- An interesting experimental proposal to finally pin down the quantum (or classical) character of gravity has just been accepted in Physical Review Letters (arxiv). I really think it is far more urgent to explore (theoretically and experimentally) whether gravity really has to be quantized, than to head on brute force quantize everything. Hence I am very sympathetic to this proposal by Sougato Bose and his collaborators (I had heard of it already a year ago in Bangalore). Anil Ananthaswamy has written a popular summary of the article for New Scientist and I am quoted (together with Maaneli Derahkshani) saying all the good that I think of such attempts.
- I have written a comment (arxiv) to correct some technical mistakes made in a couple of papers on collapse models. The trouble in the original articles came from slightly too brutal perturbative expansions of stochastic differential equations. I have tried to show different ways one could have obtained the correct results and explained what I think went wrong in the original derivations. The bottom line is that to compute the empirical predictions of all “standard” collapse models, it is never necessary to consider the full stochastic differential equation. The average of the solutions, which obeys a simpler linear master equation with smooth solutions, is always sufficient. This is really not a big deal, but perhaps this will simplify the life of people who want to make computations with such models.
On Saturday May 6th, on the Monza formula 1 track in Italy, three world class marathoners (Eliud Kipchoge, Zersenay Tadese, and Lelisa Desisa), helped by a team of Nike physiologists and bio-mechanics engineers, attempted to break the 2h barrier on marathon. Eliud Kipchoge came the closest with a breathtakingly fast 2h00’25” setting an unofficial world record (smashing the official record of Denis Kimetto by 2 minutes). A beautiful 1h documentary by National Geographic has been made on this attempt and on the 6 months preceding it. It is a beautiful ode to running, replacing the Chariots of Fire in my Pantheon of running movies.
While the 2h barrier is about to be broken by professional runners from the East African highlands, the more reachable 3h mark is still a tough target for amateur runners. This post is about my attempt to break it.
Running hard makes a priori no sense. It brings less health benefits than running moderately, is far more painful, gets you tired, and often wears down your will for other activities. The endorphines are only a mild compensation for this absurdity. They are probably not the main reason why people train: in my opinion, runners are not mainly endorphines junkies. Running is great rather because it allows to project down your value to hard numbers. It is hard for me to know how good of a researcher I am, but I know I am worth 36′ on a flat 10km. I also know quite precisely what I could do to improve this number almost deterministially. In running, progress is straightforward to quantify and well correlated with the work that is put into it.
I have been running regularly, more or less seriously, for about 12 years. But I have not really made progress in the recent years. I was decently well trained when I set my records on middle distances (mainly 1500m in 4’15”) and it has thus become difficult to beat my old self. The exhilarating feeling of slow but steady progress has faded away. Trying a new distance for which I had no previous reference was a good way to get some motivation back. Marathon training is also quite different from middle distance training, and thus provides some novelty in an otherwise dull workout routine. So I started an training plan for the Munich marathon in order to add a new “number” to my profile.
There is a lot of theory around running. Not all of it is scientific and there is quite a lot of running “tips” that are probably just superstition. That said, I think the fundamentals are more or less undisputed and so may be worth quickly explaining. I will have to be very sketchy and the reader interested in constructing a good training plan should crawl the web or get in touch with a professional coach. I will leave out the problems of nutrition/hydration, running form/technique, and gear.
My target for the marathon was 3h. This translates into 4’15” per kilometer or 14.1 km/h. At what pace should I train? Surprisingly, rarely at 14.1 km/h. What distance should I run? Counter-intuitively, never close to the marathon distance before the D-day.
The core of the training should be aimed at building the fundamental endurance without exhausting the body for the harder workouts. It should be at a pace that is easy, at which one can “easily speak but not sing”. For me, fundamental endurance is around 5′ per kilometer or 12km/h. This is much slower than marathon pace, but there is no need to go faster. Going faster would not improve fundamental endurance. It might slightly enhance other abilities I will mention later, but it would do so at the price of increased muscular fatigue. The latter would reduce the benefits of the other work outs that require a fresh body.
At the opposite end of the training pace “spectrum” lies the speed at V02 max. If you run faster and faster on a treadmill, the amount of oxygen consumed by your body per unit time will increase steadily until it reaches a plateau. The speed at which this happens is the speed at VO2max (vitesse maximum aérobie, VMA, in French). You can still go faster, because the body knows how to produce energy without oxygen. But at these faster speeds, the muscles produce massive amounts of lactic acid through the incomplete processing of glucose. Runners who specialize in distances from 400m to 1500m (and even 5000m for the finish) need to increase their tolerance to lactic acid because their race pace is faster than their pace at VO2max. For marathon, it is useless and so the fastest training pace is the pace around V02 max where the cardio-respiratory system is already at its max. It can be estimated crudely as the pace at which one can run 6 min (the half Cooper test) full blast. For me it is around 19km/h, that is much faster than marathon pace. Training at this pace puts the heart and all the respiratory system under maximum strain. By pushing the aerobic boundary, it makes the slower marathon pace easier to sustain. Training at this pace is extremely tiring and difficult and thus requires a fresh body.
The next important pace, more fuzzily defined, is the pace close to the “lactic threshold”. Actually, even before reaching the V02max, where your cardio respiratory system is at its maximum, the muscles already start producing lactic acid. This lactic acid is continuously eliminated by blood circulation but at some point it starts accumulating. The delimitation is not sharp, but for me it starts perhaps around 16-17 km/h (or the 10km pace).
At last comes the “specific” speed, that is the race pace. For me again, this is a tiny bit more than 14 km/h. Interestingly, nothing much physiologically happens at this pace so it is not great for training. One needs to run at this pace so that the body gets used to it (to make it the automatic cruising speed) and to improve the running form and running economy. But there is no need to overdo it, especially at the beginning.
Starting from a decent level on middle distance running but a recent lack of proper runs, I aimed for a 3 months training plan containing 5 work outs a week. The objective of a standard training plan is to put the previous pieces together. Here is what a typical week contains:
- 2 easy endurance run (45min to 1h at 12km/h)
- 1 “short interval” training session at VO2max pace (typically 20*[30″ fast 30″ slow]), starting with a 20-30′ warm-up
- 1 “long interval” training session around the lactic threshold (typically 6*3′), starting with a 20-30′ warm-up
- 1 long run, 1h30 to 2h15, at endurance pace (12 km/h) with a few easy accelerations inside (say 4*5′ at 15km/h). Going beyond 2h15 provides no benefits (or rather, the potential benefits are outweight by the difficulty to recover and the tremendously increased risks of injury).
The two pure endurance runs are easy and can typically go after the 3 other hard workouts. The two interval work outs, which both put a strong strain on the heart, should be spaced as much as possible.
This typical week is adapted to the first part of the training plan as it optimally develops the physiology. It is done at paces either much slower or faster than the race pace. Only in the second half of the training plan is the gap bridged and this latter speed introduced, either during the long interval session or during the “accelerations” of the long run. This plan could be improved by adding at least one session of musculation (targeted on core muscles and legs), possibly after a shortened endurance run. The benefits are more long term and so I did not put any in my 3 month plan. It made me run between 60 and 85 km a week and I could feel tremendous progress. The two weeks before the race day were 30% and 60% lighter in volume than the typical weeks to get back some freshness. I was ready.
After such a lot of training, cruising at marathon pace (4’15” per km) feels very easy, especially after two weeks of lighter work outs and overcompensation. I actually started a bit faster, stabilizing around 4’09” where I felt just fine. The first 10 km were naturally very easy, I just had to focus on staying calm and drinking properly. I clocked 41′ (3h pace gives 42’30) without any effort. Going up to the half marathon mark at the same pace required a bit more effort. From the half mark to the 30 km mark, the pain slowly ramped up. Maintaining the pace started requiring a constant pressure from the mind, the feeling of cruising seamlessly faded away. After 30 km the amateur marathoner enters terra incognita. Long runs are almost never longer than 30 km during the training months because going beyond destroys the body too much for vanishing benefits. But on race day, the end is at 42 km. From 30 km to about 38 km I almost maintained the pace at the price of a huge mental effort. At that point the pain is everywhere in the body, every single cell lacks oxygen and glycogen. Around the 38 km mark, physiology beat my mind. At some point, no matter how much the mind pushes, the chemistry in the muscles says no. My body slowed down and my mind had to agree. I struggled to stay above 4’45” per kilometer which is just barely above the usually trivial fundamental endurance pace. This tough mind body bargain brought me to the finish line.
Official chip time 2h56’55”. Mission accomplished.
It is a decently good marathon, especially for a first. The slow down happened quite late in the race and was not catastrophic. Otherwise the pace was steady. Now I can say I am worth “below 3”. This will compensate any blow to the ego from the rejection of an article by angry referees. At least for a short while. But next time, to get the same feeling of achievement, I will have to go faster.