Serieshelpmate in 19

Here’s a brilliant problem.

Consider the following chess position.

Black is to make 19 consecutive moves, after which White checkmates Black in one move. Black may not move into check, and may not check White (except possibly on his last move). Black and White are cooperating to achieve the aim of checkmate. (In chess problem parlance, this problem is called a serieshelpmate in 19.) How many different solutions are there?

This problem is due to Kauko Väisänen, and appears in A. Puusa, Queue Problems, Finnish Chess Problem Society, Helsinki, 1992 (Problem 2).

Hint: the above is quoted from Richard Stanley’s Enumerative Combinatorics.

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AE

XXVII

“Is my team ploughing,
That I was used to drive
And hear the harness jingle
When I was man alive?”

Ay, the horses trample,
The harness jingles now;
No change though you lie under
The land you used to plough.

“Is football playing
Along the river shore,
With lads to chase the leather,
Now I stand up no more?”

Ay, the ball is flying,
The lads play heart and soul;
The goal stands up, the keeper
Stands up to keep the goal.

“Is my girl happy,
That I thought hard to leave,
And has she tired of weeping
As she lies down at eve?”

Ay, she lies down lightly,
She lies not down to weep:
Your girl is well contented.
Be still, my lad, and sleep.

“Is my friend hearty,
Now I am thin and pine,
And has he found to sleep in
A better bed than mine?”

Yes, lad, I lie easy,
I lie as lads would choose;
I cheer a dead man’s sweetheart,
Never ask me whose.

---

Sanskrit pronouns and closeness

Reminded from here.

Unlike English “this” and “that”, Sanskrit has two of each. That is, there are four “degrees” of pronouns, varying by proximity:

1. very close, “this”: etad, एतद् :

m. एषः   एतौ   एते (एतेन, एतस्य, एतस्मिन्)
f. एषा   एते   एताः (एतया, एतस्याः, एतस्याम्)
n. एतत्   एते   एतानि (एतेन, एतस्य, एतस्मिन्)

2. close, “this”: idam, इदम्

m. अयम्   इमौ   इमे (इमम्, अनेन, अस्य, अस्मिन्)
f. इयम्   इमे   इमाः (इमाम्, अनया, अस्याः, अस्याम्)
n. इदम्   इमे   इमानि (इदम्, अनेन, अस्य, अस्मिन्)

3. away, “that”: adas, अदस् (rare?)

m. असौ   अमू   अमी (अमुम्, अमुना, अमुष्य, अमुष्मिन्)
f. असौ   अमू   अमूः (अमूम्, अमुया, अमुष्याः, अमुष्याम्)
n. अदः   अमू   अमूनि (अदः, अमुना, अमुष्य, अमुष्मिन्)

4. in absentia, “that”: tad, तद्

m. सः   तौ   ते (तम्, तेन, तस्य, तस्मिन्)
f. सा   ते   ताः (ताम्, तया, तस्याः, तस्याम्)
n. तत्   ते   तानि (तत्, तेन, तस्य, तस्मिन्)

Then there’s also एनम् etc., which according to MW “Grammarians assert that the substitution of एनम् &c for इमम् or एतम् &c takes place when something is referred to which has already been mentioned in a previous part of the sentence”.

रम्याणि वीक्ष्य मधुरांश्च निशम्य शब्दान् 
  पर्युत्सुको भवति यत्सुखितोऽपि जन्तुः ।
तच्चेतसा स्मरति नूनमबोधपूर्वं 
  भावस्थिराणि जननान्तरसौहृदानि ॥

Making audio louder with Audacity

(Tried with Audacity 1.3.12 beta.)

1. Open the file in Audacity. Go to Effects → Amplify.
2. The amplification set is already the maximum possible without clipping. Don’t change anything, just click OK

This makes the file as loud as possible without clipping: without the loudest parts of the “signal” getting lost. If the result is not loud enough, the problem is not with the loudest parts (they are already as loud as they can be), but with the softer parts. So you need a transformation that makes the soft parts louder while keeping the loud parts the same. This is Dynamic range compression: the dynamic range (difference between softest and loudest parts) is compressed.

So, after trying “Amplify”,

1. Download “Chris’s dynamic compressor” from here (direct link).
2. Save the file compress.ny in /Applications/Audacity/plug-ins
3. In Audacity, go to “Effects → Compress dynamics…” (or perhaps it’s called “Compress &dynamics…”)
4. The first control (“Compress ratio”) is the main one. Or just leave it as it is. Click OK.
5. If still not loud enough, go back and increase Compress ratio. Of course, increasing it means decreasing the dynamic range — increase it too much and the parts meant to be soft will be no softer than the rest.

Converting old PS files (generated with LaTeX) to searchable PDFs

pkfix fasc3a.ps fasc3a-fix.ps
ps2pdf fasc3a-fix.ps

A common (or at least, more common than it should be) scenario: you find a PostScript file of some paper, clearly written in (La)TeX, but which looks blurry on screen and you cannot copy any text. Converting to PDF with, say, ps2pdf does not help either. You curse the .ps format, and put up with the blurriness or print it out (where it looks fine) to read it.

Turns out it doesn’t have to be this way. The problem is that the PS file is using bitmap fonts, but assuming you have the scalable (Type 1) versions of those same fonts on your system, you can convert the fonts! There’s a script called pkfix, distributed with TeX Live, which will take a ps file that uses bitmap fonts and try to convert it to use scalable fonts. Just run it as

pkfix inputfile.ps outputfile.ps

This should produce a PS which isn’t blurry and is searchable, but if you prefer PDF, the usual way will work

ps2pdf outputfile.ps

or on Mac OS X if you don’t have ps2pdf for some reason, o inputfile.ps -a macps2pdf where macps2pdf comes with MacGhostView.

If the file is very old (generated with dvips from before 1996) and pkfix doesn’t work, there’s a further script called pkfix-helper that may make the file appropriate for pkfix.

BTW, if it’s your own files that are coming out blurry, something is wrong with your setup. Just install the package cm-super from CTAN—sudo tlmgr install cm-super or whatever—and no other change is needed. Or you can use the lmodern fonts with \usepackage{lmodern}, but that shouldn’t be necessary.