Infimum Jest

For the math lovers out there, this post is for you. In the footnote to a recent post ("A Visitor from Redmond") I referred to an infimum function. From Wolfram Math World¹, here's a definition of infimum (Hat tip to M.I., my finance consultant):

Infimum

The infimum is the greatest lower bound of a set S, defined as a quantity m such that no member of the set is less than m, but if epsilon is any positive quantity, however small, there is always one member that is less than m+epsilon (Jeffreys and Jeffreys 1988). When it exists (which is not required by this definition, e.g., infR does not exist), the infimum is denoted infS or inf_(x in S)x. The infimum is implemented in Mathematica as MinValue[f, constr, vars].

Consider the real numbers with their usual order. Then for any set M subset= R, the infimum infM exists (in R) if and only if M is bounded from below and nonempty.

More formally, the infimum infS for S a (nonempty) subset of the affinely extended real numbers R^_=R union {+/-infty} is the largest value y in R^_ such that for all x in S we have x>=y. Using this definition, infS always exists and, in particular, infR=-infty.

Whenever an infimum exists, its value is unique.

SEE ALSO: Infimum Limit, Lower Bound, Supremum

Note that Blogger converted some of the symbols in that definition to text, e.g., writing out the Greek letter epsilon instead of showing the Greek symbol for it.

Had I known of this back in December, when I wrote this post, "Infinite Connections or Infinite Jest", I could have used "Infimum Connections" as an alternative, obscurer post title.

Infinite Corridor

In the previous post on the Sonic situation in Northern NJ, I mentioned the late author David Foster Wallace, who was known for his well-reviewed (but, I suspect, infrequently-read) door stopper Infinite Jest, and for his copious use of footnotes in his writing¹. Somewhat coincidentally, yesterday I received an e-mail from Joshua Persky, the subject of this post from last December, "Infinite Connections or Infinite Jest?".

Persky, you may recall, was the MIT alumnus and former investment banker who gained national attention for his unorthodox job searching method: handing out resumes while wearing a sandwich board in Midtown Manhattan. In that post last December, I noted that Persky had found a new job with an accounting firm, but Persky informs me that he left that job a couple of months ago, and is currently open to job or business opportunities in "writing, inspirational speaking, career counseling, valuations and business development consulting". If you are aware of any such opportunities, and would like to contact him, below is Mr. Persky's website and contact info:

917 650 8700

joshua.persky@sloan.mit.edu

www.JoshuaPersky.com

In that post last December, I also questioned the value of MIT's alumni network (the school's alumni organization is called "Infinite Connections"; hence the post title) given the challenges of Mr. Persky's job search. In our e-mail correspondence, Persky seemed to agree, writing,

MIT's alumni network has not been as helpful as it could be. Unfortunately, although the education is wonderful and rigorous, the school lacks in social connectivity. It's pretty much up to each student to find his/her own way. I imagine that the other ivy league^[2] schools are a bit better at networking. However, MIT is trying and encourages alumni to be in touch and mentor each other.

Persky also was able to shed some light on the origin of the name of MIT's alumni organization, mentioning that the main hallway at MIT is called the "Infinite Corridor".


¹The Onion once hilariously mocked Wallace's tendency to write door stoppers and his use of footnotes, "Girlfriend Stops Reading David Foster Wallace Breakup Letter At Page 20". Excerpt:

BLOOMINGTON, IL—Claire Thompson, author David Foster Wallace's girlfriend of two years, stopped reading his 67-page breakup letter at page 20, she admitted Monday.

"It was pretty good, I guess, but I just couldn't get all the way through," said Thompson, 32, who was given the seven-chapter, heavily footnoted "Dear John" missive on Feb. 3. "I always meant to pick it up again, but then I got busy and, oh, I don't know. He's talented, but his letters can sometimes get a little self-indulgent."

^[2]Although MIT is more prestigious than some Ivy League universities, and is located close to Harvard geographically, it is actually not part of the Ivy League.

Infinite Connections or Infinite Jest?

Earlier this week, the New York Times reported that laid off investment banker Joshua Persky (the fellow on the right in the photo above) landed a new job several months after becoming famous for handing out resumes in Midtown Manhattan while wearing a sandwich board advertising his job hunt ("After Unusual Hunt, Ex-Banker Lands a Job"). You probably already know that Mr. Persky has landed a new job, since, as Mr. Persky notes on his blog today, his story has been picked up by all sorts of media outlets, including MSNBC, the front page of Yahoo!, etc.

Persky's successful job hunt is an inspiring story of persistence and originality, and that seems to be how most of the media have covered it, but as a cynic, it raises a question for me: What does it say about MIT's alumni network (here is its "Infinite Connections" website) or the prestige of an MIT degree that an MIT alumnus had to resort to such a stunt to find a job? Presumably, one can get an education of similar high-quality at a somewhat less prestigious (and less expensive) school; if the added prestige and connections of an MIT degree are of such little value that an alumnus needs to go to such extraordinary lengths to get a new job, than why pay more to go to MIT?