silver lining

It seems to have been raining constantly for months.  However, this does have the advantage that the garden is green and growing like crazy, and all those raindrops can be pretty:

shooting chocolate

I'm just back from a couple of days in Brussels, where I was at a meeting about Unconventional Computation. Brussels is a mixture of new and old buildings, as the "view" out of my hotel window shows:

New buildings at the back, packed right up against older ones in the middle.  And those older ones are indeed quite old; zooming in on the wall to the right shows some crumbling brickwork:

But what Belgium is famous for, of course, is chocolate.  I decided that photographs would be better for me than any closer interaction, and the displays themselves are works of art:

I did succumb to a hot chocolate drink, however.  Mmmm.

search history

I was writing a paper, and as a conclusion to a short section, I wanted to put "Life is a verb, not a noun".  Now, that sounds like something someone has probably said before, so I thought I would check, in case I needed to reference it.  I found the source as follows:

• I Google “Life is a verb, not a noun”.
• Lots of entries say it's by Charlotte Perkins Gilman, but none give a source (as usual)
• I Google “Charlotte Perkins Gilman wikiquote”
• I follow the link to http://en.wikiquote.org/wiki/Charlotte_Perkins_Gilman
• It’s not there
• I Google “Charlotte Perkins Gilman Life is a verb, not a noun”
• One of the entries this time looks more like like a source: I can see that it has a reference in it, to a (p. xv)
• I follow link to http://www.h-net.org/reviews/showrev.php?id=33118
• It’s a review by Cara L. Burnidge, of Charlotte Perkins Gilman: a biography, by Cynthia J. Davis, with a link to the book itself at Amazon.com
• I follow link to http://www.amazon.com/exec/obidos/ASIN/0804738890
• The Amazon page has a “look inside” version of the book, so I look to see if p.xv is included. It is, and has the quote, but no source. However, the same paragraph has several other quotes, and then an endnote reference 10.
• I look to see if endnote 10 is included in the “look inside” version. It is, on p.409, where it says “she calls 'life' a verb in HW, 203”, which sounds like it could be the source.
• I assume 203 is a page reference, and that HW is an abbreviation for the source. What is HW?
• I look to see if the abbreviations are included in the “look inside” version. They are; HW = Human Work
• I Google “Charlotte Perkins Gilman Human Work”
• There's a Google books version at http://books.google.co.uk/books/about/Human_work.html?id=IHoEAAAAYAAJ&redir_esc=y.
• I follow the link to the book; it’s not searchable.
• Back to Google Results page; there's another version at http://books.google.co.uk/books/about/Human_Work.html?id=y8Gif_Ni0L0C&redir_esc=y
• I follow the link to the book; this one is searchable.
• I search for “verb”; there are many hits; one is on p.203. And there it is:

• I go to the beginning of the book, and get the rest of the bibliographic details.

"Life is a verb, not a noun."
Charlotte Perkins Gilman, Human Work, p203. McClure, Philips and Co, 1904.

Elapsed time, less than 15 minutes.
Try that with a paper library!

Maybe I should add it to wikiquotes...

the scam returns

[phone rings]
"Hello?"
[crackle]
"Hello?"
"Hello ma'am, this is [rapid mumble I couldn't make out] check-up on your computer..."
"Do you know that this is a scam?  Are you a criminal, or are you being fooled by your employers?"
[pause]
"Hello ma'am, this is [rapid mumble I couldn't make out] check-up on your computer..."
"Do you know that this is a scam?  Are you a criminal, or are you being fooled by your employers?"
[dial tone]

background to this (I was less bored this time)

gopher tuna

I've posted about alternative lyrics to Carl Orff's O Fortuna before. However, I recently came across another version, and realised there are alternative alternatives.  There are several versions on YouTube, with their surreal lyrics (but little more so that some possibly drug induced lyrics of real songs) made even more surreal by the accompanying pictures. (A few pics may be mildly NSFW, depending where you work, but they are uniformly wonderful.)  My favourite version (which is the one I stumbled across today) has hand-sketched internet meme figures.

Realising that there are several versions, and that some extremely different readings seem to fit just as well, made me look up the original medieval Latin lyrics, and do a compare and contrast:

O Fortuna (O Fortune)	Oh, four tuna // Gopher tuna
velut luna (like the moon)	Bring more tuna
statu variabilis (you are changeable)	Statuary on his knees // Statue of big dog with fleas
semper crescis (ever waxing)	Some men like cheese // Cement like cheese
aut decrescis; (and waning;)	Hot, temperate cheese // Hot Democrat cheese
vita detestabilis (hateful life)	Vimto can taste of kidneys // Green chalk can taste like hippies // We took a taste of me knees
nunc obdurat (first oppresses)	Lukewarm two rat // You caught two rocks? // Look up, you brat
et tunc curat (and then soothes)	Bet too cool, rat // Pet two cool rats // That took cool rat
ludo mentis aciem, (as fancy takes it)	You don't get cheese or chicken // Luke don't make tea. Sore chicken
egestatem, (poverty)	Bend chips all day // Play chess all day
potestatem (and power)	Hot and salty // Hold his sock tip // Poke Tess all day
dissolvit ut glaciem. (it melts them like ice.)	Dip sore feet. Good, hot chilli // She sold me good, hot chicken
---
Sors immanis  (Fate - monstrous)	Saucy codpiece //  Saucy hot peas //  Saucy mommies
et inanis,  (and empty)	Ate spleen of neice //  Get me cod, please //  Get in on knees
rota tu volubilis,  (you whirling wheel)	Brought up too full food in me //  Rock talk to boy who believes //  Broke up to follow minis
status malus,  (you are malevolent)	Suck juice from moose
vana salus  (well-being is vain)	Fun with some goose //  Fun, handsome goose
semper dissolubilis,  (and always fades to nothing)	Second these so rude big knees //  Cement pizza? Noobie please! //   Second this, all who believes
obumbrata  shadowed)	Open bra top //  Open bar tab
et velata  (and veiled)	Get them loved up //  Get him locked up
michi quoque niteris;  (you plague me too;)	Leaking foot when near cherries //  Leaky aquariataries
nunc per ludum  (now through the game)	Look, they look good //  Look there! Fruitloop! //  Look, them look dumb //  Look there look good
dorsum nudum  (I bring my bare back)	Dogs sure look cute //  Don't sue YouTube //  Hot soup look good
fero tui sceleris.  (to your villainy.)	Farewell to knees and berries //  They wrote teh dictionary //  Farewell to ancient berries
---
Sors salutis  (Fate is against me)	Salsa cookies
et virtutis  (in health)	Windmill cookies
michi nunc contraria,  (and virtue)	They'll give you gonorrhea! //  They gave you gonorrhea!
est affectus  (driven on)	This octopus //  This know is loose
et defectus  (and weighted down)	Let's give him boots //  Let's cook this goose
semper in angaria.  (always enslaved.)	Send him a carburetor //  Send him to North Korea //  And give him half a pizza //  Send him a car or pizza
Hac in hora  (So at this hour)	Lovely Torah //  Ow, paper cut! //  Monkey, Dora
sine mora  (without delay)	Send me more of //  Sandpaper, ahh!
corde pulsum tangite;  (pluck the vibrating strings;)	Potato soup and chicken
quod per sortem  (since Fate)	What mess again? //  Go taste the dip! //  I miss old friend //  Hot mess all day
sternit fortem,  (strikes down the string)	Sing it, ugly //  It's made with cool whip!
mecum omnes plangite!  (everyone weep with me!)	Be good for Peace Monkey's sake //  Make room for a piece of lovely cake //  Be good for a piece of cake

Clearly these alternatives aren't all independent, but there's enough variety to be amusing. Most of the variation seems to be around lines that nothing fits very well.  Also, once a variant has been used, it appears to affect nearby versions: once you have rats in your head, they stay around.  I suspect that a trained historian could work out a family tree of which version influenced which.

Listening to any of the recordings whilst reading the original words is interesting: in some cases the words really being sung appear to fit just as poorly as some of the alternatives.  Presumably this is a combination of a large choir singing not quite simultaneously, in a foreign language, filtered through a non-perfect sound system.

Knowing what to listen for makes all the difference.  Once you are listening for "Vimto can taste of kidneys", it's easy to hear.  But then so is "Green chalk can taste like hippies".  These surreal lyrics are much easier to hear than alleged mumbled satanic phrases in rock music played backwards (but for the very same reason).

a jewel of a probability puzzle

I've been spending way too much time reading John Baez' Azimuth blog. It's got lots of fascinating stuff, but one piece that really caught my eye is a probability puzzle:

Suppose I have a box of jewels. The average value of a jewel in the box is \$10. I randomly pull one out of the box. What’s the probability that its value is at least \$100?

First thought, of course, is: "I don't have enough information; the answer will depend on the distribution".  But in fact you can give quite a strong bound on the answer even without knowing the distribution, using Markov's inequality: the probability is +++\le 1/10+++.

At first, this looks impossible: how can this be independent of the distribution?  Surely I can have some strange collection of jewels that violates this bound?  But no, and in the comments section there are some great explanations that give an intuition about why this is so, including David Guild's:

As long as gems have non-negative value, then (probability of pulling a \$100 or better gem > 10%) implies that (average value > \$10). Since the average is exactly \$10, then the probability can’t be more than 10%.

A very clear proof is laid out by Greg Egan. I'll rework it here, for the general case of an average value of +++a+++ (rather than the specific \$10) and a big value of +++b+++ (rather than \$100), to get the general result.

Let +++A+++ be the set of all jewels, +++\#A+++ be the size of set +++A+++, and +++V(x)+++ be the value of jewel +++x+++. Let +++B+++ be the set of "big value" jewels
$$ B = \{x\in A | V(x) \ge b\}$$We know the average value of the jewels is +++a+++:
$$ a =  \frac{1}{\#A} \sum_{x \in A} V(x) $$If we replace the sum over all jewels +++A+++ with the sum over the smaller set of jewels +++B+++, we must get a smaller answer (assuming that all the values are non-negative: necessary in the general case, and implicit in the given example).  So:
$$ a \ge  \frac{1}{\#A} \sum_{x \in B} V(x) $$From the definition of +++B+++, we have +++\forall x \in B, V(x) \ge b+++.  This implies that
$$ \frac{1}{\#A} \sum_{x \in B} V(x) \ge  \frac{1}{\#A} \sum_{x \in B} b  $$We can do this last sum:
$$ \frac{1}{\#A} \sum_{x \in B} b =  \frac{\#B}{\#A} b$$Putting this all together, we have
$$ a \ge  \frac{1}{\#A} \sum_{x \in B} V(x)  \ge \frac{1}{\#A} \sum_{x \in B} b = \frac{\#B}{\#A} b$$So
$$ a \ge  \frac{\#B}{\#A} b$$Rearranging gives the result that the proportion of big value items to all items (the probability of drawing a big value item) is:
$$ \frac{\#B}{\#A} \le \frac{a}{b}$$For the example with +++a=10+++ and +++b = 100+++, this gives us +++1/10+++.

This derivation assumes that the chance of pulling out any jewel is the same.  But, as Baez explains, the result is independent of this.  If some jewels are more likely to be picked, and that likelihood is used to define the average value too, then the result stands. (I leave the proof as an exercise for the reader.)

So, from a problem that initially looked as if it doesn't have nearly enough information, we've moved to an intuition about why a result (albeit only a bound) can be given, and a simple proof of a general result for that bound: Markov's inequality.  The power of maths!

There's also a result for values that can go negative, which requires also knowing the standard deviation: Chebyshev's  inequality.  It's all on John Baez' blog.  Go there, and you to  might spend as much time reading around as I have!