Bellerophon symbol, variation 7
Saturday 3rd October 2009

Oh, I think I meant to delete a few more of these. Never mind.
img_2626.jpgimg_2630.jpg The stuff I wrote later on about not being bothered to upload the photos won't make much sense now, as I've now got round to it. Ah well, whatever. Yep, so . . . here we are, in Bolton-le-Sands. Blah.

an accreted terrane of heterogeneous rocks
God, it's such a pain having to name these entries sometimes. Wikipedia eventually gave me an interesting article about the Franciscan Assemblage, so that'll do. Anyway, I think the morning/afternoon of today was fairly typical of a Saturday at the moment - loads of tidying up and cleaning. Yawn. Didn't we go out for a walk in the latter part of the afternoon? Probably. I'm not sure. I think we went to Bolton-le-Sands or somewhere like that. We probably took a few photos but my camera's too far away right now (several metres away). Matthew (friend from school, now living in Chorley; I'm saying this to differentiate from any other Matthews I know) popped round in the evening, not long after 7pm. This was the plan: wander into town, get a meal, followed by a few drinks. M****** was to stay at home, baby-sitting. So yeah . . . we had a beer and then headed for town. Matthew fancied something Thai/Chinese (as in food), and as M****** had recommended this new (ish) Thai restaurant on, erm . . . a street near The Bobbin . . . we went there first. They were full so (plan B) we went to the Sun Café instead . . . they were almost full there as well, but they had a couple of tables free, so it was all fine. I can actually remember what I ate there and probably what Matthew had as well . . . but it's really not that interesting, surely. Suffice to say, food was up to it's usual high standard, although my penne arrabiata wasn't really spicy at all. This is probably a fault in my taste buds rather than the food. So yeah . . . it was all fine. Then I think we went to the John O'Gaunt for a pint of bitter. There wasn't a jazz band playing (thank god) and it wasn't really all that busy but it just seemed a bit dull, somehow, so we left after that pint. Then I think we went to the Sun (the pub). It was heaving in there and queuing up to be served was an odd experience . . . it probably wasn't as long ago as I think but it seems like years since I last had to queue to be served at a pub on a busy Saturday night. So yeah . . . I think we just had the one drink there and then decided to wander home, in a slightly roundabout manner. We walked past the White Cross, heading towards Prospect Street, when Matthew had the idea to walk through Scotch Quarry. I think we would have walked through here many times whilst at school, all those years back. It wasn't quite pitch black but it still took a while to find the steps leading out of the quarry. Then we had to clamber over the wall of the University of Cumbria in order to maintain a diagonal path across their fields (quickest route) and then we were pretty much home. The wood-burner was still going so I threw some more wood in. And that was about it . . . another beer, finish off the Glenmorangie (well, there was hardly any left) and off to bed.

Sunday 4th October 2009

Somewhere up near Scorton
We invited over Helen and Stu for lunch. After lunch, we drove over to Scorton (or, specifically, Nicky Nook) for a walk. After the walk, we went to some café thing, that seemed to be also masquerading as a garden centre, some kind of gift shop and maybe a licensed bar as well. All very odd.

Tuesday 6th October 2009

Beer syphoned!
So, tonight the beer was syphoned from one beer bucket to a clean, sterilised similar beer bucket. This took a lot longer that I would have thought, probably owing to the small difference in altitude between one bucket and the other. Erm . . . I'm kind of guessing there. Anyway, all the gunk from the original beer bucket was left out, which was kind of sad (just because it's gunk, doesn't mean it's all bad, surely?! Surely?!), as there was quite a lot of it, and I couldn't help but wonder if beer gunk had been given an unnecessarily bad name . . . I hate to waste beer and wasting beer gunk . . . well, I don't whether that's good or bad . . . but, hey, I went with Lucy's advice and left it out. The beer in the new barrel is now looking decidedly clean and gunk-free. Now I just need to leave it for another week or two.

Saturday 10th October 2009

found this on an old SD card
IMG_2692.JPGSo yeah . . . I was clearing up and re-formatting old SD cards when I stumbled upon this. Thought I might as well keep it. Shame I look a bit shifty and R****** has his eyes closed, maybe that's why I never uploaded this. Ah well.

Sunday 11th October 2009

Am bless E dee
Today we went up to Ambleside to see M******'s grandparents. Today was one of those odd days where there was little or no rain. Blimey. That's quite a first for Ambleside, at least in the times I've been there. So yeah . . . we got there at about 11:30, pottered about for a bit (A****** and I playing in the garden), had lunch . . . then, in the late part of the afternoon we went for a quick walk towards Sweden Bridge, before setting off for home . . . then back again (fortunately before we had left Ambleside itself), as someone had forgot their handbag. Hmmmm.

Friday 16th October 2009

Making coffee, getting the children's breakfast sorted out . . .
img_2740.jpgimg_2741.jpg . . . and taking pictures of the fantastic sunrise this morning. I saw the tiny slither of the moon and saw the sky and thought, "Yeah, why not?" The moon disappeared about 15 minutes later, swamped by the light of the sun.

Saturday 17th October 2009

Does 0.9 recurring = 1?

img_2758.jpgimg_2760.jpgimg_2762.jpgimg_2763.jpg This very question was bugging me recently (well, not that much). So, imagine you have 0.99999... followed by an infinite numbers of 9's. For the sake of brevity, I will use three dots to represent recurring. Hence, 0.9... = 0.9 followed by an infinite number of 9's. But does 0.9... = 1? On the face of it, you would think, "Erm, no. 0.9 recurring is very close to 1 but it's not actually 1." However, consider the following proof (many thanks to Tim for this):

Let s = 1 + x + x2 + ... + x{n - 1} (Equation 1)

Then (1 - x)s = 1 + x + x2 + ... + x{n - 1} - (x + x2 + ... + xn) = 1 - xn

So, if I divide both sides by (1 - x),

s =1 - xn  (provided x is not equal to 1)

1 - x

Now suppose -1 < x < 1. Then xn tends to 0 as n tends to infinity, so s tends to 1 / (1 - x) as n tends to infinity, i.e. 1 + x + x2 + ... (going on for ever) = 1 / (1 - x). Putting this down in an equation:

s =1  (for -1 < x < 1) (Equation 2)

1 - x

With me so far? I found it easiest to go through all of this on pen and paper. Anyway, assuming all this makes sense, we can solve the equation with a specific value of x. So, let's let x = 0.1 = 1 / 10.

So, according to equation 1:

s = 1 + x + x2 + ... + x{n - 1} = 1 + 0.1 + 0.01 + 0.001 + ... = 1.1... (that is, the 1's go on forever)

Also, according to equation 2, we have:

s = 1  (Equation 3)

1 - 0.1

Rearranging slightly, we get:

s = 10 / 9

But we already know what s is from above. s = 1.1..., so therefore:

1.1... = 10 / 9

Divide both sides by 10, hence: 0.1... = 1 / 9

Multiply both sides by 9, hence: 0.9... = 1

img_2749.jpgOf course, it should be obvious that this equation only holds when we have an infinite number of 9's (but surely that's implied by 'recurring'). Recall how we were able to exclude the xn term as this tended to zero as n tended to infinity (for -1 < x < 1). So perhaps our equation could also be written thus:

0.999999 (i.e. number of 9's = n) → 1 as n → ∞ (the right arrow symbol, →, denotes 'tends to' or 'approaches').

So, yes . . . I think 0.9 recurring does indeed equal 1. That's the weirdness of infinity, I guess.

Sunday 18th October 2009

A****** in black & white
img_2778.jpg This picture was taken several weeks prior to me creating this entry, so I can't say much useful about today or this picture.

Saturday 24th October 2009

Beer bottled!
Well, that's half of it (i.e. 20 bottles) bottled anyway. M****** and I tried a little bit of the homebrew and decided it definitely needed more sugar; it was just way too . . . bitter. I added a bit of a sugar (about a teaspoon) to a small glass of beer and then extrapolated from there. Little bit of arithmetic later and a bit of guess work . . . and I decide to boil up 1lb of demerara (sp.?!) sugar in about half a pint of water and add this to the 15 litres (it's about that, perhaps a bit more) of homebrew. I've just tried another bit and it tastes much better with the sugar. So yeah . . . after a lot more sterilising and rinsing, I carted a load of bottles out to the garage and got busy syphoning beer. There was only one tragedy - one bottle broke as I was trying to use my bottle capper to push the bottle top on. There wasn't much broken glass but I've no idea if a splinter went into the beer or not, so I'll have to discard that. A splinter managed to catch my wrist somehow but it was only a light scratch. So now I just leave them in their bottles to settle for a month or two and then enjoy around about Christmas.

Sunday 25th October 2009

Ah yes, the all-important pictures . . .
img_3174.jpgimg_3175.jpg Following on from yesterday's entry, here are some pictures of the recently bottle beer, in site. Ain't garages useful, eh? There aren't many other places (besides a brewery, I guess), where you can get away with brewing beer. And, of course, a by-product of beer production is CO2, so I get to increase my 'carbon footprint'. All good stuff.

img_3179.jpgimg_3180.jpgimg_3183.jpgimg_3184.jpg So this is a boat going from Ambleside to, erm . . . Bowness-on-Windermere?! Was it? Yes, I think so. It was a boat with a licensed bar. How fantastic is that? There were a few pictures like this (i.e. the one of the far left). I kept this one because of the random, orange person in the background. I'm vaguely wondering what they're looking at . . . someone to the left of me? Turns out it was M******. Hmmmmm.

Monday 26th October 2009

Somewhere round about Grasmere probably

Tuesday 27th October 2009

A wander around Ambleside and then Brockhole

Wednesday 28th October 2009


Thursday 29th October 2009

Tarn Hows and Coniston

Saturday 31st October 2009

img_3430.jpgimg_3433.jpgimg_3436.jpgimg_3439.jpg This year's jack-o'-lantern was constructed by M****** using a turnip. I don't think there were any pumpkins left by the time we got to the local root vegetable vendor. But not to worry. I think we live on one of those streets were some families get quite into the whole Hallowe'en thing, decorating their houses, porches, drives, etc., with various bits of Hallowe'en ephemera. We just opted for the black light, as seen in these two photographs.