The answer to the puzzle makes an invalid assumption about grammar: “-est” doesn’t require a specific number of items to compare. A counterdemonstration is “x is the est and the est X in Y; how? Ans: x is the only X in Y.” (I’m not sure that this holds for the kind of picky grammarian (as celebrated in a recent HARPER’S) who maintains a difference between “less” and “fewer” or between “further” and “farther”, but as you both are mathematicians a mathematical approach is plausible.)

I think that Doug was taking the picky grammarians viewpoint. Common usage is on your side and, speaking as a mathematician, I am inclined to agree with you. Still, the picky grammarian has an argument, to wit:

The trio, “large”, “larger”, and “largest”, cover three different number modes, to wit, one, two, and many, where many is any number greater than two, these being the original number modes recognized by the English language.

Ah, the Russian mode.

I had heard that it was the Hungarian Nobleman mode. Linguistically, though, Indo-European languages had a “two” mode which mostly survives today as archaisms.

It being patent that there are two stations under consideration, the form appropriate for two is relevant. In older times this distinction between the three forms was carefully made in the teaching of English; since, it would seem, English is no longer taught (indeed, is only irregularly used)

“In America they haven’t used it for years.” (Shaw/Lerner, 1955?)

You’ve got me, boss. It’s in the musical “My Fair Lady” in one of the songs (Henry Higgins is lamenting the state of English in England) but I don’t know offhand if it is in Pygmalion and I can’t find my copy.

In fact, all three forms are relevant — given a sufficient difference in size, one could refer to “the large station”, as well as the larger and largest.

One can, of course, and be understood. I’m not sure whether the picky grammarian would be happy with you.

The mathematical logicians viewpoint may be a bit different. All three forms are comparative forms. In a sense, the “..er” form is primary because it is a direct relationship from which all other comparatives are derived. Thus the statements that “X is large” is an assertion that when X is compared in size to some unspecified set of things, X has the greater size than all of the members of some unspecified subset which may but need not be a majority of the original unspecified set. In short, the notion “X is large” is rather vague.

The “…est” form has a flaw in that it assumes that is a single maximal element. An element X of a set is maximal if there is no element in the set that is “…er” than X. However a set can have more than one maximal element, i.e., it can have several elements, all equal in size, but “…er” than any of the other, non-maximal, elements. Thus, in a class of children, there might be two boys of equal height who are taller than any of the other children. Neither of the two boys is the tallest boy in the class.

A simple rendition of “…est” is

(Ax)((x .in. S)& (x .ne. X) & (X “…er” x)) <-> “…est” X

which may be rendered in English as: X is the “…est” element in S if and only if for all x in S not equal to X, X “…er” than x. Under this rendition you are right; in a set with one element that element is simultaneously the largest and smallest element. The picky grammarian, however, insists that “…est” should be rendered as:

(Ax)((x .in. S)& (x .ne. X) & (X “…er” x) & (Card(S) >2)) <-> “…est” X

i.e., that the set S have more than two members. The mathematical logician cannot rule as to which is right, the determination of the meaning “…est” being a convention of the language.

On the other hand the picky grammarian is right about the distinction between “less” and “fewer”. The term “fewer” specifically refers to cardinality; the term “less” is a comparative which must be accompanied by a measure.

That’s a train station of a different color.

Yes, and Alexander the Great had an infinite number of limbs.

Some one of these days I’m going to have to reread “Stress Analysis of a Strapless Evening Gown”. I suspect that it won’t stand up well under rereading.

I didn’t read juveniles when I was young; I did my serious reading then. It was only when I was mature (or overly ripe as some would say) that I started reading juveniles. Be that as it may, I have read The Phantom Tollbooth and recall the passage. It plays on a different aspect of the use of comparatives.

From: “Aris Aristou” ([email protected])
Date: 5/20/2001
Subj: methodology of research articles

I found your site while surfing. VERY interesting and multidimensional. Who are you? I’m interested in METHODOLOGY of research articles and bibliography. I have some, but I left most of them in S. Africa. If you have time, send me something. Thanx!

The question “Who are you?” is one of those fundamental questions that is intimidating and almost unanswerable. It can mean so many different things, depending upon the desire of the person asking. Thus the questioner might be asking:

Q: Please place yourself in the structured schema which I use to describe society and the world around me. In other words, give me a series of tags that I can use to categorize you.

The answer to such a demand needs must depend upon the categories and tags that the questioner recognizes. Fortunately there are a large series of such tags that are commonly and conventionally recognized. Thus the categories of nationality, ethnic origin, gender, occupation, income, place of residence, marital status, hobbies and interests, religion, and political affiliation.

An answer in terms of these tags often suffices to satisfy the questioner because we all of us carry with mental schemas, lists of default assumptions about persons bearing said tags. This is a practical necessity – we cannot know everyone in intimate detail. These assumptions are only defaults; each individual represents an exception to the defaults in some respects.

This form of the question is more of a “What are you?” than a “Who are you?” – that is, it reduces the person to a list of attributes.

There is another meaning that the question might take, on the lines of “What is your essential self?”, there being an implicit assumption that people have essential selves. As an example of this kind of question I will quote from the book, Dragonsbane by Barbara Hambly. The female protagonist, Jenny Waynest, is addressing the supporting character, Gareth:

… “Who are you, Gareth of Magloshaldon?”

He started at that, and for an instant she saw fright and guilt in his gray eys. He stammered, “I – I’m Garaeth of – of Magloshaldon. It’s a province of Bemaire…”

Her eyes sought his and held them in the gray shadows of the trees. “And if you weren not of that province, would you still be Gareth?”

“Er – yes. Of course. I …”

“And if you were not Gareth?” she pressed him, holding his gaze and mind locked with her own. “Would you still be you? If you were crippled, or old – if you became a leper, or lost your manhood – who would you be then?”

“I don’t know -”

“You know.”

An irony in this passage is that Gareth, at that point, is travelling under a false identity.

The passage (and the book) assumes one of the great answers to the question of identity, which is that we have an inner essence which defines our self, the various attributes being trappings like the clothes we wear.

Another answer is that there is no essential self, that we are like onions from which you can remove layer after layer without ever arriving at an essence, an inner core.

The fictional theologian, “Bull” Morris, claimed that we wear masks and that the masks become part of our selves.

And so on and so forth. You see, your question is too hard for me to answer.

To turn to your easier but still difficult question – what about the methodology of research articles? I have a couple of web pages on the subject,
What Is Peer Review?
Abusing References

the latter perhaps being best view as advice on what not to do. If one means to write a research article one should read the “advice to authors” sections that journals regularly supply. Further, it is useful to read articles in the relevant journals to see how they are structured. I can, with some reservations, recommend Bruno Latour’s Pandora’s Hope.

… continued on next rock …

I have received your answer – very educative, indeed – and I’ll take a look in your sites. I hope I didn’t offend you with my “naive” question. It was more an expression of admiration about the “depth” of your site! Thanks about the notions and instructions.

I wasn’t offended; on the contrary, I was flattered.

From: “Paolo” ([email protected])
Date: 5/12/2001
Subj: Cybernetic theory

do you know where I can Find some information on philosophycal influences on cybernetic theory?

Ouch. That’s rather vague. If you were thinking of Artificial Intelligence rather than cybernetic theory there is a host of material. The term, cybernetic theory, is sort of passe. That is, the subject matter, feedback systems and homeostasis, is standard material in engineering curricula. You might look at Wiener’s autobiography, I Am A Mathematician, for hints as to the philosophical influences on his work.

From: “Heinz Puppe” ([email protected])
Date: 5/17/2001
Subj: God and Religion

The notion of God (and/or Satan) is an infantile illusion. (Sigmund Freud)
Religion is the opium of the people (Karl Marx)

Religion is what people did before they invented parchisi. Et cetera.

Why did you feel the need to write this?

From: Jmbolesjr ([email protected])
Date: 5/11/2001
Subj: Was a Marine?

Once a Marine forever a Marine. Semper Fi. No such thing as Ex-Marine or was a Marine. Hell I went through P.I. in the summer of 1982. From what I read, you were inlisted in the 50’s. Did you not learn that then?

I heard something like that, yes. That was a long time ago and I moved on. This notion that when you become a Marine the globe and anchor is stamped on your soul and you are permanently encased in a set of dress blues is rank mysticism. Defining who you are by what you did for a few years of your life is, well, I won’t say what it is, but it’s like the guy who was a sports hero in high school and does nothing with his life after that. You must know the type. They have a job at the local gas station, drink beer at the local bar, and fill their days talking about their glory days when they were a big star.

Saying “Once a Marine, forever a Marine” is a form of pretense, really. Yeah, you’re a member of fraternity, you’ve been there and done that, and means something. But the truth is that when you’re out and have been out for a while you’re not the real thing anymore. You don’t pass the physical or the age limits. You act like a civilian and you think like a civilian. You’re not under the UCMJ. You aren’t sharp in the way that the guys in uniform are. You don’t know the current equipment in and out. In short, you know what it is about because you’ve been there but you’re not there now and you’re fooling yourself if you think you are.

Do you want to know what “Once a Marine, forever a Marine” is about? It’s about the Corps honoring its own and never giving up on its own people. It’s about not saying, “What have you done for me lately?” It is not about being government property.

The Marine Corps doesn’t own me. It never owned me. It doesn’t own you. It doesn’t own anybody; it never has and I hope to God it never it will. Marines are not slaves to be owned. They are free citizens who freely took the oath to defend their country.

From: “Edward J. Willett” ([email protected])
Date: 4/25/2001
Subj: Awards Update

When will you be posting the Awards for 2000 & 2001?

Sometime this summer. My personal schedule has been a bit bollixed over the past year.

From: “Larry Crowder” ([email protected])
Date: 5/7/2001
Subj: A question about the role of a scientist in the Piltdown investigation

Thank you for your very interesting website about Piltdown Man. I have only recently become interested in the subject, and I hope that you will give me your opinion on one area.

In The Piltdown Forgery J. S. Weiner states (page 57), “The surface stains of a number of flints of both kinds were tested by Dr. E. T. Hall of the Clarendon Laboratory at Oxford, using his X-ray spectrographic method of analysis.” The more recent book Unraveling Piltdown by John Evangelist Walsh does not even mention Dr. Hall. The bibliography compiled by Tom Turrittin lists only two entries by E. T. Hall.

Nevertheless, a newspaper article announcing the retirement of Dr. Hall from Oxford stated, “Prof. Hall has been famous for his scientific detective work since the 1950s when he determined that the Piltdown Skull, alleged to be a relic of early man, was a modern fake.” [emphasis added]

In your opinion, is this accreditation to Dr. Hall deserved and an accurate assessment of the facts? Did he have any role to play in the investigation of the skull, or was it limited to the spectrographic examination of the flints as stated by Weiner.

Hall did a chemical and spectrographic examination of all of the Piltdown bones. He came on the scene after it had been determined that Piltdown Man was a hoax. The newspaper article is in error in that respect. However Hall’s work was critical for analysis of how the hoax was manufactured.

http://www.theregister.co.uk/content/28/18767.html

Some people are so busy and so important that they need every bit of extra help that they can get.

Snicker.