November leaves

November has been so mild that many of the trees still have their leaves.

apple tree

maple

That's not to say there aren't many leaves on the ground, and in the water.

leaves in the rill

leaves surrounded

It's not all leaves.

this tiny mushroom in the path has caught a thread

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Venus

Venus is very bright tonight.

16:52 GMT, looking south west; unretouched phone photo

Once I had checked it wasn’t an aeroplane, I was sure it was Venus.  But I thought I’d check with Google Sky map; it’s always nice to have an excuse to play with that app.  I fired it up, and pointed my phone at the bright light.

No, I don’t think so.  And not just because I knew I wasn’t looking south…

I waited a few seconds, until the orientation sensor kicked in properly, and the image slewed round to show:

That’s better!

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with just a hint mackerel

16:10 GMT, looking west

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Spoilers!

Wow!

I had been carefully managing my expectations, because The Day of the Doctor couldn’t possibly live up to the hype, excitement, and full weight of the 50 year history, could it?

Yes it could.

the 11 Doctors – but actually it should be 12!

We now have a continuous timeline of regenerations, filling in the gap between McGann and Ecclestone.  Which leads to the question: what is the official numbering now?  (That certainly promises oodles of fun for pedants in future pub quizzes!)  And the problem to do with the 13th regeneration has been acknowledged, so we have that to look forward to.

But most important of all, it is a great story, playing on the existence of time travel and time paradoxes, examining the great Time War and the Doctor’s dreadful role in it.  It is a marvelous episode, full of fun, pathos, wit, momentous moral decisions, and gorgeous nods to the 50 year history, from the cheeky opening shot in Totter’s Lane to the epic final battle around Gallifrey.  Tennant and Smith work excellently together, playing off each other.  In a clever twist it is these somewhat childish later Doctors who are the living with the memory of the terrible deed they have done, while the older, more adult Doctor (Hurt) has not yet committed the act that will scar the Doctor throughout his future regenerations.

Three Doctors – the Daleks don’t stand a chance!

Who would have thought, 50 years ago today, that the future would hold something like this?

So, I wonder: what the diamond anniversary will hold?

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found it!

After trawling through more newsagents than I would like to admit, we now have the full set of Radio Times covers:

Matt Smith found at last

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with apologies to The Four Seasons

November, 1963 (Oh, What A Night)

Oh, what a night
Late November, back in ’63
Was a very special time for me
As I remember, what a fright

Oh, what a night
You know, we never got know his name
But life was never gonna be the same
What a Doctor, what a sight

Oh, I
I got a funny feeling when he walked through the door
Oh, my
That TARDIS, inside was so much more

Oh, what a sight
Materialising: mesmerizing me
Who was everything I dreamed it’d be
So SFnal, what a night

And I felt a rush when the TARDIS sounded thunder
Spinning its light around and sparking my sensawunda
Oh, what a night

Oh, I
I got a funny feeling when he walked through the door
Oh, my
That TARDIS, inside was so much more

Oh, what a night
Why’d it take so long to do what’s right?
Beeb was wrong, but now it’s seen the light
What a Doctor, what a night

And I felt a rush when the TARDIS sounded thunder
Spinning its light around and sparking my sensawunda
Oh, what a night (doo de-do, doo de-do, doo de-do, dee di-di)

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golden anniversary anticipation

We have a small collection of small daleks

standing at the foot of our smaller collection of full sized daleks.

We don’t collect only daleks, of course.  To celebrate the 50th anniversary, this week’s issue of the Radio Times has 12 different covers.

We have 11 of the 12 different covers this week.  Matt Smith had sold out.

These will be added to our collection of other Who-covered Radio Times.

Row 2 has 4 covers from the 40th anniversary, which form a montage.

And now, we have to wait until this evening for The Day of the Doctor, which we will be watching at home on the TV in 2D, the way it is meant to be seen!  We have, of course, already watched the webisode Night of the Doctor, which provides an crucial insight into the timeline, and the number line.

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prediction shouldn't be this difficult

I have previously noted the inaccuracy of some computer predictions.  Tonight I observed how it also applies to cars.

As I started my trip, the GPS said the journey would take 2 hours 20 minutes, and the car instrument panel claimed I had 205 miles until an empty tank.

50 miles, and one hour, later, the GPS said the remaining journey would take 2 hours 5 minutes; more bizarrely still, the car instrument panel claimed I now had 215 miles until an empty tank.

So, it seems that the car thought I had taken 15 minutes to travel 10 miles backwards?

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sequestering carbon, several books at a time XIII

The latest additions:

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this is what happens when you give Computer Scientists access to piped chocolate

We had a Children in Need quiz night at work yesterday.  One round was to decorate a cake. Our team (The Flying Robots) felt that a fractal, with its infinite chocolate complexity, should be a sure winner.

Sierpinski cake

The judges, for some unfathomable reason, preferred another:

double decker artistry

Okay, maybe we weren’t taking it that seriously…

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autumn trees

Walking over to a meeting, I spotted the sun low on the magnificent tree in front of the library.

Magnificent autumn colour (and it looker oranger in real life than in the pic).  Then a few steps further on I saw another tree catching the light:

It was also brighter in real life than here.

Just, wow!

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representations, permutations, visualisations

One of the things I’m interested in is evolutionary algorithms (EAs), and how to make them better.  An EA takes a population of “genomes”, “mutates” (changes a little) and selects (based on “fitness”), and mutates and selects, and ... until a suitably fit answer is found.

A recent advance has been the introduction of “evo-devo” algorithms.  (I’m putting all this biological terminology in scare quotes, because by the time the relevant process has been translated into a computer algorithm, it is so far removed from its biological inspiration as to make a biologist wince, or even exclaim in outrage.)  Evo-devo puts a distance between the genome (the representation that gets mutated) and the “phenotype” (the representation that gets selected based on fitness).  This can help the algorithm’s performance, by allowing simple easily mutatable genomes develop into complex structured phenotypes.

A colleague of mine at York, Jillian Miller, is the inventor of such an algorithm, Cartesian Genetic Programming (CGP).  The genome is a string of numbers (numbers are easy to mutate a little bit).  The string is then interpreted as a network phenotype.  The network itself has inputs and outputs, so is a form of program.

Now, let’s consider permutations.  A permutation of the numbers 1 to N is these numbers in some specific order.  So the permutations of 1 to 3 are: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1).  A string of length N has N! (N factorial) permutations.  N! grows very fast; while 5! = 120, 10! = 3,628,800, and 100! > 10¹⁵⁷.

Permutations are common in computer science.  One classic use is in the Travelling Salesman Problem: given a bunch of N cities, find the shortest path through all of them.  That is, find the permutation of 1 to N that gives the shortest path.  Given there are N! such permutations, clearly we don’t want to try them all.  Although exact algorithms that are essentially more efficient than trying all possibilities aren’t known (and it is strongly suspected that there aren’t any), there are algorithms that come up with very good approximate (nearly shortest path) answers most of the time.  EAs are one such class of algorithms: breed for fitter (shorter) paths.

Permutations as genomes are a bit tricky, though.  A permutation has structure: it must contain all the numbers from 1 to N, and each only once.  So you can’t mutate a single entry: you have to swap two entries, or do something else that maintains the permutation structure. “Crossover” is even harder: how do you take half of one permutation, half of another, and combine them into a valid permutation?  There are various techniques, but they are not very pretty.

Using an evo-devo approach to generate a permutation seems even harder: how do you ensure that your developed system is a valid permutation?  So, for example, with CGP we can have a list of outputs, but how do we ensure that this list is a valid permutation?  (Having a single output that is already a permutation merely moves the problem back inside the network somewhere.)

We need a further representation and development step that is guaranteed to produce a permutation.  Rather than try to get the network to produce a permutation immediately, let’s break it down into two steps: the network produces a list of numbers, then that list has to go through a further interpretation step to form a permutation.  Julian came up with an idea of how to do this: given a list of (say) real numbers (easy to produce with CGP), just sort them into ascending order.  The correspondingly sorted list of the indexes gives the required permutation.  Voilà!

A string of numbers is interpreted as a network, which outputs a real vector, which when sorted yields a permutation

What is happening here is easy to visualise using a technique called parallel coordinates.  A list of N real numbers can be thought of as a vector in N-D space.  But N-D space is hard to visualise if N > 3.  (I find it pretty hard to visualise even when N = 3.)

It’s hard to visualise a lot of dimensions this way

Parallel coordinates do what it says in the name: instead of drawing the N dimensions orthogonal to each other (rapidly running out of ways to do this in our 3D physical space), draw them parallel to each other.  It’s easy to draw lots of parallel lines.  Now plot the N-D point (x₁,x₂,...x_N) as follows: plot the point x₁ on axis 1, the point x₂ on axis 2, and so on, then joint these points together with a line.  The line in the parallel coordinate plot represents the point in N-D space.

parallel coordinates view of a single N-D point

We can use these parallel coordinated to visualise how a vector of real numbers can represent a permutation by its components being sorted into ascending order.

(top) a vector of 20 real numbers, a 20-D point, drawn in parallel coordinates; (bottom) the same vector, with the parallel axes ordered so that the components are in increasing order: the sorted axis indexes are the permutation represented by the N-D point. 

The Python/numpy code that generated these plots is:

N = 20
P = range(N) # indexes
V = rand(N)  # random vector

# plot unsorted vector
for dim in range(N):
    ax1.plot([dim, dim], [0, 1], '0.5', linewidth=0.25)
    ax1.text(dim, -0.2, str(P[dim]), ha='center', fontsize=32)
ax1.plot(range(N), V, '.k', markersize=20)
ax1.plot(range(N), V, 'k')

# sort, and plot sorted vector
P = argsort(V) # sort indexes
V = sort(V)    # sort vector (for plotting)
for dim in range(N):
    ax2.plot([dim, dim], [0, 1], '0.5', linewidth=0.25)
    ax2.text(dim, -0.2, str(P[dim]), ha='center', fontsize=32)
ax2.plot(range(N), V, '.k', markersize=20)
ax2.plot(range(N), V, 'k')

Note that the code that generates the permutation is the single line P = argsort(V): the rest is just plotting code.

Here I started from a random vector, rather than the non-random output of some CGP network.  Sorting a random vector is one way to construct a random permutation, but as far as Julian and I can tell from the literature, this CGP use for representing evolved, non-random permutations isn’t standard.  Julian has been using it for several years in his module on evolutionary algorithms, and will be publishing a paper on some results next year.

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afternoon sunset II

a little earlier than yesterday, and more spectacular

16:18 GMT, looking west

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afternoon sunset

The view at 4:30pm, and it’s still over a month to the shortest day!

16:30 GMT, looking west

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the old and the new

I’m just back from a 2 day residential Theo Murphy scientific workshop held in the Royal Society’s Kavli Centre at Chicheley Hall.  It’s my first visit there, and I can certainly recommend it as a marvellous venue for a workshop: great facilities, marvelous food, and friendly, efficient staff.  The science was great fun: I learned lots of new things, discovered links between seemingly diverse areas, and had interesting discussions over food and coffee.  I’m buzzing with ideas, which is the whole point!

I did the usual “photograph from my bedroom window” thing, which had a somewhat different from usual view:

first day of the workshop, view due east, into the rising sun

Oh, and then I took a photo from the other window in my bedroom:

first day of the workshop, view due south

Blissful.  I found an amusing view from the window half way down the main stairs:

A lovely formal garden, with lawns, paths, clipped bushes and trees, and, just visible at the vanishing point of the path … a wind farm!  The old and the new collide.

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sequestering carbon, several books at a time XII

A rather small haul:

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ubiquitous destruction

I just saw the following on BoingBoing:

The “Destruct Room” in Jack Kirby’s comic book OMAC (1974)
was a place where stressed-out people could act on urges to smash things. 

It reminded me of:

A panel from “The Gabriel Set-Up”, the third story in the Modesty Blaise comic strip,
by Peter O’Donnell and artist Jim Holdaway (1964)

Clearly the urge to smash is universal.

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