Playing the Glassperlen Game

(a "musical" introduction to how an aspiring magician might play it)


People play the Enneagram Game to better understand their basic desires, fears, and tendencies that affect their relationships and personal growth. But is traditional enneagram theory aiming for a bigger game, beyond personality typing? The history of the enneagrams seems to indicate yes. There are many references to enneagrams somehow connecting to all of human knowledge in the writings of all three of the founders. These references also talk about the elevation of the soul to the Divine, or maybe the downloading of the soul from the Divine. These references to "all human knowledge" and the more general and deeper spirituality around these bridges to the Divine bring to mind Hesse's Glassperlenspiel. Similar kind of lofty structure.

Reading without love, knowledge without tribute, education without heart, those are the worst sins against the mind.
- Hermann Hesse

That quote says a lot of what needs to be said here. But to see that, a short review of Hesse's novel is needed. The Glassperlenspiel is played by the inhabitants of the fictitious Castalia. They do nothing else other than play this purely intellectual game. They make connections between music concertos, mathematical structures, paintings, physics theories, history, and so on. They want to know and understand it all. They could not care less about the chaos and the pain beyond Castalia's borders.

The novel follows the trails of Joseph Knecht, who eventually becomes Magister Ludi, master of the game. But as he ascends to the highest level of the game, he becomes increasingly troubled by the emotional isolation from the rest of the world, and begins to question whether Castalia has it all wrong.

This inner conflict leads him to resign his lofty position and return to the reality of the world outside Castalia. But just days after he returns to the real world, he drowns in a river. So all that brilliance, all that strenuous work, comes to nothing, it looks like a waste. Now read the quote above again. The story and the quote are saying that focusing on cognitive intelligence, instead of a strong emotional counterpart, is not what humans ought to aspire to. In fact we now know that people with high EQ generally do better than people with high IQ. In truth, Hesse does not give us recipes at the end, leaving it up to each of us to decipher the meaning of Knecht's tortuous journey through life.

Hesse himself stated that the game was played so that players could eventually reach God. Now let's move down a notch because reaching God and calling it the "Game of All Knowledge" sounds a bit intimidating. At its core, the game rests mostly on connections between music and mathematics. In the early 40s mathematical theories of music were developed, mainly in Europe, so like many other important ideas, this connection between mathematics and music was in the air at the time of Hesse's novel.

But in exactly the same time frame of maximum world turbulence, around 1945, an arguably more consequential conceptual revolution, this time in mathematics itself, appeared in the work of Samuel Eilenberg and Sounders Mac Lane, their theory of categories. The generalization power of these categories was extraordinary. It was like a Glassperlenspiel of making connections between ALL the branches of mathematics. And this time, the rules of the game were very precise. In fact, if you insist on playing the Glassperlenspiel based on a precise set of rules, you will sooner or later end up in the middle of category theory.

This point of view reached a peak in the work of Alexander Grothendieck, who many consider to be the greatest mathematician of the 20th century. If I went on a limb, I could say that Grothendieck was the greatest Glassperlenspiel player, at least as far as mathematics is a big part of that game (ok, so I did go on a limb!). Grothendieck was interested in finding deep patterns in all of mathematics, unifying and building bridges between various branches of mathematics in the process, which is also the desire at the core of the Glassperlenspiel play. As an aside, Grothendieck is much more than a unique phenomenon in mathematics, his life reads like the history of the turbulence that hit Europe in the 30s and 40s. But this time not as an aside, but rather as the one aspect of his life that relates deeper with our interest in this game playing is his gradual movement away from the mathematics community and into political activism and more importantly for us, into spiritual matters (he dedicated a tremendous amount of his later writings to proving the existence of a Divinity).

The clip below attempts to give us a conceptual overview of all these threads connecting Hesse's work with Grothendieck's work and with music. It's long and demanding, but if you can abstract away the specific mathematics and listen to the rhythm and the music behind those more specific mathematical forays, you'll get a good glimpse of what the Glassperlenspiel is about. I am only playing here a very short part of the clip, but if you have enough time and enough wine, it's truly worth rewinding and listening to the whole thing.



On the aibluedot site, I mention at length how humans play their personal game, the game of building their model of reality and constantly trying to improve that model in order to minimize surprise. In this case, these words (model and surprise) have precise meanings borrowed from bayesian statistics. We are trying to build equivalent models with AI. Although generally these models are mostly about cognitive intelligence, we will not be mistaken to think that soon emotional components will be added to them. Tying this back to us humans, we will not be off by much if we look at our more accessible version of the Glassperelnspiel as a game of improving the cognitive component of our model and the Enneagram game as a game of improving its emotional intelligence counterpart.

Resources: links, video clips



How Exactly is the Glassperlen Game Played?

(Just like for the Enneagram game, I am deliberately asking this question with the word "exactly" included. Because for either game, there is no such thing, there is no precise set of rules to follow. You are supposed to construct AND play your own game.)

So, with this caveat understood, how does one play the Glassperlen Game constructively, but not rigidly, and avoid a kind of futile ending as in Hesse's novel? Short answer: by trying to make connections between various life experiences and finding patterns in those connections. And then trying to leverage what has been learned in the past into the things one has to do in the future. Now, to nourish that desire to be relevant, to contribute to one's well being and the well being of those one cares about, all this leveraging will have to be done more so in the presence of that other form of intelligence, which we do not fully understand and which we may not understand until it surpasses our ability to understand it. If that intelligence takes your job away, what do you need to do? If your health is taken away because of all the stress coming from that loss, what do you need to do? If any other type of misfortune which AI may bring about hits hard, what connections can you make and what patterns can you notice which would allow you to go through it all?

So let's look at an example of such possible game playing. Say D lost his job as a lawyer to AI. Say he has always dreamed of being a park ranger, that he went to law school because both parents were lawyers and he was supposed to follow in their footsteps. How does he go about it? There is not much to connect his past experiences with the life of a park ranger. Yes, he camped by the river, and felt something. He wandered what it would be like to drive that bear away from the garbage bins. The process of reaching out to that goal goes in the opposite direction from a contemplative form of meditation. It requires effort and focus, it requires straining and some restlessness. But obviously, at some point the better way to proceed would be to combine contemplative meditation with this more strenuous form of Glassperlen play, at different times.

Just like in the graph below, the concept A="being a park ranger" appears disconnected from the rest of his inner graph of knowledge. He looks at it and cannot see any obvious patterns. Playing Glassperlen means he will strain to build tentacles, to add nodes and arrows to his graph of knowledge until those tentacles reach point A. And ideally reach it in multiple ways. So the central idea is to not let concepts we come across in our knowledge (and on which our future may depend) dangle disconnected, even if we do not need them integrated for immediate benefit. By playing the game we continuously integrate, we increase the connectivity degree of the graph of our knowledge and pay attention to the many patterns within it. This continuous adding of nodes and arrows in order to reach the concept "A" is shown below:

Before the game, concept A (red circle) is disconnectedAfter the game, A gets connected with the rest of our knowledge

The reader may say that this looks a bit contrived. But Mathematics itself has been played in this fashion. Perhaps the best way to see this is to look at Fermat's last theorem, which is very easy to state and be understood by everyone: namely, the equation

$$ z^m = x^m + y^m$$ has no solutions for positive integers (meaning 1,2,3, ...) \(z,x,y\) and \(m\), where $$ z > x > y > 0$$ and $$ m > 2 $$
Since \( 5^2 = 4^2 + 3^2 \), the equation does have solutions when \( m = 2 \). This theorem eluded proof for 350 years and because of its simplicity, it frustrated many souls. But this theorem was just like our concept A in the picture above, relative to Mathematics; it looked disconnected from the main graph of mathematical knowledge. It was only after Grothendieck (and others following him) played the Glassperlenspiel over a wide swath of Mathematics that its tentacles finally reached A, and allowed a proof to be found.

Maybe a personal story would help here. When I changed career paths, moving back and forth between theoretical math and practical software projects, I did not actually stray from a core subject. To me, Mathematics and Software (i.e. Computer Programming if you wish) are the same thing, they are fundamentally about formal systems of rules, or in other words they are games played according to specific rules.

Download and view in Acrobat Reader DC: Formal Software Development
In fact one can make this equivalence very clear and formal. Back in 2011, I wrote the outline of a fairly large program of study about this equivalence, Formal Software Development, shown on the right. This equivalence gains a significant importance in the age of AI. Because when we design powerful AI systems in the future, we will not have the luxury of allowing them to have bugs. This bug-free requirement can only be accomplished with formal methods, i.e. with lots of mathematical logic. You can find more about it at the link on the right, if that interests you.

I waffled about mentioning this personal story, because that program is only meant for professionals and we have already watched an example of more technical game playing in the video above. This may give one the impression that playing Glassperlen is a technical, mathy kind of endeavor. Many people I know have made more dramatic career changes than I have, and I admired them for doing it. Maybe that is a better way to play the game. I just have not done it, and my graph of interests and knowledge grew less dramatically.

In fact you are playing it too, consciously or subconsciously. Our brains synthesize knowledge and make connections all the time. They are wired that way. We have approximately 100 billion neurons in our brains, but a far larger number of connections (called synapses) between these neurons, up to 15,000 synapses for one neuron. So the degree of connectivity in the brain is very high, the graph looks very dense. About 95% of all the activity in the brain is in the subconscious, so you are playing a lot of Glassperlen without knowing it. It takes extra effort to play it with more awareness, to play it in the conscious rather than let it be played in the subconscious.

For the Enneagram game, we have been a bit more precise, and wrote down its set of traditional rules, with an invitation for the reader to change the rules to their liking. As it was already mentioned above, if you really insist of finding the rules of Glassperlen, you will sooner or later end in the middle of a mathematical theory, namely category theory. In fact, that connection is made in the video above quite eloquently, and if you watched it, you saw that the first candidate subject over which to extend the mathematical game is music. The problem I am having right now is translating the verbiage associated with category theory into a more digestible math-free language. The main concepts of functor and natural transformation require good examples in order to be understood, and right now those examples are abstract and not easy to explain to a non-technical audience.

Category theory has been referred to half-jokingly as "abstract nonsense". Don't read too much into that, it is abstract in the most powerful sense, precisely because it reveals so many connections and patterns between apparently disparate subjects. But to invoke the main results of category theory outside of mathematics, and show their immediate application to categories found in life is a bit stretching right now. I am still trying to find that verbiage, so in future versions I hope to add it here. You can find a video clip of a nice lecture on this theme, titled "Category Theory in Life" as the last clip on the Resources: links, video clips page. See how much of it jives with you.

Maybe by now you may also look at the Glassperlen as a game of increasing awareness about the things that matter to us individually, and at the Enneagram as the game of increasing awareness about the people who matter to us individually, including ourselves. Of course, there are crossings between the two, making all this game playing even more fun and more useful.


Glassperlen and the Enneagram Void

Hesse published an earlier novel, Narcissus and Goldmund, in 1930. He looked at the two as opposite and complementary types. "We are sun and moon, dear friend; we are sea and land. It is not our purpose to become each other; it is to recognize each other, to learn to see the other and honor him for what he is: each the other's opposite and complement." Narcissus typifies the Thinker (enneagram type 5) while Goldmund typifies the Artist (enneagram type 4).

We have already touched on the void between the 4 and the 5 at the bottom of the enneagram, where the 3-based symmetry is broken and no arrows cross. I mentioned that this void (especially its being diametrically opposed to the type 9 on the enneagram circle) is very important in my own game playing. But the void has fascinated many others since the enneagrams have appeared. You may want to chew a bit on these borders between various centers, including the border between the Instinctual and the Thinking centers and the border between the Instinctual and the Feeling centers (shown as red dots below). And also, why is it that the border at the bottom seems to play a larger role than the other two? Does this say something deeper about people?





You would think that those whose types and wings fall in this void area should be more complex, more volatile, and harder to understand. They straddle this major border between the Thinking and the Feeling centers. They may be the most naturally inclined Glassperlen players, because their wider cognitive and emotional ranges allow them to make more and deeper connections. But again, more complex does not mean superior, as we have already agreed in the Equality rule. And as we also agreed, any type can behave like any other type (including a 4 or a 5) under certain situations. Part of this game playing is to try to understand those situations better.

Would it surprise you, after all this mentioning of Hesse and Grothendieck, that both of them belong to the void!? Most people type Hesse a 4w5 and INFP in the MBTI. Most people type Grothendieck a 5w4 and INTP in the MBTI. In terms of MBTI, the difference between them is in the Thinking/Feeling dimension of MBTI, which is completely lined up with the enneagram typing. If you think of their calling in life and the things that they have achieved, that makes a lot of sense, doesn't it?


The Connection with Artificial Intelligence

I have spent the past two years jotting down my thoughts about AI at aibluedot.com. And I lose a lot of sleep about AI and the various directions it may go. Given that an astonishing number of jobs will vanish because of it, the normal reaction people usually advocate for is to join the AI race and focus our education system on STEM (Science Technology Engineering and Math) subjects. That way, the thinking goes, we can better compete within the new global economy, which we can safely assume it will be based on AI. But I think, as many of my colleagues do, that an increased emphasis on STEM subjects in our education system, at the expense of humanities, is NOT the way to go.

Here is why. We know that the Industrial Revolution has replaced human muscles in the economy with machines, and that the AI revolution will replace human brains in the economy with all sorts of computational devices. So what's left? What's left is really what makes humans special, what separates us from the muscle/brain animal kingdom. Call it the "heart" if you wish. So the idea would be to fortify this special gift that we have. And if we do want to fortify the human character, in the face of an unprecedented assault on our sense of worth, which is still being based on our ability to work and produce something of value, then subjects of humanities will be needed even more. In fact, my personal opinion is that humanities will be needed the most exactly in those programs which are focused on STEM subjects. Simply put, we would like the people who design AI systems to bake human-centered values into those systems. How could they do that without more seriously observing and understanding themselves first?






Although I have been searching for more specific ways in our education system which could be used to fortify character, the connections with the cognitive aspects of the Glassperlen game and the emotional aspects of the Enneagram came late. So I'm looking at these two games as a possible requirement in education, maybe in the junior/senior year of college. We play the Glassperlen game to build bridges between the things we know, to reach the things we desire to know, or that we would have to know in order to make a career transition; it's all about enhancing our cognitive intelligence. And we play the Enneagram game individually or with dear ones in order to enhance our emotional intelligence and our human connections, to build the needed human support system around us. Our mental resilience depends on both the cognitive graph and the emotional graph having high degrees of connectivity, similar to the dense synaptic connectivity in our biological brains.









Write me if you are interested in discussing various aspects of these ideas (or any other ideas YOU may have about the kinds of education initiatives we would need in order to better navigate our AI future) at the address on the left above. I use this email address nowadays mainly for this particular purpose, to talk about AI matters with respect to education (but, if we communicated via this address before, we can still carry on the older thread about formal software development, or the equivalence between math and software). For all other AI matters, like policy, governance, ethics, or security, please use the address on the right above.

(We reached the end of the section about games. We looked at two games, each requiring some effort to play. But all throughout this section, 3 has been our favorite number, not 2. And so there is a 3rd game to be played, but we all play it naturally, not just magic-ians and music-ians. The game of love. It's a bit out of scope here, so I say a few words about it on the side and tie it with the concept of instinctual drives, therefore completing the enneagram personality typing.)