What Makes A Brilliancy?

Beauty and Creativity

Beauty is deeply linked to creativity. Creativity can be defined. Creativity is the stuff dreams are made out of.

It is commonly defined as a combination which is original and useful (within a domain). Researchers have accepted this generally. One smack down is the idea that this misses the fact that art can be creative. Art can be creative, but is it useful? What is 'useful'? Useful means humans value it. Valuing something taking actions to keep it. It leads to realizing that usefulness is whatever goes.

The above definition has a good correspondence with some frameworks from neuroscience. When investigating brain changes when people were creative, they found the influence of two brain networks: the default network and the fronto-parietal network. When creative ideas are generated, the default network has greater activation, when creative ideas are evaluated the fronto-parietal network has greater activation. The 'construction system of the brain' brings together different elements. The fronto-parietal network evaluates these ideas. A creative idea can only be invalidated if there is something wrong with it. This is a common description of creativity in neuroscience.

Mind-wandering as spontaneous thought: a dynamic framework. Christoff et al., 2016

One fundamental question of creativity, is the exact mechanism by which it operates. A fact which needs to be accounted for is that creativity can apply to everything. Is this brain mechanism applied to everything, or is there an individual creativity that emerges for every subject.

Turns out that's a false question. Creativity is not one process. The approaches to creativity in neuroscience has been criticized by some researchers as presenting creativity as 'monolithic' entity in the brain. There are different types and different stages. We have creative idea generation and creative idea evaluation. We have this occurring not as a single process, but many processes based on the domain of creativity, doing chess or music or whatever. There are two kinds of generation, one that is purposely and consciously driven to find a solution to a problem, and one which is spontaneous and arises by itself such as shower thoughts, daydreams, and dreams. So creativity refers to many things. In chess we can compose puzzles, or we can come up with creative solutions over the board. We may a dream of chess puzzle. We may judge how creative a chess puzzle is.

Some researchers have said that "we know next to nothing about how brains generate creative ideas" and criticized the field of creativity: "the neuroscientific study of creativity finds itself in a theoretical arid zone".

There are so many factors that goes into creativity. Like what we know. Clearly we know more creative themes compared to olden times because we have the internet and so can see many more compositions. It would be much harder to create compositions in 1600 compared to now. There is the question of is it creative when everyone knows. Smothered mate, everyone knows. They already knew about smothered mate from at least 1497 as it was described in Lucena's book, Repetición de Amores e Arte de Axedrez, which is the oldest chess book that we know of. We have more knowledge now. However creativity is still valued, human nature didn't change, just what we have to work with changed.

The Scale of Aesthetics and Creativity in Chess (SACC)

Beauty is assessed by asking people what's beautiful. Or creative. But now we need a scale to measure it. This is the first scale that has been created in the domain of chess. Previous studies assessed beauty/creativity in chess, but did not create a scale/survey that could quantify beauty/creativity. This scale takes aesthetics and creativity to be part of the same coin. And they are. Beautiful chess compositions are creative compositions.

They created six dimensions, based on their review of aesthetics and creativity research in chess. The Scale of Aesthetics and Creativity in Chess (SACC). They gave positions to players of different levels and asked them to give the move they'd play. The positions chosen were from real games, and the solution was a surprising unexpected move.

They then had three experts rate the answers of the players according to the six dimensions, to assess the responses for their creativity.

Reliability coefficient across scale dimensions.

The values show how consistent each dimension is with each other. Overall they are consistent and the analysis showed that the scale is uni-dimensional which means that it measures one thing. Originality has a lower value compared to the rest meaning that between the expert raters, the rating for originality of the moves given by the players varied more.

For some reason beginners got more creative scores for their responses than intermediate players overall. The authors said maybe this is due to the Einstellung effect where intermediate players come up with more automatic responses as opposed to experts who think out of the box more, and beginners who have less constrained thought patterns due to knowing less. The dimensions are ranked separately so even ideas that don't work could be ranked as original. Correctness must be given as a necessary condition, rather than a dimension that is part of creativity. Otherwise this happens, where beginners are ranked as more creative than intermediates which doesn't make sense.

The scale nicely shows elements of creativity in chess. Heuristic violation is when something that you expect doesn't occur (e.g. normally you don't sacrifice a queen for a pawn). Economical win means the line is efficient, it doesn't drag out. This is related to correctness, the line must not be flawed, it must work for all the variations. Themes are tactical ideas like forks, deflections etc. But what about creative chess generation?

In Sicilo Creativity

Chess compositions are where creative puzzles are created by humans. This takes place outside of a game.

A common composition method is to work backwards, start with a final position and engineer some tactics in reverse. This ensures that creative elements will appear with certainty. This is a process which requires making sure that the creative tactics adhere to the standards of compositions. For example, it should ideally be a unique line that wins and the tactics should work out, there shouldn't be a 'cook'. A cook is a term for a composition which has a flaw. This happened in olden times when they didn't have computers. But now 'cooks' are no longer a thing as you can check with the Fish. Commonly the lines will have some strategic themes which is supposed to be the cherry on the cake, and there can be multiple possible responses from an imaginary opponent that don't work in glorious fashion.

The day came when they had neural nets have a go, have a try. As usual this was brought to us by the DeepMind Crew (TM). The authors of AlphaZero.

1. Neural nets learned from 4 million puzzles here on Lichess.

2. Reinforcement learning was applied to reward counterintuitive, realistic and unique puzzle generation which were assessed using Stockfish and seeing how different the FEN strings are from other FEN strings. They also applied a diversity filter to stop the same high-reward puzzle from being generated over and over again.

3. They further filtered for good puzzles by using a reward function to rank the puzzles and applied theme detectors (e.g. looking for deflections as an example).

4. They created a booklet of the best puzzles by choosing the top 50 ranked puzzles based on the above criteria, validated by expert players.

5. And that's how we get some nice platinum synthesized creativity, ready for delivery to your doorstep. The mental image of someone looking at a chessboard with a puzzled Sherlock Holmesian expression vanishes into the wind. Replace that with sheer, bit-coded numerical brilliance.

They got some nice puzzles. One shining gem was a rook sacrifice and long queen move which all the experts agreed was amazing.

The Deadly Queen Dive

Queenie dives in the pool. Ends up finding a King.

IM for Chess Compositions Amatzia Avni describes this as a “short, yet challenging puzzle” with an aesthetically pleasing ‘long’ move, performing both attacking and defensive missions; while initiating a vicious threat, it continues to guard against the black Queen checks.

GM Matthew Sadler liked the retreats and the geometrical motifs (2 Qa1 3 Qf6+), noting that they are very engine-like and tricky for humans to spot, requiring vision over the whole board. The touch of leaving the Rook on f7 en prise while covering the check on d4 with the Queen on a1 is particularly fine.

GM Jonathan Levitt described this position as a very good combination involving the paradox (and limited depth) of the initial sacrifice, the geometry of the long queen move, and one or two nice variations before the final goal is established. The initial sacrifice needs to be accurately calculated, you need to see the long queen move (2 Qa1), which is not at all typical and thus harder to see than a normal move.

Evaluating In Silico Creativity: An Expert Review of AI Chess Compositions, Veeriah et al., 2025

Smothered Mate with a lil' Twist

The Zigzagging Bishop

The experts’ feedback was generally positive; they noted the innovative fusion of aesthetic themes and the "over-the-board" vision. Nevertheless, the reviewers also provided constructive criticism, pointing out that some positions were trivial, while the collection overall lacked the profundity and complexity of traditional endgame studies. They also remarked that certain puzzles were unrealistic. For future development, they recommended increasing the complexity and depth of the positions, incorporating problems with more complex sidelines and robust counter-play, and wanted to see more surprising theme combinations.

Evaluating In Silico Creativity: An Expert Review of AI Chess Compositions, Veeriah et al., 2025

The neural nets had a distribution of what creative puzzles look like. They had to add things to it like reward functions and theme detectors and unique move detectors to get it good. And even then it wasn't perfect. Only 2.5% of the generated positions were usable. The puzzles above are the best of the harvest. They are nice. The experts remarked that overall the top tier of the harvest was not fully there in terms of human level creativity. Clearly this is a emulation of creativity, but not the way humans know it. We benefit from knowing what we are doing. We have meta-cognition.

The Algorithms of Creative Idea Generation

Three conditions are necessary: a mechanism for introducing variation, a consistent selection process, and a mechanism for preserving and reproducing the selected variations. In what follows we shall look for these three ingredients at a variety of levels.

Donald Campbell, Blind Variation And Selective Retention In Creative Thought, 1960

Campbell's article talked about the parallel between creativity and natural selection. Organisms that can't adapt to their environment disappear, while the ones who can survive, which means that traits suitable for survival carry on. A protozoa is a unicellular organism. But in spite of its one cell, it has a broad outlook on life. When trapped in a crevice, a Protozoa finds its way out by randomly going in different directions until it can keep on moving. This is an example of a mechanism that introduces variation (going in different directions), a consistent selection process (go in the direction where movement occurs) and preserving selected variations (genes which produce this mechanism). Campbell took this evolutionary idea and thought about applying it to explain how creative thought works.

The tacit assumption that has been driving creativity research, however, is the opposite. Creativity is obviously special and there must be something, somewhere, that makes it so. This way of thinking betrays the commitment to a distinct factor, an extra something – the creative bit, if you like – that’s specifically added to the plain mix to make the sparkling difference. Powered by this instinctive hunch, creativity is routinely treated as a monolithic entity and assigned to some brain network (e.g., default mode network, DMN) or associated with a particular cognitive process (e.g., divergent thinking). The fact that such conclusions are based on “creativity tests” that combine a false category formation with a compound constructs, effectively renders this research paradigm phrenology.

A Neurocognitive Framework for Human Creative Thought, Arne Dietrich, Hilde Haider, 2017

The current paradigms are flawed as they involve contrived tasks such as the alternate uses tasks which ask subjects to come up with different uses for an object, or the remote associations task where you have to find a word that relates to a set of other words. But creativity can also happen spontaneously without effort. And can also occur through convergent thinking which does not generate many possibilities, but settle to one solution.

Creativity has different stages and is not one process. Creativity for different domains will involve different neural circuits which are dedicated to those particular tasks. Dietrich and Haider came up with a framework to make progress towards a fruitful understanding of creativity. This framework uses the analogy that Campbell discusses, comparing creative thought to the process of natural selection in evolution. However they introduced the concept of 'partially sighted' variation. Instead of the random variation, we have the ability to constrain the direction of the creative process when deliberately looking for creative ideas.

Dietrich and Haider talked about scaffolding. This is the concept that in evolution, an organism must pass through stages. For example before having a brain that can predict future scenarios, an organism must have a body first which responds to chemical signals for example. A brain would not evolve by itself without a body, as the body is what survives or doesn't through natural selection. In creativity, they proposed a form of cognitive scaffolding that would allow such bypassing of intermediate states to be able to find solutions. This scaffolding would occur when deliberately seeking creative solutions.

Another concept is a fitness function. Meaning what will survive. In natural selection this is done by the environment. If the organisms survive their traits will carry on. The environment makes the organisms fate. For the brain, there is the question of what the fitness function for creative idea generation is. What allows an idea to be selected as creative, when generating ideas in an unknown solution space.

A unifying concept for these tasks is the concept of Representations of Predictive Goals. This takes place under the framework in neuroscience of the brain as a prediction machine, generating a model of the world so that stimuli does not need to be constantly decoded, the brain can save energy by simply signalling prediction errors. When the stimuli doesn't match the model. So if the brain is seeing a chess board, it doesn't constantly 'send' that a chess board is there as that is given by the brain's generative model, a signal of change would only be sent due to a prediction error which occurs when doesn't match the models expectation (table collapses in the middle of a game).

A Representation of Predictive Goal is a top-down bias that acts on independent encapsulated modules, biasing them to act in a certain way. Modules are a coalition of neurons can perform a certain task automatically but do not know anything outside their area of expertise. Predictive goals creates advanced heuristics that simplify a problem space and allow fitness of creative ideas to be assessed. An example of a heuristic in chess is 'look for forcing moves'. This creates 'partially sighted' variation, analogous to Lamarckian vs Darwinian variation (experience gained in the lifetime of an organism can be transmitted to offspring, vs natural selection by the environment on organisms with individual differences). On the other hand, 'partially sighted' variation means that some solutions will be blocked out, as a necessity of reducing the problem space. In spontaneous thought, independent modules in the brain can operate on a blind variation algorithm, meaning less constrained ideas that are more varied. The downside is that they may be less useful, but the upside is that there will be more novel ideas. This is what happens in dreaming or flow states with less attention.

Principles of Beauty

Here is another look at the principles of beauty in chess. Margulies distilled some principles from having chess players choose the more beautiful solution.

Principles of Beauty, Stuart Margulies, 1977

Thirty expert chess players examined pairs of chess positions to select the more beautiful solution of each pair. Eight principles of beauty were derived from these judgements:

1. successfully violate common strategies
2. use the weakest possible piece
3. use all the piece's power
4. give more aesthetic weight to the critical pieces
5. use one giant piece in place of several minor pieces
6. employ themes
7. avoid stereotypes
8. neither strangeness nor difficulty produce beauty

Is there a hidden element behind all these disparate factors? Is there an underlying factor.

When elements occur together it is fruitful to think about whether they are all related somehow. This may provide new insights that can unlock the nature of creativity and beauty.

The Illusion of Beauty

Comparative psychologists have found that, in almost every species studies, animals will work to be exposed to novel sensory stimuli. Indeed, 'stimulus novelty' is the most universal reinforcer of behaviour which is known. In my own work with monkeys I have found that monkeys will even work to look at abstract paintings and prefer such pictures to pictures of appetising, but familiar, food.

Recent experiments strongly suggest that when monkeys work to look at pictures they do so because the picture presents them with a challenge to incorporate new material into their model of the world: pictures of familiar objects hold their attention far less long than pictures of objects for which they have no readily available category. But while they do not spend long on thoroughly familiar things, neither, I should say, are they interested in looking at a total jumble.

Nicholas Humphrey, The Illusion of Beauty, 1973

Humphrey discussed how monkeys are interested in novel objects that are within the domain of their world model. Unusual things that still fit into the outer edges of their experience.

Humans through meta-cognition reflected on the fact that we have a drive for seeking things out of the norm. Then we deliberately create situations where we seek things out of the norm. Things that are unusual like a queen getting sacrificed, tactics, something that wasn't seen before. All these are things out of the norm.

Now what is beauty? Depends on the way you see it.

We have the ability of meta-cognition, the ability to monitor our own states. This leads to reinforcing mechanisms being 'bashed' for all their worth.
Artificially processed foods create levels of sugar that we never had before. We did have a drive towards glucose, as organisms which favoured glucose rich foods, got more energy leading to higher chances of survival for those organisms, propagating the tendency to favor glucose-rich foods. However, we gained the ability to realize this fact, once this happens, the brain then deliberately creates scenarios which activate these reinforcing mechanisms. Leading to artificially processed foods with unnatural levels of sugar.

But as we learned more complex concepts, the same tendency applied. Despite the fact that evolution never developed for those things specifically. Resulting in chess positions, being seen as 'beautiful'. The beautiful positions are actually unusual, out of the norm positions which we are reinforced to look at through an old evolutionary drive to pay attention to novel situations to support survival.

The subjective experience of beauty arises out of 'consciousness', which creates an illusion that we are looking at 'essences', that what we see has a subjective experience . The user illusion simplifies neural processes so an organism can co-ordinate it's actions. When look at a chess board, you do not know the visual processing that goes on, but see the chess board as a singular essence, which is intrinsic and simple. When you have the concept of smothered mate in your mind, you do not know what goes on in the brain neurochemically. Consciousness is a second-hand summation of brain wide activity. Color, shape, texture are all processed in different regions of the brain.

However we are reinforced to look at out of norm situations which still have some realism. The monkey was not "interested in looking at a total jumble". In order to learn from unusual events, we must have some frame of reference to understand them and learn from them. This is why chess positions with extremely contrived compositions are seen as less beautiful. This is why positions that are beautiful have economy and harmony. Beauty can also be in positional play. The surprising manouvres and deep strategy are reinforcing as they are novel. People will have variation in what they consider beautiful depending on their experiences, how well they can comprehend the position and how novel the ideas are.

Beauty is in the eye of the beholder.

Or rather, beauty is in the degree to which the self-reinforcing drive towards novel stimuli is activated in an individual.