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The say of the week March 30, 2009

Posted by dorigo in games, humor.
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“I read in the newspapers they are going to have 30 minutes of intellectual stuff on television every Monday from 7:30 to 8. to educate America. They couldn’t educate America if they started at 6:30.”

(G.Marx)

Ten photons per hour March 23, 2009

Posted by dorigo in astronomy, games, mathematics, personal, physics, science.
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Every working day I walk for about a mile to my physics department in Padova from the train station in the morning. I find it is a healthy habit, but I sometimes fear it also in some sense is a waste of time: if I catched a bus, I could be at work ten minutes earlier. I hate losing time, so I sometimes use the walking time to set physics problems to myself, trying to see whether I can solve them by heart. It is a way to exercise my mind while I exercise my body.

Today I was thinking at the night of stargazing I treated myself with last Saturday. I had gone to Casera Razzo, a secluded place in the Alps, and observed galaxies for four hours in a row with a 16″ dobsonian telescope, in the company of four friends (and three other dobs). One thing we had observed with amazement was a tiny speck of light coming from the halo of an interacting pair of galaxies in Ursa Major, the one pictured below.

The small speck of light shown in the upper left of the picture above, labeled as MGC 10-17-5, is actually a faint galaxy in the field of view of NGC3690. It has a visual magnitude of +15.7: this is a measure of its integrated luminosity as seen from the Earth. It is a really faint object, and barely at the limit of visibility with the instrument I had. The question I arrived at formulating to myself this morning was the following: how many photons did we get to see per second through the eyepiece, from that faint galaxy ?

This is a nice, simple question, but computing its answer by heart took me the best part of my walk. My problem was that I did not have a clue of the relationship between visual magnitude and photon fluxes. So I turned to things I did know.

Some background is needed to those of you who do not know how visual magnitudes are computed, so I will make a small digression here. The scale of visual magnitude is a semi-empirical one, which sets the brightest stars at magnitude zero or so, and defines a decrease of luminosity by a factor 100 per every five magnitudes difference. The faintest stars visible with the naked eye in a moonless night are of magnitude +6, and that means they are about 250 times fainter than the brightest ones. On the other hand, Venus shines at magnitude -4.5 at its brightest -almost 100 times as bright as the brightest stars-, and our Sun shines at a visual magnitude of about -27, more than a billion times brighter than Venus. The magnitude difference between two objects is in a relation with their relative brightness by a power law: L_1/L_2 = 2.5^{-M_1+M_2}; the factor 2.5 is an approximation for the fifth root of 100, and it corresponds to the brigthness ratio of two objects that differ by one unit of visual magnitude.

Ok, so we know how bright is the Sun. Now, if I could get how many photons reach our eye from it every second, I would make some progress. I reasoned that I knew the value of the solar constant: that is the energy radiated by the Sun on an area of 1 square meter on the ground of the Earth. I remembered a value of about 1 kilowatt (it is actually 1.366 kW, as I found out later in wikipedia).

Now, how many photons of visible light arriving per second on that square meter of ground correspond to 1 kilowatt of power ? I reasoned that I did not remember the energy of a single visible photon -I remembered it was in the electron-Volt range but I was not really sure- so I had to compute it.

The energy of a quantum of light is given by the formula E = h \nu, where h is Planck’s constant and \nu is the light frequency. However, all I knew was that visible light has a wavelength of about 500 nanometers (which is 5 \times 10^{-7} m), so I had to use the more involved formula E = hc/\lambda, where now c is the speed of light and \lambda is the wavelength. I remembered that h=6 \times 10^{-34} Js, and that c=3 \times 10^8 m/s, so with some effort I could get E=6 \times 10^{-34} \times 3 \times 10^8 / (5 \times 10^-7) = 4 \times 10^{-19}, more or less.

My brains were a bit strained by the simple calculation above, but I was relieved to get back an energy roughly equal to that I expected -in the eV range (one eV equals 1.6 \times 10^{-19} Joules -that much I do know).

Now, if the Sun radiates 1 kW of power, which is a thousand Joules per second, how many visible photons do we get ? Here there is a subtlety I did not even bother considering in my walk to the physics department: only about half of the power from the Sun is in the form of visible light, so one should divide that power by two. But I was unhindered by this in my order-of-magnitude walk-estimate. Of course, 1 kW divided by 4 \times 10^{-19} makes 2.5 \times 10^{21} visible quanta of light per square meter per second.

Now, visual magnitude is expressed as the amount of light hitting the eye. A human eye has a surface of about 20 square millimeters, which is 20 millionths of a square meter: so the number of photons you get by looking straight at the sun (do not do it) is 1.2 \times 10^{14} per second. That’s a hundred trillions of ’em photons per second!

I was close to my goal now: the magnitude of the speck of galaxy I saw on Saturday is +15.7, the magnitude of the Sun is -27, so the difference is 43 magnitudes. This corresponds to 2.5^{43}, which you might throw up your hands at, until you realize that every 5 units of the exponent the number increases by 100, so you just do 100^{43/5} which is 100^{8.6} which is 10^{17.2}… Simple, isn’t it ?

Now, taking the number of photons reaching the eye from the Sun every second, and dividing by the ratio of apparent luminosities of the Sun and the galaxy, I could get N_{\gamma}=10^{14} / 10^{17} = 10^{-3}. One photon every thousand seconds!

Let me stress this: if you watch that patch of sky at night, the number of photons you get from that source alone is a few per hour! With my dobson telescope, which intensifies light by almost 10,000 times, I could get a rate of a few tens of photons per second, and the detail was indeed detectable!

If you are intested in the exact number, which I worked out after reaching my office and the tables of constants in the PDG booklet, I computed a rate of N_{\gamma}=3.4 \times 10^{-3} photons per second with unaided eye, and 22 per second through the eyepiece of the telescope. Without telescope, that galaxy sends to each of us about 10 photons per hour!

UPDATE: this post will remain as one clear example of how dangerous it is to compute by heart! Indeed, somewhere in my order-of-magnitude conversions above I dropped a factor 10^2 -which, mind you, is not horrible in numbers which have 20 digits or so; but when one wants to get back to reasonable estimates for reasonably small numbers, it does count a lot. So, after taking care of some other (more legitimate) approximations, if one computes things correctly, the number of photons from the galaxy seen with the unaided eye is more like two hundred per hour, and in the telescope it is of about 350 per second.

The say of the week March 19, 2009

Posted by dorigo in games, humor, internet, italian blogs, physics, science.
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“Questi c’hanno sistematici che fanno provincia”

[These fellas have got county-wide systematics]

(Xisy, from a comment in M.Dal Mastro’s blog)

The four pawns attack as black likes it March 7, 2009

Posted by dorigo in chess, games, personal.
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The four-pawns attack of the Alechin defense arises after the sequence 1.e4 Nf6 2.e5 Nd5 3.c4 Nb6 4.d4 d6 5.f4. White goes all in for a direct attack, exploiting the wandering black knight to gain space in the center. This variation has received a lot of attention since the early days of the Alechin Defense, and it has seen in particular some interesting developments during the seventies, by the sapient hands of Jugoslav players.

I play the Alechin defense as black, and I often find myself struggling in extremely sharp positions when the four-pawns attack is played. It is white’s choice to enter that variation, and one should be prepared well on the main variations, since one faux pas may be fatal. However, these days I cannot afford the luxury of spending time on chess openings, so I have to rely on my experience on the general ideas of the positions that arise.

This evening I played a game that turned out to be a clear (although most probably not clean) example of the thematic tactical motives of the positions that arise in the four-pawns attack. It was a 5′ blitz game on the ICC, so I should be forgiven (as should my unnamed opponent) for any unchecked blunders -I have not fed the moves to a chess engine yet. So here are the moves of the game, with minimal commentary.

1.e4 Nf6 2.e5 Nd5 3.d4 d6 4.c4 Nb6 5.f4 dxe5 6.fxe5 Nc6 7.Be3 Bf5 8.Nc3 e6 9.Nf3 Be7 (see diagram below)

We have reached a tabiya, a standard position in the four-pawns attack. Here white has the choice of the solid, positional play that arises after 10.Be2 0-0 11.0-0 f6 12.exf6, or the more aggressive, bold play involving a central push and a swift assault on the black kingside. My opponent chose the second way.

10.d5 exd5 11.cxd5 Nb4 12.Nd4 Bd7 13.e6 fxe6 14.dxe6 Bc6 15.Qg4 Bh4+ 16.g3 Bxh1

We are still playing moves that are in most chess textbooks. White has given up the exchange -the difference in value between a rook and a light piece- but he has a positional advantage and the initiative for it.

17.0-0-0 Qf6 18.gxh4 0-0 19.Be2 Qe5!?N 20.Bh6

Here I vaguely remembered a game I played six or seven hundred years ago, at a national tournament, when I was taken by surprise by the last move of the white pieces. The most used move here, I recalled -and the only one I was prepared to answer- is 20.Bg5. I tried to squeeze my brains for the textbook variation, but I only recalled that the black rook used to end invading the second rank. The move 20….Rf2 did not look that bad, so I played it, letting my opponent spend time to think on its merits. However, I was wrong. The move 19….Qe5 was a mix-up of two variations, and turns out to be a novelty in this position: not a bad move, however.

20…. Rf2?! 21.Rxh1 Kh8 22.Bg5?

Black’s twentieth move was not good, since now, instead than 22.Bg5, white could have acquired a sizable advantage by 22.Nf3!, attacking the queen while she is still forced to defend the g7 square. Instead the move chosen by white justifies black’s sortie on the seventh rank: black has free hands to attack now.

I felt pretty sure of what I needed to do. The pivot of the white position is the Nd4: it is an octopus rather than a knight, but kick it away from there, and it causes white more trouble than benefits. The move I played is a thematic push in this position, aimed at taking control of the center, defending the black Nb4 from horizontal attacks by the white queen, and caressing ideas of a pawn storm of the white king. I felt it in my bones that this move should be played. Of course a computer might prove it a blunder: but at blitz, these moves bring home a lot of points.

22…. c5! 23.Nf3?

This move is very bad, and is the cause of white’s loss. Now, disregarding the attack on the his queen, black takes total control.

23…. Nxa2+! 24.Kc2? Rxe2+ 25.Nxe2 Qxe2+ 26.Kb1

And what now ? The black Na2 is under attack. Black is a pawn up, but he needs to be precise. On 26….Nb4 27.Qf5 white seems capable to hold. But here comes a silent killer:

26…. Nc4!

White is powerless: he has no means to defend the b2 square from the simple threat of Qxb2 mate. White played

27.Bc1 Nxc1 28.Kxc1

but after the precise

28….Rd8!

he had to resign. There is no way to avoid Qb2 mate, other than sacrificing the queen. Note that 28…. Nb4! would also have been an excellent move. Here many continuations win for black.

I was pleased with this short game, which shows that the position arising from the four-pawns attack is dangerous for white just as much as it is for black!

The say of the week March 3, 2009

Posted by dorigo in games, humor, literature.
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“A black cat crossing your path signifies that the animal is going somewhere.”

G.Marx

Think as an experimental particle physicist: results! February 27, 2009

Posted by dorigo in games, humor, physics, science.
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I know you are impatient, and the weekend is coming, so while I still hope more of you will leave their results in the comments thread, I give below the key to compute the score of the two-part test I offered in the two previous posts. Each answer has from zero to three of the following symbols: E,T,S,C,D. Just sum each category for now:

(more…)

Think like an experimental particle physicist – second (and last) part February 27, 2009

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While putting together the scores to evaluate the answers to the 11 questions of the previous post, I realized that they are not enough for a fair classification. So here are a few more quizzes for those of you who found my effort worth paying back with five more minutes of your time.

  • K) You are found in the library of your Department. Why was that ?
  1. Why, I had an hour to kill…
  2. I am just checking out the new librarian (he/she’s cute).
  3. They told me there are coupons to cut away for free radioactive samples on this month’s issue of Physics Today.
  4. They threatened to expel me if I did not bring back the overdue copy of DH. Perkins’ book.
  • L) How much is 87 times 945 ?
  1. About 80 thousand.
  2. About 82 thousand.
  3. I left my pocket calculator in the office upstairs.
  4. (after a minute)  82,215  (ignore my fast breathing).
  5. 82 215 (mind the space -I take pride in following AIP style rules!).
  6. More or less 10^5.
  • M) The mean-looking airport cop finds an electronic board wrapped in a sweater in your carry-on.
  1. You go back to the check-in counter: you came early on purpose.
  2. You try to explain it is innocuous HEP hardware.
  3. You manage to power it up by fiddling with the laptop power cord to show the two-digit LCD mounted on it does come alive.
  4. You start arguing that the sign with red crosses on lighters, firearms and batteries mentions nothing even vaguely resembling a CAMAC module.
  5. You let them dump it, too bad for science -and whoever uses CAMAC nowadays, after all.
  • N) Your paper draft receives really nasty comments from your collaborators
  1. You write down the names of the bad guys on your small red booklet in the bottom drawer – their time in front of the muzzle will come one day!
  2. You answer in kinds on a rage, with carbon-copy to the spokespersons, making a fool of yourself.
  3. You answer as politely as you can in a very detailed manner, cursing yourself softly while you feel like you’ve bent over.
  4. You decide the paper really is not worth that much and forget about it for a month or two.
  • O) After your presentation is over,  the session convener asks a tough question and you do not even know what he or she is talking about.
  1. You say you do not know the answer and display your best smile, hiding the sweating.
  2. You repeatedly pretend you did not understand the sentence until he or she decides it’s time to move on.
  3. You think it wasn’t such a good idea to grab that last-minute chance for a plenary talk.
  4. You go to a random back-up slide and discuss it in detail for five minutes, trying to look meaningful.
  • P) A science reporter calls and asks you information on the  hunt for supersymmetry.
  1. You feel flattered, get carried away, and end up disclosing reserved information from your experiment.
  2. You direct him or her to the experiment spokespersons.
  3. You pretend you’re the switchboard operator.
  4. You ask what magazine is that for, and after hearing it’s “New Scientist” you hang up.
  • Q) They sent you a paper to be reviewed. It sucks big time.
  1. Feeling true to your duties, you implacably point out each and every imperfection with rigor and an occasional bit of sadism.
  2. You reckon nobody’s going to read the paper anyway, so you send back two lines saying the paper looks ok but would they please use AIP style rules ?
  3. You are fought between your duties and your compassion for the poor post-doc who did most of the work  to get the paper to your desk, and try to balance the two things, ending up screwing both -the author feels raped and the paper does not get any better from your review.
  4. You would never accept to get into an editorial board, it’s just such a waste of research time.
  • R) You are on owl shift and your colleagues are out of the room for coffee and cookies, when every screen turns red, alarms sound, and an ominous-looking warning sign start flashing on the silicon cooling contol panel.
  1. You run to the silicon crash button and press it.
  2. You silence all alarms and fetch the emergency procedures folder, then start reading it
  3. You rush to call your colleagues.
  4. You sneak out, join your colleagues and serve yourself a coffee, then look over the glass door and mention there appears to be  something flashing inside as if you just noticed it.
  • S) You feel you think like an experimental particle physicist because…
  1. You do not work in HEP, but at least one answer in each of the 19 questions above made a lot of sense to you
  2. You read this blog and you think it really does not take much to be a HEP physicist.
  3. You are a theorist and although you have trouble with practicalities you think experimentalists have similar thinking processes.
  4. You are a scientist from another field and you know how to tie your shoes.
  5. You are a scientist from another field and you wear sandals.
  6. You are sure you do not think like an experimental particle physicist in the least.

Think like an experimental particle physicist! February 26, 2009

Posted by dorigo in games, humor, physics, science.
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In my ongoing effort to convince my readers that experimental high-energy physics is easy and fun, and to make it more appealing to everybody, I am presenting you with a small test, which should measure your ability to think as an experimental particle physicist. These questions  should be enough to sketch your profile as a HEP worker. You are invited to use five minutes of your time to give your answers in the comments thread below. I will provide results in a couple of days.

  • A) You need to insert in your analysis code the width of the Z boson. What do you do ?
  1. you google “Z boson width”
  2. you go to pdg.lbl.gov and download the Z boson table
  3. you dig under a pile of preprints for your copy of the PDG booklet
  4. you write “=1.0; // REVISE: Z boson width!!! ” and leave it to a better day
  • B) What is the muon mass ?
  1. 0.105658367 GeV
  2. 0.105658367 GeV/c^2, silly you
  3. 105.658367 MeV/c^2
  4. 0.1134289256 u
  5. “sqrt(0.01116369);” which is a number you retrieved from an old piece of code
  6. about 100 MeV, give or take a few
  • C) How does the Higgs boson decay to a pair of photons ?
  1. by first splitting into a pair of top quarks
  2. by first splitting into a fermion loop
  3. by first splitting into a pair of W bosons
  4. it cannot, the Higgs is not electrically charged
  • D) A primary cosmic ray with an energy of 10^17 eV hits the atmosphere. It is determined to be a neutron.
  1. it must come from inside our galaxy
  2. it is a Nobel prize winning discovery
  3. it produces a shower like a proton would
  4. all of the above
  5. all of the above except 1.
  6. all of the above except 2.
  • E) A detector is being decommissioned and is being taken apart at a facility near your office.
  1. you wear a surgical mask when you walk by -activated powder might be dangerous
  2. you drop by and try to scavenge a gadget or two
  3. you mail the ex-spokesperson to ask for those yellowed scintillator planes
  • F) The code won’t compile…
  1. you check the error messages carefully
  2. you try it on a different account
  3. you hit the “save” button on your editor again and retry
  4. you go to the coffee machine and ponder
  • G) You are scheduled to talk at a conference, on a topic that is not your own
  1. you start reading material one month before
  2. you start looking for slides on the same topic a week before
  3. you email the authors of the relevant analyses for help four days before
  • H) You are on day shift at your experiment next October. What is your main worry right now ?
  1. Get on par with the latest safety procedures and make sure your training has not expired
  2. Find a substitute for that week for your course of the first semester
  3. Find the cheapest flight early on
  4. Look for entertainment options for all those evenings
  • I) You walk by a colleague’s desk in the evening and find out he’s not logged off his account.
  1. you use his email to send himself a reminder
  2. you log him off
  3. you notify the sys admin
  4. you open his mozilla browser to a porn web page
  5. you go back to your own desk, remembering you did not log off either
  • J) A histogram of the invariant mass of jet pairs  in events containing just two energetic jets shows a compelling peak at 120 GeV.
  1. It’s the higgs!
  2. It is a statistical fluctuation
  3. It is a bug in your code
  4. This was a sample of Z boson decays to electron-positron pairs, and those are electrons corrected as if they were jets
  • K) What does a significance of three sigma mean ? Four sigma ? Five sigma ?
  1. something not so rare; something quite rare; something exceptionally rare.
  2. evidence of some new phenomenon; strong evidence of same; observation of new physics!
  3. evidence of something fishy;  a bug in the code; a horrible bug in the code.

A pretty knight journey February 21, 2009

Posted by dorigo in chess, games, personal.
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I give below the moves of a blitz game I played tonight on the Internet Chess Club. The moves are not accurate, as we had just five minutes each to complete the game, and we are both dilettantes. But the attack I played was so simple it played itself, so maybe this is a good training example… I am white against a first-category player (HerrTrigger his ICC handle).

1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Nxd4 Nf6 5.Nxc6 bxc6 6.Nc3 Bb4 7.Bd3 0-0 8.0-0 d5 9.exd5 cxd5 10.Bg5 c6 11.Qf3,
Up to now, nothing of our own making – you can find the above sequence on any chess opening book. It is called “Scotch game”; this particular variation is not known for causing black any particular opening problem, but white’s setup is solid and lends itself to a quick kingside surge, if black does not play the most accurate moves.

11….Bd6
Sub-optimal. Black has to be careful of his dark squares, and the pin of the Nf6 required more attention. Now white gets a clear initiative.
12.Ne2!
The start of a straightforward idea – Ne2-d4-f5 will further weaken the dark squares around the black king.
12…. Rb8 13.Nd4
Now Nxc6 is threatened, and the queen cannot defend the pawn since it is tied to the defence of the Nf6.
13….Bb7?
But this is surely a mistake. Black places the lightsquared bishop on a passive square, blocking the open b-file for some counterplay by the Rb8, and totally leaves the f5 square undefended.
14.Nf5 Be5

This is the position bfore the  start of the final attack. First of all, the black bishop is targeted, gaining a tempo with the rook.
15.Rfe1 Qc7
Now black threatens Bxh2+, but this is not really a problem for white. Instead, the logical conclusion of the knight manouver is in the air…
16.Nh6+!
If now black takes the N, white wins both by 17.Qf5 and by means of the pretty 17.Rxe5! Qxe5 (17…. hxg5 18.Rxg5+ Kh8 19.Qxf6 mate) 18.Bxf6, and black is soon mated (18…Qe6 19.Qg3+).
16….Kh8 17.Bxf6!

The simplest way to win. Black resigned, since on both 17….Bxf6 and 17….gxf6 there follows 18.Qf5 and there is no way to avert Qxh7 mate, while on 17….Bxh2+ 18.Kh1 Qf4 19.Qh5 Qxf6 (19….Qxh6?20.Qxh6) 20.Nxf7+! Kg8 21.Bxh7+ is mate. The Nc3-e2-d4-f5-h6 manouver is pretty in this game, since all the moves are active, and by threatening in turn the c6 pawn, the d6 bishop, and the king the knight takes the lion’s share of merit for the attack.

One word of warning: the above variations are the result of some thoughts on the game diagram, without even moving pieces on a real chessboard, let alone running a check with Fritz. So I am most likely going to be refuted by deeper silicon analysis… To me, the game and the variations still look quite logical in their development and conclusion!

Small satisfactions February 12, 2009

Posted by dorigo in chess, games, personal.
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This evening I worked out some small satisfaction for myself by routing in turn an international master, Guido Kern (Dorot his ICC handle), and the South Carolina State champion of 2007, Timur Aliyev (gatorchess his handle), at blitz chess on the Internet Chess Club.

The game with Kern was not very correct: we both committed several mistakes. Normal stuff, when you have an average 5 seconds per move. Here is a position from the game:

I am white, and it is my turn to move. The move sequence is very simple to guess, so I will give it without further ado. I played simply 17.Nxe4! Nxe4 18.Bxe4, having seen from the start that after 18….Rae8 19.Bxd5+ Kh8 20.Qg5 I would end up with a large advantage. The game continued 20…. Bg6 21.Bf7! Qe7 22.Bxe8, and with an exchange and two pawns of advantage I converted to an easily won ending in a few more moves.

In the game with Aliyev, I played a much more impressive kingside attack. Here is the position after black’s 26th move. I am white.

The plan plays itself, and in fact here is how the game finished: 27.Rc1, Rgg8; 28.Rcc7, Rgf8; 29.Re7, Qd6; 30.Rcd7, Qc6; 31.Rxf7, resigns. In fact, there is no way to parry the mate on h7.

So, it is true that at the mature age of 43 years I feel my neurons abandoning me one by one… But those left can still give me some small satisfactions now and then!