With Fermat's Last Theorem now proven (not by Fermat!) and formalized (not (yet) by Kevin Buzzard's project! see also this post), it may look like we are at a risk of running out of questions concerning sums of like powers, i.e., expressions of the form $x_1^p+\cdots +x_k^p$ for some $k$ and $p$.

At least, recent developments motivated me to look into such problems, and it turns out that, fortunately (?), there are still many things we don't understand at all. This post is a kind of tour of the numerous open problems that remain about sums of like powers.

Disclaimer: I am not a mathematician. This post talks about a topic well-suited to recreational mathematics in the sense that the statements of the results are elementary (at least I hope I understood them correctly), but the proofs are much more difficult and I don't claim to have the necessary prerequisites. I'm just a curious onlooker, but I may of course be wrong about some points.

Our starting point is Fermat's Last Theorem (FLT). I will give its statement below in case you are not familiar with it (but in this case you should also look at the Wikipedia page to learn about the historical story involving Fermat's margin notes!). FLT shows that there are no positive integer solutions to the following equation for $p>2$:

By contrast, there are infinitely many solutions for $p=2$, which are called Pythagorean triples (they are the triples of integers that can be the length of the sides of a right triangle). This post is divided in four sections covering the following generalizations:

• allowing more terms on one side of the equation, i.e., $x_1^p+\cdots +x_k^p=y^p$
• allowing more terms on either side, i.e., $x_1^p+\cdots +x_k^p=y_1^p+\cdots +y_l^p$
• not forcing the right-hand side (RHS) to be a $p$-th power but in fact aiming at achieving all integers as a sum of $p$-th powers $x_1^p+\cdots +x_k^p$
• looking more generally at the number of ways in which we can achieve each integer as a sum of $p$-th powers

Equations $x_1^p+\cdots +x_k^p=y^p$

For arbitrary powers $p$, how many positive integers to the power $p$ do you need to sum to get another positive integer to the power $p$? Of course we exclude trivial solutions by imposing $k>1$ and requiring that the numbers are strictly positive. FLT then tells you that, for $p>2$, two numbers are not enough, so you need at least 3 numbers, i.e., $k\ge 3$.

Euler conjectured that, in fact, you need at least $p$ numbers, i.e., $k\ge p$. That is, you need to sum three cubes to obtain a cube, four fourth-powers to obtain a fourth-power, and so on. And indeed, for cubes ($p=3$), we do know by FLT that we must have $k\ge 3$. But it turns out that Euler's conjecture is wrong: I'll review this below following Wikipedia's summary. The first refutation came when a computer search in 1966 by Lander and Parkin on the CDC 6600 led to a two-sentence paper giving the identity:

Thus, summing four fifth-powers (i.e., $k=5-1$) is sufficient to get a fifth-power (i.e., $p=5$). In fact, it also happens that there are counterexamples for fourth-powers, though this would only be found two decades later: Elkies developed a construction of infinitely many counterexamples, and did a computer search to find a concrete one:

Later, the smallest possible counterexample of a sum of three fourth-powers giving a fourth-power was discovered:

Of course, for fourth-powers, having three terms on the left-hand-side (LHS) is best possible because two is impossible by FLT. By contrast, for fifth-powers, we don't know whether four terms on the LHS is optimal: two is impossible, but three is open.

Also note that, while we know infinitely many counterexamples for fourth-powers, we only know two counterexamples for fifth-powers (including the one given above) if we restrict to positive integers and if we disallow solutions where all terms have a common factor. If we allow negative integers, we know precisely two more counterexamples; I'll come back to this issue of negative numbers later.

What about sixth-powers? We don't know. More accurately, we don't know whether it is possible to use strictly less than 6 terms on the left-hand side (thus giving other counterexamples to Euler's conjecture): in fact we don't know of counterexamples to Euler's conjecture with other powers than 4 or 5 (and for 5 as I explained we only know a handful). But there's more: we also don't know whether we can write a sixth-power as a sum of six sixth-powers; the best known expression is a sum of seven sixth-powers. By contrast, we do know how to write a seventh-power as a sum of seven seventh-powers, and likewise for eight. For all larger powers, we no longer know; all known solutions use more terms than the value of the power.

To sum up the number of terms needed in the LHS:

• $p=2$: two terms possible
• $p=3$: two terms impossible by FLT, three terms possible
• $p=4$: two terms impossible by FLT, three terms possible
• $p=5$: two terms impossible by FLT, four terms possible, three terms open
• $p=6$: two terms impossible by FLT, seven terms possible, everything else open
• $p=7$: two terms impossible by FLT, seven terms possible, everything else open
• $p=8$: two terms impossible by FLT, eight terms possible, everything else open
• $p\ge 9$: two terms impossible by FLT, all known solutions involve strictly more than $p$ terms

Such results are reviewed here and more exhaustively by the venerable EulerNet project (table "KNOWN LOWER BOUNDS", column 1), a volunteer computing project using BOINC to search for solutions to these problems.

In terms of general results, as far as I can tell, there are no known lower bounds on how many terms are necessary beyond what is given by FLT (i.e., two terms never suffice for $p>2$); and there is no known general upper bound on how many terms suffice as a function of $p$ except for what follows from Waring's problem (as I'll summarize below). See also the discussion here.

Equations $x_1^p+\cdots +x_k^p=y_1^p+\cdots +y_l^p$

A relaxation to the previous equation is to study equal sums of like powers, where both sides of the equation are sums of potentially more than one power (but all powers are still the same). Of course, we then look for nontrivial solutions, i.e., solutions where we cannot use the same number on both sides, and we want to find the smallest possible numbers $k$ and $l$ of terms on each side to have a solution. How large do these get, depending on the power $p$? Do we get solutions with a smaller total number of terms than in the case of the previous section (where we impose $l=1$)?

This rephrased problem is also more robust in presence of negative numbers. Allowing negative numbers of course has no impact when $p$ is even, but when $p$ is odd it could make a difference. However, when $k$ and $l$ can be greater than 1, then we can always make all numbers positive up to moving them to the other side of the equation. For this reason, allowing negative numbers makes no difference in the current section, whereas allowing them in the previous section reduces (for odd $p$) to the current section.

So what do we know? There is the Lander, Parkin, and Selfridge conjecture which asserts that we must have at least $p$ total terms for power $p$, i.e., $p\le k+l$. Contrast this to Euler's refuted conjecture: the latter only talked about equations with one term in the RHS ($l=1$), but it claimed that solutions needed $p$ terms in the LHS, i.e., the stronger bound $p+1\le k+l$.

The Lander, Parkin and Selfridge (LPS) conjecture has not been refuted yet. None of the counterexamples of the previous section refute it, because they beat Euler's bound by just one term, i.e., they ensure $k+l=p$. By contrast, achieving a fifth-power as a sum of three fifth-powers would refute the LPS conjecture, because the total number of terms would be 4. We also do not know whether for $p=5$ we could have $l=k=2$, i.e., a nontrivial solution to $a^5+b^5=c^5+d^5$. This amounts to asking whether there is an integer that can be written as a sum of (positive) fifth-powers in two different ways, which is a long standing open problem that I'll mention again at the very end of the post.

The LPS conjecture is not interesting for squares, and for cubes it is true (and not tight) because of FLT: you need at least two terms on each side so at least 4 terms in total, whereas the LPS conjecture makes the weaker assertion that you need at least 3 terms. For fourth-powers and fifth-powers we know solutions matching exactly the bound (e.g., the counterexamples to Euler's conjecture from the previous section), and for sixth-powers we had no Euler counterexample in the previous section but we do know a solution with 3 terms of each side (i.e., with $k=l=3$):

See this Wikipedia list for other similar solutions.

More results are in the EulerNet table "KNOWN LOWER BOUNDS". In particular for sixth-powers we don't know a solution with two terms on one side (i.e., $k=2$ and $l=4$ or vice-versa). We also know according to this table that eight total terms are possible for eighth-powers, but it is open whether seven total terms suffice for seventh-powers -- and the higher the powers, the less we know.

As far as I can see, we have no general lower bounds whatsoever on this problem, i.e., we have no weakening of the conjecture which is known to be true, except again from FLT when requiring one side to have only one term ($l=1$). In the current state of affairs no proven results seem to rule out that there could exist solutions to $a^5+b^5=c^5+d^5$, and more generally to $a^p+b^p=c^p+d^p$ for every $p\ge 5$. It also seems that we don't know whether there is any difference in the number of terms required when imposing $l=1$ like in the previous section, compared to the general case -- though as I explained we know some expressions using $l>1$ for which there is currently no known analogue with the same $k+l$ but with $l=1$.

Also, we do have bounds on the related Prouhet-Tarry-Escott problem, but I'm not covering this one here because it involves equations with multiple powers at the same time (see also this for multiple powers).

As for upper bounds, as far as I understand the only ones that we do have are the ones deriving from Waring's problem, which is the next question I'll talk about.

Achieving all numbers as $x_1^p+\cdots +x_k^p$

So: instead of finding sums of a small number of $p$-th powers that are equal to a $p$-th power, we could instead wonder how many terms are needed to express all positive numbers as a sum of that number of $p$-th powers. This is related to equations of the form $x_1^p+\cdots +x_k^p=y^p$ from the first section: if the LHS ranges over all numbers, then in particular it ranges over $p$-th powers, so the equation with $y^p$ on the RHS will necessarily have a solution.

For squares ($p=2$), the situation seems reasonably well-understood. We understand:

• Which numbers can be written as the sum of two squares;
• Which numbers can be written as the sum of three squares;
• That all numbers can be written as the sum of four squares.

For this last point, we allow the squares to be zero. If we only allow nonzero squares, we still get all numbers but with a small infinite list of exceptions¹, and allowing five nonzero squares suffices to achieve every number greater than 33. See this paper for a more general discussion of what happens when we disallow zero terms; I won't discuss the issue further and will always assume that zero is allowed.

For cubes ($p=3$), the situation immediately gets more messy:

• For numbers that can be written as the sum of two cubes, there is a Wikipedia page and a paper giving a characterization
• We do not know which numbers can be written as the sum of three cubes
• What we do know is that every natural number is a sum of at most 9 cubes of positive numbers, and 9 terms is the smallest possible number of terms in general: see Waring's problem

What about higher powers? Well, Waring's problem precisely asks us to figure out, for each power $p$, the minimal number of terms $g\left(p\right)$ that we may need in sums of (possibly zero) $p$-th powers in order to achieve all integers. We know that the function $g$ is well-defined in the sense that for every $p$ there is a finite number of terms $g\left(p\right)$ that suffices², and there is even an explicit formula that is conjectured to give the value of $g\left(p\right)$ for arbitrary $p$.

There is also a variation where, instead, we ask for the number $G\left(p\right)$ of terms in sums of $p$-th powers that allow us to achieve all sufficiently large integers. This is far less understood: we do know that this function is well-defined and admits upper bounds, but the exact values are unknown except for squares (where we know from the above characterizations that $G\left(2\right)=g\left(2\right)=4$) and for fourth-powers (where $G\left(4\right)=16$ is known). For cubes we do not know how many terms are needed: we could achieve all numbers with $g\left(3\right)=9$ terms, but we know that 7 cubes suffices for all but finitely many numbers; however this does not match the best-known lower bound of $4$. So $4\le G\left(3\right)\le 7$ and the exact value is not known.

There is another variation: we can allow negative numbers, and more generally (to have a version which is also interesting for even powers) we can ask how many terms we need to achieve all integers when we also allow minus signs in front of the terms. This is the so-called easier Waring's problem. It is "easier" in the sense that it is less difficult to prove that indeed for every power there is a number of terms that will always suffice, but it is otherwise less understood than the original problem described earlier. For instance, when allowing minus signs, we do not know whether 4 terms are needed for $p=3$, i.e., whether every integer can be written as a sum of four cubes of (possibly negative) integers; as this paper reviews, we know that 3 terms are not enough and that 5 terms suffice.

It then seems natural to combine both variants and ask for the least number of terms (positive and negative) that is needed to achieve all numbers except a finite number of exceptions. This variant appears under the name $W(\cdots )$ on page 6 of these MIT course notes, but it does not appear to have been otherwise studied.

How many times can we achieve numbers as a sum of like powers?

Beyond the study of how many terms are required in sums of like powers to cover all integers (or almost all of them), there is the question of the number of different ways in which we can express every integer.

For squares, we have some understanding of the number of possible ways in which numbers can be written as sums of squares, and of the number of ways in which they can be written as sums of 3 squares (with zero being allowed).

For cubes, again, our understanding is more sparse. The question relates to the famous anecdote of the taxicab number between Hardy and Ramanujan about the fact that 1729 is the smallest number that can be expressed as the sum of two positive cubes in two different ways. (Note that if we allow negative numbers then 1729 is no longer the smallest, because 91 can be expressed as $3^3+4^3$ and as $6^3-5^3$, see here.) The sequence of taxicab numbers studies more generally the smallest numbers $Ta\left(n\right)$ that can be written as sums of cubes in $n$ different ways.

The question extends to generalized taxicab numbers, with $Taxicab(p,j,n)$ being the smallest integer that can be written as the sum of $j$ $p$-th powers in $n$ different ways. Of course we know very little about these, and they happen to be related to the conjecture that we saw earlier by Lander, Parkin and Selfridge. Indeed, nontrivial solutions to $x_1^p+\cdots +x_k^p=y_1^p+\cdots +y_l^p$ with $k=l$ are in fact giving us a way to write the same number as sums of $k$ $p$-th powers in two different ways. Thus, the LPS conjecture would imply that $Taxicab(p,j,2)$ is undefined unless $2j\ge p$. In particular one open question is whether $Taxicab(5,2,2)$ is defined at all: this is again the open question of whether there is an integer that can be written as a sum of two positive fifth-powers in two different ways.

The goal of this post is to describe my experience with psychotherapy in the past few years, structured as questions and answers. It is written from the perspective of in-person psychotherapy in France, for problems that are not too severe (nothing life-threatening), and from someone with the financial resources to pursue it (more on this below). It is meant as a personal report of how I see psychotherapy and how I feel about it – it is certainly not authoritative and I do not have any specific legitimacy to write about this.

The post covers mostly the meta aspect of my experience with the therapeutic process, and does not really say much about the nature of the problems.

What is this, in factual terms?

In the spring of 2021, I finally managed to act on an idea that I had considered for years: I took an appointment on the Web to see a psychologist (chosen at random among those close to where I lived).

Since then, I have been consulting a therapist on a regular basis, once every 2-3 weeks on average with some variation. (In particular, I stopped for 6 months as I was traveling abroad and used this as an opportunity to see whether stopping made a difference. That said, eventually I felt that seeing a therapist again was a good move.)

Over that time, overall, I have been seeing three different therapists, in two different cities in France. In all cases the modalities were similar: talk therapy (which I would classify as supportive therapy), for 50-60 min sessions. The cost was 70-75 EUR/session.

Which kind of therapists can you find in France?

There are plenty of resources online to help you navigate the many different kinds of psychotherapy that exist, but let me just write here what I understand as a non-expert user.

The broad categories include:

• Psychologue, which are the ones I went to. They are not medical doctors and cannot prescribe drugs, but they must have a university diploma (it is a regulated title). They can have different therapeutic methods, with, e.g., cognitive behavioral therapy being one of them.
• Psychiatre, which I have not tried; the main difference with "psychologues" seems to be that they are medical doctors and often include drugs in their approach (and in particular they can prescribe psychiatric drugs). Note that other medical doctors in France (e.g., médecin généraliste aka GPs), can also prescribe such drugs.
• Psychanalyste, which follows the specific practice of psychoanalysis. I have not tried these either.

I'm assuming that the practitioners listed on established therapy websites have some form of credentials, though of course I have not checked. Beyond the above, there are other kinds of neighboring professionals, e.g., life coaches, that I am not familiar with.

I have only seen psychologists in-person, though you can also see them online. (Many in-person psychologists also offer online sessions, and there are also purely online services.) This was a deliberate choice — to me it felt like interacting with the therapist in person was an important part of the experience (and it also drew me more out of my comfort zone), but of course online therapy can also have advantages (it can be more convenient, it can be cheaper, it can be easier to find available therapists depending where you live, etc.).

Many therapists will have some kind of schedule about when they can see patients (during the day or at night, online or onsite, etc.): the schedule can also be a factor when choosing the right therapist.

Did you try psychiatric drugs?

No. I'm scared of them, it is somewhat irrational but at some level I think it's a reasonable worry. I thought I would rather try talk therapy first, and things never got dire enough for me to consider trying psychiatric drugs.

That said, I would definitely try them if I felt like there was no other option. And it is entirely possible that I have been missing out on some immediate benefits that could have been obtained more easily using drugs.

How different were these therapists?

The three psychologists I have seen were, to me, surprisingly similar in terms of how they operated. There were of course some small differences: they were different people, following somewhat different processes (one practices EMDR which did not convince me, another practices CBT which convinced me more). Overall, though, I was more struck by the uniformity of the process than by individual differences. This relates a bit to the dodo bird verdict, i.e., the various psychological theories seem to end up having roughly similar effects on patients. (Note how much this contrasts with physical health, where the efficacy of treatments is obviously different depending on what the underlying illness is — e.g., appendectomy is a very effective treatment for appendicitis but a very ineffective one for pneumonia.)

Somewhat more subtly, depending on the therapist, the areas of my life that we would end up talking about most regularly were not the same. However, it is hard to tell whether how much of this was connected to differences in therapeutic approach, vs differences in what were the main problems in my life at a given moment when I was seeing them. I also suspect that the first sessions with a therapist tend to initiate a dynamic that will tend to be followed for longer afterwards, but which is reset when changing therapists.

Another common point between these therapists is that they all adhered to the basic framework: the sessions started on time, ended on time, the therapist listened actively, focused on what I was telling them, were welcoming towards what I disclosed, reacted appropriately, etc. And there was no interaction with the therapist outside the sessions. This being said, I have heard of people who experienced wildly inappropriate behavior from their therapist — so I know this also exists and unfortunately one needs to consider the possibility that things may not go well.

Does it help?

I would say it does... probably. That said, after all these years, I'm still not sure how much. Part of the problem is that there are lots of confounding factors: some problems got better but it's unclear how much this was thanks to therapy (vs thanks to my own efforts, or thanks to changes in circumstances). I would say there was an immediate improvement in the first few months (though I only say this in hindsight, and it wasn't so clear in the moment). Again, though, it's unclear whether things improved thanks to the therapy, or whether me starting the therapy was a sign that I was ready to take action and get better.

I think there are clear benefits immediately after sessions: I tend to feel relieved, and feel like I have more clarity about the problems discussed. I get some "fresh start effect" giving me confidence that I'll manage to make progress on these problems in the following weeks. I also get a self-esteem boost, simply because someone gave me (against payment) the feeling that my problems were important enough to deserve some attention.

In the longer term, I think there are other changes. Here are the main ones I can think of:

• More clarity about where you and your worldview come from. It is a bit cliché that the therapist wants you to talk about your mother, but in fact talking about family relationships turned out to be far more enlightening than I would have expected. Here is how I would summarize it: when you grow up as a child, you take a lot of things for granted about the environment in which you live, your family, your caretakers, etc; and this affects a lot how you see the world later. It requires some deliberate effort to reexamine things and see your life from an adult angle. (E.g., "what's happening in the lives of my adult friends right now is what happened earlier when I was a kid and now it makes more sense"; or "This thing that happened to me as a child was a pretty big deal, even though I couldn't tell at the time and hadn't taken the time to reflect on it since") So I got the opportunity to realize that many points in my behavior and my problems could be better understood in the familial and sociological context that I come from. (The problem with this kind of epiphanies is that it's hard to notice when you have them - your perspective shifts on things that were "hidden in plain sight", and afterwards it feels like you always knew about them at some level.)
• Getting an outside perspective about things. You may be going in circles stressing over problems and then you realize that these problems sound very different when you explain them to a neutral third party. Maybe this exercise helps you to remember why the problems matter to you. Maybe you realize that they don't matter so much in the end. Often you will realize that your way of seeing the situation is not universal: it's not necessarily invalid, but it's more personal than you thought. On the other hand, sometimes you will get outside confirmation from the therapist that your situation is objectively difficult and that your feelings are a healthy and understandable reaction to the situation. This turned out to help: in some cases in real life, I could use my mental model of the therapist to estimate how they would react to what happens and do an outside view visualization exercise. It also helps me to make some distinction between who I am as a person in the long term, vs how I am feeling in the present time about the problems of the moment.
• Emotional literacy. Trying to get the habit of mentally checking on myself how I am doing at an emotional level: accepting that I have emotions, noticing them, understanding them. You may benefit more or less from this depending on how connected you are to your emotions: I had a long way to go, so there were some "noob gains" that were easy to unlock.
• Being more open. I think it is easier for me now to talk about life stuff to others (e.g., to friends, or on my blog ;)) without fear of judgement. At some level this is just about trusting other people; and opening up to the therapist was a (very scary) first step. In fact, the extent to which it scared me was (with hindsight) pretty good evidence that I needed to make progress on that front. So I think it was useful training for me to say deeply weird and inappropriate things to a stranger and have them react in a welcoming and non-judgemental way. (Also, given that people overall are weirder than it looks, talking to a therapist can help you realize that your seemingly very unusual personal problems are rather mundane when seen in the very wide space of all the things that people may need to talk about.)
• Useful pointers, concepts, and theories. Sometimes the therapist will point out that what you are saying/thinking sounds like [problem category X], and will explain to you briefly what this is about. These labels can be good pointers to read more about the topic yourself if you didn't know about it. This proved useful to me, despite all the Wikipedia-backed self-diagnosis I'm capable of. Indeed, it's one thing to know that an abstract concept exists, and another one to have someone point out to you how that concept can relate to a very specific thing that you just lived or said or did.
• Better self-knowledge and more clarity about your life problems. You're probably already aware of the fact that some things in your life are not how you would like them to be. However, I have the impression that in many cases you become accustomed to your problems and you no longer realize that you have them. Or, more viciously, you had never realized that you had these problems in the first place, but they were still taking their toll. Indeed, therapy was for me the occasion to notice many obvious problems that I wasn't noticing (e.g., a fish not having the concept of water), and that these problems were not universal and maybe even fixable! Further, the immediate problems that I would complain about would often be a consequence of these larger problems, and I hadn't connected the dots. (Of course, awareness of a problem doesn't mean you can immediately fix it, but it's an important prerequisite.)

Why can't you take care of yourself on your own?

I sympathize with the hope that one should always be able to fix all personal problems on one's own. Self-sufficiency certainly looks like something desirable! Further, psychological problems look like they should obviously be self-fixable, simply by introspection and willpower. (This is not like material problems, e.g., it feels less like a failure to ask friends for help if you need to carry something that's physically too heavy for you to carry alone.)

You can also get the impression that therapy isn't necessary for you if you already have some reflexivity about your life (as opposed, e.g., to people who aren't interested at all in their own psychology) and already have some of the theoretical concepts (as opposed, e.g., to people who don't know how to find documentation about human psychology). If you already do things like journaling, and if you're already able to find information online by yourself, then why would you need help?

I have been this person for a long time — but I have changed my mind about this. I now think that it's OK to ask for help. And I think it's acceptable even in cases where it's not an absolute life-or-death necessity, e.g., something that you could possibly do on your own but which will be far easier to handle with some help. I think that the myth of self-sufficiency can sometimes come from the fact that asking for help is scary.

I also think that the inability to ask for help, and the years of procrastination before finally seeing a psychologist, have a lot to do with me having been raised as a man. The statistics I've heard seem to suggest that men in France are much less likely to see a therapist, even when corrected for gender differences in the prevalence of some psychological problems. In fact, hearing about this masculine stereotype and recognizing myself in it was part of what encouraged me to try psychotherapy in order to escape it.

There are other bad reasons not to see a therapist (which I suspect can also have some connection to gender), including:

• Imagining therapy as a battle of wits where the therapist would lose.¹ If you have a high opinion of your intellectual abilities, you may think that seeing a therapist is a waste of time: how could they possibly find something clever to say about you that you wouldn't have been able to deduce on your own? In particular, if you are trained as a scientist, it's easy to want to take a scientific view on everything, and be contemptuous towards people who study inferior topics such as psychology. In any case, part of the therapeutic process is to accept that someone may be able to help you with things that you are not managing well on your own. I think you can be both highly intelligent and find yourself unaware of your problems or unable to make progress on them.
• Imagining that the therapist can't possibly understand you. A variation of the above argument, based not on the lack of intellect but the lack of familiarity. How could a stranger find something relevant to say about your life when you see them one hour every two weeks, compared to you living your own life 24/7 for decades, or compared to friends or family who have known you for years? The counter-argument is that therapists actually understand and remember very little factual detail about what you are telling them — but your general approach and feelings can be pretty obvious to spot for a trained professional. It's disconcertingly easy for them to tell you something about the situation that was not thinkable from your perspective
• Imagining that the therapist can't solve your problems. Maybe you have it all figured out: the problems in your life are XYZ (something something job, something something relationship), and these problems are hard to fix, indeed you're already working at fixing them. How can a psychologist help? Well, not by solving your problems directly — but it's important to realize that active listening (as opposed to problem solving) can already help a lot. Of course sometimes part of the road in getting better is indeed to fix some already-identified problems that don't depend on you, e.g., being stuck in a bad financial situation, in a harmful job, in a toxic relationship, etc. But you may need help in order to actually get it done, and you may also need help in figuring out what the real problem is.
• Worrying about confidentiality. Part of my self-sufficiency fantasy was worrying too much about secrecy, e.g., I was uncomfortable with the risk and vulnerability involved in disclosing my feelings or private details about my life. In this light, deliberate disclosures to an untrusted stranger sounded like the worst breach of security imaginable. Of course, therapists are supposed to observe strict confidentiality about the contents of sessions — but in my view this was not a strong security guarantee (especially judging from the standards of computer science, e.g., compared to a cryptographic protocol). So part of the process of seeing a therapist, for me, was accepting that my problems were not so terribly confidential that I couldn't tell them to someone else — and that I wasn't such an important person and so it didn't matter so much if someone else knew.
• The therapist doesn't really care about you. I admit that this is true — for all three therapists, I got the impression that they were doing the job seriously during the session, but I wouldn't imagine that they would "care" beyond the boundaries of the session.² Which is normal — it's just their job. Still, like all professionals, it doesn't mean that they cannot do their job well.

In contrast with the above, there are of course some good reasons not to see a therapist, e.g., if you can't afford it, or if you legitimately don't need it.

OK, why can't you get help from friends then?

I sympathize with the view that professional psychotherapy is not an ideal system because it's based on a financial transaction: it leaves out those who can't afford it, and appears to compete with the non-commercial help you can receive from friends (or other people you may have various kinds of social relationships with, in particular romantic partners — I could quip that this is especially true for men in heterosexual relationships, as we tend to disproportionately benefit from free emotional labor by women).

I sympathize because I think it's important to cultivate friendships where you can be open and vulnerable and receive the same kind of benevolent help that you get from professional therapy. With loneliness becoming more prevalent, and social ties getting weaker, it certainly sounds like therapy is the wrong solution — and being closer to your fellow humans without a mercantile crutch is a better answer.

However, this argument isn't so convincing when you look at other areas of life. Cooking for instance: you can cook with friends and share meals, or you can use money to buy a sandwich or go to the restaurant; it sounds like it's OK that the two approaches would coexist and may be more or less appropriate depending on circumstances. Further, while there can be some common points between a therapy session and emotional support from a friend, there are also some important differences:

• There is no expectation of reciprocity. You're not supposed to "use" friends to vent about your problems, or for one-sided emotional support. Of course, doing it at some level is normal, but it's also normal for friendly conversation to stray away from your problems towards other topics (in particular towards the problems of the other person). Asking for friends for help too often feels (to me) like I am burning some social capital and could eventually degrade the friendship. Not so with therapy: it's all about you, and the social obligation to care about the other person is replaced by financial payment. The therapist is officially here to help you for some set period of time — which your friend didn't sign up for.
• The goal of therapy is explicitly for you to get better. This is in contrast with many friendly interactions with people, which pursue other goals (e.g., having uncomplicated fun). Of course, friends can support each other and help each other to improve their lives, but not all friendships are like that (and not all friends are interested in this kind of topics, and they are not interested all the time).
• The therapist is completely exterior to the rest of your life. There are some things that it's difficult to say to friends. Say you want to talk about a mutual acquaintance: it can be difficult for them to keep a secret. Or say you want to talk about your relationship with the friend themself... These can be mitigated if you have a diverse enough set of friends to ask for advice from people that are sufficiently far away in the social graph, but this is not always possible. Or say you want to say something embarrassing, which the friend may find inappropriate, or which could worsen their image of you if you told them... In brief, saying something to a friend can have some irreversible side effects. By contrast, the therapist doesn't know anyone else about your life, you don't have a strong duty to them and you can stop seeing them if you want: so in a way you don't have to strategize about what you tell them and what you don't.
• The therapist has psychological training. Unlike your average friend, the therapist is a professional who is trained in helping people with their psychological needs. You may have some friends who also happen to have such qualifications, or to be naturally good at this; but most of your friends probably are not.
• The therapist has a neutral relationship towards you. Your conversations with a friend are part of an ongoing relationship with the friend. Depending on that relationship, there can be some emotional intensity going on which could blur the psychological help that you receive. E.g., maybe what you are saying resonates with another shared experience, maybe your friend is mad at you for some unrelated reason... The therapeutic relationship is different because it has some level of distance, and the therapist will work to maintain that distance and stay in their role without letting their own emotions interfere.

So, broadly speaking, therapy sessions have a clear agreed-upon framework, which your interactions with friends generally don't. Your mileage may vary here: some people do not have trouble with the ongoing negotiation of giving and receiving help from friends; but personally I'm much more comfortable when the framework is clear and I don't need to second-guess.

This leads to the obvious question of whether you could get your friends (or strangers) to agree to such an explicit framework in order to exchange mutual support. This is the idea of co-counselling as I understand it, and it sounds promising but I have never practiced it.

But what makes psychotherapy work?

I'm not sure, really:

• What I say during sessions sounds a lot like introspective self-monologue, but the difference is that I'm putting it out loud in front of someone who listens, which forces me to articulate it more.
• Having someone else involved in the process makes me accountable (e.g., genuinely trying to make progress), like getting classes from a teacher to learn how to play an instrument vs trying to learn on your own.
• The therapist's outside perspective seems to make it easy to say things that must look obvious from the outside but are not obvious to me from the inside.

In any case, it's not because the therapist would have some magical solutions to fix the specific problems that you have. They will often just state the obvious, e.g., remark "this problem seems to be bothering you a lot" (perhaps with the implication "other people could have the exact same problem but it wouldn't be an important topic to them"). Such observations seem trite, but somehow they can help me realize, e.g., that I had been spiralling non-stop about the problem but that this was neither proportionate nor necessary. Alternatively, it can force me to articulate the problem more and understand what's really bothering me.

Astral Codex Ten has an interesting article with a subjective take on why some people seem to benefit from therapy more than others. (The author, Scott Alexander, is a psychologist — and he is also a central TESCREAL figure, so you should probably take the blog with a grain of salt.) Of the reasons mentioned, I identify a bit with the "external reassurance" part: having someone else telling me something never has quite the same weight as when I say something to myself.

Why didn't you start psychotherapy earlier?

For most of my adult life my #1 reason for not doing psychotherapy is that I felt like I didn't need it. Further, I didn't even see it as an option — I thought this was only for people with major problems, or for rich people, or generally not for me. In retrospect, I think it could have helped me a lot to get started sooner. Probably some of my friends would agree — at the time I think I did not have many friends who knew me closely (mostly by lack of self-disclosure from my part), but even then some probably suspected that something was amiss. I think I just didn't have enough perspective to ask myself how I was doing, whether things could be better, or whether some outside help could be useful.

I'm not sure when is the first time I started imagining that seeing a therapist was something I could actually try. From a personal diary I know that I had the idea at least in summer 2018, and the idea regularly recurred from then on, but it took me around 3 years at least to act based on this idea. (This kind of negligence in following my goals and taking care of myself is of course part of the issue as you might have guessed.)

Starting therapy was also easier because some of my friends were doing it, and because broadly speaking it had progressively become more culturally acceptable. (To the extent that people now talk about therapy speak and therapy culture to criticize how much the approach of therapy has percolated in everyday life.)

Overall, more sarcastically, one could say that I had now transformed into the kind of person for whom therapy was a good fit sociologically speaking.

In any case, I think a large part of what blocked me was fear: psychotherapy, and the vulnerability it entails, were really outside my comfort zone. Doing frightening things is hard — and I'm still not very good at it.

What do you talk about during sessions?

It's very unstructured. Usually I will spend a few minutes just before the session to remind myself of what happened since last time, and whether some particular things stick out. (It would probably be a good idea for me to do this more consistently, but I haven't managed to form the habit yet.) Depending on the session, sometimes there will be obvious problems that I'm struggling with, and sometimes it's less clear. When there isn't too much pressure from bigger crises, the session will sometimes explore some longer-term issues, or more conceptual territory about broader topics.

There is some variance between sessions: sometimes I feel like I understand things in a new light, sometimes I'm disappointed because I feel we didn't really connect all that well. I guess that this is inevitable. It's also interesting to see how sometimes the main topic ends up being something completely different from what I would have anticipated; or to see what are the topics that we apparently managed to conspicuously avoid.

I have heard from friends that it sometimes happened that they would run out of things to say during a session, and I think it is a common worry about therapy sessions. So far this has never happened to me: I don't seem to ever run out of things that I need to talk about. (This may be a good or a bad thing.)

I have seen therapists giving some "home assignments", e.g., asking me to make progress on one concrete objective by the next session. That said, I didn't get the feeling that they were enforcing this very closely — they would not necessarily bring it up the next time.

When does it end?

I'm not sure. Of course one can ask whether it's a normal thing for therapy to go on indefinitely — isn't this a sign of its ineffectiveness?

After about 5 years I'm not sure how much I still "need" therapy, but I still feel that there are things holding me back, and I don't feel confident enough yet about being able to address them on my own — which is why I haven't stopped yet. The 6-month break I took in 2023 also gave me the impression that, in the long run, it made sense for me to start again — though I used this as an occasion to switch to a different therapist.

I do not know, from the therapist's side, how much they optimize for patients that "need" them more, and whether they can "sack" you if you're managing well enough or if you don't seem to benefit a lot from therapy. (I know that some therapists have a clearer protocol about how many sessions the therapy will last and what is the expected trajectory, but I have not encountered this yet.)

Is therapy a good use of money?

First, the answer to this question depends of course on how much money you have. I have enough money that paying for therapy sessions is not a financial problem, but I realize that this is definitely not true for everyone.

It is of course awful that people who need care (psychological or otherwise) are prioritized depending how much they can afford to pay for help, rather than how much they would benefit from it. For this reason, I have wondered whether it was acceptable for me to ask for this care, given that there were certainly other people who needed it more (e.g., people with real issues that were genuinely putting them in trouble!), and also that the money I was spending could have been used in different ways (e.g., donating to a good cause).

In fact, this question was the occasion for me to go on a spiral of doubt: is it OK to spend a significant amount of money towards the specific goal of improving my life? I think that, to some extent, this kind of doubts were connected to the issues that caused me to seek therapy in the first place. This may be related to another reason why therapy can be effective: paying money to get help is a way to prove to yourself that your well-being has some value (at least financially), and that it is worth the "investment". (Still, this can't be all that there is to it: I would expect that paying for therapy works better than indulging in other expensive things with no long-term benefits.) In fact I can think of situations afterwards where psychotherapy loosened a bit my relationship to money: I felt OK paying for something that might make me happier, because I was "already" paying significant money for psychotherapy so it wasn't a huge investment in comparison.

On the negative side, however, psychotherapy is branded as "healthcare", which I think can make it easier for people to accept whatever it costs. At least, personally, I find it hard to be rational about money when help is involved. So I don't really put the 70 EUR I pay per session in balance with other ways in which I could have benefited from spending this money. There is also a question of habit: it's easier to continue once you've started.

Anyway, looking at the bigger picture: I have paid a few thousand euros in total (and also invested time, around 100 hours overall over the course of five years), with the outcome that it probably helped me feel better and improve in the problems that I had. When phrased in this light, I don't regret the investment.

Why are you writing about this?

The idea to write this post came from discussions with friends about my experience with psychotherapy. Despite the normalization of therapy (at least in the social circles around me), these conversations gave me the impression that it could still be useful to share my personal experience with therapy — especially coming from someone who doesn't typically write about this kind of topics, or who might radiate (at least in some contexts) the impression that I'm not the kind of person who "needs" it. Indeed, I hope that this can help readers of this blog to think about whether they may benefit from therapy, e.g., some people who might be in the same situation where I was a few years ago.

Anyway, let me reiterate that this is just personal experience: the point isn't that you should absolutely do therapy, or that I endorse it wholeheartedly. (As you can see, despite the overall positive impression, I also have mixed feelings.) The point is to share my perspective in the hope that it can be useful, and of course in the process to help myself to understand better how I feel about therapy.

[This post is written in English but is given from the perspective of someone living in France. The situation in other countries may differ.]

I'm writing about an unusual topic: the choice to use cash (rather than payment cards) when paying at businesses. Over the last few years, essentially since COVID, more and more businesses seem surprised when I pay with cash -- I feel a kind of social pressure not to use it. Hence this post: I will explain why it's legally allowed to pay with cash, why I do it, and why I sometimes don't.

The law

Are businesses required to accept cash payments? In France, the answer is yes, with some exceptions:

• They can refuse coins or bills in bad condition, or money suspected of being counterfeit
• They can refuse payments with too many coins
• They can refuse payment if you don't have change (but I guess this is only if the customer doesn't have the exact amount)
• In some loosely defined cases, cash can be refused when it's inconvenient (e.g., some vending machines, etc.)
• There is a limit to how much you can pay using cash (the maximal amount depends on the type of purchase)

In practice, this law still seems to be respected: I have not seen many places who refuse cash payments outright. However, I see more and more places that don't have change, or complain and ask whether I couldn't use a payment card instead.

The reasons

Here are the main reasons why I think it's important to be able to pay using cash:

• It avoids giving money to payment card companies. On card payments, a percentage of the money goes to the payment card company (instead of the seller). Of course, these companies¹ are an oligopoly: they are hard to compete against because of the network effect. In other words: essentially all customers have a card from one of the major payment networks, so essentially all shops have to accept these networks, and starting a new payment network is complicated because you need both shops and customers to coordinate. By paying in cash rather than card, I make sure that the entire payment goes to the seller rather than payment card companies. I think this is usually a better way to allocate my money.
  • Some shops give discounts to customers who pay cash (because they get 100% of the payment amount). However, in my experience the practice is pretty rare. I assumed that it was because merchants were forbidden to do it because of the contracts that they sign with payment card companies, but this does not seem to be the case, at least with Mastercard or Visa².
  • I am aware that handling cash isn't entirely free -- many businesses pay third parties to handle their cash for them. There is one big difference however: as opposed to payment cards, I am more confident that this is a market with fair competition. Indeed, businesses can switch to a different provider when they want, and their customers will not notice.
• When I pay cash, it does not leave a trace³. This means my bank knows less about how I spend my money -- and indeed, this is none of their business. It's also not the business of merchants to know the history of my payments with them, as some sellers seem to be tracking customers using their payment means. It's also none of the business of the many third parties to which I imagine banks and shops are reselling the payment habits of their customers.
• Cash is more resilient. This makes sense both at an individual level and at a social level. At an individual level, if your bank decides that it no longer wants to do business with you for some opaque reason, or if a technical problem means that your card no longer works, then you can be in trouble. At a social level, cash works better whenever there's a crisis: this was demonstrated, e.g., during the 2025 Iberian Peninsula blackout.
• Many people don't have cards. It's important that these people can also pay and receive payments without needing cards or bank accounts.

The Cash Matters initiative lists many other reasons, more or less convincing, to prefer cash.

The counter-reasons

There are some reasons that sometimes make me reconsider the choice to pay cash:

• For some consumer goods that you buy in-person and which can be returned, some shops will refund you in money when you pay by card, but when you pay cash they will only refund you with a voucher that can only be used in the same shop (and often has an expiration date). For obvious reasons, actual money is better than a store voucher, so I will often compromise and use payment cards for purchases where I might change my mind later.
• Of course, sometimes paying cash is inconvenient, e.g., when I am in a hurry, or when I forgot to stop by an ATM.
• Online payments obviously don't work with cash.
• For some purchases (e.g., related to travel), some payment cards provide some built-in insurance but only if the payment is made with the card. (Of course, such payments are usually made online anyway, so the previous point applies.)
• Some banks offer cashbacks when you pay by payment card. However, for now the amounts have been too small for me to care. Some other banks charge you for ATM withdrawals, but mine does not.

There are other systematic reasons to prefer card payments, but I don't find all of them convincing:

• Cash may make some crime easier. This can happen at an individual level, i.e., you can fall prey to crime (e.g., theft, extortion). It can also happen at a social level, e.g., by making organized crime easier⁴. That said, I tend to find the erosion of personal freedom much more concerning -- I'm more afraid of states and big corporations than I am afraid of criminals.
• Hygiene -- this was a big concern with COVID. However, again, I find it hard to be concerned (see previous point).
• As a computer scientist, I agree that it's unpleasant that cash relies on the difficulty of replicating a physical artefact. Protections against counterfeit money feel a lot like security through obscurity. Still, somehow, it mostly works. You could have expected that the Internet would make it easier for counterfeiters to exchange restricted information, but in reality the opposite seems to be happening: counterfeit euro notes are at a historic low.
  • I understand the intellectual appeal of replacing cash by a digital solution that addresses the current shortcomings of payment cards -- probably involving some form of cryptocurrency with zero-knowledge proofs or something of the sort. Yet, at present, I find it hard to be enthusiastic about cryptocurrencies: I'm disgusted by their huge environmental cost, and the amount of speculation they attract, in comparison with the actual services that they provide. (And yes, I am aware of systems like proof of stake to reduce the environmental impact of cryptocurrencies, but all of this seems pretty far away in the future -- whereas the question of whether to use cash or card payments is a very immediate one.)
• Environmental impact. Measured in terms of greenhouse gas emissions, it seems that paying in cash may have more impact than paying by card. That said, the amounts seem pretty negligible (see, e.g., here): at a few grams per transaction, this is probably very small compared to the environmental impact of whatever you are buying.

Conclusion

Unlike other political issues, I don't see many people around me who care about cash payments -- which is what gave me the impression that this post may be worth writing. To summarize, the cash ecosystem looks like something that would be almost impossible to reinvent today if it didn't already exist. It is a simple but effective way to anonymize transactions and ensure that payments aren't taken over by payment card companies, so I hope it lasts.

I don't know if the right to use cash is seriously endangered in the short term, at least in the EU: the European Central Bank says pretty clearly that they want to keep cash around⁵. However, from what I can see around me in the past years, I'm getting a bit worried that it may become more and more difficult to pay with cash in practice. The move towards a cashless society also seems to be pretty advanced in some countries such as Sweden (see also this critical article from the BBC).

I leave you with some related work, as I searched for other groups who might be advocating for cash payments or investigating the matter. The answer seems to be that such groups exist:

• There is the Cash matters initiative that I already mentioned above.
• There is a KEEP CASH campaign in the UK, which unfortunately seems to be only organized as a Facebook page.
• The US-based ACLU has a piece about cash.
• The US also has a proposed bill to enshrine the right for customers to pay by cash, but I don't know whether it stands a chance of being adopted.
• There is a comparison of the right to pay by cash in EU countries here.

Thanks to Marc Jeanmougin for feedback on this post.

I tend to write a lot about my opinions about academia in my area (theoretical computer science), e.g., about open access, about general problems with academia, etc. If you are interested in this topic, I just contributed an interview to the latest Bulletin of the EATCS, the European scholarly association for theoretical computer science (of which I am now a vice-president).

You can read the interview in PDF format here.

I have read the book Politiser le bien-être by Camille Teste. A possible English translation of the title would be: “Making wellness political”.

I found the book interesting, so I wrote this blogpost to summarize it. Maybe this can help make the book's message available to a larger audience: the book is written in French, and not freely available online. Of course, these notes are just my personal work: I am not affiliated to the author, and they do not claim to be a substitute to the book.

The high-level structure of the book is in three parts:

• Define wellness as it is usually understood, and present its shortcomings.
• Analyze how and why activist movements reject wellness, even though wellness can be useful to such movements.
• Propose how to build a political form of wellness, which can address its limits, support political activism, and enable change.

Wellness and its shortcomings

Wellness can be understood as health in the far-reaching sense of the constitution of the World Health Organization: “Health is a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity.” It can also be understood as encompassing various sectors, inspired by the list of the Global Wellness Institute (a wellness trade group):

• Beauty salons, cosmetics, anti-aging products;
• Nutrition, dieting, dietary supplements;
• Exercise;
• Traditional medicine and alternative medicine¹;
• Preventive medicine;
• Mental health, self-help, meditation, etc.;
• Workplace wellness;
• Spas and thermal/mineral springs;
• The list also includes some sectors indirectly connected to wellness such as wellness tourism and wellness real estate.

These practices are a significant sector of economic activity. Indeed, they represent an economy whose worldwide value is estimated by GWI to be $4.9 trillion in 2019, with expectations of growth despite a dip during COVID. This amounts to a few percents of the world economy, which the World bank estimates to $133 trillion in 2019.

So, there is a large industry that aims at making people feel better. What's not to like about it? The book argues that wellness can be criticized in at least three main ways:

• The need for wellness nowadays is made more acute by the capitalistic system² which is powering the wellness industry:
  • One leading cause is wage labor, which pushes people to work long hours at demanding and sometimes physically harmful jobs, sacrificing their well-being.
  • More insidiously, we can suffer because of the loss of meaning at work, and the possible harmful effects of one's work on the planet.
  • Other social trends makes wellness more necessary to some groups. For instance, patriarchy has negative effects on the well-being of women specifically, e.g., mental load, social pressure (e.g., to conform to beauty standards), and of course aggression risks. So women are especially in need of what wellness can offer³. One can make similar points about racism. In other words, the wellness industry exists in a system that actively works against the well-being of some people.
• Well-being practices are normative and not inclusive:
  • They drive away many people who do not conform, e.g., physical practices (yoga, etc.) are not marketed towards people who are too fat according to dominant standards.
  • Also, they are expensive, so they mostly cater to the needs of the rich, even though they are typically not the ones who need it most.
• Some wellness practices are actually a Trojan horse for problematic doctrines:
  • Essentializing gender or biology;
  • Cultural appropriation of non-Western practices;
  • Quackery, e.g., people favoring ineffective alternative medicine over effective conventional treatments, and facing dire health consequences;
  • Taking advantage of psychologically vulnerable people, e.g., selling them expensive therapy, or enlisting them in cults.

So, the effects of the wellness industry are self-defeating because they happen in a system that works against wellness; they are misallocated, often problematic, and mostly try to alleviate the symptoms rather than fixing the root causes of unhappiness. The book further points out the deeper problem that our perception of well-being is wrong:

• The wellness industry leads people to believe that well-being is something that they can buy⁴, reducing happiness to a financial question: you will be happy if you earn enough and consume enough. This makes us forget about alternatives such as downshifting or simple living: doing less, working less, simplifying our lives, being happy with less, etc.
• Well-being is presented as a purely individual pursuit, with approaches focusing on the self (think of exercise, dieting, meditation, yoga, etc.). This can give us a fake sense of control, i.e., it gives the impression that we can be happy through our individual actions. However, the wellness industry is in fact neglecting the collective factors of happiness: cultivating meaningful relationships, being connected, feeling helpful, etc. It is also distracting us from the political causes of our unhappiness. For instance, it put individual workers in charge of dealing with their problems (e.g., working conditions, work-life balance), even though these are better understood as a collective struggle (e.g., via labor unions).
• The individual approach to well-being comes with a form of moral imperative: you have a personal responsibility towards others to become the best version of yourself. Instead, we should see this more at a collective level (again: caring for each other), and at a political level (aiming for a system which would make it easier for everyone to be happy).

This warped perception of well-being is part of a individualistic trend where we are less and less willing to rely on each other⁵ and to believe in the value of collective action, or even in the fact that collective action is possible.

Wellness and activist movements

Having presented this picture of wellness, the book moves on to the question of how wellness is perceived by activist movements. (The book uses “the left” as shorthand to talk about activist groups that seek to effect change towards some worthy goals, but I find this a bit polarizing so will stick with more neutral terminology.) It starts by a concrete example: a wellness week-end organized by Extinction Rebellion for its members, which drew significant criticism from other activist groups:

• The spiritual overtones of such initiatives are seen with skepticism because they are perceived as incompatible with a rational, fact-based approach. This may make the movement less effective (e.g., if spiritual practices are substituted to evidence-based practices), and may also harm the credibility of the movement (e.g., on scientific issues like climate change).
• Further, they are reminiscent of organized religion, but left-wing movements (in particular marxism) typically see religion as a tool used by those in power to justify the current world order (e.g., via promises of a happier afterlife).
• Last, the use of spirituality by cults, and the closeness between wellness and cultish practices, may mislead outside observers and make them see activist groups as cults.

There are other apparent reasons why, arguably, activist movements should not focus on wellness:

• Wellness activities are less urgent and less effective than direct action, e.g., an activist group should focus on its goals first and foremost, and not the well-being of its members. Likewise, the public perception of individual activists is often that they should be ready to give everything to support their cause, instead of wallowing in self-care.
• Focusing on one's well-being is a privilege, and one that the underprivileged typically do not have. Hence, activist movements may be seen as hypocritical if they present to act towards social justice but end up focusing on wellness activities that are intended for their privileged members.
• In any case, pragmatically, in an individual sense, activism is often tiring and disheartening, so it is often not a good way to be happy.

The book proposes the following retorts to these arguments:

• The goal of progressist movements should be, ultimately, to promote some form of well-being. In this light, wellness practices are a way to stay in touch with the long-term goals of the movement. It is short-sighted and productivist to aim to effect “maximal change” without stopping and paying attention to the conditions in which this change takes place and which effect it has on the members of the movement⁶.
• We should not accept the “warrior monk” image of tireless activist leaders who give everything they have. It is probably influenced by toxic masculinity, given that many of these charismatic leaders are male. In fact, they would often be better inspired to do less, spend less time in the spotlight, and be aware of their own limits, emotions, and weaknesses. Further, activist movements should make it possible for their members and leaders to express vulnerability instead of pressuring them to project an image of flawlessness. In fact, the common perception that activists must be perfect (in French, “pureté militante”) is really a double standard that we should reject.
• Typically, activists are in need of wellness, more so than the general population. First, activism is often done in addition to a full-time job, so activists will be more busy than non-activists; further, activists are often overwhelmed because there is too much to do for the cause and not enough helping hands. Second, specifically in activist movements that campaign for the rights of minorities, the members often come from the minorities in question, so this is especially hard for them: they must shoulder both the disadvantages that society imposes to that minority, and the work that must be done in order to effect change.
• In the long term, movements are not effective if their members burn out. Further, if they are too demanding, then they may also scare away potential newcomers. For this reason as well, paying attention to the wellness of activists is a good long-term strategy for activist movements.

In fact, the book argues that it is necessary for activist movements to openly talk about wellness and care. Indeed, there is a risk that this emotional labor will be done anyway in an invisible fashion (and, disproportionately, by women), and that it will not be recognized. Further, the very act of taking care of oneself and of other community members can be a political act, namely, saying that your well-being matters: especially if you are from a minority that society does not care about.

Building a suitable form of wellness for activists

After defusing this criticism of wellness in an activist context, the book concludes by presenting its end goal: developing a notion of wellness which both addresses the problems pointed out in the first part, and can serve activist movements as explained in the second part. That is, wellness should be compatible with the end goal of activist movements (i.e., with the world that they want to make happen), and also be compatible with the path to get there (i.e., it should help political struggle, make activists stronger, and make activist movements more attractive).

The book offers some general guidelines for wellness practitioners (e.g., teachers):

• Wellness practitioners should strive at welcoming all people, including those who do not conform to the conventional idea of attractiveness. They should make this explicit and visible in their communication, and focus on exercises that all their participants can do, including those who have a disability. This means that, instead of leaving some behind, wellness should cultivate the art of caring for each other and including everyone (e.g., when going for a walk, going at the pace of the slowest person).
• Wellness should respect people's boundaries: practitioners should only touch participants with affirmative and easily revocable consent, and making it easy to opt-out or leave instead of being trapped by group dynamics. Of course, in the current majority culture, participants may find it difficult to feel what they genuinely want, or to express their needs: for this reason, wellness practitioners should explore communication approaches that aim at empowering participants. The general idea is that participants should not be asked to ”let go” and passively receive what is offered, but that they should be actively choosing what will happen.
• Wellness should be horizontal rather than vertical. It should not be organized as an all-knowing teacher having hierarchical power over students. It should be more horizontal, with teachers and participants working towards a common goal. It should also aim at empowering students, making them autonomous in the practice, instead of making them dependent on the teacher's knowledge.
• Wellness should be financially available to those who need it most, e.g., with fees that depend on revenue. Wellness professionals should also think about how they structure their activity, e.g., investigating cooperative models.
• Wellness practitioners should be careful about which ideology they promote. For instance, they should eschew the law of attraction which claims that wanting something is enough to get it (hence making individuals responsible for their misery by not “wanting” the right things); they should avoid gender essentialism; etc.
• Wellness practitioners should be aware of the risk of cultural appropriation. This is the situation where Western practitioners teach non-Western practices (e.g., yoga) and often misunderstand them, or bowdlerize them to be compatible with a Western capitalistic worldview.

The book thus identifies deeper positive functions of wellness that are needed in today's society and in activist movements:

• Wellness approaches can reconnect us to traditional roots that we have lost in the name of modernity and rationality. Indeed, the use of non-Western esotericism in wellness can be understood in a colonial way. Specifically, we have assimilated non-Western cultures, we have essentialized their exoticism, and we give them the role of helping us escape from our purely rationalist worldview, while still considering them as inferior. In the face of this, wellness practices can help us acknowledge the fact that the path to our own well-being is sometimes beyond the reach of rational thinking.
• Wellness approaches can reconnect us to our body, and remind us that we are embodied beings. They should make us rediscover pleasure, especially physical pleasure, e.g., via sex positivity. They should encourage us take our time and do less, e.g., via silent walks, meditation, etc. They should free us from the tyranny of having to constantly improve, and leave us space to just live. This goes against a productivist view which makes us forget the needs of our body and tame it to follow the rules of the system. They can also help us change our mindset by making our bodies stronger, training them to take more space rather than being subdued (especially for women and other minorities), and teaching them to defend us (e.g., with self-defense, in particular for women).
• Wellness approaches can make us aware of the true causes of our suffering, in particular systemic causes. They can also help us support one another with our vulnerabilities. They can also help us notice and accept how we are currently influenced by the system that we wish to change. In so doing, they can lead people towards collective political action.
• Last, wellness approaches can reconnect us to the importance of spirituality. The book argues for a personal form of spirituality, in particular one intended to connect us to nature. It perceives spirituality as a way to give importance to what matters to us, and thus to support political action.