The world has certainly lost one of its greatest thinkers, and many of us have lost a dear friend, colleague, and mentor.
I was getting concerned that I hadn’t heard back from Sol for a while, particularly after emailing him late last week, and then I ran across this notice through ITSOC & the IEEE:
Solomon W. Golomb (May 30, 1932 – May 1, 2016)
Shannon Award winner and long-time ITSOC member Solomon W. Golomb passed away on May 1, 2016.
Solomon W. Golomb was the Andrew Viterbi Chair in Electrical Engineering at the University of Southern California (USC) and was at USC since 1963, rising to the rank of University and Distinguished Professor. He was a member of the National Academies of Engineering and Science, and was awarded the National Medal of Science, the Shannon Award, the Hamming Medal, and numerous other accolades. As USC Dean Yiannis C. Yortsos wrote, “With unparalleled scholarly contributions and distinction to the field of engineering and mathematics, Sol’s impact has been extraordinary, transformative and impossible to measure. His academic and scholarly work on the theory of communications built the pillars upon which our modern technological life rests.”
In addition to his many contributions to coding and information theory, Professor Golomb was one of the great innovators in recreational mathematics, contributing many articles to Scientific American and other publications. More recent Information Theory Society members may be most familiar with his mathematics puzzles that appeared in the Society Newsletter, which will publish a full remembrance later.
A quick search a moment later revealed this sad confirmation along with some great photos from an award Sol received just a week ago:
As is common in academia, I’m sure it will take a few days for the news to drip out, but the world has certainly lost one of its greatest thinkers, and many of us have lost a dear friend, colleague, and mentor.
I’ll try touch base with his family and pass along what information sniff I can. I’ll post forthcoming obituaries as I see them, and will surely post some additional thoughts and reminiscences of my own in the coming days.
I’ve been a proponent and user of a variety of mnemonic systems since I was about eleven years old. The two biggest and most useful in my mind are commonly known as the “method of loci” and the “major system.” The major system is also variously known as the phonetic number system, the phonetic mnemonic system, or Hergione’s mnemonic system after French mathematician and astronomer Pierre Hérigone (1580-1643) who is thought to have originated its use.
The major system generally works by converting numbers into consonant sounds and then from there into words by adding vowels under the overarching principle that images (of the words) can be remembered more easily than the numbers themselves. For instance, one could memorize one’s grocery list of a hundred items by associating each shopping item on a numbered list with the word associated with the individual number in the list. As an example, if item 22 on the list is lemons, one could translate the number 22 as “nun” within the major system and then associate or picture a nun with lemons – perhaps a nun in full habit taking a bath in lemons to make the image stick in one’s memory better. Then at the grocery store, when going down one’s list, when arriving at number 22 on the list, one automatically translates the number 22 to “nun” which will almost immediately conjure the image of a nun taking a bath in lemons which gives one the item on the list that needed to be remembered. This comes in handy particularly when one needs to be able to remember large lists of items in and out of order.
The following generalized chart, which can be found in a hoard of books and websites on the topic, is fairly canonical for the overall system:
Mnemonic for remembering the numeral and consonant relationship
s, z, soft c
“z” is the first letter of zero; the other letters have a similar sound
t & d have one downstroke and sound similar (some variant systems include “th”)
n has two downstrokes
m has three downstrokes; m looks like a “3” on its side
last letter of four; 4 and R are almost mirror images of each other
L is the Roman Numeral for 50
/ʃ/ /ʒ/ /tʃ/ /dʒ/
j, sh, soft g, soft “ch”
a script j has a lower loop; g is almost a 6 rotated
k, hard c, hard g, hard “ch”, q, qu
capital K “contains” two sevens (some variant systems include “ng”)
script f resembles a figure-8; v sounds similar (v is a voiced f)
p is a mirror-image 9; b sounds similar and resembles a 9 rolled around
Vowel sounds, w,h,y
w and h are considered half-vowels; these can be used anywhere without changing a word’s number value
There are a variety of ways to use the major system as a code in addition to its uses in mnemonic settings. When I was a youth, I used it to write coded messages and to encrypt a variety of things for personal use. After I had originally read Dr. Bruno Furst’s series of booklets entitled You Can Remember: A Home Study Course in Memory and Concentration1, I had always wanted to spend some time creating an alternate method of writing using the method. Sadly I never made the time to do the project, but yesterday I made a very interesting discovery that, to my knowledge, doesn’t seem to have been previously noticed!
My discovery began last week when I read an article in The Atlantic by journalist Dennis Hollier entitled How to Write 225 Words Per Minute with a Pen: A Lesson in the Lost Technology of Shorthand. 2 In the article, which starts off with a mention of the Livescribe pen – one of my favorite tools, Mr. Hollier outlines the use of the Gregg System of Shorthand which was invented by John Robert Gregg in 1888. The description of the method was intriguing enough to me that I read a dozen additional general articles on shorthand on the internet and purchased a copy of Louis A. Leslie’s two volume text Gregg Shorthand: Functional Method.3
I was shocked, on page x of the front matter, just before the first page of the text, to find the following “Alphabet of Gregg Shorthand”:
Gregg Shorthand is using EXACTLY the same consonant-type breakdown of the alphabet as the major system!
Apparently I wasn’t the first to have the idea to turn the major system into a system of writing. The fact that the consonant breakdowns for the major system coincide almost directly to those for the shorthand method used by Gregg cannot be a coincidence!
The Gregg system works incredibly well precisely because the major system works so well. The biggest difference between the two systems is that Gregg utilizes a series of strokes (circles and semicircles) to indicate particular vowel sounds which allows for better differentiation of words which the major system doesn’t generally take into consideration. From an information theoretic standpoint, this is almost required to make the coding from one alphabet to the other possible, but much like ancient Hebrew, leaving out the vowels doesn’t remove that much information. Gregg, also like Hebrew, also uses dots and dashes above or below certain letters to indicate the precise sound of many of its vowels.
The upside of all of this is that the major system is incredibly easy to learn and use, and from here, learning Gregg shorthand is just a hop, skip , and a jump – heck, it’s really only just a hop because the underlying structure is so similar. Naturally as with the major system, one must commit some time to practicing it to improve on speed and accuracy, but the general learning of the system is incredibly straightforward.
Because the associations between the two systems are so similar, I wasn’t too surprised to find that some of the descriptions of why certain strokes were used for certain letters were very similar to the mnemonics for why certain letters were used for certain numbers in the major system.
One thing I have noticed in my studies on these topics is the occasional references to the letter combinations “NG” and “NK”. I’m curious why these are singled out in some of these systems? I have a strong suspicion that their inclusion/exclusion in various incarnations of their respective systems may be helpful in dating the evolution of these systems over time.
I’m aware that various versions of shorthand have appeared over the centuries with the first recorded having been the “Tironian Notes” of Marcus Tullius Tiro (103-4 BCE) who apparently used his system to write down the speeches of his master Cicero. I’m now much more curious at what point the concepts for shorthand and the major system crossed paths or converged? My assumption would be that it happened in the late Renaissance, but it would be nice to have the underlying references and support for such a timeline. Perhaps it was with Timothy Bright’s publication of Characterie; An Arte of Shorte, Swifte and Secrete Writing by Character (1588) 4, John Willis’s Art of Stenography (1602) 5, Edmond Willis’s An abbreviation of writing by character (1618) 6, or Thomas Shelton’s Short Writing (1626) 7? Shelton’s system was certainly very popular and well know because it was used by both Samuel Pepys and Sir Isaac Newton.
Certainly some in-depth research will tell, though if anyone has ideas, please don’t hesitate to indicate your ideas in the comments.
UPDATE on 7/6/14:
I’m adding a new chart making the correspondence between the major system and Gregg Shorthand more explicit.
Furst B. You Can Remember: A Home Study Course in Memory and Concentration. Markus-Campbell Co.; 1965.
The inventors of error-correcting codes were initially motivated by problems in communications engineering. But coding theory has since also influenced several other fields, including memory technology, theoretical computer science, game theory, portfolio theory, and symbolic manipulation. This talk will recall some forays into these subjects.
Elwyn Berlekamp has been professor of mathematics and of electrical engineering and computer science at UC Berkeley since 1971; halftime since 1983, and Emeritus since 2002. He also has been active in several small companies in the sectors of computers-communications and finance. He is now chairman of Berkeley Quantitative LP, a small money-management company. He was chairman of the Board of Trustees of MSRI from 1994-1998, and was at the International Computer Science Institute from 2001-2003. He is a member of the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences. Berlekamp has 12 patented inventions, some of which were co-authored with USC Professor Emeritus Lloyd Welch. Some of Berlekamp’s algorithms for decoding Reed-Solomon codes are widely used on compact discs; others are NASA standards for deep space communications. He has more than 100 publications, including two books on algebraic coding theory and seven books on the mathematical theory of combinatorial games, including the popular Dots-and-Boxes Game: Sophisticated Child’s Play.