If, like me, you download a lot of reading material online (books, articles, papers, etc.), you’ll probably also have run into the frustrating issue that most authors of PDF douments simply haven’t given any thought to page numberings. More specifically, it’s very often the case that although page numbers are graphically included on each page in a sensible manner, they’re completely out of sync with page numbers displayed in your desktop/mobile PDF reader. These are the so-called logical page numbers: they are used in the table of contents, and when you want to jump to a specific page, amongst other things – crucially, they can be specified by the creator of a PDF document. Now, the physical page numbers are simply the counting numbers, starting at one and increasing, and are the same for all documents. Both of these types of page numbering systems are distinct from graphical page numbers, which are the aforementioned visible markings on pages in a document.
FC Barcelona has for some time now been the sole passion I’ve permitted myself in the world of sports fandom. The club has recently undergone a great deal of upheaval, due to the sad circumstances of former manager Tito Vilanova’s relapse with cancer, and a new manager being appointed this year. There has been plenty of both media praise and criticism directed at the Blaugrana of late, though the sensationalist news seems to be winning out, and many who don’t follow the club’s ongoing course through the footballing tournaments now believe that the “Golden Era” of the club’s dominance has come to an end. Regrettably, what has transpired over the past year or so has only helped confirm this view, be it valid or otherwise. Vilanova’s team of the 2012-2013 season kicked off with dazzling form, yet his extensive absences among other factors led to a decline in form, culminating in a 4-0 and 3-0 loss to Bayern Munich in the semifinals of the Champions League that season. No doubt, winning the league with a record of 100 points (tying Real Madrid’s record of the previous year) was an achievement, but it was dwarfed by the humiliating loss to Bayern Munich and the several losses and draws with arch-rival Real Madrid. The strange relating to style, tactics, and line-up that the team employed (in particular towards the end of the season) was subject to much criticism, and while we should not be overly harsh on the poor man, it surely does seem like he was a little out of his depth.
After tonight’s rather insipid performance against AC Milan in the Champions League, and only days after an even more lacklustre draw with Osasuna in La Liga, doubts are starting to creep in to the minds of those Culés who unanimously praised the appointment of manager Tata Martino just a couple of months ago. Before these two games, this year’s team had been continuously praised – at least by pro-Barça media – for its evolution in style and winning streak, but in fairness major problems have been apparent since the start of the season. Again, we should not be too critical on a new manager, especially one with such limited experience in European football and who was forced to take over the reigns under such dire circumstances. Nonetheless, I shall best the rest of this article off a sound if unsympathetic premise: resistance to fully embrace change when the context demands it can only lead to stagnation and weakening. Perhaps the era of what some journalists and fans have hailed as the best club team to ever play football is over, but intuition says this need not be the case at all, especially to those acquainted with Barça’s unique style and paragon of a youth academy, La Masia. I dare say that to most Barçelonistas (at least the cynical ones, of which there are many), we seem to be on the verge of relinquishing our domination of world football – if we have not already.
Now, to the crux of the issue here. In my view, we can identify the following problems holding Barça back from reattaining the zenith of its powers, seen as recently as 2011 (or 2009, for some).
- The team is not waking up to the fact that other elite European clubs, as well as many smaller ones, have already learnt well how to combat Barça’s style of Tikitaka football and ceaseless possession of the ball. The strategies largely fall into two camps: park the bus and press aggressively and physically off the ball. Both, although particularly the latter, involve a fair bit of violence, that if referees were a little more sympathetic to FC Barcelona, might often earn such teams a slew of yellow and red cards. Alas, for whatever reason, most referees seem to rejoice in seeing the largely diminutive and technically ingenious Blaugrana players get routinely fouled, kicked, and bullied by their opposition (recent examples include Real Madrid, Atlético Madrid, Celtic, and AC Milan). That’s a contentious subject for another day, however. What is more important is that the Barcelona management and players wake up to the absurdly self-evident fact that their usual approach of passing the ball around in midfield until the opponent gets fed up of chasing it simply does not work. Tata Martino may already be working on this, and signs are that he seems to be keen to restore the high-pressing tactic off the ball, and introduce more directness and long-passing into their game. Certainly, these updates are welcome, but most likely they are not sufficient.
- The determination, grit, and verve that marked the Barcelona team from 2006-2009 looks gone. The legends that are Xavi Hernández and Andrés Iniesta have not reached their heights for some time, and while we may be able to excuse the former for age, there is little explanation for the latter of any sort. Perhaps it’s not surprising, given the majority of the team has won a number of La Liga titles, Champions League’s, and even European Cups and a World Cup with Spain. Yet surely neither the club’s millions of fans, nor the management, nor even most of the players are content with achieving only what they have so far. Tata is a new coach, unknown, and originating outside the club (despite having the connection with Messi and his old club) – and together with his genuinely affable and approachable disposition (it would seem), one can perhaps see why he is not whipping the team to get the most out of them. His soft approach, if continued even as he establishes his position and respect within the club, may backfire on both the club and himself if allowed to persist for much longer. Particularly evident in the last two draws with AC Milan and Osasuna was the lack of desire in the players. The few constant exceptions to this: Neymar (being a young and new player at the club), Messi, Puyol, and Alexis (simply by their characters), Bartra (by his willingness to break into the first team) are much appreciated, and crucial to the team’s success, but there are 11 players on the team, and if the majority do not put their heart into their performances, it will severely and adversely affect the performance of the team. Additionally, we might put down the lack of influence by Neymar and Alexis in recent games to the so-called “FIFA virus” (returning after internationals), but given that every player has seen his fair share of rest even at this early stage in the season, I am not one to buy that argument.
- The ever-talented youth products of La Masia are only being integrated into the first team with great reluctance. The typification of this problem may be the careers so far of centre-back Marc Bartra and midfielder Sergi Roberto. Of course, some would argue that Thiago Alcântara was forced out by lack of playing time and trepidation in making him a starter for the first team, but in reality he was given a great deal of playing time for his young age, and was perhaps a bit over-eager to find playing time at all costs, moving away from the club after continual pressure from his father Mazinho, it is suspected. Marc Bartra and Sergi Roberto on the other hand, born and bred Catalans, have only ever impressed in their first-team performances when given just a little opportunity to find form. Finally the club may be realising what a talent Marc Bartra could be, and part of the solution to the ongoing centre-back “crisis”. Sergi Roberto represents a rather novel type of midfielder to the current incarnation of the club and its style: he is box-to-box and highly dynamic, while still capable of accurate and quick passing in the mould of Busquets, Xavi, or Iniesta, the giants of Tikitaka.
- A refusal to bench, retire, or sell off long-standing players who have consistently and markedly underperformed for a long time is hurting the performance of the team. This situation is particularly exasperating, given the profusion and diversity of superb young talent at the club. Notable examples of players who have very rarely performed to an adequate level over the past two years are Gerard Piqué and Pedro Rodríguez. Rightly lauded as being top players and major contributors to the success of both FC Barcelona and La Roja over the past 5 years or so, their respective forms have since declined enormously, and show no signs of returning. Perhaps it is complacency, perhaps they were never as brilliant as many of us thought, or perhaps something else altogether, but the crucial point is that neither Piqué nor Pedro have shown enough skill or form of late to warrant their automatic placements in the line-up. In fact, I personally have thought Piqué has long been a much over-rated centre-back, and should never have been bought back from Manchester United some four years ago, at least not to play as a centre-back (which he does a rather poor job of imitating these days). Pedro seems capable of little other than continuous back-passing, occasionally losing the ball, and defending with vigour on a good day. Well, maybe we should try him out as a full-back, but he is certainly doing our front line no good. Now, the form of Xavi is a very contentious issue; he is a club legend even while still playing, and has contributed so much to the team over the past 10 years, he deserves the utmost respect of all Culés whatever happens from now. The same goes for Andrés Iniesta. Yet the former in particular, and also the latter to some degree, have shown lack of inspiration on the field for a great deal of the last 6 months, if not longer. Might not guaranteeing their automatic starting positions for every big game do a bit of good? When undoubtedly hugely talented young stars, full of energy and eagerness to prove themselves, are waiting on the sidelines, it could hardly get more exasperating for them and the fans alike.
Now, I do not intend to address the solutions to each of the above problems individually and in detail, but they are certainly something I would hope every player at Barcelona and the managers have at the forefront of their minds, if they wish to continue the great success of the club in coming months and years. Let me now propose two teams that I think should be given tries as soon as possible. That is, I am of the firm view that playing these line-ups with the appropriate formations and tactics would do much to strength and reinvigorate the team, while providing much-needed competition for the players who feel their starting spots are guaranteed for every important game until the day they retire.
Trial Team for this Season
I strongly feel that this team would address some of the key problems, focused around certain positions and areas of the field. For a start, the problems rampant in central defence, which seem to stem from Piqué’s casual attitude and lack of speed, along with Mascherano’s occasional awkwardness in a role he has only recently adopted, could be hugely reduced or even eliminated by a pairing of the talented-yet-callow Bartra and the stalwart-yet-old Puyol, who would seem to complement each other perfectly. At the RB position, Alves is undoubtedly a world-class position and still far superior to Montoya, yet Alves still managers to great significant tactical and positional problems for the teams by his surging (and often heedless) runs down the right wing. Montoya is far more measured in these, perhaps due to his age, or perhaps by his nature, but irrespective of his talent, we will very soon need a new RB to replace the ageing Dani Alves, and why not try the promising La Masia graduate? As for Midfield, I have already alluded to the issues with Xavi and Iniesta, and whilst being two of the best players of their generation, it is becoming all too apparent these days the lack of penetration and attacking flair that more direct, box-to-box midfielders like Cesc Fàbregas and Sergi Roberto ought to be able to provide without difficulty. In the worst case, this midfield pairing would prove ineffective, but at least inspire our usual midfield duo of Xavi and Iniesta to break out of their highly conservative style that has solidified over recent years. As to the forwards, I have opted for a pretty conservative (arguably first-choice) trio; Tello should be given plenty of opportunities to show his worth, but I am not sure he is the solution to any of the team’s problems, especially given he brilliance of Neymar there.
Trial Team for Next Season
This team is rather more speculative, and by no means am I suggesting it is best team we could product next season (it is certainly not) – but it is certainly worth experimenting with (along with variations), for the sake of developing and enhancing Barça’s playing style, as well as the talent and skill diversity in the squad. Indeed, I am not so much suggesting this line-up be played, but that bits and pieces of it be incorporated in various matches. The abundance of alternatives also suggests (as it should) that who to play in what position, even experimentally, depends a lot on their progress over the current year, and form coming into next season. Regardless, there needs to be a strong desire to experiment with the squad, at the very least to the extent Pep Guardiola did in his tenure. If we introduce young players and give them the chance to shine in the first team while still only 18, 19, or 20, we may encourage the blooming of these stars, rather than forcing them to languish in the B team until some rigidly mandated age of 21 or 22, as seems to be the case of late. As a final remark, I should add that it is certainly with experimenting with a true centre-forward at the helm (such as the current B-team talent Sanabria, or a purchased tall striker) in place of Messi, and pushing Messi either to right wing or a “No. 10″/playmaking role behind the striker.
While it would be premature and largely a pointless exercise to list my thoughts on the entire squad for net season (to be clear, I am not even claiming that all of the above players should be promoted to the first team next season, only trialled), I will just make a brief case for Carles Puyol and José Pinto becoming player-coaches in their respective positions. They are both hugely well-respected and well-liked players (in particular Puyol), top-class players, and inspiring characters in the dressing room, not to mention on the pitch. Moreover, they would both provide crucial experience and mentorship for the youngsters entering into the first team and starting to secure their places, such as Bartra, Masip, and potentially Oier and Bagnack too.
Alright, I think I’ve rambled long enough for now! What do you think, fellow Culés?
This post is just a brief nod to the IEEEXtreme Competition that I took part in at the end of last year with a couple of like-minded students at my university. Queen Mary, University of London were kind enough to host the participants from Imperial College. (Unfortunately just a single team, since the others didn’t manage to get their registration through in time!
The event was a gruelling but undoubtedly challenging and enjoyable 24 hours of programming solutions to a range of small problems given to us by the competition organisers. Alas, we were restricted to C++ for our solutions (the lesser of two evils when compared to Java), but considering than myself and one of the two other team members were far from regular users, I thought we did a fair job of coping. (We were constantly refreshing ourselves on much of the basics!)
The results were published not too long ago, and I must say I was amazed we managed to rank as high as 71 overall (out of some 1,500 teams). In fact, I gather we were somewhere in the 20s at one point, but evidently slipped dramatically when we all lost the desire to keep going about four hours from the end. What’s even more astounding is that our lone Imperial College team managed to rank first among the teams from the United Kingdom. Admittedly, this says more about the popularity of this relatively new contest in the UK, especially when one notes how many British teams entered. Eastern European countries unsurprisingly put forth a host of participants. Still, I was moderately pleased with our effort. Our phenomenal team spirit more than made up for any shortcomings, of course.
Oh, and as it turns out, a power outage in that area of London induced a delay of some two hours, mainly spent dashing around the campus. The fire alarm and standing around in the freezing area wasn’t much appreciated, though I doubt it affected our success in any real way. Though that isn’t what I’ll be telling the electricity company, of course, when I claim full competition-related damages.
Most annoyingly of all during the marathon competition, there was a singularly irritating problem relating to dynamic programming that none of our team was able to solve throughout the event — despite persistent efforts and the fact that the great majority of other team had no problem! The contest had its faults too; the arbitrary swings in difficulty level of many questions often took us by surprise, as the times taken for us to fully solve the questions ranged from 20 minutes to 5 hours to never. I hear most were rather better specified than their counterparts from last year, however.
In all, my day of IEEEXtreme was a perversely enjoyable exercise in frantic coding and sleep deprivation. Probably not one I’ll repeat in its current form (even if I were still in university), but not one I’d take back either. I daresay I’ll be revisiting the similar but less biologically demanding Google Code Jam contest this year, only to fail utterly in the second one, when facing up against some truly super-human competitors.
Some time ago I wrote a post about the well-known logic puzzle of The Traveller’s Paradox and attempted to derive and justify a solution using the formal methods of propositional calculus (zeroth order logic). I return today to another intriguing and somewhat challenging problem within the realm of mathematical logic, albeit with what I hope is a much clearer approach and argument.
Although “The Hardest Logic Puzzle Ever” is scarcely a logically verifiable statement, the puzzle does indeed have a reputation as a rather tricky logic puzzle (at least among those encountered by laymen) and in any case has a non-trivial solution. The problem has some notable names attached to it, having originally been published in The Harvard Review of Philosophy by the logician George Boolos, but originating with the popular mathematician Raymond Smullyan, and altered slightly by the late computer scientist and AI pioneer John McCarthy.
The puzzle is commonly stated as follows.
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.
At first glance, the problem may appear insurmountable due to the behaviour of god C, yet when we notice that his behaviour is not truly random, but rather only his veracity is — he otherwise follows all rules of logic. Boolos clarified: “Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.”.
Encountering this puzzle for the first time just in the past week, I made an effort to solve it on my own using a formal approach, as much as possible. As it turns out, I had some success, and hence thought I might share my reasoning here in the form of an article.
Let us begin by setting up the puzzle in the standard language of propositional logic (that is, Boolean algebra). We first define our useful propositional variables and predicates, which are
- , whether the da response corresponds to yes (absolute truth). $R$ is thus true if da means yes and ja means no, and false if da means no and ja means yes;
- , whether a given god (we consider them independently) is telling the truth. Note, this has a well-defined value even for Random (god C), since the context is a specific question and corresponding response.
- , the question (propositional predicate) that is asked to a given god.
Note that the latter two variables are semantically valid within only within individual questions. However, because we shall only utilise them within the context of question-response pairs, we need not concern ourselves with this.
There is a number of ways to convert the verbal problem statement into a set of formal logical expressions, but I shall adopt a fairly direct and unambiguous one here. We start by noting two simple facts regarding the truthfulness of a particular yes-no response .
Note that the biconditional () can be interpreted as material (syntactic) equality. This is precisely equivalent to the non-fundamental XNOR () operator in propositional logic. With a bit of manipulation it can be shown that
In other words, the yes-no of any response shall be the absolute (true) answer to the question XNOR whether one is asking a truth-teller.
We must then note the complication to the puzzle introduced by the fact we do not understand the language of the gods; indeed, ‘da’ could mean either yes or no and ‘ja’ the opposite. To account for this, we can write two more statements specifically about the da-ja response (denoted ), which take virtually identical forms to before;
Unsurprisingly, this can be rewritten in the same way to use the XNOR operator;
Note that the value of represents the actual response; that is, it is the single observable of the logical system we have constructured to represent the puzzle.
While we could restrict ourselves to the use of the primitive Boolean operators (AND, OR, and NOT), the use of the XOR operator here facilitates things considerably, due to its special properties (notably commutativity and associativity) and the simplicity it gives our theorems.
Now, combining the two expressions (theorems) for and (this can be seen easily by considering the biconditional as equality), we can factor out the negations and use associativity of the XOR operator to write
We now have an easily manageable form for the da-ja response of a given god. The question now becomes, how do we extract the absolute truth value of the response from this observable variable? Clearly, one has no control over the and variables, which are predetermined by god being asked the question (and possibly by the flip of a coin) as well as the language of the gods. However, we do have direct and full control over the question to ask, the predicate .
In order to extra meaningful (absolute) truth value we first note that any propositional variable XNOR itself is false, thus disappearing from its containing expression. Given that we wish to eliminate the variables and from the final expression, we can decompose the predicate ; that is, give it an explicit form.
Let . Hence, we can say
At this point we almost have a solution to the puzzle. We have shown that one can obtain an accurate true-false response to any question we wish to ask any god. As long as we ask a question of the form , then a response (effectively to question ) of ‘da’ always corresponds to truth and ‘ja’ always to falsehood.
There are a number of ways to use this to reveal the identities of the three gods. The simplest and most direct, I feel, is to ask gods A and B whether they are Random. This definitively indicates the Random god (since if both answer in the negative, then it must be god C by elimination). One can then simply ask either of the remaining gods (not Random) whether he is True, deducing the identities of the True and False gods in a single question. Hence, we have totally and provably solved the puzzle within the desired three questions.
The iPhone 4S model was released by Apple just under a month ago here in the United Kingdom. Having gotten over the general disappointment of a late (delayed?) release and no new hardware (the widely-rumoured iPhone 5 model), I was soon excited by some of the new software features offered by iOS 5 on the new iPhone model, most notably the advanced voice recognition system Siri. The much-improved processing power, not to mention updates to the camera and external antenna were also appreciated, though in some sense just reaffirmed what the more demanding technical consumers were expecting in the original iPhone 4 release.
Warning: Rant ahead. Apple fan-boys, avert your gazes.
Four weeks later, and I’m still sitting here with my two-and-a-bit year old iPhone 3GS. I was due for an upgrade on my O2 contract just a week after the initial release, and contacted both O2 directly and my local Carphone Warehouse retailer to find out what the status of this upgrade was. Apparently, not only was the retailer entirely out of stock of the new iPhone 4S (in its warehouses or otherwise), but they had no word on when any further shipments would be arriving soon. In the ensuing three weeks, I’ve made the personal effort of checking for new stock updates every few days, only to be told that a new delivery should be coming soon. Besides a brief restocking a week ago (that didn’t include any of the 64 GB versions), I have repeatedly and consistently been told to come back and enquire again in a few days regarding stock. Now, it’s hard to blame this on Carphone Warehouse, since every employee I spoke to seemed about as perplexed as me.
To me, the simple fact that Apple has failed to sufficiently stock one of their primary UK retailers with the new iPhone model for almost 4 weeks now is absolutely shambolic. I mean, how can one of the largest companies in the world, which prides themselves on customer satisfaction, make such an atrocious mess of logistics? It’s not like Apple has just entered a technology sector with a minor new product no-one has heard about or might consider buying. While undoubtedly initial sales figures for the new iPhone have been quite impressive, I can’t help but think Apple has severely damaged customer relations in the UK, if not suffered a notable loss in sales. At this point in time, I’m really struggling to find that irrational love for a company that so many Apple fan-boys have latched onto over recent years. Sure, my current phone is an older iPhone model and my laptop a MacBook Pro, but I bought these products mainly because they far ahead of the field at the time of release and merited their price tags. With outstanding-looking Android phones currently on the market, and some impressive Windows Phone 7.5 models just released, I’m quickly rethinking whether to let myself be led around by Apple any more.
In short: get your act together, Apple, and don’t expect to remain the dominant player in consumer technology whilst sitting there and twiddling your thumbs. You’ve done of good work to earn the respect of millions of users throughout the world (not least through clever marketing), but realise that you’ve no god-given entitlement to keep it in the future.
So this is sort of an overdue update where things are with my life, as well as a bit of self-promotion for the work I’m going to be doing over the next 9 months or so…
The first thing that needs to be mentioned is my total relief at no long being a student of physics. Well alright, it wasn’t all that bad. To be fair, there were many parts of my degree I enjoyed, yet unfortunately my current feelings seem to be dominated by a few painful lecture courses and exams! In any case, I am now happy to announce that I’ve graduated with 2:1 honours in theoretical physics at a world-class university.
Before I commit myself to the unavoidable drudgery of a full-time career, or more likely (given my talent for procrastination) a PhD course, the plan is to take a very non-committal year out — post-university gap year if you like. More on future plans to come in another post, but for now I wanted to mention that I’m going to be doing some part-time month over the coming year. Specifically, I will be working as a private tutor in the areas of mathematics, physics, electronics, computing, and English language/literature. My plan is to do this on an ad-hoc basis alongside other potential freelancing work. Learning and particular pedagogy is something I’m very passionate about. For anyone that may just happen to stumble across this post, I am offering to tutor secondary school students as well as adult learners in the N/NE London and SW Essex regions in these subjects, focusing on GCSE and A-level courses, but willing to accommodate to other courses.
If you’re at all interested, you can check out my profile on First Tutors. Feel free to contact me either via the contact form on this website, or via the First Tutors website.
Moving forward in time to the 1950s, we return with this piece to the style of Vivaldi and Bach. Albinoni’s Adagio in G minor was for some time thought to be be a work of the well-known 18th century Italian composer Tomaso Albinoni, yet is now accepted as a Neo-Baroque work of the modern biographer of Albinoni Remo Giazotto (with just perhaps some inspiration from an original Albinoni manuscript). The name and common attribution have nonetheless stuck, even to this day.
Though often described as a musical hoax, passing off a work as one by a famous master was a relatively common practice by lesser-known composers from the 19th century onwards, done in order to gain widespread recognition. In this sense, Giazotto has certainly succeeded, but moreover, he has created a masterpiece of modern classical music and an unforgettable melody of sombre.
(Performed by the Leningrad Chamber Orchestra.)
It’s a universal fact that computer wallpapers never stay fun for long. No matter how pretty the picture is, staring at the same desktop each day can get a little tiresome. (Okay, so if you’re anything like me, the desktop is continuously obscured by masses of windows, but we all know that’s irrelevant.)
NASA have for years now run the wonderful Astronomy Picture of the Day website, featuring a new (and almost invariably stunning) image of outer space or some astronomical phenomenon – from our own moon, to neighbouring planets, stars, and galaxies. Even better these days, the pictures are inevitably high-resolution, making them ideal for desktop wallpapers.
As it happens, some clever guy came up with the idea of creating a program to run in the background and automatically update your desktop each day with the latest astronomical picture, published by NASA on their website. The application, called APOD Wallpaper, is available to download and install on your Windows machine, and having used it for roughly a week now, I can already highly recommend this handy little app. As a student of physics (and someone with a particular interest in astrophysics and cosmology), this has quickly become a must-have for my laptop; yet who could not appreciate the beauty of these pictures?
May you never tire of your desktop again!
Having just gotten hold of my lovely new MacBook Pro, I’ve had a chance to play around with getting an automatic APOD wallpaper on OS X too. As it turns out a certain scripting guru (Harold Bakker) has written a script to automatically update the OS X desktop wallpaper with the latest APOD and has kindly put it on his website. It’s slightly less trivial to setup than the Windows app, though he provides clear instructions on how to create a cron job for automatic updates… it’s been working perfectly for me so far!
It’s been some time since my last installment in this series, but despair not, there is more to come — beginning with a new modern masterpiece. Let me also say that I fully intend to restore a bit of regularity to this series!
Joaquin Rodrígo is arguably the greatest composer in the history of Spanish guitar music, though it was far from all he composed. His life, spanning almost the entirety of the 20th century, produced two great and enduring works. The more popular is the Concertio de Aranjuez, but it is his Fantasia para un gentilhombre, which I prefer and which I wish to introduce here. The name literally means “fantasy for a gentleman”; the gentleman in question here being the virtuoso guitarist Andrés Segovia. The piece itself draws inspiration from Spanish folk music, retaining both its lively and lyrical characteristics while making superb use of the classical orchestra. All in all, a true delight.
Watch and Listen:
(Performed by Narciso Yepes.)
(Unfortunately I couldn’t find any freely available download, so YouTube will make do! If you’re looking for a good performance to buy though, I can definitely recommend one by Pepe Romero and the Academy of St. Martin in the Fields.)