Shape is actually something we have not talked about, so fascinated were we by the battle between Hebe and the Philosopher King. One of the problems of sdp(f) is that it is wider than it is high. It is even worse with sfdp or fdps. This means that either it has to be squeezed down to fit on a printed page, which is normally higher than it is wide, or it has to be printed sideways and the book has to be turned through 90 degrees. (Of course the same is not true of a poster or a computer screen.)

One of the many virtues of Valery’s Adomah is that it is higher than it is wide – actually twice as high, but the boxes could be widened. It means reading the sequence of numbers downwards, but one soon gets used to that. In fact columns of numbers are frequent in scientific publications. For the computer screen, Adomah can be printed in its horizontal version.

Most spirals are circular in outline, which is also the wrong shape. I designed my Chemical Galaxy specifically so that it would fill a sheet in the An series. (For Americans, this is a series of rectangles in which the long axis is 1.414… times the short axis, so that each size is exactly half as big as the previous one. A0 is one square metre and An is 2^n square metres; yet another reason for you to adopt the metric system!) I thought a poster would be easier to read in the ‘landscape’ version. Now, with the printed page in mind, I am designing a ‘portrait’ version.

I thoroughly enjoyed our conversation today. You mentioned Valery’s “Perimeter Rule”:
For Z through 120, block depth plus half block width equals 9.
It’s one of several mathematically equivalent ways to state periodic tables’ arithmetical regularities.

One-half block width is (1/2)[2(2 l + 1)] = 2 l + 1.
Block depth is 2D – 2 l, where D = the ordinal number of the LSPT’s last dyad.
For D = 4, block depth = 8 – 2 l.
Adding one-half a block’s width, 2 l + 1, yields 8 + 1 = 9.

Linguist analysis adds new dimensions to one’s understanding of controversies regarding the periodic table. Revealed are insights into deep linguistic features of languages, and, perhaps along the way, into the sociology of scientists and philosophers of science.

Henry

It’s not me or a few PT designers that Bent needs to convince but editors of journals and university presses.
Good luck doing that Henry.

(1) A CORRECTION. Scerri is, strictly speaking, right. He did not say EXACTLY what I’d said (from memory) he’d said (in Sci. Am. (?)). But really, that’s sort of beside the point, his ref. to Sci. Am., and perhaps not quite the whole truth. Here’s what he wrote in JCE, Feb. 1991, p123:

“The proposed new fdps version shown in Figure 2 does not yield any new predictions as to chemical or physical behavior of the elements [not true by the time of the publication, 2006, of NI, subtitled "An Introduction to Leading {New} Uses of the Left-Step Periodic Table"], and this in itself argues against its adoption. Moreover, the proposed version leads to grouping together of the element helium with the alkaline earth metals, which is a little difficult to accept in chemical terms. . . NOT SURPRISINGLY [emphasis added] this proposed electronic form of the periodic table has not been generally adopted by chemists . . .”

(2) SIGNIFICANCE OF A CHEMICAL ROUTE TO THE LSPT. One of NI’s leading contribution to chemical pedagogy may be its provision of grounds for dropping the phrase “electronic form of the periodic table”, through the book’s demonstration of chemical captures of the left-step periodic table WITHOUT REFERENCE TO ELECTRONS OR ORBITALS. That’s in the spirit of Feynman’s remark that sometimes it’s useful to see how little theoretical machinery one really needs in order to obtain a given result. Chemical capture of the LSPT is what makes the consilience between ordinal numbers generated by Chemical Periodicity and the quantum numbers of atomic physics so extraordinary.

(3) DEFINITIONS of “n” AND “r” IN TERMS OF NODAL SURFACES. Scerri complains that I’ve introduced new definitions for quantum numbers. So I have. My book’s title is, after all, “New Ideas”. Included are new ideas (Mine and mine alone? I’m not sure.) regarding two definitions. The question is: Are the “new ideas” useful? Judge for yourselves.

Eugen points out that Scerri and I can both use the relation n = r + l. So far so good. But that’s not the entire story.

In my identification of n and r, n is the total number of nodal surfaces and r is the total number of radial nodal surfaces. In the alternative definitions that Scerri prefers, n is the total number of nodal surfaces NOT COUNTING THE ONE AT INFINITY and r is the total number of radial nodal surfaces NOT COUNTING THE ONE AT INFINITY. What’s the gain in that, for students? If the inelegance of the latter definitions were the only issue at hand, Scerri’s tantrum would be a tempest in a teapot, over an issue of taste. But, as with periodic tables, inelegance in this instance hides deep physical principles.

Strictly speaking, SCERRI’S PREFERRED DEFINITIONS OF n AND r, FROM THE LITERATURE, DO NOT CORRESPOND TO PHYSICAL REALITY! That fact has an immediate kicker. (The proof of the usefulness of definitions is in the pudding.)

I can write, in terms of nodal surfaces, that r ≥ 1 and n ≥ 1.
Scerri must write, IN TERMS OF NODAL SURFACES, that r ≥ 0 and n ≥ 0.
But, in fact, never is n = 0!
And that’s only the beginning of the story. The most significant part follows.

One of the famous relations in quantum mechanics that drops out of solutions of Schrodinger’s equation for the hydrogen atom is the relation l ≤ n – 1. It’s widely used by students in working out atoms’ electron configurations. They couldn’t get very far in Chem101 without it.

[Consequently, it’s a huge weakness in chemical education today that that relation, l ≤ n – 1, just appears out of the blue. Students must accept it. There’s nothing else that they can do. They can’t understand it. Chem101 is a faith-based course. It may be, indeed, worse than no course at all! Students arrive fearful of what they are about to encounter and leave confirmed in their fears. “Chemical educators” should be advised: “Above all, do no harm!”]

Both Scerri and I, to repeat, can write n = r + l. I can write, in addition, as mentioned, r ≥ 1. Add that to the previous relation. Presto! n ≥ 1 + l; i.e.: l ≤ n – 1. Q.E.D.

[It’s that simple. If you frame definitions in strict accordance with physical reality, nice things tend to happen. If I knew that I’d pass into the history of chemistry for that derivation alone, I’d be happy. (I’ve not checked the literature to see if others have used it. I first used it in a graduate course in quantum mechanics at UConn in 1953, and later in general chemistry. Over the years many students have seen it, from me, if from no one else.)]

What can Scerri do? Adding r ≥ 0 to n = r + l yields l ≤ n. Wrong!

How, then, does a Scerri introduce freshmen to the relation l ≤ n – 1? With a wave of the hand? (Quantum mechanics used to be called “wave mechanics”.)

My prediction is — if past performance is prologue — that our provocateur will respond with complete and absolute silence regarding this situation in which his choice of definitions of the quantum numbers n and r IN TERMS OF NODAL SURFACES leads to the incorrect relations n ≥ 0 and l ≤ n.

Historical Note: I sense that it may be correct to say that the nodal-surface interpretation of the principal and radial quantum numbers “n” and “r” FOLLOWED introduction in discussions of the hydrogen atom of two integers one less than my “n” and “r”. It’s rather like He/Be following He/Ne. Science progresses. It gradually cleans up its act. I’m grateful to our provocateur for instigating what might be correctly described as a small part of that clean-up.

To “domesticate” the AAE for people unfamiliar with it, one might start with the traditional s(f-footnoted)dp table and proceed through the sfdp and fdps tables to the AAE, followed by its planar projection, which, stretched out in one dimension, is Mendeleev’s Line, easily curled up to Philip’s spiral. Along the way one could branch off to step-pyramid tables, and Valery’s table, and its sequels. That might bring everybody together, and illustrate that all representations of the Periodic Law, of ordered Z-values, are topologically equivalent to each other.

Illustrating an old adage, Philip, are your comments of March 19, 8:05 am that –

“You [ES] have rearranged [the periodic table] by (1) removing the f block to a footnote, (2) slicing the p block in two, between groups VI and VII and (3) moving the four groups on the right of the cut to the left of the table. All that for the sake of bilateral symmetry and a couple of triads! I’m sorry, but I can’t see the point. What is a learner to make of ‘periods’ such as F-Ne-Na-Mg-[gap]-Al-Si-P-S?!

“SEEK SYMMETRY AND DISTRUST IT.”

[One thing to say for the F-Ne-Na-Mg . . . Al-Si-P-S table: It does list the most commonly named Groups first. The LSPT lists them last.]

Sanderson’s truncated table for beginners, with both its f- and the d-blocks footnoted, and with H above Li and He above Ne, has “bilateral symmetry” — granted certain restrictions on atomic numbers. That restriction in itself suggests that such tables may not reflect fundamental features of the Period System.

Latent in Mendeleev’s Line are several deeply significant REGULARITIES. But the Line itself exhibits no symmetry whatsoever! On the contrary, exactly contrary to what one must have for true and exact symmetry, elements occur in the Line ONLY ONCE.

We seem to need new(?) terms to describe particularly shapely representations of the Periodic Law.

Centering the LSPT’s dyads yields a step-pyramid table, with bilateral symmetry — if one doesn’t look closely at the Table’s entries; and, again, subject to restrictions on Z. Needed to guide the eye down a Group are vertically separated dyads tied together by tie-lines.

Elevating the LSPT’s blocks by an amount equal to their l-values (corresponding to plotting vs. l the quantity n rather than n+l) yields Valery’s table with, again, bilateral symmetry — if, again, one doesn’t look closely at the Table’s entries; and, again, subject to restrictions on Z. Needed to guide the eye along periods are horizontally separated blocks tied together with tie-lines.

That said, because the Periodic System’s fundamental explanation lies in atomic structure, where symmetry plays an important role, perhaps one should consider carefully Valey’s suggestion — and Jess’s — that symmetry does, indeed, become manifest in some representations of the Periodic Law.

Henry

A reader might wonder, however: Why would a “clear and concise” and convincing article on such an important topic as location of the s-block in periodic tables appear in an obscure journal, The Chemical Educator, rather than in the Journal of Chemical Education, location of many articles on periodic tables.

You and I know the reason for that, Eric.
Gary tried to get his article published in JCE, and failed.
Why?
An unfavorable review by a referee.
Namely? You know. Tell us. Go ahead. Tell the truth.

This is ridiculous!
Changing your mind all the time is one thing.
And stating irrelevant and partial truths is another failing.
But surely this is beyond the pale!
It doesn’t add one iota to the advancement of science.

With apologies to the rest of the gang for dwelling on an issue of no scientific significance whatsoever — or maybe not?
(One likes to know, in science, how reliable one’s sources really are.)

Henry

Needless to say, Sciencebase is “Sb”

The speed with which this post went viral is quite amazing, I tweeted about it first thing this morning (about 8am UK time I think it was). And like, I say only a couple of handfuls of elements yet to find bloggers. I’m only adding them if people specifically ask, so please don’t send suggestions unless they’re yours and please don’t send for any elements that are coloured bronze or gold on the PT as they’re already taken.

Chemists have traditionally made a big deal out of Periodic TABLES vertical columns and horizontal periods. Columns have meant primary kinships: same number of valence-shell electrons of, generally, the same type. That’s what “verticality” has meant.

The electronic interpretation of secondary kinships is: same number but different types of valence-shell electrons and, to be chemically significant, same maximum oxidation state.

The electronic interpretation of tertiary kinships is: same number of valence-shell vacancies and hence, sometimes, same minimum oxidation state.

“Primary”, “secondary”, and “tertiary” indicate kinship closeness, not kinship strength.

Why are “secondary” kinships ranked “ahead” — as to closeness — of “tertiary” kinships?
In the history of periodic tables they have been MUCH MORE IMPORTANT than tertiary kinships — at least until recently (with the helium issue).
Also, secondary kinships FAR outnumber tertiary kinships.

Secondary kinships create periods of different lengths.
Periods of different lengths have led to the creation of some 700 periodic tables.
Imagine the absence of secondary kinships.
We’d have have one, simple, rectangular table, the same for everyone —
except, perhaps, for the location of H and He? At the far right or the far left?.
(Electronic structure might place them at the far left.
Maximizing number of triads would place them at the far right.)

I’ve never been particularly moved by “knight’s move”. The reason for it? Sort of vector addition of the traditional “diagonal relation” and the “inert-pair effect”? The first move takes one down and to the right one space, the second one to the right two spaces. The completed move: 1 down and 2 to the right (if 1 + 2 = 2). That model predicts that knight’s move is always associated with atoms that exhibit the inert-pair effect. Is that so? I’m not up on the move. What are the leading examples of it? Perhaps I need to give it more thought. I recall seeing it discussed in Scerri’s book. At the time I took that as a mark of poor judgment.

Henry