.

The comic book Queen & Country is based on the British ITV series The Sandbaggers.

First: I can find the comic book and TV series mentioned in resources that describe other such things. Second: There are similar characters, plotlines, or settings between them, according to a notion of "similar" that I'm not actually prepared to analyze right now.

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter is a good book.

People who read it, drawn from some reference class I'm not prepared to analyze right now, are not disappointed.

"A Visit from St. Nicholas" (a.k.a. "Twas the Night Before Christmas") was written by Clement Clarke Moore.

If I go to the library and look it up, I get results that agree with the proposition. Standard references express less disagreement on the matter than on the authorship of Shakespeare's plays, since Clement Moore is more recent.

Herbert Hoover was left-handed.

Museums likely to have artifacts from Herbert Hoover's administration include writings written with left-handed penmanship styles, or have specific instruments such as scissors in left-handed orientation.

Basically agree with your (A) answers, though I'd also add that even if a person hadn't read GEB, they could also expect that a long-lasting following for a book is more likely for a good book.

As far as (B), it cashes out for me into a complex of descriptive and normative claims. Among the descriptive claims are that it is possible for someone to excel legendary band X in their own genre (it would be hard though not theoretically impossible to find a good judge of genre quality who wasn't biased by knowing the legendary band).

That's reasonable.


Very, very nice! One quick suggestion: could you change the order of exercise A slightly so that it's in ascending order of difficulty? Judging from the other comments on this page, #2 and #5 are the most vague (and thus more difficult) and #7 was very easy.

Minor quibbles aside, I highly approve of this endeavor--well done!

Thank you!

The reason why #2 appeared so high on the list was because I wanted a case where the statement really didn't constrain expectations much to appear early in the list. As for #7 - yeah, you got me there. When I revise it, I will be sure to move that up.


I keep trying to vote this post up, but as far as I can tell it hasn't worked.