When I first had the idea of writing a text with such title,
a month or so ago, I had a completely different thing imagined. I was enjoying
some ‘me’ time while reflecting on the pointless nature of life. The setting
must have had it’s say too. A freezing walk through a charming old town of a
city I’ve never been to before, an unexpected stop at an underground pub, and some
whisky menu with prices I was more than willing to pay. How long it’s been
since the last time I took a flight of stairs down to enter this obscure place
with filthy tabletops and basses whispering to one’s soul- an eternity! Proof
of the ephemeral nature of time served my being almost the oldest breathing
object there. After ordering some Scottish liquor to a much too young and much
too knowledgeable bartender, I trusted her enough to surrender my phone under
the reasonable pretense of charging.
Singularity you say. Must be a fancy way of expressing the
state of being alone. “It must be what I am and feel right now”, I thought.
Please I can, love I could and cherish if must. Who’d imagine the depth of my
being wrong and right at the same time?
That flight of stairs opened Pandora’s box, teleporting me
into those times when happiness was as simple as that, when meaning was as
tangible as a glass of cheap liquor. As dividing by 0 is undefined in
mathematics because there are no such numbers which multiplied by zero would
produce a non-zero dividend, we follow this law too, dividing our time, our
lives and ourselves by something different than zero. Singularity can mean a
whole lots of things. What I have just described in mathematics is one example.
Applied to physics, it is the moment when gravity and density become so strong
that physical laws break down, as for example in the centre of black holes. Regarding
AI, singularity is a point where artificial intelligence surpasses human
intelligence leading to uncontrollable and irreversible technological growth.
Now back to the underground bar, filthy table and gravitational liquors. Applied to me, singularity isn’t something intelligent enough to need surpassing. To start the loop I only needed to take a flight of stairs down. But that’s not all. I am lying.
Irina,
ReplyDeleteIf we speak about singularity in a truly mathematical sense, then chess is one of the rare human systems where singularity can be *experienced*, not merely defined.
In mathematics and physics, a singularity is not an object, but a boundary: a point where local laws cease to be sufficient, not because reality disappears, but because description becomes incomplete. Chess contains similar points — subtle, silent, and decisive.
Most chess positions obey local principles: material balance, initiative, space, tempo. Cause leads to effect. Improvement is measurable. But there exist rare positions where these principles no longer determine the future. Evaluation stabilizes. Strong moves repeat. Progress vanishes. This is not ordinary equality — it is a **singular position**.
Such a position can only be understood holistically, through a small set of global invariants.
One invariant is **parity**: whose move it is, how time is structured, and how reversibility behaves. In these positions, time stops being linear. A single tempo does not change evaluation, yet it changes the entire horizon.
Another invariant is **structure**: relations between pieces and pawns that remain unchanged under all “reasonable” continuations. These structures do not invite improvement; they only permit preservation or irreversible rupture.
The third invariant is the most delicate: the **transcendence of equality itself**. Equality ceases to be a number and becomes a logical object — true within the system, yet undecidable by local means. Engines recognize it. Humans sense it. Neither can force it directly.
The hierarchy among these invariants defines what might be called the **total strategy** of the position: not a plan, not a move, but an ordering of what cannot be changed.
Tactics, in contrast, need not be fully revealed. It is enough to say that tactically such positions are characterized either by the *distance to mate* becoming undefined, or by the appearance of a repetitive double locus — a nodal point where the next step preserves the invariant in a Gödelian way. What matters is not calculation, but proximity to the boundary.
Seen this way, chess resembles a geometry with negative curvature: locally flat, globally rigid. One small action — a single move — can radiate consequences far beyond the visible horizon, not because it is brilliant, but because it touches the structure itself.
Engines reach these singularities and grow silent. Not from weakness, but from completion. The human player, however, may still choose to cross the boundary — not by calculation, but by sacrificing a local invariant to break a global one.
Perhaps this is the true singularity in chess: not superiority of intelligence, but the encounter with a position that contains more time than can be played.
With respect,
Veaceslav