WHO IS THE G.O.A.T – the long introduction
Please visit my new site/blog: The Tennis GOATs
The discussion about the tennis GOAT – the greatest of all time – is prone to raise huge polemics. And this is true not only for tennis but for whichever sport you choose to debate!
One tends to be discouraged by many obstacles:
How to compare players of different generations?
How to compare their respective qualities, their respective achievements?
Because of all the difficulties involved – and they are many –, there are those who argue that this is a silly, unreasonable or even impossible discussion.
But is it?
Well, it all depends on how you think about the question, on how the comparison is to be made, on which criteria are to be used.
There are people who imagine that the discussion about the GOAT is a sort of an imaginary tournament, where all the greatest players of each generation play against each other. In this scenario, the GOAT would be the one to win the tournament.
Now, how to pick who would win a match between, say, Laver vs. McEnroe, Borg vs. Ashe, Federer vs. Connors, Lendl vs. Nadal, Djokovic vs. Rosewall, Sampras vs. Pancho Gonzales?
Now, this truly seems to be an impossible thing to decide, an implausible task to accomplish!
How could one possibly tell – or at least establish reasonable criteria under which to decide – who would perform better in this imaginary tournament?
Different generations, different styles, different equipment (rackets, balls), different courts, even different physical possibilities…
How could we even start the discussion?
Laver has the best backhand, McEnroe the best net game, Nadal’s the best athlete, Borg has the best mind-set, Sampras the best serve, Djokovic the best all-round game? And could we even hope to agree on who’s got the best what?
How could anyone find a way to, by analysing the different and complex qualities of a player, decide which player has the “better set of qualities”?
If the discussion takes this direction, I agree, I don’t see how we could possibly reach any kind of consensus!
I love sports and no wonder I love spending time speculating on all kinds of things: who is the best soccer player of all time: Pele or Messi (or Di Stefano, Garrincha, Puskas, Maradona, Ronaldo)? Who is the best Formula 1 driver: Senna or Schumacher (or Piquet, Prost, Fangio, Lauda)? The best basketball/volleyball player? Who would be in your dream team: in soccer, volley, or basketball?
All those discussions are fun to have and spend time on, but the first thing I realised is: how difficult it is for people to agree! And this is so even when we have people with (apparently) similar lines of thought.
So the next thing I realised is: we can never reach a consensus – whichever the subject may be – if we don’t agree, beforehand, on the criteria we are going to use to judge the respective assets involved in the debated topic.
- GOAT in soccer/football
Let’s spare a few minutes here and indulge ourselves in speculating on who is the best soccer player of all time.
Now, we could start the discussion by selecting a few legends everyone would agree to be among the greatest: Leonidas, Garrincha, Pele, Di Stefano, Puskas, George Best, Cruiff, Zico, Maradona, Ronaldo, Messi, to name a few.
But after that, how could we go on when two or more people disagreed?
For example, how are we to decide whether Pele or Messi is the better player?
By analysing their respective qualities such as the ability of dribbling, shooting, passing, assisting, scoring?
By analysing and comparing their numbers and achievements, such as goals scored, assists, titles?
Any discussion would obviously have to contemplate all those things, but I’m sure the reader already sees where the problem lies.
The first criteria, for example, are far too subjective, and it seems very hard – if not impossible – to find a common ground we can all agree on.
If I say/think that Messi dribbles better than Pele, whereas one friend is convinced that Pele is the best and another one chooses Ronaldo instead… how could we try to persuade each other? Which kind of (more) objective arguments or evidence could we give in support of our respective opinion? We could watch as many videos as we wanted and I bet no agreement would ever be reached!
Resorting to numbers would seem to be a good move, for numbers bring a more objective kind of data. After all, there can be no doubt that Pele scored more goals or won more important titles than Messi or any of the others in that list. Actually, there’s this famous response Pele gave to a reporter when asked, provocatively, who was the best, Maradona or him: “when Maradona scores more than 1,000 goals and wins 3 World Cups, he can come and talk to me”.
But should numbers settle the question so easily? And, maybe more to the point: which numbers are or would be able to help?
The first and obvious problem here is the fact that soccer is a collective sport and hence it does not seem to be completely fair or appropriate to solely judge a player’s merit based on accomplishments that were reached as/by/in a team.
Indeed, based solely on the “important titles criterion”, for instance, Brazilian Cafu – with two World Cup titles in three finals – would be considered a (far) better player than Argentinian Messi. However, nobody who understands just a little bit of soccer would be capable of uttering such blasphemy!
But there are other difficulties to take the numbers “at face value”, even considering only the more individual achievements, such as goals scored.
The average number of goals scored in a match before the seventies was far higher than in today’s game, which could raise the question whether a goal scored back then should have the same value as a goal scored today.
On a similar reasoning, one could raise the question whether a goal scored in the Spanish Premier League (or Portuguese, Turkish, Japanese…) should be worth the same as one scored in the Italian or English ones, when all the stats point out to the fact that goals in the latter are scarcer than goals in the former.
Obviously a “mix and match” of both subjective and objective criteria could be used, but… how much weight would we give to each?
We are also all well aware that numbers don’t “speak by themselves”, that numbers need to be interpreted to mean something. But what do we do in those cases when it’s not even obvious how to interpret them?! Can anyone think of a clear – and persuasive – way of balancing all available criteria in the cases above-mentioned? The collective aspect, as well as the wild variation in the strength of the different leagues in different countries are definitely complicating factors in judging a player’s achievements!
The only sure thing in all of this is that if people are unable to reach an agreement as to the criteria, then there’s really no way to agree on all the rest.
- GOAT in Formula 1
What about other sports, say, Formula 1?
Who is the best: Schumacher or Senna? Fangio or Prost? Lauda or Piquet?
Schumacher has the obvious edge in terms of titles and other numbers and records, but Senna died young and could be thought of as being capable of the same (or even bigger) exploits.
On the other hand, one could argue that after the 1990’s Formula 1 has become more a race of the constructors than of the drivers: whoever has the best car wins, in stark contrast with the previous decades, when up to five different drivers from up to five different constructors would fight to the last race to see who would be crowned the champion.
Indeed, when a driver is able to win (more than) half of the season’s grand prix, should we ascribe this (more) to his talent or to his car?
And the reverse question: when, in a season, the driver managed to be the champion with only a few wins and a lot of second/third places, should this equilibrium among the candidates count for or against the champion?
Nelson Piquet’s case is an interesting one.
Prost and Piquet were contemporaries for most of their careers and their rivalry started in an era when there seemed to be more “true competition” among the constructors and, therefore, drivers. However, despite the fact that Piquet got his third title before Prost got his second, Piquet is never mentioned in any top-five list of the best of all time, whereas Prost is in almost all lists… Go figure!
Anyway, Formula 1 is also a very difficult sport to use numbers as the sole (or main) criterion because – and we all agree at least on that! – the quality of the car has (at least) as an important role in a driver’s success as his talent.
Ok, we all also know that the best driver has a fundamental role in developing a car and we all also know that the best driver tends to get hired by the best constructor. However, that did not prevent us from seeing Damon Hill being crowned champion in 1996… And I guess, here too, we can all agree that he was far from being the best driver back then!
- Now, what about tennis?
Of course, here too there are pitfalls.
Nevertheless, here we have, to start with, at least one crucial advantage: it’s a one-against-one sport, where, moreover, no player can blame lack of access to the best available equipment for not having achieved success in his career. Indeed, we can without fear say that any player within the top 100 can use the best equipment money can buy and an athlete can wish for.
In that case, it seems fair to conclude that their “objective” achievements – titles, #1 awards, and other records – are a suitable way of assessing his overall success and, therefore, their quality/efficiency of play.
Now, this is a very important point, so let’s not be afraid of being redundant and repetitive here.
Normally, in informal discussions about who is the best, it’s common to focus on a player’s individual and observable qualities, such they are presented in a match: backhand, forehand, serve, footwork, mind-set, physical capacity… you name it!
This is a fascinating and amusing debate to take part in and I personally love it! But it is also a dead-end when it comes to more manifold comparisons.
There is no way for two people, even with slight differences of opinion, to reach a consensus based solely on these so-called subjective criteria on who is the best player. For one reason: it’s already very hard for two people to reach consensus as to which player is the best at any specific criterion – say, the best serve –, let alone as to who has the best set of such different qualities!
Do you think I am a pessimistic person? Ask ten friends (or read ten renowned tennis critics) about which player has the best backhand/forehand/serve/etc./etc. Now compare their answers. Now try and take into consideration the opinion of the people who are older and also saw the players of yore. Reached any consensus? Good luck! As the French say: “autant de têtes, autant d’avis” (as many minds, as many opinions).
Does that mean that we should then give up? Not at all!
The good (the great) thing about tennis is that we can – and should – rely on the following premise: all the qualities (or lack of them) a tennis player possesses, they will – inexorably – be reflected in his accomplishments. If a tennis player is good, by the end of his career, he’ll have won a few titles. If he’s very good, he’ll have won many and important titles. If he’s one of the greats, this will accordingly be translated in many unique achievements and records.It cannot get any simpler than that!
Unlike soccer, where you can blame your National team for not having won a World Cup during your career, or Formula 1, where you can blame your car or team, there is no such excuse in the tennis world. If you fail to win tournaments, to reach #1 in the world, to put your name on the records books, there’s no one you can blame… but yourself. It might be your mind or your body that fails you. Or both. But, in the end, it’s you and only you.
It’s the whole of you that will succeed; it’s the whole of you that will fail.
The same body that allows you to make astonishing things on court is the same one that may get injured; the same mind that allows you to keep your cool inside the court is the same one that may prevent you from training hard or even urge you to quit your career abruptly.
So, although it’s very intuitive – and almost irresistible – to imagine that your idol could’ve won more titles “if his body/mind/whatever hadn’t let him down”, it’s neither practical nor fair to indulge in such speculations.
You may say it was bad luck and it might well have been. But listen: you did not complain when he accomplished off-the-chart feats because of this very body/mind duo.
An athlete is both his body and his mind. They are both needed to make him great. It can take either of them to make his ruin.
At any case, we are not here to discuss “unfulfilled talents” or players that could be/have been better or could have reached higher levels if…
There are no “ifs” in the history books!
Anyway, what we observe in tennis is that we appear to have this ideal situation, where the whole set of qualities of an athlete, mind-and-body-in-all-their-intricate-and-complex-interactions, will invariably be translated into titles and other kind of (measurable) achievements.
So, here’s the first and crucial move by means of which we may somewhat escape the pitfalls of the more subjective discussions and criteria: instead of talking about a player’s multiple qualities, we’ll talk directly about what he (has) achieved because of those qualities.
Instead of talking about style, beauty of play, separate strengths such as observed in his backhand/forehand/footwork/mind-set… we are going to talk about his feats and triumphs, namely his titles, records, and awards.
So we will not worry or speculate about why a player achieved what he achieved. We will talk about and reason on the fact that he did. We will list and count what he did accomplish, how many titles he won, how many weeks/years he spent as #1, how many records he’s got to his name. And then and only then rightly conclude that he achieved that much because he was incredibly talented. The more success, the more talent (and work ethic).
Obviously, we may want to mention or talk, here and there, about certain specific attributes and qualities of a player – Federer’s beautiful footwork or Nadal’s incredible mental strength – but if and whenever we do that it’ll be only to illustrate or complement the scenario, never as part of the underlying criteria.
- What about comparing players of different generations?
This first move – achievements as the ultimate proof of talent/efficiency – is key to our purposes. However, this does not mean that we don’t have challenges ahead of us. We still have to answer some tough questions, and one of the most difficult is:
Are the achievements within a generation really comparable to the achievements within another generation?
This is a tricky and fair question to ask.
Indeed, we all have the right to wonder why or if merely listing the achievements of a particular player is a good way of measuring his (relative) success among players of different generations.
Now if, by “really comparable” you mean an “absolute” criterion to reach an “absolute” conclusion, then the answer is, obviously, “no”.
But then, I guess, you are the kind of guy who should rather be in the metaphysics business, not here. In metaphysics, you can wonder whether Achilles will overtake the tortoise in a race, but in real life, the tortoise always finishes second!
Jokes aside, if you are the “absolute” kind of guy, for whom it’s “either perfection or nothing”, then surely this book is not for you, and I’m really sorry for that.
It’s not our intention – or pretension – to have the final and absolute word on the matter.
Instead, this book is for those (like myself) who think that we can reach a reasonable, educated conclusion – even if not perfect – when we base our reasoning on solid evidence and judicious, practical criteria. That’s our aim here.
Let’s not close this parenthesis quite yet, for it is very important to clarify things so nobody gets frustrated in the end.
For that matter, as important as saying what I do intend to accomplish here is saying what I do not intend to accomplish.
– I’m not comparing backhands, forehands, footwork, service, or beauty of style.
– I’m not comparing or speculating about athleticism, mind power, under or over-achievements, sheer talent, or artfulness.
– I’m not taking into consideration speculations about what could have happened if… he hadn’t retired, got injured, married or had children…
It’s not that those facts and factors are not important. They are. Very.
But a crucial premise in this book is that, for all their subtle complexity, those facts and factors will inevitably be reflected in a player’s global achievements. And global achievements, of course, translate themselves into titles and records, into numbers and stats!
So our strategy is that, instead of engaging in those complex, multi-faceted, and subjective-tainted debates, we’ll try to simplify and “cut to the chase”.
So instead of discussing and debating, as separate topics, the different qualities a player may or may not have, we’ll discuss the consequences, the result of all those qualities put into action, that is, how those qualities and characteristics transform themselves into titles, finals, weeks as #1, etc.
By analysing how they translate (or not) into numbers – and most importantly into the big numbers (e.g. Grand Slams titles, weeks/year-end as #1) – we may be able, in the end, to build up our evidences as to how dominant a certain player is/was over the adversaries of his own generation.
I do apologise if I repeated myself here, but when I talked about this project to friends the misunderstandings about what I didn’t intend to do sometimes robbed their attention and prevented them from analysing and judging what I do intend to do.
- Parenthesis closed, back to our question.
Are the achievements within a generation really comparable to the achievements within another generation?
Leaving aside the stubbornness of the “absolute-seekers”, I do believe we have very good reasons to answer positively to that question.
And the main reason I vouch for that is:
Whenever a player wins a title, it means that he was better, at that tournament, than all his adversaries of the moment.
Whenever a player is the #1 in the rankings, it also means that he was better, or more consistent if you prefer, than all his adversaries during the past 52 weeks.
So titles, records, rankings, and other numeric achievements are, all of them, a pretty good way of keeping track of how dominant a player is/was in his own time, in his own generation.
So the more dominant a player is/was, the more titles and records and weeks as #1 he will have written in his resume, in his CV.
In a word, the better, the more dominant a player is, the better numbers he will have compared to his peers.
So what else, what better could we ask from the GOAT than to have the best resume among all the players that ever played the game?
- Comparisons and uniformity of data
Before we proceed, we have to face one more problem, a big one.
As a sine-qua-non prerequisite for any comparison to succeed, we’ve got to have some uniformity along the period studied.
If we are to use titles and records of the players as our basic evidence, it is crucial that a title, say, of a Grand Slam, obtained in 1920 involves as much difficulty as a title obtained in 1980 or 2010.
The question that concerns us is:
Do we have such uniformity along the different generations, along the different eras?
Now, I do think we have very, very good reasons to assume that this “uniformity requirement” is satisfactorily met in the case of the Open Era, that is, the period that started in 1968 when the distinction between amateurs and professionals ceased to matter, meaning that the participation at any tournament was from then on permitted – open – to any player.
After the Open Era, especially after ATP started the computerised rankings, we have indeed reached a sort of “standardisation of the game” – in terms of tournaments, rules, rankings, competition – so it seems to be a fair assumption that all achievements within this era are very much “comparable”.
So when a player wins a Grand Slam, it means that he won one of the four most coveted tournaments of the year. It means that he prevailed where the other players – the very best competition at that moment– failed, despite all their desire and effort.
So if a player won a Grand Slam in 1980, or 1990, or 2000, we are well supported in assuming that those titles have the same symbolic value, that is, the value of having triumphed among the best competition available at the time. And the same reasoning applies to other titles and achievements, respecting, naturally, their respective importance and difficulty.
It’s in that sense that winning a Grand Slam will obviously have more importance than winning a Masters Series or an ATP500/250 (I’ll get back to that), as well as (if less obvious) being the #1 shall have more importance than winning a Grand Slam (I’ll also get back to that).
Now, if a player did that – if he won Grand Slams etc. and was ranked #1 –, not only once, but multiple times; and not only multiple times, but more times than his peers, we might well be tempted to say that he was not only a great player, but the greatest.
* * *
Now the tricky part: what about the pre-Open Era, about the period we could call the Pro-Amateur Era?
Do we find a “smooth-enough” continuity of standards from that era to the Open one?
And here the answer unfortunately is: not quite.
As the name suggests, the Pro-Amateur Era (before 1968) is a time when the field was divided between amateurs and professional players, meaning that there were Grand Slams to be played only by amateurs and Grand Slams (the so-called Pro-Slams) to be played only by professionals.
Or, that immediately makes one raise an eyebrow for it entails that (1) the best players at a certain point may not be contesting the same tournaments, in which case (2) the overall level of the competition/difficulty of the tournaments concerned is consequently and proportionally lowered.
Surely that wouldn’t be a true problem if, say, the professional players were always and indisputably the best of the field, or vice-versa. But that was not the case, not at all.
There were too many situations where some of the biggest names of the game were professionals whereas some other big names played as amateurs.
So we have this situation where the best players in the world were split between the two categories and, as a result, often the very best players were not competing at the same time, at the biggest and most important tournaments.
But let’s not speak in the abstract, let’s give concrete examples. And I think the perfect example is this:
Three of the biggest legends of the sport – Rosewall, Emerson, and Laver – never competed (at their prime) at the same tournament, not at least until the Open Era began!
Or, if we are reminded that the three of them, all combined, account for 55(!) Grand Slam titles (in 83 finals), we may have a pretty good idea of what was at stake.
So the problem of taking into consideration the data before 1968 is not as much a matter of being Amateur versus being Pro; it’s a matter of answering the following question: when a player won his biggest titles, did he play against the best possible adversaries at that time?
And in the case of the Pro-Amateur Era, the answer is, unfortunately, “no”.
Let’s take a quick look at the table below so you can draw your own conclusions.
Green = Amateur era; Blue = Pro era; W = champion; F = runner-up
First of all, we can immediately notice that these three greats didn’t quite compete for the big prizes simultaneously, at least not in their prime years (prime years = at least a grand slam final reached).
Let’s break this table down and get some startling facts.
Emerson: he won 12 Slams, all as an amateur, but in 10 of those (1963-1967) he did not have to face neither Rosewall nor Laver. In the other 2, he didn’t face Rosewall.
Rosewall: In 8 of his 15 major titles as a professional (1957-1962), he didn’t have to face neither Laver nor Rosewall. He never played against Emerson in his (Emerson’s) best years.
Laver: he won 6 majors as an amateur without having to face Rosewall and in his 9 titles as a professional he didn’t play Emerson.
To grasp the full dimension of this, it may suffice to add:
- Without facing neither Emerson nor Laver, Rosewall went undefeated in majors’ finals;
- The 3 finals that Emerson lost, he lost to Laver;
- The 2 finals that Laver lost, he lost to Emerson.
- The duo Laver-Emerson won 7 of the 8 Slams of that period (French Open 1961 was the exception).
- Without facing neither Rosewall nor Laver, Emerson went undefeated in Grand Slam finals, amassing 10 of his 12 GS titles;
- The 5 finals that Rosewall lost, he lost to Laver;
- The 6 finals that Laver lost, he lost to Rosewall.
- The duo Rosewall-Laver won all 16 pro-majors of that period (Wimbledon Pro was held only in 1967, hence 16 Pro Slams in that period, not 20).
What is to be made up of this?
That those three are among the greatest players of all time, there can be no doubt.
Nevertheless, it’s also indisputable that some of their greatest titles were achieved without some of the best competition then available.
Now it does not take a genius to conclude that if the three of them were competing at the same time at the same majors, their final tally of titles would be less than their actual numbers.
So what I am saying is:
Whereas in the Open Era we can assume that:
(1) all the best players are competing against each other and, therefore;
(2) to win a Grand Slam a player has to beat the best of the best at that time;
the same does not hold true in the case of the Pro-Amateur Era.
Now, two important consequences from that:
- Winning a Grand Slam in the pre-Open Era – be it a pro-major or an amateur major – cannot have the same value than winning it in the Open Era.
In other words, it would, then, be a crucial error of judgement to take the Slam titles obtained during the Pro-Amateur Era at “face-value” and give them the same status/difficulty as they’ve come to have during the Open Era.
And because of that, we decided that the pre-Open Era data should be analysed separately from and interpreted under a different light than the Open Era data.
* * *
- A silly thought experiment
If we want to extend this reasoning, we could try a little “thought experiment”.
Let’s imagine that something of the sort happened during the Federer-Nadal-Djokovic rivalry during the period between 2003 and 2018.
In that period:
- Federer amassed 20 titles and 10 more finals. Of those 10 lost finals, he lost 9 to either Nadal (6) or to Djokovic (3).
- Nadal amassed 17 titles and 7 more finals. Of those 7 lost finals, he lost 6 to either Federer (3) or Djokovic (3).
- Djokovic amassed 14 titles and 9 more finals. Of those 9 lost finals, he lost 5 to either Federer (1) or Nadal (4).
Now, let’s imagine that Federer was an Amateur from 2003 to 2005, a “Pro” between 2006 and 2011, and Amateur again from 2012 to 2018.
Let’s imagine that Nadal was an amateur from 2003 to 2015 and a pro from 2016 to 2018.
And let’s imagine that Djokovic was an amateur from 2003 to 2008 and a “Pro” from 2009 to 2018.
We would then have a table like this:
Here, for the sake of the argument, we are assuming that a final lost to either of the rivals would be converted to a title.
So, for instance, during the period 2006-2008, Federer won 7 titles and made another 4 finals, all of them lost to Nadal (3 in Roland Garros, 1 in Wimbledon). Without Nadal in his path, we could speculate that Federer would have 11 titles in that period.
Applying this reasoning to the whole period (see table above), where Federer doesn’t face Nadal during 2006-2011 and doesn’t face Djokovic in 2006-2008 and 2012-2015, Federer would jump from 20 to 28 titles !
Similarly, Nadal would jump from 17 to 22, whereas Djokovic would jump his tally from 14 to 19 titles!
In this surreal scenario, it’s not difficult to imagine that any of them — Federer, Nadal, or Djokovic — would have many, many more Slam titles if they didn’t have to face each other in certain key years or tournaments.
Now… Does it sound a little bit far-fetched? It most certainly does! But in a way, that was precisely what happened in the Rosewall-Laver-Emerson years, when they were not competing against each other at the same time!
This — certainly silly — thought experiment has only one, and easy, point to be made.
Without your main adversaries on the battlefield, having (many) more titles in your resume would be the natural consequence.
Or, that’s precisely what happened in Laver, Rosewall and Emerson’s careers.
Although that cannot be used to prevent them from being among the greatest, it’s a plausible enough reason so as not to take all their Pre-Open-Era numbers and titles at “face value”.
Mind you, I am not here saying that we should consider that Federer has 28 GS titles instead of his actual 20, or Nadal 22 instead of his actual 17. Not at all. But I am saying that the titles — and other records — obtained in the so-called “Pro-Amateur Era” should have less weight than the ones obtained after the Open Era. And that’s basically why I decided not to include Laver (or Rosewall) as GOAT candidates here (although, later on, I shall dedicate a special chapter/post to Laver’s feats).
* * *
SUMMING THINGS UP…
Let’s make things simple.
The GOAT is not about some absolute measure or standard. There’s none.
The GOAT is very simply about who’s got the best resume, about who was the most dominant player within his own time.
And let’s add: the best resume in the history of tennis until this present moment. So, at any point, a player who was once considered the GOAT might lose his title.
Now why is that people cannot agree on who’s got the best resume in tennis?
Quite simply: because there’s no player with a flawless resume.
Federer has a terrible H2H against Nadal; Sampras never made a final in Roland Garros; Nadal spent far less weeks atop the ranking; etc. etc.
So, what’s the real job here?
Try and get our priorities – the main criteria – clearly stated.
Which aspects of one’s resume shall be more valuable?
Which flaws counts more or less against each player?
In other words: our main task here is to discuss and establish the main criteria after which we are going to assess each player’s resume.
Does it sound a good strategy?
I do hope so.
For those who also agree and are curious about it, please follow along!
A quick reminder:
This is an open, live work.
By that I mean not only that every year I may have to update the relevant numbers and stats of the players here concerned, but also that I may be persuaded by some of you that the criteria here used are not quite as sound or all-encompassing as I first thought.
So let me here and now thank you all who are willing to give me feedback!
Should any one want to criticise, comment, or eventually make a compliment 😉 about any of these posts/chapters, please write to firstname.lastname@example.org and I’ll be more than please to answer your questions or discuss your arguments with you.
And last but not least: I hope you’ll all enjoy. I did!
 Maybe with one unfortunate exception: Monica Seles, who was stabbed by a coward man. I have no words to express my anger related to this episode.
 In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.