Münchhausen trilemma
That&#x27;s not a true trilemma. A trilemma is a &quot;choose two out of three&quot;. Therefore a trilemma is always depicted as a triangle where the vertices are the things you would like to have and the edges are the possible combinations.<p>A trilemma is an extension of the concept of a dilemma, which is &quot;choose one out of two&quot; .<p>Example: [good, fast, cheap]: you can have good and fast, but it&#x27;s going to be expensive. Or good and cheap, but it&#x27;s going to take longer. Courtesy of Jason Kottke[0], some more simple trilemmas:<p><pre><code>    Elegant, documented, on time.
    Privacy, accuracy, security. 
    Have fun, do good, stay out of trouble.
    Study, socialize, sleep.
    Diverse, free, equal.
    Fast, efficient, useful.
    Cheap, healthy, tasty.
    Secure, usable, affordable.
    Short, memorable, unique.
    Cheap, light, strong.
</code></pre>
----<p>Ultimately the generalization of a trilemma is a (3-)budget. I will show this.<p>An n-lemma is &quot;choose (n-1) out of (n)&quot;. Geometrically&#x2F;topologically the things you would want in a n-lemma corresponds to the vertices in an (n-1)-simplex. A dilemma is represented as a 1-simplex, i.e. a line segment with each alternative as one end. In this case alternatives are points and so are the choices;  in the 3-case alternatives the choices are segments. I&#x27;ll leave you to imagine 4 and 5-lemmas geometrically.<p>An n-simplex can be defined in a n-dimensional vector space as the region of points whose coordinates sum to 1. So for example a 2-simplex (a triangle) is the set of points (x,y,z) such that x+y+z = 1. In a n-lemma, only vertices are allowable choices -- i.e. x,y,z must be all either 0 or 1.<p>In an n-budget, we can have partial allocations -- rather than have to choose two out of study-socialize sleep (i.e. sleep deprivation, loneliness or failing classes), I can spend my finite time as P% study, Q% social, R% sleep. Note: we can still represent budgets as points <i>inside</i> (n-1)-simplices.<p>Of course, some trilemmas are not <i>easily</i> seen as extremizations of budgets. In some cases this will be because certain alternatives are fully binary (either you have floating exchange rates); in others, it&#x27;s because we need to think a little more about the trade-offs (cheap, light, strong) -- we need to think harder about how lightness works against strongness.<p>---<p>We can next imagine how to model slightly more complicated decision structures as n-lemmas. For example, I might have to decide between being married or single (each with its delights) and single people might have to decide between intelligence, looks and agreeableness. (This is terribly sexist but presumably very beautiful people don&#x27;t have the same pressures to be smart and carve a space for themselves; and people who are intelligent <i>and</i> hot are full of themselves. Bear with me please). In this case we&#x27;ve connected a 1-simplex (married or single) to a 2-simplex. This is known as a simplicial complex, and it turns out we can (roughly oversimplifying) rebuild topology from the ground up by chaining simplices like that.<p>So the choose-one-out-of-three &quot;trilemma&quot; in the OP isn&#x27;t a trilemma at all. It&#x27;s some decision structure that arises out of a complex of dilemmas. Possibly because every choice is connected to every choice, it even has the geometric contours of a triangle, but a hollow one, one where the segments are not connected. Therefore it doesn&#x27;t generalize as a budget. What <i>is</i> the trade-off structure then? What is the finite thing that makes having everything impossible? What are these people talking about?<p>[0] <a href="https:&#x2F;&#x2F;www.kottke.org&#x2F;05&#x2F;04&#x2F;pick-two" rel="nofollow">https:&#x2F;&#x2F;www.kottke.org&#x2F;05&#x2F;04&#x2F;pick-two</a>