Last set of *GEB* notes for the night. Yet another essay/side story from the book.

### Bach’s *Aria with Diverse Variations*

- Popularly known as Goldberg Variations
- All of the pieces, except the final one, are based on a single theme
- In the last variation is a sort of “post-ending ending” that contains extraneous ideas (two German folk tunes) that are outside the original theme. Variation called a “quolibet”
- Written in 1742, when Bach was **Cantor in Leipzig**

### Copper, Silver, Gold themes

- Kupfergödel, Silberescher, Goldbach - Copper, Silver, Gold: an Indestructible Metallic Alloy - Indestructible Metallic Alloy - Eternal Golden Braid - Giraffes, Silver, Gold (G - Gödel) - Copper, Elephants, Gold (E - Escher) - Copper, Silver, Baboons (B - Bach) - Silva and Gould, who are coppers### Goldbach

- In 1742 sent letter to Euler (who was at the court of King Frederick the Great) with the conjecture: “Every even number can be represented as a sum of two odd primes” - Never been proven - Schnirelmann in 1931 proved that any number, even or odd, can be represented as the sum of not more than 300,000 primes#### “Vinogradov property”

- Vinogradov in 1937 showed that every “sufficiently large” odd number can be represented as a sum of no more than three odd primes. - It has not been determined what number is “sufficiently large,” only that it must be finite### Predictably terminate

#### Goldbach property

- Look at all numbers less than 2N to determine property within a fixed amount of time

- Recognizable

### Connection with Zen Dualism

- Statement that a number has the “Achilles property” involves infinite amounts of information - Same with “29 is prime”, etc…### Chaos integral part of beauty and harmony

- Order and Chaos by Escher### Does not predictably terminate

#### “Goldbach variation”

- Contrived by Hofstader?

- Is every even number the difference of two prime numbers?

- Hofstader does not state whether this holds for all numbers or not

- “Tortoise property”: Number is the difference of two odd primes

- “Achilles property”: Number is not the difference of two odd primes

#### WONDROUS numbers

- If n is odd, make it 3n+1

- If n is even, make it n/2

- If it reaches 1, it is a WONDROUS number, otherwise it is unWONDROUS

- Seems to expand chaotically, and thus does not predictably terminate

### Very Asian Gold Box variation

- very gold Asian box

- then becomes very Asian gold box

- finally, Very Asian Gold Box

- What did Hofstader mean by this final variation?

### Real ending:

- “Good night”

- “Sufficiently assiduous” reader can spot.

- Misspellings spell out “end”:

- Whatver (e)

- Outstanding (n)

- Golbach Conjecture (d)

### False ending

- Introduction of extraneous event and characters which are inconsistent

- Isomorphism with Bach’s *Aria with Diverse Variations* (“Post-ending ending”)

- Isomorphism with recognizable/predictably terminate theme. “Sufficiently assiduous” search will always terminate, though cannot predict when it will terminate, thus ending is recognizable

### Complete List of All Great Mathematicians

- De Morgan - Abel - Boole - Brouwer - Sierpinksi - Weierstrass - Hidden mathematician in diagonal: Dboups (-1) = Cantor (mathematician who invented diagonalization argument) (**“Bach in Liepzig”**)

## Comments (1)

Look up Kupfergodel and Silberescher in the Index, and you find their first names are Roman and Lowen - or did I get that backwards? (I don't think they're real, though.)

The Very Asian Gold Box was the "variation Goldbach's".

"Sufficiently large" means there exists a 'v', above which all odd numbers have the Vinogradov property.

WSClark.

Posted by W.S.Clark | July 27, 2012 9:03 AM

Posted on July 27, 2012 09:03