Photo by Caroline Taillandier @caro972
Asli Bilgin, a great heart and community leader in New York City (via Microsoft) dined via candlelight in a charming French Restaurant in the heart of Gramercy, Park Avenue, NYC. Alissa Emerson trudged through the snow with a 5 inch by 5 inch Tiffany-blue plastic box neatly packed in her editfashion.com-approved hand bag, joined by Michael, her husband, to sit among friends at the restaurant’s inner balcony.
There, Alissa introduced an interesting gift idea that is simple and elegant – yet can be distilled into binary. Asli was treated to a projected slide show of pictures and a usb drive made of Philips metal embossed by Swarovski crystals so that as she jet-sets to Dubai to educate global leaders on new Microsoft technology – her friends go with her – a fun way to bring back old traditions like watching slides with one another. The best wishes for her in her travels.
Speaking of binary, and since Asli also loves math, on vacation, I happened across a superb explanation for binary, by Brian Hayes in his collection Group Theory in the Bedroom. On page 180, he writes:
The most important numerals are all constructed according to a place-value system. In decimal notation, the numeral 19 is shorthand for the expression:
( 1 x 101 ) + ( 9 x 100 )
Or, as you might recite in a primary-school classroom, “one ten and nine ones.” Likewise, the binary numeral 10011 is understood to mean:
( 1 x 24 ) + ( 0 x 23 ) + ( 0 x 22 ) + ( 1 x 21 ) + ( 1 x 20 )
which adds up to the same value. The ternary version of the same number is written 201, which expands as follows:
( 2 x 32 ) + ( 0 x 31 ) + ( 1 x 30 )
In this case we have two 9s, no 3s, and one 1.
The general formula for a numeral in any place-value notation goes something like this:
d3 r3 +d2 r2 +d1 r1 +d0 r0 …
Here r is the base, or radix, and the coefficients d i are the digits of the number.
Hint: Brian is a balanced ternary fan, which is very pretty and arguably more efficient than binary, and on which he continues to write on page 189:
the digits of a balanced-ternary numeral are coefficients of powers of 3, but instead of coming from the set {0 1 2}, the digits are -1, 0, and 1 (sic)
The decimal number 19 is written 1101 in balanced ternary, and this numeral is interpreted as follows:
( 1 x 33 ) – ( 1 x 32 ) + ( 0 x 31 ) + ( 1 x 30 )
