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Listener 4071: Five Dots by Franc

Posted by Gareth Rees on 19 February 2010

After several straightforward weeks, I have the feeling that we are due a difficult puzzle, and this looks like it’s going to be the one. There are extra words in all the clues, “the first and last letters of which contribute to a common version of a thematic statement attributed to a name.” The name, or rather “six contiguous cells” of it, is to be found and highlighted. There are four clashes in the grid, with dots to be entered at the clashes, and a fifth dot to be discovered.

The grid has numbers but no bars. Why no bars? If I understand the rubric correctly—“Numbers in brackets give the numbers of cells used for the grid entries”—I should be able to just fill in the bars right away based on these numbers. Surely the setter wouldn’t just omit the bars to create a mechanical task for the solver? There must be some thematic reason that I don’t yet understand, some need to disguise the lengths of entries, perhaps.

So to be careful, I’ll only enter the bars that I believe are absolutely necessary: that is, the ones to the left of across entries and the ones above down entries.

The clues, now that I come to them, are really hard. I guess it’s my inexperience, but I find clues with extra words very difficult. My clue-solving technique depends on parsing all the words to form theories for the structure of the wordplay, but the extra words thwart this. After an hour of staring at the paper, I have only half an answer. 47 down, “Husband sources of manganese, uridines and nitrates (3)” is MAN (if the extra word is “uridines”) or MUN (if it’s “and”).

By Wednesday evening, I’ve spent about three hours on the puzzle so far and I have only thirteen entries, with no clashes yet discovered.

However, the letters from the removed words are suggestive. If I take them in order by clue, first—last—first—last— etc, then I get nonsense, for example, …LEILELVEECTTHH at the end of the across clues. So maybe I need to take all the first letters and then all of the last letters?

Across, first: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _LIEVETH
Across, last: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ELLECTH
Down, first: _ _ _ _ _ _ _ _ _ _ _ _ _H_ _ _S_ _ _ _ _EDUS
Down, last: _ _ _ _ _ _ _ _ _ _ _ _ _O_ _ _G_ _ _ _ _RUSE

This is suggestive of the words BELIEVE and INTELLECT. There can’t be all that many quotations with these two words. So, off to Google, and sure enough, it’s by Galileo:

I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use…”

This is an extract from Galileo’s 1615 letter to Madame Christina of Lorraine, Grand Duchess of Tuscany. Galileo is arguing that in the physical sciences, the accumulated evidence of our senses, and the conclusions we can deduce from them, are to be preferred to conclusions derived only from unclear passages in the Bible. He continues:

“… and by some other means to give us knowledge which we can attain by them. He would not require us to deny sense and reason in physical matters which are set before our eyes and minds by direct experience or necessary demonstrations. This must be especially true in those sciences of which but the faintest trace (and that consisting of conclusions) is to be found in the Bible. Of astronomy, for instance, so little is found that none of the planets except Venus are so much as mentioned, and this only once or twice under the name of “Lucifer.” If the sacred scribes had had any intention of teaching people certain arrangements and motions of the heavenly bodies, or had they wished us to derive such knowledge from the Bible, then in my opinion they would not have spoken of these matters so sparingly in comparison with the infinite number of admirable conclusions which are demonstrated in that science. Far from pretending to teach us the constitution and motions of the heavens and the stars, with their shapes, magnitudes, and distances, the authors of the Bible intentionally forbore to speak of these things, though all were quite well known to them.”

Back at the crossword, the quotation identifies all the extra words, making the pace of solving merely very slow, rather than glacial.

After another hour or so, I’ve filled getting on for half the grid, but I still haven’t found any clashes. However, I can see Galileo’s name starting to appear in the unchecked letters at centre left.

Let me think a bit more about the rubric. I need to find five dots associated with Galileo. The obvious possibility is that the five dots represent JUPITER and the four Galilean moons, IO, EUROPA, GANYMEDE and CALLISTO, which Galileo first saw through his telescope 400 years ago, some time between December 1609 and January 1610. Each of these moons has a name that’s even in length, so could be indicated by a clash with half the name in each part, for example I clashing with O, or CALL with ISTO.

Now that I have this idea, it’s easy to spot SCALLOP clashing with BISTOURY in the lower left to give CALLISTO, and MASSEUR clashing with OPACITY in the middle to give EUROPA.

And the disconnected cell in the very centre of the grid must be JUPITER. I’ll draw it a bit bigger.

(So the question I asked at the beginning remains unanswered: why have the bars been omitted from the grid? It turns out that I can just draw them in based on the numbers after the clues. I suppose the intention was to not reveal the disconnected central cell right away, but I think it was an unnecessary and somewhat misleading complication, because of the doubt it created as to how the numbers and clashes worked.)

After solving a couple more clues I consider 27 across, “Corrupt Idaho satirist”, the answer to which has to fit into _V_ _AL. It looks like it ought to be •VENAL with the dot representing JU. And yes, the clashing answer at 15 down (“Capital ombu tea”) is CHAPITER.

So this clash is JUPITER, and so the dot in the middle must instead be IO, which can be understood to represent a clash between GALILEO and GALILEI. How delightful!

And now that these dots are in the right place, their arrangement looks much more satisfactory, because the dots for the moons that I’ve found so far look as though they are in positions that are approximately to scale. Let’s check that:


Semi-major axis

(10⁵ km / cell)











This seems to be about as good a fit as you could expect from a crossword grid. So GANYMEDE, with a semi-major axis of 1,070,400 km, must lie between 3 and 4 grid cells from Jupiter. If I draw two circles with radii of 3 and 4, Ganymede most likely lies between the circles, in one of the three positions indicated by the red dots.

Are any of those positions right? Yes, 11 down, “Good fish? Rather old”, is SOMEDELE, and 17 across, “Gypsy exfoliants blasted zit”, is TZIGANY.

I can see now why the grid is not symmetric: getting the Jovian system to scale must have been a tricky constraint.

The remainder of the crossword is still no pushover. There is one clue I don’t understand. 23 across, “Ratify losing part of Ogilvie clan” is SEAL. “Ratify” is the definition, but how does the wordplay work?

It was a horribly difficult puzzle to start with, and for a long time I thought I wouldn’t be able to do it, but guessing the quotation saved the day. It all looks straightforward now I understand it, but as the great scientist said,

“All truths are easy to understand once they are discovered; the point is to discover them.”


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