More on Really Big Numbers
After Daddy Cockburn (Zero Gravity, April 2001 APS News) told his ten-year old that 10 to the 5th power is ten thousand, Constant Reader was left with serious doubts about all the rest of the numbers. Is an erratum planned?
a.k.a. Virginia Trimble
Chair, Division of Astrophysics (the unit of APS charged with considering astronomical numbers)
Editor's Note: We're pretty sure it was a typo. That's our story and we're sticking to it.
In the April 2001 issue (Volume 10, No. 4) of APS News, page 4, there is a trivial but amusing typo in the "Zero Gravity" column. In the middle of column 2, a father-son dialog is reported: "Dad, what is 10 to the 5th power?" The reply is "Ten thousand"!
Okay, we all know it's one hundred thousand. The irony is that this error appears on the same "Letters" page in which we find the first letter titled "Science Textbooks Riddled with Errors."
The letter, from David A. Lupfer, ends with the admonition, "...Where is the attention of the APS members and directors? We must attack this problem in our own back yard!"
We hear you, David.
Alistair Cockburn's commentary on really big numbers addresses a need for names for these numbers not only for children but for journalists and media people who have trouble differentiating between million and billion. I applaud his approach and the definition he applies. I have a suggestion, however, concerning the name he chose: "fuga" unfortunately comes within an epsilon of a derogatory term for a person involved in a sex act, as pronounced by a person with a Boston accent.
I suggest that 'fugar' be avoided as well, since that just exacerbates the pronunciation problem. Perhaps 'gugar' might work, and it has the sound of science-fictionish technobabble that seems to be appreciated, as in "Captain, we are within gugar-10 of the asteroid!". Other combinations might also be used, such as 'fugoo', although this sounds more like a Chinese dinner than a number. Personally, I favor 'fugol' since it suggests the already familiar googol. In any event, my thanks to Alistair for an entertaining and useful commentary. I await his commentary on adolescent number crunching.
A. G. Jackson
I found the Zero-gravity article by Alistair Cockburn in the April 2001 edition of APS News very interesting and humorous. I also have two small children who enjoy playing the I-know-a-number- larger-than-you-do game. It appears however, that in defining the Fuga-number, either the typesetters missed the equations or Dr. Cockburn has not arrived at a largest number scenario. In the article, Fuga-number is defined as "that number raised to that number that number of times." The example of Fuga-3 is given as ((33)3). This would be, using the included parentheses, (27)3=19,683, or 39. However, a much larger number could be obtained if the order of the parentheses were reversed. I therefore propose another larger number, which I will call Gufa-number. Let's define Gufa-number as "that number raised that number of times to that number". Gufa-3 could then be written as (3^(33)), and Gufa-4 would be 4^(4^(44)). Switching the order of paranthesis makes Gufa-3 = 327, or 7,625,597,484,987, a number considerably larger than Fuga-3. Therefore, as our children will eventually say, "My space commander rules a Gufa-fuga-gar-googolplex of stars!
Michael B. Ottinger
Missouri Western State College
Concerning the photographs of four of the participants in the 2001 APS Lead-Scientist Institute on page 3 of the latest APS News (Volume 10, No. 4): How exactly were they able to weigh the items mentioned in the article when their hands were located so as to prevent the proper operation of the spring balances? In particular, in the bottom picture the spring was completely inoperative. Perhaps the Editor should have been a little more careful in choosing a photograph to illustrate the article.
University of Southern California, Los Angeles
Edward Lee of the APS Education Department replies: It does appear in these photos as if the participant's fingers are pushing down on the spring during the measurement, which indeed would prevent the proper operation of the scale. However, the spring is actually inside a thin-walled, clear plastic tube, so the participant is holding the tube, not the spring.
Time of Flight Beats the Competition
It is gratifying to see William Stephens' 1946 invention of the time-of-flight mass spectrometer recognized by APS News1. However, one might extend the comment "...yet the technology is generally unknown among the educated public" to point out that it is also unknown to most physicists, in spite of its origin in nuclear and atomic physics. It may surprise your readers to know that there were almost 300 papers involving time-of-flight mass spectrometry (TOFMS) presented at the most recent annual conference of the American Society for Mass Spectrometry. They may also be surprised to learn that commercial versions of the most sophisticated TOFMS instruments (actually quadrupole/TOF hybrids), which cost ~0.5M$ each, are selling briskly at a rate exceeding 30 per month, primarily for the study of biomolecules. Such instruments have in fact become essential measuring tools in the emerging field of proteomics2,3.
The author has done a good job of describing the present technology in the limited amount of space available, although he or she fails to mention the most recent advances (collision cooling and orthogonal injection). However, the final paragraph gives an impression that is considerably out of date and is seriously misleading. The reason for the present popularity of time-of-flight instruments has little to do with "lack of access [to] sophisticated magnetic sector machines", or "lower cost". Rather, it is because of the fundamental advantages of TOF instruments, particularly for the study of biomolecules. These include:
- Effectively unlimited m/z range;
- Almost complete absence of truncating elements such as slits, as well as "simultaneous" observation of the whole m/z range without scanning, thus giving greatly increased sensitivity for most applications;
- Considerable improvements in TOF mass resolving power R and mass accuracy [delta]m. The commercial versions of the hybrid machines mentioned above have R >10,000, and |m/m < 10ppm or [delta]m < 10mu.
For the above reasons, sales of magnetic sector machines for biological applications have plummeted almost to zero, and it has been difficult even to give away used four-sector spectrometers, million-dollar instruments that represented the state of the art only ten years ago.
Interested readers may wish to read personal accounts of these developments4,5 or consult review articles that summarize some of the most recent progress6-8.
University of Manitoba, Winnipeg
1 "This month in physics history", APS News, April 2001 p.2
2 A. Shevchenko, A. Loboda, A. Shevchenko, W. Ens and K.G. Standing, Anal. Chem. 72 (2000) 2132-2141
3 T.J. Griffin, S.P. Gygi, B. Rist, R. Aebersold, A. Loboda, A. Jilkine, W. Ens and K.G. Standing, Anal. Chem. 73 (2001) 978-986
4 R.D. Macfarlane, Braz. J. Phys. 29 (1999) 415-421
5 K.G. Standing, Int. J. Mass Spectrom. 200 (2000) 597-610
6 R.J. Cotter, Anal. Chem. 71 (2000) 445A-451A
7 I.V. Chernushevich, W. Ens and K.G. Standing, Anal. Chem. 71 (2000) 452A-461A
8 M. Guilhaus, D. Selby, and V. Mlynski, Mass Spectrom. Rev. 19 (2000) 65-107