What is a Dotted Word™?

Question

_{This is based on the What is a Word/Phrase™ series of Phrase™ and Word™ puzzles, started by JLee.}

If a word follows a certain rule, then I call it a Dotted Word™.

Use the example word lists below to find the rule. Each word can be tested for whether it is a Dotted Word™ without depending on other words in these lists.

Dotted Word™, Not Dotted Word™
ONLINE, DIGITAL
HOWDY, HEY
URGES, INSTINCTS
NASAL, BARITONE
FROG, TOAD
POLAND, UKRAINE
WATER, LUBRICATE
FOLIO, DOCUMENT
COBRAS, PYTHONS
REBIND, UNSEAL
PRATTLER, BABBLER
LUAU, FIESTA
RECEPT, RECEIVING
KNIFE, SPOON
FRAMES, BOXES
LANDLADY, DUCHESS

Hint:

The number of possible Dotted Words™ is relatively small.

Hint 2:

This is a very elementary puzzle. You don't need more than one hint.

Is the fact that the words are presented in all caps relevant/intentional? — MercyBeaucou, Jan 05 '17 at 23:59
Perhaps the fact that "recept" is included in the list indicates that Dotted Words are relatively hard to find and/or that they were found using a very wide net. — DyingIsFun, Jan 06 '17 at 03:31
@Silenus I don't understand, what do you mean by hard to find? — , Jan 06 '17 at 16:07
@tilper, the fact that the word is very uncommon may suggest that Mike Q had trouble finding words with this property, and so needed to resort to an uncommon one to fill out his list. This suggests to me that the words might have been found with CPU aid, using a large lexicon. — DyingIsFun, Jan 06 '17 at 16:12
@Silenus That may be true to some extent. Is that a problem with the puzzle itself or are you making an observation about the solution? — MikeQ, Jan 06 '17 at 16:38
@MikeQ, it's not a criticism at all! I'm trying to help others by reverse engineering your path to finding these buggers! — DyingIsFun, Jan 06 '17 at 16:39
By the way, I like how you streamlined this question format—very elegant! — DyingIsFun, Jan 06 '17 at 16:41
I'd say the fact that the word pairs are generally pretty close conceptually indicates both sets of words are quite common. — Neil W, Jan 07 '17 at 11:26
By just seeing the name's I felt it was something related to Morse :) — Techidiot, Jan 07 '17 at 13:19
Just curious...does 'dotted' by any chance refer to musical notation, where a dotted note gets 50% more length than its un-dotted counterpart? — wildBillMunson, Jan 08 '17 at 06:14
I tried something with Top Level Domains but I couldn't get it to work. — Glorfindel, Jan 12 '17 at 12:39
@Glorfindel Nope, that's the wrong direction, but you almost have the correct kind of "dot". — MikeQ, Jan 12 '17 at 12:45
Doesn't seem to be anything to do with the periodic table (just in case hint 2 was being cryptic). FIESTA can be spelled with element abbreviations — Joe, Jan 12 '17 at 12:58
@Joe Sometimes when I'm stuck on a puzzle, I find that taking a break and stretching may help. — MikeQ, Jan 12 '17 at 13:39
Not sure if I can ask this, so feel free to leave it unanswered, but would the word "Haters" be dotted or undotted? — user33280, Jan 12 '17 at 14:00
Cool concept for a puzzle :) I don't think it'd be realistically solvable without hint 2. — Rubio, Jan 12 '17 at 18:13
@Rubio Most of my comments and replies today were intended to be hints. — MikeQ, Jan 12 '17 at 18:16
(Oh, I know. Just noting that, ideally, a puzzle should be solvable without added hints - or they're not just hints, they're more or less essential. Something to be aware of going forward. I hope to see more from you, this was really good!) — Rubio, Jan 12 '17 at 18:18
@Rubio It was meant to be relatively easy from the start. I've followed these puzzles for a while, and consider most of them almost impossible to solve logically, so I expected the more experienced puzzlers to crack this quickly. Maybe "Dotted" was too misleading? — MikeQ, Jan 12 '17 at 18:29
I only realised why they were called Dotted in hindsight. It's hard to estimate how good such hints are beforehand. Had you called it "Periodic Word", it might have been too obvious, after all element symbols from the periodic table are a bit of a staple here at PSE. Dotted made me think of Morse and Braille first. — M Oehm, Jan 12 '17 at 18:33

score 12 · Accepted Answer · edited Jun 19 '17 at 13:22

The last hint and also Gareth's answer make it clear that ...

... all Dotted Words can be split into symbols for chemical elements. But this is not a sufficient condition, because some of the non-dotted words, but not all, can also be "elementarily split".

The distinguishing trait is ...

... that all elements used in the dotted words must be of the same period, i.e. they must occur on the same row in the periodic table:

O·N·Li·Ne: Oxygen (8), Nitrogen (7), Lithium (3), Neon (10): period 2
Ho·W·Dy: Holmium (67), Tungsten (74), Dysprosium (66): period 6
U·Rg·Es: Uranium (92), Roentgenium (111), Einsteinium (99): period 7
Na·S·Al: Sodium (11), Sulfur (16), Aluminium (13): period 3
Fr·Og: Francium (87), Oganesson (118): period 7
Po·La·Nd: Polonium (84), Lanthanum (57), Neodymium (60): period 6
W·At·Er: Tungsten (74), Astatine (85), Erbium (68): period 6
F·O·Li·O: Fluorine (9), Oxygen (8), Lithium (3), Oxygen (8): period 2
Co·Br·As: Cobalt (27), Bromine (35), Arsenic (33): period 4
Re·Bi·Nd: Rhenium (75), Bismuth (83), Neodymium (60): period 6
Pr·At·Tl·Er: Praseodymium (59), Astatine (85), Thallium (81), Erbium (68): period 6
Lu·Au: Lutetium (71), Gold (79): period 6
Re·Ce·Pt: Rhenium (75), Cerium (58), Platinum (78): period 6
K·Ni·Fe: Potassium (19), Nickel (28), Iron (26): period 4
Fr·Am·Es: Francium (87), Americium (95), Einsteinium (99): period 7
La·Nd·La·Dy: Lanthanum (57), Neodymium (60), Lanthanum (57), Dysprosium (66): period 6

(There are several possible divisions for some words, but only one that makes it count as a Dotted Word.)

Why are they called Dotted Words?

No, it has nothing to do with Lewis dots, which would describe the electron configuration in an atom and therefore would refer to the columns in the periodic table.

They are called Dotted words, because some people call a dot a period.

I think you missed the link to the Lewis Dot. – Sid Jan 12 '17 at 18:10 — Sid, Jan 12 '17 at 18:10
There is no link to Lewis ... oh, I see. Fixed, thanks! – M Oehm Jan 12 '17 at 18:14 — M Oehm, Jan 12 '17 at 18:14

Gareth McCaughan · Answer 2 · 2017-01-12T17:46:25.183

I thought, after looking at just a few of the words, that a Dotted Word might be one

made out of chemical element abbreviations.

Thus, e.g.,

ONLINE = O/N/Li/Ne and FRAMES = Fr/Am/Es.

Hence the hint saying that the puzzle

is "elementary".

However, this is demonstrably wrong; see below.

ONLINE = O/N/Li/Ne; DIGITAL fails because neither D nor Di exists.
HOWDY = H/O/W/Dy; HEY =He/Y.
URGES = U/Re/Ge/S; INSTINCTS fails because none of {Ct,T,Ts} exists.
NASAL = Na/S/Al; BARITONE fails because none of {It,T,To} exists.
FROG = Fr/Og; TOAD fails because neither T nor To exists.
POLAND = Po/La/Nd; UKRAINE = U/K/Ra/I/Ne.
WATER = W/At/Er; LUBRICATE = Lu/Br/I/Ca/Te.
FOLIO = F/O/Li/O; DOCUMENT fails because neither D nor Do exists.
COBRAS = C/O/Br/As; PYTHONS =P/Y/Th/O/N/S.
REBIND = Re/B/I/Nd; UNSEAL = U/N/Se/Al.
PRATTLER = Pr/At/Tl/Er, BABBLER fails because none of {Bl,L,Le} exists.
LUAU = Lu/Au; FIESTA =F/I/Es/Ta.
RECEPT = Re/Ce/Pt; RECEIVING fails because neither Ng nor G exists.
KNIFE = K/N/I/Fe; SPOON =S/Po/O/N.
FRAMES = Fr/Am/Es; BOXES =B/O/Xe/S.
LANDLADY = La/Nd/La/Dy; DUCHESS fails because neither D nor Du exists.

There are several counterexamples. But this seems to be close to working, and it's hard to believe it's coincidence. I suspect the intended answer is a variation on this theme and perhaps the variation explains why "Dotted Word" is the name.

It's very noticeable that

all the counterexamples are non-DWs that have decompositions, suggesting a rule of the form "a Dotted Word is one that has an 'elementary' decomposition such that ...". (This would also explain how it's possible that relatively few Dotted Words exist, even though a substantial fraction of all words have 'elementary' decompositions.)

A substantial fraction of the counterexamples

are non-DWs whose only decompositions involve noble gases, which (approximately) never form actual chemical compounds. But not all, and O/N/Li/Ne depends on Ne, so this is probably coincidence and in any case can be at most part of the answer.

A related conjecture would be

something along the lines of "a DW is a word with an 'elementary' decomposition that would be a possible chemical compound" or "... where each consecutive pair of elements can actually combine together somehow", but (1) that seems rather complicated and (2) S/Po/O/N seems like it fits any criterion of that sort at least as well as, say, O/N/Li/Ne does.

I notice that

all the Dotted Words have decompositions into at most four elements, and some of the Non-DWs with decompositions require more. (But note e.g. that Fr/Og uses only two elements; and that B/O/Xe/S requires only four but isn't a DW.) This is kinda suggestive of IP addresses, which is particularly interesting given Mike Q's comment to Glorfindel.

An obvious guess if it had worked in every case would be that "Dotted Word"

is just meant to hint at abbreviations, which are often indicated by trailing dots.

Or, more specifically,

conventionally one puts a dot at the end of an abbreviation exactly when its last letter is not the last letter of the thing abbreviated, so perhaps we could allow "Ra" but forbid "Rn" since it comes from Radon and wouldn't be dotted if we followed that convention for element abbreviations.

But clearly we need something smarter...

What about BOXeS, HeY, and LuBrICaTe? You should check all of the words first. — MikeQ, Jan 12 '17 at 16:03
I already put a comment on the original post - FIESTA can be comprised of chemical element symbols — Joe, Jan 12 '17 at 16:04
Yup, I found some counterexamples once testing. But it's ... surprising ... how large a fraction of words seem to be classified correctly by this criterion. Perhaps it's a deliberate red herring, though. — Gareth McCaughan, Jan 12 '17 at 16:05
No problem - I don't know about it being deliberate, I suspect that you can make a LOT of words from chemical element symbols, although I don't know the stats :-) — Joe, Jan 12 '17 at 16:06
@GarethMcCaughan You are on the right track. I suggested that Joe should take some time and stretch before trying to answer again. Maybe you should try that too? — MikeQ, Jan 12 '17 at 16:07
There is something in chemistry called "dot notation," apparently. Coincidence? https://www.google.com/search?q=dot+notation+chemistry&ie=UTF-8&oe=UTF-8&hl=en&client=safari probably not. — DyingIsFun, Jan 12 '17 at 16:08
Actually Th exists and is the chemical symbol for Thorium. Yt used to exist before.. — Sid, Jan 12 '17 at 16:18
@Silenus Coincidence. "Dotted" is intentionally vague, but designing a rule that involves solving chemistry problems seems too complicated for this type of puzzle. You should expand your mind, otherwise you'll miss the big picture. — MikeQ, Jan 12 '17 at 16:18

What is a Dotted Word™?

2 Answers2

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