Been one bloody week since my DSL connection last behaved itself. Every time I call up the Tata Indicom Customer Service folks and tell them that the bloody DSL connection only works for half-an-hour or so in the mornings, they promise to look into it, and they promptly close the complaint when I login the next morning. Grrrr. It’s so very irritating to have a non-functional internet connection. Let’s see now, they were supposed to fix the damn problem yesterday. I’m hoping that the connection is still up later in the day… it would be very painful for me to log off now (which I’m going to do) and then find out a few hours later that the connection is on the blink again. Dear DSL connection, Please, PLEASE work. Do your FFTs in peace and keep that goddamn light on the modem glowing steady.

Update: For once, it wasn’t really the ISP’s fault. Figured this out one fine evening when I turned the computer on, hoping against all hope that my DSL modem would behave itself. It didn’t. Just as I was about to power the computer down, a transformer blew somewhere in the neighbourhood, and we were left without electricity. Lo and behold, the DSL light started to burn a bright green! Things were hunky dory until an hour or so later, when the power came back, preventing my UPS from cutting itself out. The moment the power returned, the DSL light went out. Curious, I thought, and made my way to the balcony – the KEB guys had installed new lampposts, and their power cables were overlapping my internet cable! It looked like powerline interference was pushing the SNR in my internet cable way, way down – it also explained just why my internet connection went kaput every evening at 6, and came back the next morning at 6 – these were the exact times when the street lights went on and off. Now, I need to confirm this hypothesis – but it looks like the experiment agrees with the theory.

A Close Brush with After Shave

I was at the neighbourhood store today, shopping for after shave. Yours truly shopping for after shave is something of a joke, as my better half says. It does happen to be funny, because I shave once in a blue moon. More often than not, I wander around looking like an unshaven bum. I do this for many reasons – for one, I like to irritate my better half. I also happen to be lazy. For some other insane reason, my favourite brand of after shave has been off the shelves for some time now. I was a staunch user of Nivea Balsam, and was willing to die unshaven if only I could get hold of a bottle or two of the sweet smelling stuff. A wait of more than two months yielded no results with all known peddlers of this liquid. I was deeply sorrowed, for Nivea was the only blessed after shave I knew of that did not sting. I absolutely hate the sting of alcohol on freshly shaved, vulnerable skin. Left without a choice, I decided to pick up a different after shave today. Hence my presence at the neighbourhood store. I settled for a sleek black cardboard box labelled “Mercury”. The labelling said that it was a gel that contained a moisturiser. Anything that contains a moisturiser shouldn’t sting much, I thought. The other side of the box screamed at me in bold lettering – “HARMFUL IF TAKEN INTERNALLY”. I thought back to high-school chemistry and methanol, and hooch deaths. I shrugged, and paid the price for my choice – it was twice as expensive as what it ought have been. I cursed myself, the people responsible for the Nivea shortage, and the world in general (in that order) and went home. I lifted the covering flap, prised open the lid to the bottle, and sniffed. I choked. It was one of those overpowering fragrances that trails its wearer like a comet’s tail. Or a dog’s. I gingerly lifted the bottle out, and laughed – it was shaped like a hip flask. I never did understand these designers. Anyway, the bottle being shaped like a hip flask lessened some of my guilt at having splurged a couple of smiling blue Gandhis – something designed with a sense of humour deserves appreciation. After much ado about my face with the Gillette, the other Gillette, water, and a pair of scissors, I proceeded to my rendezvous with the after shave. I up-ended the bottle above my palm, to little avail. The ridiculously small opening in the bottle was blocked by a bright bluish-green jelly-like liquid, that was reminiscent of radioactive waste. The smell was tempting, however – so I shook the bottle a little, and managed to extract some of its contents into the hollow of my palm. I repeated the procedure and recapped the bottle. Evenly dividing the gel between both my palms, I proceeded to make contact with my cheeks, and was promptly stung. I didn’t know where the hell the moisturiser in the gel was – it stung, and it kept stinging. Bloody hell, they named it just right – Mercury is closest to the Sun. My inner self was screaming at me to run to the bathroom and wash the after shave off, but something – perhaps it was foolish pride, or perhaps it was the cinnamon, aloe vera and whatever crap in the after shave – prevented me. I looked again at the black hip flask. Only a demented mind could have imagined such a perverse prank. The thought that I’d paid up what was a small fortune ten years ago stopped me from throwing the hip flask into the garbage bin. Maybe the cinnamon, aloe vera and assorted crap also contributed to that decision, I wasn’t too sure.

I’m roaming the streets again for that elusive bottle or two of Nivea. These days, the only Nivea product for men on the shelves seems to be something called Nivea Whitening Moisturiser For Men. The insecure adolescent male’s equivalent of Fair and Lovely. Who in his right senses wants that crap? Not me. Ugh. Shudder. Oh well, hopefully my cherished Nivea after shave hits the shelves soon.

The bright green light on my ADSL modem has been highly indicative of the schizophrenic mental processes within. It’s been winking at me for the past hour or so. At times it is peaceful and appears a solid green, this is when I like it the best. At times it gets angry with me and shuts off. At other times, it goes crazy and flashes invective at me in a code that I cannot understand. It’s not Morse, I did my Code Practice in the high roofed attic that housed the Coimbatore Amateur Radio Club, more than a decade and a half ago, and I haven’t forgotten. Yes, it’s true that electronic equipment have rights, that they can’t function like mindless machines day in and day out, that their masters must be considerate towards them – BUT THAT’S NOT WHAT I PAID FOR, DAMN IT. I seem to have gotten my message through, because the DSL light is now a bright green. At least for now. I feel like a manager – but yes, we all have to do evil things now and then.

Tomorrow I find out what it takes to get a BSNL connection

QOTD

The last words of Evariste Galois – Ne pleure pas, Alfred! J’ai besoin de tout mon courage pour mourir à vingt ans!

Translation – Don’t cry, Alfred! I need all my courage to die at twenty!

This and that. More of “this” than “that”, though.

The room is dark save for the glow from the monitor on the table where I sit, as I type this. My better half is engrossed in Taarein Zameen Par, an Aamir Khan movie that I refused to watch. The last AK movie that I enjoyed was Dil Chahta Hai, and I intend to leave it that way. The notes from Schubert’s Impromptu No. 4 in A Flat waft through the excellent JBL Duet speakers perched atop the metal and plastic box that houses, among other things, an SMPS. I’m a dedicated audiophile, not much of a speaker snob – but even so, I find myself in a self-congratulatory mood whenever I chance to look at my latest acquisition.

Thanks to the JBL, I’m rediscovering many forgotten pieces from my music collection. The speakers are truly a good buy, though they’re a tad expensive. They don’t sound bad even when I push the volume control to near maximum – I’m impressed! They also deliver reasonably good bass, midrange and treble.

One of the first pieces that I try out on a new piece of audio equipment is the Overture from Mozart’s The Marriage of Figaro, partly because it sounds good regardless of the quality of the equipment – one has to have outrageously bad speakers to make the Eggtimer Overture sound bad. Picture then, my state of pleasant surprise when I could actually feel the violins kick in after the the horn and the clarinet! The notes from Satie’s three Gymnopedies were clear and distinct – truly piano e forte. I’d given up listening to my extensive Chopin collection ages ago, for lack of good speakers. The last pair (or should I say triple?) that I had was the Creative Inspire 2.1. Though a subwoofer was part of the package, it did precious little for me, the music was just louder and maybe there was good treble. A close relative did me a great favour by (unintentionally) knocking the subwoofer off the bookshelf where it was located. I did go without speakers for the better part of a year, before splurging a little money on these two babies. Thankfully, I did have the Sony headphones that my wife had thoughtfully gifted me on a birthday a few years past. That ensured that I did not go without music. The head tires of headphones, however.

I started my day yesterday with Astrud Gilberto, and ended it with Zakir Hussain. A Saturday well spent! My hitherto infrequent listening sessions at home have now become more frequent, and I’ve recovered sufficient enthusiasm to go hunting for that elusive Manuel de Falla CD. I would love to listen to El Sombrero de Tres Picos, now that I have a decent pair of speakers.

A few precious hours remain of this Sunday, and then the grind starts all over again.

One of the Funniest Videos I’ve ever seen

I haven’t laughed this much in ages.

Silence! I Kill you!!

Stuck.

I’m stuck. This is probably trivial, but I’m just not able to get it. Yet.

Consider , with addition and multiplication defined thus – , the quantities in parentheses being ‘ordinary’ addition and multiplication. Halmos [1] then asks his readers to show that is a field if and only if is prime.

It’s fairly straightforward to show that if is a field, must be prime – one way to do this is to show that if is composite, then any that divides will not have a multiplicative inverse. Another way is even simpler – is the minimum number of times must be added to itself to produce . Consider . Now, . Also, . This means that either or , which is a contradiction. (The second “proof” is more elegant than the first, but is unfortunately not mine.)

I’m stuck trying to show that being prime implies that is a field. The only thing that needs to be done is to show that a multiplicative inverse exists for all ; in other words, such that .

Let’s see, there’s only a day’s work left before the weekend. Maybe a strong shot of coffee on a chilly Saturday morning will do the trick. I peeked into Halmos for a short respite from a few dry sections in H&K, and look at what happened. It does feel a little embarrassing to admit that I’ve spent more than a day on this. Sigh. Okay, not quite a day – because the only time I get to spend thinking about this stuff is early in the morning and late in the evening. Ha. Sigh. Oh, the things that I left undone when I was young.

Update [06 Jan 2008]:

Nothing yet. Thought about this half-heartedly for some time. Trying to resist the temptation to google for the answer. Crap, it looks like you either learn these things when you’re studying, or you don’t at all. Let’s see. Anyway, for the time being I’m just going to go ahead. I’m happy to know that the characteristic of a field is either zero or a prime number.

Update [09 Jul 2008]:

Thanks for your comment, Guppy! Both the times that I tried to respond in a comment, the comment got mangled. Here’s what I was trying to write:

I was thinking of a proof using Euclid’s algorithm, like so:

, prime and .

Hence we can find integers such that

The rest follows… but I’m not really happy with this proof, I think I’ll give the Guppy Method a go.

—
[1] Paul R. Halmos. Finite Dimensional Vector Spaces. Springer, 1974.