Week 2 (4/1,3): Computation Creativity

[Gio-Choi]

In order to extend the power of enhanced computation, theologians, natural philosophers, artists and engineers engaged in efforts to profitably turn everything into number. This week we consider the efforts of Ramon Lull, Roger Bacon, Gottfried Leibniz and others through modernity to quantify reasoning and creativity for computation. What does it mean to turn qualities into quantities? What is lost and what is gained in the translation? And how do we turn them back into qualities once computation is complete. And who is the discoverer—who deserves (and culturally receives) credit in works driven by computation—the computer, the user, the computer (or program) designer, or the one who implemented the design? And if and when computation model the imagined physical and metaphysical worlds, can it cause them?

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[suryachinnappa]

The readings this week showcase the turning-into-number of rich(er) information from a variety of sources and disciplines, as well as reflecting on the significance of this practice and its implications. The key concept seems to be abstraction–as we have learned in class, numbers themselves are concepts that derive from the natural world, and arbitrary aspects of numeric representation are indicative of the particular sociocultural pressures under which a given numeric system emerged (for example, base-10 number systems being dominant across the human population, likely on account of the fact that we have 10 fingers on which to easily count). Once these abstractions are constructed, they can be applied to enumerate any of the things in the natural world. Another leap of abstraction comes in when conceptualizing of collections as units, and as parts as units; this allows for the enumeration of things that are not directly (pragmatically) countable, whether because they are too large (grains vs bags of rice) or too small (pies vs slices of pie). A further leap of abstraction is involved in establishing the continuous nature of numbers, and so on and so forth. What we are left with is a diverse set of fully abstract representations with which to make sense of the natural world. However, it is evident in representing tangible objects and phenomena as pure abstract formalism, it seems inevitable that some richness is lost. The underlying questions here become: to what extent is richness lost, and to what extent is richness lost relevant to the purposes towards which this abstraction is used? We see two possible solutions developed through the readings.

Varshney et al.’s paper “A Big Data Approach to Computational Creativity” tackles this issue in one way, a direction which has become very popular in the modern age of rapidly increasing computational power. By leveraging an impossibly large quantity of culinary data relating to flavor profiles, cultural backgrounds, and many other factors, Varshney et al. develop a computational model that can create novel recipes, approximating and even surpassing the creativity of human participants by their metrics. In doing this, they solve the problem of potentially losing richness of data through abstraction by simply directly encoding all of the richness deemed relevant.

The chapter on Ars Combinatoria in 18th-century music addresses the issue in a somewhat inverse way, showcasing the ways in which the system of 18th-century music allowed for artful composition based on random number generation. This is done by restricting the options for concrete phenomena that the numbers could possibly represent. In doing this, they address the issue of richness disparity by making the signified phenomena as informationally “poor” as the numbers themselves; rather than requiring the numbers to determine all aspects of the practice of musical composition, the designers of this system have fixed most aspects of the system such that those aspects which are interpreted through the numbers, and the specific interpretations given for the numbers, are such that these surface as artful contributions to the music.

Discovery: I had heard about musical "puzzles" posed by composers in the baroque and classical periods before through prior reading, but the readings from this week provided additional insight as to just how plausible it was to work with their musical systems in algorithmic, formal ways. I find connections with the content I'm learning in my music theory class, in which there are very few solutions deemed as "correct" for any given situation in the musical system we are using (18th century European classical music). Music then seems to be a uniquely accessible point of proximity between the formal and the human, as there is a sense of intuitive satisfaction in music which satisfies the formal properties set up in such systems. It makes me think of natural language, as another uniquely algorithmic but emphatically human phenomenon which operates on similar formal rules, though we seem to find that in this case, these rules are emergent from our own cognition, as opposed to socioculturally prescribed as in the music-theoretic tradition (though linguistic prescriptivism is no stranger to anyone who has been through an American elementary school, and conversely there is evidence that some of the rules imposed in this system are indeed reflective of deeper emergent cognitive factors; it seems like the relationship between prescription of formalism and natural emergence thereof, in both music and language, is somewhat contrapuntal).

[ucachyut]

Leibniz and his contemporaries sought to develop a "language of nature" that would allow humans to systematically discover and express the laws governing the world. For Leibniz, this language was deeply tied to numbers. From a modern perspective, this raises a fundamental question: What are numbers in the first place?

Even if we take numbers as primitive, their utility arises from operations like addition and ordering, which themselves require a deeper foundation. Modern mathematics provides this foundation through set theory and mathematical logic, which can be seen as our closest approximation to a universal language. Starting with sets as the only fundamental objects, we can construct mathematical structures that model physical phenomena. For example, the state of an electron or photon—containing all information about its behavior—is represented as a point in a complex Hilbert space, a construct derived purely from set-theoretic axioms. Rather than speaking of numbers alone, I will refer to quantities as the broader mathematical framework encompassing set theory and formal logic, while qualities are the human-language interpretations of these mathematical structures.

When translating qualities into quantities, little to no information is lost. However, when reversing this process, significant loss occurs. This is because the very act of translation depends on human language, which is inherently ambiguous. Even if set theory were the perfect universal language, we would still require natural language to express its meta-rules. For instance, set theory defines primitive formulas using the following rules:

• Every primitive formula is a primitive formula.
• If $P$ is a primitive formula, then $\neg P$ is a primitive formula.
• If $P$ and $Q$ are primitive formulas then $P\land Q$, $P \lor Q$, $P \rightarrow Q$ and $P\leftrightarrow Q$ are primitive formulas
• If $P$ is a primitive formula and $v$ is a variable, then $(\exists v)P, (\exists! v) P$ and $(\forall v)P$ are primitive formulas

Without these meta-rules, set theory would be meaningless. This highlights a paradox: the search for a universal, precise language is constrained by the imprecision of human language.

Moreover, the assumption that every statement is either true or false leads to Gödel’s incompleteness theorems, which prove that no sufficiently expressive formal system can be both complete and consistent. This suggests that the universal language may operate beyond the binary logic we currently use, perhaps through probabilistic or alternative logical frameworks.

Both the designer and the implementer deserve credit. The designer establishes the rules of translation between human language and formal structures, while the implementer brings the system to life. Computation would be impossible without both roles working in tandem.

At first glance, computation seems purely descriptive rather than causative. However, consider a counterexample from quantum mechanics. A quantum system initially exists in a superposition of multiple possible states. Upon measurement, the system "collapses" into a definite state. Measurement is effectively a computation—translating the abstract mathematical state of the system into an observable quality. This process is irreversible, meaning that computation does, in a sense, change reality.

A more intuitive analogy is a coin flip. Before landing, the coin exists in an uncertain state—its final outcome unknown. Once it lands, the result is computed into a definite value: heads or tails. Computation, in this sense, irreversibly assigns reality a specific outcome. Thus, it is not impossible that computing has physical consequences.

Discovery:
While I was aware of Godel's efforts to characterize the entirety of mathematics and language using numbers, I was not aware of Leibniz's efforts to do the same. It also came as a surprise to me how similar the goals of a 17th century mathematician were to that of modern day mathematicians and physicists, though they had fewer tools available to them. Arthur C Clarke's description of his visit to Tibet also reveals that even monks had a similar goal - of finding the ultimate language.

[Noah48841]

For Leibniz, turning qualities into quantities was a way of truly understanding those qualities—better, even, than what could be achieved with “optical instruments” (p. 23). He saw quantification as a way to build a universal language that could illuminate fields like moral philosophy and metaphysics through an “infallible method of calculation” (p. 23). In his view, this would allow us to compare things that previously seemed incomparable (p. 24). Precision and clarity are gained through this process, and Leibniz seems to believe that little, if anything, is lost. I probably disagree with this, however. While this might be true in principle (I think there are good arguments for reductionism and physicalism), in practice this mindset seems like it leads to a lot of Goodharting –the process by which one aims for some proxy (towards some end) to such a high degree that it stops being a good aim for the true end.

In Arthur C. Clarke’s “The Nine Billion Names of God,” there’s an implicit suggestion that even the most sacred things—like the names of God—can be reduced to numbers. But there’s also a kind of irony here. The monks, seen as naive by the engineers, turn out to be vindicated in the end. The stars start going out, as they predicted. So perhaps Clarke is suggesting that the mathematical or engineering mindset, while powerful, can lead to overconfidence. Just because you can represent something numerically doesn’t mean you’ve grasped its full significance. I think the story shows that this culture of quantification sometimes overlooks the truth—or at least the deeper meaning—of what it reduces to data. Once again, I’m probably gonna have to disagree over here – I largely think that 1) religions usually don’t make enough falsifiable predictions for this to be the case and 2) that this irony is overstated – you can, I believe, quantify these very sacrosanct things.

In Chance and Choice, we see how something extremely qualitative—like music—was historically transformed into a kind of computation (p. 346). The benefit here is that it opens up new forms of creativity that might not be easily accessible through pure intuition. In theory, someone with a good grasp of mathematics, but no musical background, could still produce a beautiful composition. This suggests that computation can help generate new insights or creations in spaces we once thought depended purely on “feel.” I probably largely agree with this point. The brain, and therefore the algorithms associated with liking vs disliking music, can probably be broken down into its computational parts, so this is possible. One thing to worry about is using some other metric (say melody) that is correlated with someone liking music but not actually the base algorithm used in the brain. This might take you off course or just limit one’s ability to quantify the niceties of music in practice.

In the piece on big data and computational creativity, the authors argue that translating creativity into something quantitative increases the range and scalability of human creative potential—especially in domain-specific contexts (p. 2). One concern, they note, is the possible loss of surprise (p. 2), but they think this can be addressed. In general, they’re optimistic that the costs of quantifying creativity are low, if it’s done carefully. That said, their “4 Fs” framework for creativity might work well for edge cases, but may be harder to apply when thinking about radically new or “far” forms of creativity. I found their definition of creativity—“decomposing artifacts into their constituents... then recomposing and reconstituting new artifact ideas” (p. 7)—interesting, though perhaps it dodges some of the deeper philosophical questions, since the process still involves human input (p. 10). As they write: “Creativity is easy neither for people nor for machines, but the challenges are different” (p. 14). Also, for what it’s worth, some of those recipe examples looked really good!

Discovery:

One thing I learned from these readings is how early the Enlightenment-era thinkers embraced the idea that quantification could be the key to truly understanding human knowledge. I had always associated this mindset more with the age of computers—when algorithms started doing things we once thought only humans could do, and when we began reframing even non-mathematical problems as computational ones. But it was striking to see how deeply this way of thinking had already taken root centuries earlier. Without making any claims about whether this shift is good or bad, I just found it fascinating to realize how long this mindset has been shaping our approach to knowledge.

[mhmanek]

Original Materials
(In writing this memo I re-read parts of my favorite book, Gödel, Escher, Bach, that were closely related to the ideas around music theory, quantifying and formalizing ideas mathematically and whether meaning resides in the message or the interpreter).

Leibniz begins his musing by noting that while weight and measure are not universal properties, number, in fact, is. He envisions "a language which would embrace both the technique of discovering new propositions and their critical examination". This is reminiscent of mathematical logic and the Gödel numbering system.

As Chance and Choice explains, the efforts to codify music and construct a mechanical process for musical composition were closely tied to games and 'canon puzzles'. Such efforts seem justified, since there seems to be something inherently mathematical about such compositions. Pieces that are staggered in time (phase difference), have different pitches, different speeds, are inverted (one jumps up whenever another jumps down and vice versa), or are retrograde (played backward in time relative to the original) can all be expressed in the language of mathematics. Indeed, one could ask the question concerning 'canon solutions', of whether there is a music-theoretical analogy of the theorem that a polynomial of degree n has at most n solutions? One is also reminded of Kepler's notion that the planetary orbits resemble musical harmony.

But there may be limits to the possibility space of music that can be reached solely through such mechanical efforts, and this is what may be lost in the translation. For example, in Gödel, Escher, Bach, Douglas Hofstadter writes "The two fugues in the Musical Offering (by J. S. Bach) are outstanding examples of fugues that could never have been 'composed by formula'."

On the other hand, there may also be something to be gained from the translation between quality and quantity. In lecture, we discussed metrology - the study of units, measurements - and how sharing a standard unit of measurements enhances interoperability and hence collaboration/trade (e.g., foreign trains on local tracks). Analogously, the translation of qualitative factors into numbers provides a common ground and shared linguistic vocabulary for different fields, namely, mathematics.

In the fictional story 'The 9 Billion Names of God' by Arthur C. Clarke, we see that when all the 'names' (that is, combinatorial permutations) of God have been enumerated and printed by the computer, the stars in the sky start to die out and the world ends. The monks' spiritual and religious beliefs prevail over the engineers' coldly rational logic. The story seems to suggest that computation not only models the world passively, but, in fact, causes it actively.

More interestingly, in my view, Clarke's story teaches that profound things can be done by combining quality (monks' meditation, spiritual and religious traditions) with quantity (their use of the computer for combinators). Rather than viewing the translation problem as a question of substitutes, it may be more valuable to think in terms of complements.

Discovery
There is this recent notion of the 'revenge of the nerds', whereby mathematicians, physicists and computer scientists have revolutionized many 'soft' fields. This is evident in the rise of fields like computational linguistics, computational biology (AlphaFold etc.), quant hedge funds, AlphaGo, AI-generated art (Sora etc.) and so on. We have made many breakthroughs by systematically, quantitatively and rigorously studying such 'soft' domains. Math is being applied to everything. I did not know, however, that this 'revenge of the nerds' trend of applying math to everything was an idea that dated as far back as Leibniz, so it was fascinating to discover this.

[eeengland1]

Lebniz attempted to approach metaphysics and discursive thought by constructing a language of logic involving characters that both contain meaning and dictate some relation or performable “operation” similar to algebraic and hyperoperation symbols. Through this means of reducing (or perhaps refining) the medium of thought and discussion to the strict and quantifiable, Leibniz would fix issues such as uncertainties and fumblings, shortcomings and errors. Leibniz claims that logical fallacies will become obvious as a result of the system and mistakes will render themselves apparent as soon as they are made or viewed. While such a method of discourse and communication does seem useful, I believe that communication in some sense would be restricted and that some aspect of the discourse would be lost. The expression of ideas and statements would be affected in some way, as how they are expressed currently isn’t in a completely rigid rational form, and this current means of expression carries (desirable) data that can not be expressed purely through Lebniz’s means, or at least not concisely.

“The Nine Billion Names of God” offers an intriguing view on computation, its significance, and the effect it can have on the world. We can clearly take from this short story points worth thought: for one, the computer brute-forced the task of life (as the monastery’s speculation about the role of humans in the universe was proven to be correct), implying that computation has a very physical and direct effect on the world around us. Could this story be suggesting the dangers, or perhaps highlighting the significance of computation through an unusually extreme example? It seems as though certain remarks on this paper focused on the theology of the story, in my interpretation, and not as much the role played by computation— so the amount of significance Clarke meant to place on the role of the computer is up for debate. Perhaps Clarke meant to show how the computational benefits machines bring to society can enhance our more qualitative or social goals, but perhaps in time computers will take even this too.

In comparison, “A Big Data Approach to Computational Creativity” seems to approach the problem of developing creative recipes for culinary activities in a similar manner: by utilizing a method reminiscent of the human creative process, an AI is trained on the abundant data in the culinary arts to develop absurd amounts of possible recipes, and after a refinement process, cull and retain the ones that would be considered “creative”. The rules and specifications model what would be considered “creative” “surprising”, and “tasty”, and the AI accelerates the task, once again highlighting how computation can provide very physical effects on civilization in more than just a quantifiable way. The thought that creativity can be decomposed and quantified is, albeit perhaps not surprising, a topic of nagging interest.

Discovery: I had no idea that attempts were being made to automate creative recipe-finding as I assumed that the task of doing so in a safe and efficient manner was slightly beyond the reach of modern-day AI’s, but the Authors of this paper seemed to have incorporated all of the possible concerns I’d have about such an endeavor into the AI’s training. In practice, do people view the recipes produced sufficiently “creative”? Also, isn’t there an aspect of supply and volume to creativity, that is, if a sudden influx in creative items occurs in a community, doesn’t the value of each creative item diminish, or isn’t it at least harder to find creative items as a result? What possible implications could this have on computation and automating creativity?

[cavanbgon]

Humor persists among attempts to transmute “pure” reasoning or creativity into numbers. Much of last week’s reading dealt with prejudices among intellectual disciplines – chiefly against “dirty” practical science but also against “mechanical” math operations. That such humor persists can be thus partially attributed to both the tacit acceptance of such conventional attitudes (the mixing of “high and low”) and the corresponding irreverence that frees one from conventions. This humor seems hardly incidental. Humorous absurdity – “follies,” to borrow Arthur Clark’s pejorative – is inherent to the productivity of quantification.

Leibniz describes this succinctly. Whether or not one takes his assertions of math’s privileged position seriously, namely in providing a “statistic of the universe,” one cannot but accept the remarkable strength of essentially abstract numerical reasoning for attacking physical problems (Wiener, 17). Thus, especially if you accept Leibniz’s metaphysics, the application of this remarkable system to areas where one’s doubts have not been satisfied (Wiener, 19). That being said, Leibniz’s optimistic description of the deep descriptive powers of mathematics effectively elides the basic strangeness of any truly novel mathematical representation. Insofar as the mathematical representation is effective in expanding the range of possibilities of expression, it seemingly must assume bizarre forms. Otherwise, the mathematical expressions would take the form of familiar statements but translated into a new language without producing anything truly novel. The case of automated musical composition effectively demonstrates the latter possibility. In the classical period, the desired qualities of music had been retroactively formalized in a sufficiently mathematically well-described manner that it was possible by a few random permutations to mechanize the creation of “acceptable” musical material (Ratner, 345). Yet, once the shock of semi-autonomy and an arbitrarily large number had worn off, it became clear that what music could be produced by such narrow constructions was essentially uniform and stylistically derivative (Ratner, 352). Rather than discovering at any discernible pace great new music, the process quickly demonstrates the often-absurd triumphal rigidity of classical forms. It is thus fitting that Mozart, one of the two towering geniuses of the classical period, would choose to leave a musical feature in what can in some sense only be understood as a combinatorically random position to allow it to serve a new function (Ratner, 360). The only way the broadly random/autonomous music of note arises is first as an “absurd” musical joke (a cadence that is not a cadence).

                  Clark’s story can be told in terms of the above dynamic. In search of the ultimate, elusive truth – for the Tibetan monks at the center of Clark’s story, the names of God – endless outwardly absurd tasks are taken on. Clark’s story further explores the terror of this. With the assistance of even semi-autonomous machines, a task that would otherwise fill human history may be completed relatively quickly. This questions any notion of individual or collective human achievement in the face of machines. It is thus apropos that, even for the great naming machine’s engineers, the stars should disappear first.

Discovery:
I should acknowledge the other article we read for this week. On a rather shallow basis, I found the materials a little less interesting. I found the deep rigidity in the formulation of the recipes discussed perhaps evidence of a potential basic inadequacy of food for demonstrating human creativity. The far greater emphasis on palatability more quickly restricts one to pretty obviously derivative culinary “inventions”. All the new recipes are identifiable by a descriptively familiar culinary base modified by some novel, imported flavor profile. Largely ignorant of progress in gastronomy, I can’t comment on whether this is representative of human creativity. Still, superficially, it seems rather unsatisfying.

[Alex7692]

The translation of qualities into quantities implicates measurability, and thus facilitates a kind of "intersubjective validity" above the whims of imprecise observation. Indeed, one might argue that qualities are fundamentally quantitative (e.g. temperature as really about measurable changes in kinetic energy; musical notes as mathematically defined, etc.), and hence the translation would deepen our understanding of these qualities by grounding our discourse upon the most primitive level of description of everything. The most radical proposal, as we saw in the Leibniz reading, seeks to achieve just that by envisioning a logico-mathematical language of everything.

Nonetheless, many would also seek to resist the temptation of this form of reductionism. On one note, what quantification rules out is the intuition of a kind of primary "structure" to reality that could only be spelled out conceptually (N.B. this is not to say a mathematical language neglects concepts or structures, but that mere reduction to "numbers" is not in itself adequate without constitutive rules). Another problem would be a practical one: that is, how do we then interpret the results, which intuitively requires the translation of quantities back to qualities.

Perhaps Mozart's proposal (among other musicians of 18th century Europe) of composing music by an ars combinatoria is an interesting case to consider at this point. It does seem to permit the translation of quantities back to qualities, and specifically in the form of an auditory experience. Back it still does not capture the concrete "harmoniousness" we experience from a piece of music as given to me. There is no way of "interpreting" what is going on at the computational level, except that it has happened. It is therefore at best "a rational, intellectual device that can help to spark musical feeling" (362). Arguably, it would seem like we cherry-picking an example where numbers are not necessarily linked with the nature of qualities. What about measurement of temperature? Without going into a rigorous proof, an anecdotal example may help to elicit the intuition here. Growing up outside of the states, I've have no intuitive sense of temperature measured using the Fahrenheit scale. Understanding of measurements must be coupled by experience.

While the perfect ars combinatoria of music seems like a distant dream, it does prompt us toward questioning the authorship of computationally generated contents. In fact, an attempt to resolve the question indicates a greater philosophical concern; that is, what to make of the intertwinement of human and technology in the contemporary world? Should technology be regarded as extensions to the capacity of human reason and kinesis? Or do technical objects possess a certain autonomy out of its invention? Perhaps creativity may still be the decisive factor: that for one work to stand out among all creations using a specific tool and to engender a kind of inimitable "aura". This is when computation model may "cause" changes to the world-ontology by broadening the space of real possibility; and at the same time revising our previous metaphysical concepts of "sapience" via a further inquiry into the potentials of human spirit.

Discovery

The Clarke story was an interesting one that I've never read before –––– although highly implausible in terms of setting, as Buddhism is famous for not having a transcendent God. It does make me think of another essay I've read in a religious studies course by a Sufi, who basically argued that human (Ādam) is unique as we can enumerate all of God's names. If that is so, it would seem like such a machine would be basically equivalent to an algorithm that probes into nature of humanity.

I've also not heard about the use of ars combinatoria in 18th century Europe, though it does remind me of that very (in)famous "cross-talk / comedy algorithm" some Chinese doctoral students developed years ago. Can humor be quantifiable? Or is comedy based on a kind of elusive contingency and extraordinariness that stands definitively against "hard-boiled" logic?

[Laurelli7]

Starting from the scientific revolution, philosophers began employing quantitative methods to observe nature, leading to the rise of mechanical philosophy. The overall attempt to quantify everything stems from this mechanistic viewpoint. Gottfried Leibniz, a prominent mechanical philosopher, specifically proposed turning qualitative ideas—such as their meanings and interrelations—into quantitative symbols and formulas. This shift, articulated in his work "Towards a Universal Characteristic," argued that complex ideas could be built from a finite set of primitive concepts, similar to assembling words from letters of an alphabet. By assigning each basic concept a specific symbol or number and setting rules for combining them, reasoning could effectively be reduced to computation.

Yet, it remains questionable whether we can genuinely define such a finite set of primitive concepts. Determining which concepts qualify as "primitive" is inherently challenging. Many suggest mathematical concepts are most fundamental due to their abstract and generalized nature. From mathematics, people develop basic logics applicable to more specific fields, positioning mathematics as the foundational basis for science. Undoubtedly, significant benefits arise from this quantitative perspective: theories become easier to summarize and communicate, efficiency and logical consistency improve, and science gains greater rigor. Leibniz himself appreciated how disputes could be clearly resolved—arguments reduced to equations and solved straightforwardly. Similarly, Clarke's monks achieved efficiency by compressing a 15,000-year task into mere months through computation. Furthermore, formalization exposes hidden assumptions, deepening understanding; for example, algorithmic composition requires explicitly defining musical style rules, potentially unveiling new theoretical insights.

However, quantification risks overlooking humanity’s intrinsic intuitions or alternate interpretations beyond mathematics. Algorithmic composition, despite its efficacy, often misses moments when human intuition offers profound insights that elude quantitative explanation. Ironically, Large Language Models (LLMs)—constructed entirely through statistical, quantitative means—lack clear quantitative explanations of their internal "thought processes." Additionally, as Professor James highlighted in class, research directions have begun converging since the advent of LLMs, signaling a potential loss in the diversity of innovative ideas.

Interpreting computational outcomes qualitatively poses another considerable challenge. In fortunate scenarios, qualitative interpretations emerge intuitively—such as appreciating algorithmically composed music through our sensory experiences. Conversely, qualitative meaning can sometimes be irretrievably lost. For instance, performing PCA on datasets occasionally results in clusters whose qualitative meanings remain obscure. Here, data visualization and other analytical tools become essential.

The issue of authorship and credit in computationally produced work sparks ongoing debate. Generative AI models raise complex questions about intellectual property, with ambiguity surrounding whether credit belongs to the company owning the model, the individual prompting the model, or the original artists whose works inform the model's training data. Varshney et al. note systems like Chef Watson occupy a central creative role, suggesting credit might reasonably belong to computational entities. I partially agree but argue we must reconsider intellectual property frameworks entirely. New laws and a fresh perspective are urgently required.

Finally, regarding whether computation can generate or influence physical and metaphysical worlds, Clarke’s "The Nine Billion Names of God" serves as a compelling thought experiment. While computational models currently don't create entirely new worlds, their outcomes significantly influence real-world decisions and actions, demonstrating computation’s powerful role in shaping reality.

Discovery:

I used to think that questions about authorship and creative credit emerged only recently with generative AI and computational art. However, after reading Leonard Ratner's Ars Combinatoria: Chance and Choice in 18th Century Music (1970), I discovered that these debates date back to the 18th century. Even then, composers and audiences grappled with similar concerns, debating who deserved credit—the creator of the combinational system, the one rolling the dice, or perhaps even chance itself. This historical insight significantly broadened my understanding of how deeply rooted these questions are.

[benkim04]

In discussing the conversion of quality into quantity, I found the example regarding culinary creativity to be especially illuminating. Here, we observe an attempt to convert the qualities in food which are sense based to values which can be applied to mathematical equations. To do so, we must distill what we perceive as sensations to a number. This is done so by not applying qualitative descriptors like sweet or salty, but instead entails identifying certain compounds and pheromones. This process seems quite inhuman; we don’t ordinarily perceive a food as an amalgamation of specific compounds and pheromones. Still, this is necessary to perform the machine-enabled creativity that they desired. Turning the quantities back into qualities again presents a challenge. It is certainly possible that the combination of compounds and smells could be represented by any range of possible food combinations, and thus could result in differing dishes, some better than others. This process also removes the aspect of texture, in which now it may choose two foods that combine to an unpleasant texture, or at worst, something that is inedible. The portion that I found the most compelling was the portion regarding human-computer interaction to forge semi-autonomous creativity. This is analogous to reinforcement learning in many ways. It is suggested that the human could help in “picking a key ingredient”, “selecting the best ideas”, and synthesizing the instructions into actual, step-by-step recipes with proper proportions (Varshney, 10-11). In all of these steps, the human can steer the machine in a more reasonable direction and avoid pitfalls that arise from reducing qualities to quantities. In an attempt to be creative, which they define partially as something being novel, the machine could provide a combination of compounds and subsequently foods that in reality have historically been separated for good reason. That is, they simply do not belong. This knowledge and intuition is unique to humans and is not necessarily the result of an equation. Thus, it can be especially helpful in steering the machine to be effectively creative rather than simply creative. This system however blurs the line of who gains credit. It is obvious that the creator of the algorithm, the algorithm itself, and the humans who provided input are all members of the creative process. It is difficult to assign credit to something like an algorithm. I also find it difficult to assign credit to those who help the machine along the way, as they are only partially constructing the recipe. However, should the human’s at the end of the chain (writing down the steps, figuring out proper proportions) play a significant role in the process, I would argue that they deserve creative credit. Although the machine may suggest which foods or compounds may suit each other, it is the synthesis of the recipe itself and importantly the refinement that is crucial to the end product.

Discovery:
Also within the same discussion surrounding culinary creativity, I was intrigued by the framework of the creator and the assessor. That is, there was an algorithm that spawned creative recipes, and there was importantly another algorithm that was constructed to assess the creations. It reminds me of Generative Adversarial Networks, which employ an analogous system of generations and an adversary which attempts to determine if it is a generation or genuine. To my knowledge, GAN’s can be particularly fickle and difficult to train due to their inherent nature. This then suggests that a similar system as proposed within the paper may fall into similar traps, in that the assessor and generator may diverge in ways in which the assessor will never approve a recipe generated.

[TonyYZ]

Response
Leibniz and the Tibetan monks in Clarke’s short novel are similar in grasping the unimaginable source of creativity with symbolic combinatory systems. While we are unsure of the underlying belief system Clarke was conceiving, the nine billion divine names of God could be compared with all true propositions Leibniz attempted to produce through his ambitious Characteristica Universalis. In the end, unlike the recipe and eighteenth-century music generation algorithms in our readings, their projects remained incomplete or successful only in fiction. A crucial difference between these two paths is the requirement of subjectivity: Leibniz and the monks wish to ultimately produce a fixed system or a list that would not be affected by human alteration, while the recipe and music algorithms involve humans who make decisions in the dynamic generative process. This comparison suggests that it is necessary to maintain subjectivity to be creative because of the essential role of an interpreter.

As we turn the world’s qualities into quantities for creativity, it results in signs that require an interpreter who attributes meanings to them. The propositions produced by Leibniz’s system are signs that belong to a language system. They are products that emerged through the long evolution of language, motivated by the need for daily communication. While syntactical rules of a language could be formulated and fixed, semantic comprehension is rooted in the human’s subjective experience with the world by which connotations and subtleties differ on an individual level. When Leibniz describes his early imagination of the universal alphabet’s purpose, he claims that “every [human thought] can be discovered and judged” after “the analysis of words which are composed out of [his alphabet]” (20). However, he did not explain how the analysis and judgment of human thoughts could be done given the subjectivity embedded in the concept of human thought: moral standards and aesthetic preferences, for example, seem impenetrable through mere logical inferences.

Computational output is not the final result but an intermediate product of the creative process, as the interpreter also engages in the analysis and evaluation of the data. The continuous improvements of the recipe algorithm’s results are driven by the human feedback in “novelty” and “odor pleasantness” (Varshney et al. 7:9). Yet, while it is possible to summarize the population’s average judgments of the recipe in these aspects, they are highly dependent on the culture and individual life experience. The food that they have tried before shapes the Bayesian surprise. Also, a food may trigger a different response even for the same individual with a different intent – “I just felt nostalgic. I crave a recipe that is familiar yet creative”, for instance. Similarly, eighteenth-century musicians employ their “skill and taste” to select the suitable combination of musical elements in creation despite its superficial reliance on a random algorithm (Ratner 361). Computation becomes an instrument that mediates the creative process in human thought, whose subjective factors – intent, emotions, experience, etc. – are irreplaceable by the computations.

Discovery
I explored Leibniz’s progress on developing the universal language, which fascinates me as I have also created a conlang. The project was not fleshed out very thoroughly, although he discovered relationships between symbolic systems like the binary system and I Ching, which imply universality. While it may seem far-fetched to turn concepts of the world into simply numbers in Leibniz’s age, the vectorization of words in LLMs does seem promising, echoing his dream. While these projects both produce a comprehensive representation of the world in the language of numbers. Leibniz focuses on enlightening everyone with the universal language to produce rational thoughts and decisions, whereas LLMs’ ability extends further. After converting the world of human experience into a world of data so that a machine can manipulate the data through computations, turning them back to the experiences means substantializing the data. It is fabricating “the ultimate tool” through which its user can transform their experience in any way they like.

[malongo03]

Leibniz believed there must be a way to transform every day conversations and arguments into equivalent characteristic numbers so that every argument can be solved by rigorous proofs rather than going in circles. To make a connection outside of readings, this reminds me of the later mathematician Godel's future efforts to assign a Godel number to all statements in set theory and first-order logic. However, unlike Leibniz's program of resolving all debates using his characteristic numbers, Godel used this to achieve the opposite goal. He managed to prove by operating on Godel numbers that any logical system of axioms powerful enough to express Peano arithmetic has a true logical expression roughly equivalent to "this statement is unprovable". This was his first Incompleteness Theorem.

What I mean to say about this is that quantifying reason has been definitively proven to not be able to solve all logical debates. There exists truths that can never be proven using strictly numbers, or even strictly reason. And I suspect this the case for almost every real world debate, where mathematical truth of full certainty is impossible, meaning at some point a human being has to make a judgement call on what to trust and assume.

Assigning credit for creative projects using computation ultimately depends on the kind of computation used. For image AIs, who have been caught training their models off of artworks they had no permission to use and which have been demonstrated to be engaging in a kind of, I would morally assign credit for every output to the conglomerate of artists whose work was yoinked and the neural network itself producing the Frankenstein outputs, since none of user, network designer, and network implementer had any control over the output of the model. For works generated by a humanly constructed generator (e.g. the music discussed in Ars Combinatoria, Minecraft world generation), the creative credit for the music lies in the constructor of the formula for generating the music. Otherwise, if some process of discretion and editing was used to produce a work using computation rather than solely consisting of it, the user is the artist under a fair use doctrine.

In regards to universe modelling, I fail to see a clear metaphysical difference between a computer modeling a universe and (sorry for my third extra-source relation) the philosopher Berkeley's concept of all things being ideas in the mind of God, aside from the computer lacking agency and the plethora of infinite qualities traditionally assigned to God. "The universe is a simulation" belief just sounds like theism (or polytheism if they believe a whole society constructed the simulation) crouched behind a veneer of atheism. So yes, a computer running a model can be said to be "causing" that model, though in a subservient sense to whatever is causing our own universe.

Discovery:
Before the reading Ars Combinatoria, I did not know random permutations of rhythms and melodies were ever popular as an inspiration technique in creating music, but it makes sense in hindsight: artists of all types often try out a few different different brush strokes or word choices or clay shapes (and etc.) before settling on something in particular. The sophistication of efforts to systematize this process of experimentation for music during the eighteen century did surprise me, though I was more interested in how these systems factored in letting human create new works rather than how they could produce new works independent of humans. I think more tools and techniques should be developed like this, presenting artists that request it with a range of potential choices for minor adjustments after they make a brush stroke or type a new sentence.

[meeradasgupta247]

Is Computational Creativity Oxymoronic?
Meera Dasgupta

The Creator is an omniscient monolith to many; the creator, in contrast, is usually construed as human in nature. Hence, if we were to consider “computational creativity”, the question then arises as to whether this phrasing is oxymoronic. In other words, can computers be creative? Though the readings for this week provide compelling evidence as to the affirmative, by pointing to the augmentation of human creativity and human-like accumulation of ideas by machines to form new constructions, what is unrealized by these arguments is the idea of the creative being recognizable. As in, for something to be considered creative, there must be a standpoint where someone looks upon another as a creator; for a creator to be creative, it seems as though they must be able recognize and differentiate the creative from an unmarked other. Thus, if creativity is a two-way street, then, in not being able to recognize or form opinions about creativity as a member of the audience, so to speak, the argument can be made that a computer cannot yet be creative.

To begin, in “Towards a Universal Characteristic” by Gottfried Liebniz, Liebniz explains how the art of combination or, “ars combinatoria” (p. 20) seeks to uncover a way to characterize questions using numbers. In doing so, he seems to imply that his discovery is a creation which illuminates the Creation of all things by God (p.17). Though one may claim that the discovery itself is enough to consider Liebniz as being creative, the more fervent claim which he makes to this point is not found in the discovery itself but rather in Liebniz’ recognition of his unique, long withstanding rumination over questions in combinatorics. He explains that through “strenuous reflection” (p.21) and by “intuiting [combinatorics’] whole significance” (p. 21), he was able to differentiate himself from other great thinkers who had missed the same line of logic.

Hence, Liebniz recognizes the creativity of his life’s work through comparison. Though his discovery was certainly due to the accumulation of ideas in mathematics and philosophy,it is through his understanding of others’ and his own efforts, that Liebniz is able to identify himself as a creator. For the sake of comparison, “The Nine Billion Names of God” by Arthur C. Clarke also portrays combinatorics as a means to bring about the end of the world. In this story, machines are commissioned to take “a hundred days” (Section 1) to write all possible names for god - a feat which would have taken people “fifteen thousand years” (Section 1). Despite the machines finding new combinations of letters for names on their own, it is clear that, to Clarke, the machines are tools for the augmentation of the human endeavor.

Though, at this point, one might then wonder if the pursuit of knowledge within a highly structured, rationalist paradigm - one which seeks to explain everything concisely - can be construed as creative at all. For the monks and Liebniz, the answer is yes as their ideas still incorporate a vision for the world which is perceived by others and themselves; though both attempt to characterize the abstract with numbers, ironically, their idea of rationality remains subjective and open to internalized and external perception. In that same vein, the monks are not perceived as creative by Dr. Wagner because he dehumanizes them into customers who are always right (Section 1); in essence, the transactional nature of the machine approaching a creative task is mimicked in Dr. Wagners’ approach towards the monks. Neither understand the gravity of the task put forth before them and are unable to be deemed as creative due to their inability to recognize creative pursuit and discern it from the drive to produce some result that is asked of them.

Discovery
I never knew that Leibniz was also a philosopher and that he contributed to fields apart from mathematics! Personally, his characterization of the art of combinatorics was very interesting to me as he seemed to be very assured that it would solve arguments, bolster religion, etc. Especially pertaining to religion and the creation of the world through numbers, I had not read an account where numbers were so deeply entrenched with the supposed key to the universe. Though, of course, outcome spaces can be mapped to real numbers and combinatorial proofs can liken two expressions of scenarios with each other, I do wonder/ am unclear on how he envisioned characterizing things with numbers (ie. would this be a collection of numbers, distinct numbers, etc).

Citations

‘“The 9 Billion Names of God” by Arthur C. Clark. 1967

“Towards a Universal Characteristic” by Gottfried Liebniz [1685] in Leibniz: Selections, ed. Philip Wiener, New York: Charles Scribner’s Sons, 1951.

[ciara-kinney]

Most scientific papers following standard contemporary format include a section on the work’s significance and the benefits it will likely produce. I found the paper “A Big Data Approach to Computational Creativity” ’s response to this question quite interesting as the aim of its research is not without controversy, thus their answer necessarily takes a particular stance on the issue. The value the authors cited of developing creativity in computers was generally that the “limited availability of human creativity resources” hinders efficiency of product development cycles, which in turn reduces a stakeholder’s ability to compete in global markets, thus, introducing an artificial creativity which transcends human abilities can make stakeholders more competitive in a global economy (Varshney, et al, 1). (It also adds that studies of artificial creativity might help to further elucidate the nature and mechanism of human creativity, but this didn’t seem to be their primary point).

Although focusing on the concrete benefits of a scientific investigation is appropriate for this sort of writing, I was still surprised by the relatively limited scope of the author’s statements. Focusing on the quantitative economic impact of products of computational creativity without discussion of the value we assign the process through which they are developed (being human or machine made) is taking a position that regards product as primary and process as secondary, or perhaps not relevant at all. Although this paper centered on the development of recipes, which is just one creative domain, it emphasized the applicability of the methods the authors developed to other creative domains. This extends the conversation from just product development to other creative pursuits, such as science and art. Focusing primarily on the outcome of computational creativity in science is potentially less controversial, as comparing the impact of a product against some abstract notion of integrity of process is much easier when the product is something objective with significant ability to positively impact humanity. The value of pure art generated by a computer, on the other hand, is highly contentious, and many people regard it without value, or at least with only a fraction of the value of human made art, because it is meant to convey some “meaning” and they believe its creation process to be more integral to its worth. Whether something that exists for the sake of its meaning alone must flow from human hands to be valuable is controversial, and a question that follows discussions of computational creativity very closely.

This question also surfaces in Arthur C. Clark’s The Nine Billion Names of God. The story presents a stark contrast between two methods of obtaining all nine billion names for God: the first, excruciatingly laborious, spanning fifteen thousand years, and accomplished by the painstaking work of the monks, the second, automated, easy, and completed in three months by a machine. The ultimate equivilence of these two methods is quite shocking. That the end of time could be brought about with basic use of a computer means that it was just the outcome that mattered, not the method at all. The time invested, the devotion, the meditation, and the human character required to devote oneself so thoroughly to such a monotonous and intangible task, are all irrelevant and forgotten once the end was achieved by other means.

This story’s treatment of human generated vs. machine generated content is significant. In it, the realization of God’s will, which is often understood as some sort of ultimate meaning, is achieved more easily by machine than human. Abstract notions of human’s inherent relevance to this end are dismissed and we are forced to acknowledge that there is nothing unique about human capabilities in this regard. Only outcome is important. Applying this perspective to current questions of artificial intelligence yields interesting results.

Discovery:

I feel slightly bad sticking to taking about just two texts, but I thought that the definition of creativity used by the authors of “A Big Data Approach to Computational Creativity” was quite interesting. They defined creativity as “the generation of a product that is judged to be novel and also to be appropriate, useful, or valuable by a suitably knowledgeable social group”. Creativity defined in this way is thus entirely based on the perspectives of whatever social group you are asking to evaluate your product. I hadn’t previously thought a lot about how one can judge something’s creativity, so although this answer felt somewhat unsatisfying, I don’t personally have a better one (although that, of course, doesn’t mean that one doesn’t exist). I do wonder, however, whether this definition is using the knowledgeable group as a means to access something inherent about creativity that is just obscure, but still definable, or if relying on the opinions of others is impossible to avoid (which would maybe(??) imply that creativity is a socially determined thing without much meaning outside of that??).

[rshah1869]

In the readings for this week, I noticed how synthesis of a wide variety of compositions into numerical patterns has a kind of universalizing characteristic. According to Leibnitz, the number is a “fundamental metaphysical form” (Leibnitz, 17). This approach to the universal language quality of mathematics centers the individual in the utilization of mathematical concepts. To Leibnitz this is the only incorruptible kind of understanding. “For all other gifts may corrupt man, but genuine reason alone is unconditionally wholesome for him” (23). This universality can be understood as a closeness to God, which is a common theme that Leibnitz shares with Arthur C. Clarke’s The Nine Billion Names of God. In this story, the numerical translation of the names of God using a computer that creates permutations of 10 letters from AAA… to ZZZ… is subject to a number of rules that are inherently cultural. The monk nicknamed “Sam Jaffe” says that the machine must “eliminate ridiculous combinations. For example, no letter must occur more than three times in succession.” While this rule seems arbitrary to the Westerner selling the machine to the monks, the combinatorial nature of this limitation allows for it to be easily computable using a machine. Here we see the translation of cultural factors into the numerical as a means to an end goal.

This theme is consistent with Western musical culture. Francesco Galeazzi utilizes a number of musical phrases to assist with students who struggle with composition. This application is a practical one that allows for a kind of synthesis of recognizable musical phrases into a greater piece of music with much less effort. “We find many who can proceed with a given figure with little effort but how have insuperable difficulties when they have to invent new material. Here is something…with which one can discover a hundred, a thousand in the twinkling of an eye” (Ratner, 348). While this kind of musical shortcut is looked upon as a last resort by Galeazzi, it’s utility is in “unlocking the imagination of the student.” We see this principle of ownership and creativity in Leibnitz as well, who sees himself as the inventor of a new kind of logic “I have invented an elegant artifice…” (25).
Discovery
During this historical exploration, one surprising discovery was the extent to which early computational thinkers like Roger Bacon and Leibniz anticipated modern AI concerns. Bacon’s emphasis on empirical observation as a means to structure knowledge prefigures data-driven machine learning approaches today. However, unlike contemporary AI, which often operates as a “black box,” Bacon emphasized interpretability, insisting that understanding must accompany quantification. This contrast highlights an ongoing issue in AI ethics. As computational models become more complex, ensuring transparency and human oversight remains a critical challenge. As AI increasingly mediates knowledge production, revisiting these historical perspectives may provide valuable insights into designing systems that balance quantification with meaningful interpretation.

[aadarwal]

The sort of flow of a common thought process I found after going through the readings was really just
quantifying ----> gains and losses ----> reintegration. I found the readings to be particularly emphasizing on the quantifying part and maybe because of a bias, but I found that to be the underlying problem throughout the whole question of computational creativity. Firstly, with an emphasis for quantifying as "computational creativity" the whole process is generally applied to all sorts of human emotions, expressions and feelings. Leibniz idea of universal characterization is precisely this - trying to find data / make sense out of these qualities in the form of some sort of data. Again, very similar to the whole Big Data Approach to Computational Creativity. In fact, I think this is precisely what leads to the next step that the readings emphasize where the same quantifying principles are applied across a range of fields whether philosophy or theology, and that is not just a process that leads to loss and error, but the larger question in my opinion would be whether the loss is in the quantification process itself or more applicable to the fields? That is, I think there is a generally larger question of whether everything can in the first place even be quantified and represented as part of some computation. This branches off into two possibilities then based on the answer. If yes, then I would think that the problem creating the error or loss is architectural in the sense that the process of quantifying is not good enough yet. (This could also make sense given how much we have given better at it today then the argument could just be made that all we need to do is scale from here) but if the answer is no then I guess there is a general consensus that the loss is inherent, and that left me a bit confused in terms of whether the loss was what was creating the creating the creativity itself, or this was something that could actually be done. I think its the same kind of problem that Arthur C Clarke addressed here in saying that he was afraid of the possibility where there was a general lack of soulfulness and depth because of a purely computational creative world, sort of like a persistent belief that the human being is capable of that deeper nature and "actual" creativity. Based on this then I think I struggled a bit with the whole aspect of the reintegration in the readings. Because so far I was reading that the problem was in the computational process itself and so to me the reintegration was just some sort of reverse process of that quantifying, and the error could arise from either of these processes, but the nature was the same - the lack of an accurate quantifying tool. I am not sure if this is a correct reading- but I did feel like some instances from the passages supported it - for instance I found the idea of a feedback loop to be a representation of this where the reintegration could lead to further quantifying.

Discovery
I have been thinking about computational creativity a lot in the past, specifically from the point of view of what AGI timelines today even mean when models have been exposed to the vastness of the spectrum of human knowledge, significantly more than a single human could ever gain, and yet we see that they do not have the ability to act on that creatively in terms of creating new knowledge beyond hallucinations. Personally I have always felt that the reason for this is lack of the correct architecture for these models themselves, but these readings have really made me think long and hard about why I hold so many of these views. For instance, the fact that people from the time of Leibniz have made the assumption that turning deeper data into purely computational representations strips away parts of that complex representation that was initially available to our brains. Its fascinating to see that this architecture problem has been constant, and it looks like creativity in that regard of actual understanding (and the creating of ideas I said) has been unique to the human domain since the time and even today. Beyond this I had not actually thought of who gets credit for these things, and so the latter part of the reading was a real discovery for me in terms of making me understand and question the kinds of things that I was actually promoting. Because if the argument is that creativity lies within the human itself like I think, then the benefits of it must also go to them clearly. But if the goal is to build more computational architectures, clearly some of that credit would have to be sacrificed to build these out, and so I reached this kind of impasse as a result that I was not too sure how to get over and was hoping to get a better understanding of in class.