Fucking shit day. ‘xcuse the language. A double bill of The Libertines’ Time for Heroes on coming out of Clapham Common tube (with a bit of joyful singing from myself), followed by Otis Redding’s That’s How Strong My Love Is and Squeeze’s Up The Junction put pay to that.

# Matching birthdays

Mat asked me yesterday what the chances were that if 11,000 one-second-long events occurred randomly across the course of a day, two or more would overlap. Even though there are 86,400 seconds in the day to go at, the chances of none of the events overlapping are phenomenally remote.

To make calculations easier, I assumed that events occur on the second rather than starting at the millisecond level. I don’t think this simplification affects the calculations greatly, if at all.

To work things out, it’s easier to calculate the chances that all events happen in distinct slots, than it is to find out the chances that two or more events happen at the same time; take the former number from 1 and you have the latter.

Anyway, the probability that events will not collide is:

1 – ((86,400!/(86,400 – 11,000)!) * (86,400^11,000))

or generically:

1 – ((X!/(X – Y)!) * (X^Y))

where X is the number of slots and Y is the number of events.

This is so close to 1 that it doesn’t bear thinking about. I can’t calculate it, as neither my calculator nor Excel can cope with such large factorials.

The puzzle is very similar to quite a famous birthday problem. If you ask random people in the street their birthdays (day and month only), then you only need to ask 23 people before the chance of having two matching birthdays is over 50%, assuming that birthdays are evenly distributed throughout the year. The fact that there are slight deviations in birth rates throughout the year only serves to increase these odds.

If you ask 30 people, your chances go up to 71%, 40 people gives you 89%, 50 people gives you 97%, 69 people gives you a 99.9% chance of matching birthdays. At school, I shared my birthday with someone in my class of 26 (60% chance) at the age of 10, but also shared the same first and middle name. Not sure what the odds of that are!

(As an aside, the reason I can remember the number of people in the class is that I just realised that after 23 years, I can still recite the class register for that year: Allison, Aslam, Bywell, Caunt, Cheema, Chitsabesan, Crann, Cullen, Greenhalgh, Halliday, Harrison, Howarth, Jackman, Khaliq, McNeill, Mahmood, Mene, O’Neill, Pollard, Riley, Saughman (sp.), Sutcliffe, Taylor, Tilney, Troy, Verity.)

# Kylie, Irene Cara and shuffling

I wonder if anyone I walked past on the Pavement in Clapham could hear I Should be so Lucky or Flashdance (What a Feeling) pumping into my ears yesterday morning? They certainly saw the smile that it brought to my face, amidst those of my miserable fellow commuters. On my Most Played 25 playlist, Tiffany’s I Think We’re Alone Now has just kicked in.

I wonder if people’s setting their iPod/alternative MP3 player to Shuffle as a matter of course is a strong psychological indicator. I would have thought so.

# Tesco’s personal hygiene

Tesco’s operating principles are highly revered, such that everyone in the organisation is geared around, and aligned to, its core values.

However, it seems that they’ve missed out on one particular detail: personal hygiene. For the last two days, very early in the day, I’ve been served by someone whose odour can only be described as rancid.

# The new M&S TV advert, part 2

It inspires unbridled joy in me. My wife informs me that the clothes on display are dreadful, but she’s completely missed the point.

# Today’s emotions

The morning started well. There was a lady who boarded the northbound Northern Line with me at Clapham Common, who was clearly pregnant. The tube was rammed, and I offered to negotiate securing a seat for her. She was genuinely thankful for the offer, but said she was fine standing. Then, when a guy barged on to the train at Clapham North, I reprimanded him, suggesting he be more careful. The lady disembarked at Stockwell feeling pleased. I was both happy for her impending joy at bringing a child into the world, and proud that I’d done the right thing.

Had a meeting with my boss. She was very empathetic and supportive, which made me feel confident and valued.

I enjoyed some banter with a colleague in a meeting, but felt constrained and frustrated at needless bureaucracy and process.

My friend is going through some tough times right now. I chatted to her, and felt sad for her situation, but confident that the tough times will be brief and good times are ahead for her.

And this afternoon, someone tried to close my laptop in a meeting. This made me quite angry.

Finally, I felt despair at the weakness of some individuals in the workplace.

That is all.

# Who needs forums when you’ve got a popular blog?

Matt Cutts asks a question about CSS as a post in his blog, and gets 50 comments in response, in the space of 18 hours. Impressive.

I don’t think my blog is sufficiently popular for me to do away with forums just yet…

# Dr. Aynsley-Green

It was interesting for me to see Dr. Al Aynsley-Green on the BBC news recently, talking in his capacity as Children’s Commissioner about the failure of the education system on autistic children. Dr. Aynsley-Green treated me at Newcastle’s Royal Victoria Hospital as a child; maybe he should have focused on my mild Asperger’s symptoms a little over 20 years ago. Mild??, I hear you cry.

# Short loop across the river

I strained my left calf muscle slightly while running in my new trainers a couple of weeks ago. I think it was down to lack of stretching beforehand, as opposed to the nu shooz. Anyway, my first time back on the road was up in Telford in driving rain on Thursday morning while on a business trip. I followed this with runs on Friday morning and this morning; I’m definitely a morning runner.

On Friday, I did the 6.32km Round Battersea Park run seen here in 28 minutes. I did the 7.28km Short loop across the river run this morning in 33 minutes. I don’t take any technology with me (iPod, heart-rate monitor, watch etc.), so rely on the start and end times according to our analogue clock in the living room; not overly accurate, but it does the job.

I’m aiming to go out three times a week for the next three weeks until the Nike 10km run on 8 October, doing the 9.82km 10km loop across the river run once a week, which I’m currently taking around 47 minutes to complete. (Not sure why, but my maps are not working showing on Firefox; they’re working in IE though. Frustrating!)

If you’ve not yet sponsored me, you can do so from here, all proceeds going to the NSPCC.

# The new M&S TV advert

It’s fantastic. It’s completely fresh, one of the models (Noémie Lenoir) is stunning, and the music (my wife reliably informs me that it is Sailor’s 1975 hit, A Glass of Champagne) is inspired. Not sure which agency created it, but I approve.

As an aside, music has become a far more significant element of TV advertising in the last two years.