Pulling into St. Hilda’s; off of The Plain last week …
Here’s map of my route…
The Crucial bit is where I’m leaving the The Plain, passing the Iffley Road, but then heading into Cowley Place.
Now, I was always taught to indicate *only* when you were adjacent to the previous turning – which in my case, was Iffley Road. Whilst I realise that the distance between those two roads is ‘slight’, it’s A) better to obey the highway code in case of an accident, and B) if I were to have indicated opposite the Cowley Road, and then crash into something coming out of Iffley Road; well, it’d have been my fault.
So, there I was taking it very easy around the roundabout, and then signalling left as soon as I was able – opposite Iffley Road; and there he was too; a damn cyclist, evidently late for a lecture, or just ‘pumping peddles’ in training for a possible trip in an Oxford Eight. I saw him, and hit the brakes, and he saw me, and did the same. Now, four disk brakes at a speed deemed below their mildest interest vs. 2 times 4 wet rubber blocks against a wonky wheel made of tinfoil. Guess who won? Yes, I pulled up – having done nothing wrong; saving his life perhaps. Was I annoyed? No, Was I annoyed when he gave me a ‘you wanker’ look through the rear end! Yes!
So, I wound down the Window and shouted ‘What!?’, ‘What’s your problem?’
He replied, ‘You indicated too late!’
Now, let’s just recap a bit on the turning I wanted. Probably, coming down from the High Street, 50% of traffic goes on to the Cowley Road, and 49.9% goes onto the Iffley Road — um, very few cars turn into what is actually a dead-end street, but that happens to lead to an Oxford College. ‘I indicated too late? Rather than you never expect a car to go down this road, and don’t even bother to look 99.9% of the time! I’m a driver who sticks to limits; whilst you’re a young man who’s late and doesn’t usually encounter someone coming around that roundabout doing a 270. And, even in that 0.1%, you either beat them, or they beat you — yet you say ‘you didn’t indicate early enough’!’
So I described how I could have not have indicated any earlier, as the Iffley Road turning is quite stupidly close to the one I wanted. To be fair, given that most people never go this turn, it was a reasonable bet that I wouldn’t! Still, if it hadn’t have been good brakes – and my expecting an idiot to arrive at any moment, I would have ‘had him’ – but there he was giving me that ‘you wanker’ look. We exchange another few words about how he’d been lucky, and about he was a safe cyclist, and I just decided that there were too many witnesses to my killing him!
Imagine tossing a fair coin successively, and waiting until the first time a particular pattern appears; say HTT. For example, if the sequence of tosses was HHTHHTHHTTHHTTTHTH, the pattern HTT would first appear after the 10th toss.
Ok, now let’s take two such patterns – HTT and HTH. Given both these sequences, and a lot of trials [where you conduct this, "it first appears when" experiment, and then average the number of tosses], is it more likely that you’ll:
- hit HTT in less tosses than HTH;
- hit HTH in less tosses than HTT;
- find that the number of tosses is the same?
Most people [many mathematicians amongst them] will pick the third option. Surely, any such pattern is equally likely to show up in some yet to be discovered average number of tosses!
Actually, it’s not the case – that they’re equally likely. In reality the average number of tosses required to see HTH is 10, whilst for HTT it’s 8! How can that be???
Let’s see why.
Note that HTH overlaps itself, i.e., if you got HTHTH you’ll find that you’ve got two occurrences of the pattern in only five tosses, i.e., HTHTH and HTHTH. Ah, so doesn’t this sound like HTH is more likely then, rather than the other way around?
Well, with HTT there isn’t such an overlap – and it turns out – perhaps unintuitively – that that’s important; in a way that leads to HTH‘s downfall. So, let’s run a couple of experiments to see how this works.
Let’s go looking for HTH
Best scenario:
| Toss |
Result |
Comment |
| H |
1st token in our pattern |
excellent start! |
| T |
2nd token |
quite excited! |
| H |
3rd token |
We won! |
Second best scenario:
| Toss |
Result |
Comment |
| H |
1st token in our pattern |
excellent start! |
| T |
2nd token |
quite excited! |
| T |
|
Bugger!
Now we’ll need to continue tossing the coin until we see an H; as that’s the first token in our sought-after sequenc |
Now let’s go looking for HTT
Best scenario:
| Toss |
Result |
Comment |
| H |
1st token in our pattern |
excellent start! |
| T |
2nd token |
quite excited! |
| T |
3rd token |
We won! |
Second best scenario:
| Toss |
Result |
Comment |
| H |
1st token in our pattern |
excellent start! |
| T |
2nd token |
quite excited! |
| H/H |
|
Bugger!
However, and this is the important bit, at this stage we don’t need to toss the coin again in order to get to find our starting token – we just threw it – an H! |
If you doubt any of this, here’s a little simulator I wrote [CoinToss.zip contains CoinToss.exe].
Watched 21 last night – not a bad film, in fact, regarding entertainment vs. cost value [it ran us just £3 from Matalan!] it was rather good.
The film is based upon the MIT Blackjack team, and as I’ve read/and-seen quite a lot about them before, I was quite happy to have the film thicken the plot [maybe that should be 'have one'?] – and there’s a nice twist or two at the end. As to the film’s inspiration, you can’t do much better than watch the BBC Horizon documentary on this:
Making Millions the Easy Way
I wish ‘Oxford types’ would get up to stuff like this [of course, they might do (would they tell their lecturers?)]; it’d be so much more fun!
Probability
I was quite pleased to see some probability stuff in the film being partially explained, i.e., their running through the Monty Hall problem [although the implied cleverness of the student here is a bit hard to swallow really].
Anyway, here’s the problem:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the other two, goats. You pick a door, say number 1, and the host, who knows what’s behind all of the doors, always opens another door – to reveal a goat – let’s say that’s door number 3. He then says to you, “Do you want to swap?”, i.e., swap your initial choice of door number 1, and change to door number 2? The crux being – is it to your advantage to swap?
In the film, the problem is presented in this clip. By the way, the answer is in this too, so if you want to think about it, get ready to hit the pause button at the 44s mark!
The explanation I find that works quite well here [and I've had my Oxford stats students scratching their heads over this problem initially (as do most people I believe)] is:
Given this scenario: when you pick a door, you’re more likely to pick a goat-door than sole car-door, i.e., you’ve a probability of .66 [or 66% chance if you prefer] of picking one of the two goat-doors vs. the only car-door. Hopefully, that’s obvious.
So, if chance [substitute luck of the draw/fate/the odds/divine-intervention ...] did the right thing here, and you picked a goat-door, you know with a decent probability that the car is behind one of the two remaining doors – but which one? Now, when the host reveals another goat behind one of the two remaining doors, the car’s obviously [again, if the odds etc worked for your initial pick] behind the other door!
Basically, it comes down to this: if you picked a goat-door initially [which you will 66% of the time], by swapping later, you’ll always win the car. Conversely, and given once again that you initially picked a goat-door, if you don’t swap, you’ll lose 66% of the time. Or, one other way … by swapping, you’ll only lose if you picked the sole car-door as your first pick [which you're likely not to have done].
Update: Just found a nice little simulator of this [Internet Explorer only] at http://www.grand-illusions.com/simulator/montysim.htm
Just pondered how many shares I’d have to sell to pay for one term’s worth of schooling for my son. Roughly 80,000.
The depressing bit is that when these were ‘new’, the same amount would have raised enough to have bought me a new Ferrari!
Some things in life are truly not very fair!!!
BUT, at least – AT LEAST I was a millionaire once. And I *could* do it again – I’m sure. But, do you know what, I don’t want to or need to – a very much stress-free and life with Harriet is enough for me … actually, for anyone who might have Harriet for a partner – well – it should, really should fullfill their dreams.
At Oxford Geek Night 10, I’m giving a talk – if you can call it that; as actually it’s more like an ‘elongated cough’ … it’s a 5 minute spot! I mean I’ve told jokes that were longer than that [and if you weren't there, 'yeah': well - they were actually very well received! {for geek jokes}]. However, what can one say in five minutes – esp. when one has lots to say on the subject at hand? Ok, so it makes one ‘concentrate’ – but what to leave in and what to leave out? FIVE MINUTES! [G]eeeeek!
So, I’ll be [speed] ‘talking’ on some subset of subset of subset of subset of the Windows 3.0 development experience [mainly] … you know the kinda thing: ‘hidden stuff’ [oh how we wanted to switch some stuff on in the final build!!!]; stuff that went into its development; stuff that certainly *wasn’t* appreciated at the time! Blah …
However, I think folks might be more receptive now – but we’ll see!!! Blah again!
I’ll be taking a few ‘trophies’ along though …. like a few things I made sure I ferretted away at the launch on 22nd May 1990 – ahem – several copies of the ‘on the day’ [and for one day only] Windows 3.0 box – complete with the ‘I witnessed the Event’ stickers. Oh, and my ‘Magician’ shirt! Side point: I also have a ‘MakeProcInstance Spoken Here’ shirt somewhere I think — um, maybe – I emptied what was probably a fair fraction of a quarter of a ton of old Microsoft shirts into Oxfam’s clothing recycle thingmy a while ago – of course I did have a little ‘I bet they’ll be collectable sometime’ in my mind; but, hey, there ya go! At least I’ve kept the very personal ones.
I do hope it goes well, and that I get some very ‘deep’ questioning – esp. from the girls! Hey, that’s OK – Baby Love‘ll be flying back from ‘Up North’ while I’m in Oxford!
Bloody hell!
Just been watching the Royal Institution’s Christmas Lectures and saw a demonstration of a tool called Dasher.
Very cool, but a bit of a kick in the nuts, and a wake-up call for me really. The reason? Well, I had a system doing more or less the exact same thing in 2000 [it was better than what was demonstrated too]! I even showed it off to various Computational Linguistics folk at Oxford [who said "nice, but" ... [who'd use it|so what|it runs on Windows!|you've got too much spare time on your hands|etc]].
Crap!
I love Oxford [University], and, although I’ve published this more locally before, I thought I’d make it more public now. It’s probably of very little interest to non-Oxford people, but, you never know; it might give someone ‘out there’ a laugh [or provide vital information to a future Oxford applicant perhaps?]
Oxford University Terminology.
Let me know if you’ve got any questions!
A new series, Britain from Above starts on the BBC one this Sunday at 9.00pm.
In the main, GPS data is used to reveal traffic-information; on the sea [through the Dover straits], in the air, and even by London cab-drivers. The GPS data are overlaid, and visualised against a backdrop of the country. Additionally, there’s an interesting bit showing how the telephone system lights up during a working day.
A taster clip on the programme is here.
Going back to taxies, it reminded me of a piece of game-theory software I once wrote for a professor of economics here at Oxford. He had too many variables for which he/we needed to find some sensible constraints/limits for, or, better still, turn into constants! The game was about n cab-driver’s choice of strategies, as they drove around Belfast … such that they weren’t A) robbed [of their cash] B) robbed [of their cash *and* their taxi] C) shot, killed, i.e., robbed of their cash *and* their taxi *and* their life] You get the idea. The game-theory bit worked alongside a social sciences experiment examining moreorless the same thing [except that their experimenters had to be in Ireland].
Anyway, watching the clip, I couldn’t help but be reminded of that system, as it played itself on our cluster many 1000s of times a second, in either role; the cab-driver or the robber [and later the police], and in how it might suddenly switch into some very complex behaviour; perhaps as a result of a robbery, generated randomly by the system. Oh, fun times indeed!
One of the cool things about being at a university [still] is that people discard rubbish that’s someone else’s ‘treat’.
Recently I found a ‘Programming Languages’ Volume 2 manual for the PDP-8 – and it’s become my essential bedtime reading for now.
The book’s full of great stuff about how you should ensure that you’ve a teletype attached, and that you’ve got the steam-pressure just right before turning the thing on in the first place!
It takes me back to a time when programmers were, um, ‘novel’, men were ‘chaps’ and girls wore petticoats [actually, I got a bit carried away there!]
On languages, the book talks mostly about Focal; which I’d forgotten about altogether [a blessing really], here’s the Focal code for the Towers of Hanoi …
I loved the PDP-8 though – keying in the bootstrap and forgetting to load the punched-tape was a great way to spend a half hour or so [oh, how I WOULD LAUGH at times like those!]
If you fancy playing with a real PDP-8[E] albeit remotely, then have a look here [you can even watch the machine operate via a webcam]: http://www.pdp8online.com/run.shtml
Having recently dropped his old one in the English Channel [don’t ask], one of my friends just emailed me – would I please email him with my phone number; so that he could re-enter it?
You know, in this age of technology and interconnectiveness, phone numbers really suck! Aside from the example above, here’s another ‘why’: I’ve recently changed network operators from Virgin to T-Mobile, and, whilst I’m very happy about changing operators, I was more than a tad disappointed that it took over a week to have my number transferred from one operator to the other – it’s MY number, so why doesn’t it just move to my new phone with ME?
What we need is some sort of DNS [Domain Name System] for phones.
DNS is what your computer uses when you want to see, say, the latest BBC headlines. The BBC’s website actually sits at the end of a number – just like a phone does. In the BBC’s website case, the number is 212.58.253.73, and, if it helps, you can think of the various parts of that as being country-code, area-code, and then the number [although they’re nothing of the sort]. Now of course, you don’t want to have to remember 212.58.253.73 when you want to check the BBC news, and thanks to DNS, you don’t have to.
When you enter www.bbc.co.uk into your browser this easily remembered ‘phrase’ – www.bbc.co.uk – is resolved into the ‘internet address’ 212.58.253.73 via a DNS server. If you like, DNS is a directory-inquiries service for computers: you send it www.bbc.co.uk, and it sends you back 212.58.253.73. Once that’s been done your browser knows the BBC’s number and from that point on it sends its requests to 212.58.253.73 i.e., ‘www.bbc.co.uk’ is no longer relevant. If you’d like to prove this – that your browser/computer uses these numbers, enter http://212.58.253.73 into your browser and see what happens when you hit enter [or just click the link].
Another nice thing about DNS is that if the BBC changes its internet address it just has to update its entry in your DNS Server. So, if the BBC changes its number, www.bbc.co.uk will be ‘automagically’ pointed to the new address.
Now let’s think about phones again.
The friend that lost his phone had his own mobile-like ‘DNS’ on his phone – although he had to create and manage it manually: it’s usually called an ‘Address Book’ or ‘Contact List’.
When he last got my telephone number he created an entry in his phone’s book/list for me, e.g., Name = Peet, Number = 07883642639. Then, whenever he wanted to call me, he didn’t have to recall my actual number, but queried his phone’s ‘DNS’ instead – by asking for Peet’s number. Then, just like the real internet DNS, his phone resolved Peet into 07883642639 and from that point on his phone used the numbers to make contact.
But what happened when my friend dropped his phone into the briny? Well, once he’d shelled out for a new phone he had to email all his friends, and ask to be sent ‘reminders’. His ‘DNS’, like his old phone had gone to meet the fishes.
So, how might this be fixed – I mean, why in this day and age of interconnectiveness are we still stuck with having to manually manage our phone’s ‘DNS’? It’s archaic when you think about how the world-wide-web does it!
So, to the ‘fix’.
Ideally the solution would be to do away with phone numbers, and instead use something unique – ‘something like’ a special email address – that’s ‘mapped’ to a person’s phone? For argument’s sake, let’s say there’s a mobile.ph domain and say that I’ve registered peet.morris@mobile.ph, and then linked it to my mobile number, 07883642639.
To call me you’d simply punch in peet.morris@mobile.ph and, as I’m not ‘ex-directory’ my phone would start ringing. Nice! Of course if I didn’t like any of this, I’d simply be ex-directory [no entry at mobile.ph].
All this would need is some sort of directory-service [a single table at its simplest], i.e., your mobile network-provider realizes you’ve not sent it a number [easy] and all they have to do is lookup the person’s phone number in the table and connect you.
Isn’t this harder than simply storing Name = Peet, Number = 07883642639? Three responses. 1. how about if I change my number? 2. what happens if you lose your phone? 3. what if you don’t actually know my number in the first place? By inserting an indirection-point [the table maintained at mobile.ph here] none of the above is a problem – and we can effectively forget using unique numbers to identify people, and start using names instead – just like the real DNS does.
So, why don’t we do this?
Problem 1:
The Directory
As I’ve said, in its simplest case this is just a lookup table, and it’d be easy to do if my network-provider had such a table – and that’s one of the hard bits – having this regulated and centrally managed [and this is totally avoided in the rest of this mumble].
However, let’s assume for now that such a service exists: how about privacy issues?
In order to call me this way you’d have to know my special registered address – that is ‘registered in the lookup table’, well, this surely isn’t totally desirable. After all if we know about mobile.ph my registered address is rather easy to guess [and that’s the whole point] – but, do I really want to use that address – and risk any Tom, Dick or Harry [or double-glazing salesperson] being able to find/call me; anytime?! Well, yes, I probably do want peet.morris@mobile.ph and so this DNS-thingmy would have to be more complicated [how do we do the ex-directory thing for example], and that’s another problem.
You see in order for it to work great I’d have to add some extra data to the table, perhaps that only persons x, y, z, … should be able to gain access to my number. I want to be found by ‘friends’, but do I want to have to maintain this list myself! Sure, I don’t want anyone calling me, but perhaps there are people I haven’t remembered to add to the permissions bit of the table; but would want them to find me anyway?
Perhaps we should bring some AI [Artificial Intelligence] to this? Perhaps some intelligent agent could scan my existing call-history, and maybe my old emails as well – and maybe ‘it’ could discover whom I’d like to be able to call me? Maybe it could maintain my data?
Problem 2:
Uniqueness
The trouble with peet.morris@mobile.ph is that where there is only one bbc.co.uk [and it’s probably the one the majority of people in the world would assume it is], there are plenty of people called Peet.Morris – but only one peet.morris@mobile.ph entry in the lookup table. Would I want to tell people I’m peet.morris6236@mobile.ph; because peet.morris@mobile.ph has already been taken? Well, if we were happy with that we might as well stay as we are as we’d be back to having to remember numbers again!
To put this another way; we’re used to having numbers arranged in arbitrary ways: plus it’s easy to identify things/us using unique numbers – whether it’s your phone, your Visa card or something else. Numbers are great when it comes to identifying single items in a set, i.e., in the set of all telephone numbers only 07883642639 is MY mobile phone number. On the other hand letters have special and ‘popular’ orderings [plus a few ordering rules], e.g., as a name, I assume Peet Morris is rather more common than its backwards version of Teep Sirrom! Additionally, people usually have short names – think of Chinese names especially, and if you’re old enough; see if the joke about Wing Wong and Winging the Wong number still brings a smile to your face!
Using names as unique identifiers we’d get masses of what computer scientists call ‘name collisions’ – and whereas computer scientists might use things called ‘hash tables’ etc to get around such problems, humans can’t [believe me].
So, are we stumped on the idea of having unique identifiers for people? Well no[ish] I believe.
Why don’t we just use our normal email addresses, after all peet.morris@comlab.ox.ac.uk uniquely identifies me right now. But hold on, comlab.ox.ac.uk is tied to me via my job at Oxford – how about if I leave and say go to that ‘Poly on the Fens’, I’d most likely get peet.morris@cam.ac.uk there – and that’s just like changing my phone number: it’s hard to discover, and not necessarily unique [imagine that after I leave, another Peet Morris joins the comlab in Oxford]!
What we need are email addresses that:
- are unique
- stay with us
- are easy to remember
So, how about using a ‘for life’ email address – like the one I have at Gmail [Google’s email system] – there I’m known as peet.morris@gmail.com. Say I use that one then. My Gmail address isn’t tied to a job so if I leave Oxford [God forbid] I’ll still keep that one – surely I could use that?
Well no, as we’re back to the peet.morris6236 thing again – but this time the suffix is @gmail.com instead of the mobile.ph I used earlier. For example, I just tried signing up to Gmail as a new user, and said that I’d like peet.morris as my email name. Google’s response – “the computer says ‘no’” [Little Britain reference]. Instead Gmail asked me if I’d like one of the following:
- peetmo
- peemor
- pt.mrrs
- peet.morris12
- morris.peet
Hmmm. Well, I guess telling someone they can call me using peet.morris12@gmail.com is better than if I’d given them 07883642639 – it gives them a fighting chance of remembering me – but it’s ‘sub-optimal’.
Brian Clegg [‘Brain’ Clegg] has a quite lovely idea on the uniqueness thing though –
“I think the format problem could be partly solved by restoring the medieval concept of ‘of’ as part of a name. The trouble with @ is that it’s location specific. When I move I have to change my @. So I could be brian clegg#rochdale (where I’m using # as ‘of’) or brian clegg#wanborough if I wanted. Note that this doesn’t refer to where I live or you would have to keep changing it. It’s more like Lord X of Shugborough – you can choose wherever you like as long as people associate it with you and they can lock it in memory easier. (Note, by the way, the space – I think it’s pathetic that email addresses can’t cope with a space. We’ve managed in English for a long time.)”
“Of course there may be duplication still – the Brian Clegg who regularly beats me at the top of a Google search is a company based in Rochdale, and there could be one in Wanborough, Mass (if there were such a place). So I would add an optional qualifier. So if I didn’t get in first I could be brian clegg#rochdale/author or brian clegg#rochdale/bignose or whatever.”
P.S. in case you’re Tom, Dick, Harry or a salesperson, my mobile number isn’t 07883642639!
Here’s a link to brian clegg#rochdale/bignose‘s blog
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