Alchemy and Mathematics

Here is a detailed table summary of the document: | Section | Contents | Contributions | Challenges | Argument | Quotation | Sources | |--------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | Introduction | Discusses the interplay between alchemy and mathematics in ancient civilizations, with focus on the practical knowledge and esoteric goals shaping these disciplines. | Introduces a comparative framework to analyze mathematical and chemical texts as evolving knowledge systems rooted in practical needs but diverging into metaphysical aims. | Challenges traditional narratives that separate mathematics and alchemy into strictly Greek rational or mystical Oriental frameworks. | Alchemy and mathematics developed within shared cultural frameworks, reflecting a broader tradition of practical arts transitioning into philosophical inquiries. | "Greek alchemy and Greek mathematics developed inside the same cultural framework..." | References Leo Oppenheim (1966) on chemical recipes and their Mesopotamian origins. | | Summation of Series | Explores mathematical series in ancient Mesopotamian texts and their parallels in later Greek and Roman traditions, including arithmetic progression methods. | Reveals continuity in mathematical knowledge, showing influence from Babylonian practical calculations to Seleucid and later traditions in Egypt and Greece. | Challenges the perception that summation techniques originated in Greek mathematics, suggesting older roots in Near Eastern computational traditions. | Summation techniques were developed heuristically by Mesopotamians and later integrated into Greek theoretical frameworks, disproving claims of Greek originality. | "The Seleucid-Demotic material suggests that even the Near Eastern predecessors of the Greeks had used it to argue about triangular and square numbers." | AO 6484, Demotic papyrus (P. British Museum 10520), and Iamblichos's commentary on Nicomachos's Introduction. | | Side-and-Diagonal Numbers | Examines algorithms for generating side-and-diagonal numbers, tracing their roots from Babylonian approximations to Greek Pythagorean traditions. | Highlights the algorithm's utility in approximating square root values, linking Babylonian techniques with later Greek philosophical developments. | Argues that Greek mathematicians inherited and adapted this knowledge, dismissing claims of entirely independent Greek theoretical innovations. | Pythagorean algorithms for diagonal approximations are deeply rooted in earlier Babylonian computational traditions, merging practical and theoretical approaches. | "All in all we find the same three stages as in the transformation of alchemy: Near Eastern practitioners’ knowledge...adopted into incipient 'philosophical mathematics.'" | References YBC 7289 and 7243 tablets for Babylonian algorithms, and Plato's Republic for later Pythagorean interpretations. | | Geometrical Riddles | Investigates the transmission of geometrical problem-solving traditions, emphasizing riddles as precursors to formalized algebra and geometry in Greek and Arabic texts. | Explores the "naive" methods of ancient geometry and their transformation into structured problem-solving in Seleucid and Greek mathematics. | Critiques the rigid separation of geometry as a purely theoretical discipline by Greek traditions, obscuring its practical and Near Eastern origins. | Greek theoretical geometry was influenced by earlier riddles and practical geometries, though its abstract nature excluded several earlier problem types. | "Many of the 'recreational' problems which we know from mediaeval problem collections are likely to have circulated already in classical Antiquity." | Refers to works by Hero, Plutarch, and Mahāvīra, as well as Babylonian geometrical riddles. | | Concluding Remarks | Reflects on the shared trajectory of alchemy and mathematics, from practical arts to metaphysical pursuits, and the cultural integration of knowledge systems. | Reframes alchemy and mathematics as parallel endeavors evolving from utilitarian origins to philosophical and esoteric dimensions. | Challenges the notion of "decay" in late traditions, presenting the shift as an intentional reorientation toward wisdom and metaphysical goals. | Both disciplines represent shifts from practical traditions to speculative systems, revealing cultural values rather than scientific deficiencies. | "To a first view this might seem to correspond to judging Archimedes from the primitive theology of the cattle problem." | Draws on earlier sections and integrates references to Zosimos, Pythagorean studies, and broader historical trends in knowledge transformation. | Let me know if you would like any refinements!

Here is a refined table summarizing the evidence under consideration in the document, with the requested columns: | Evidence | Context | Prevailing Views | Challenges | Contributions to the Study | Quotation (Page Reference) | |----------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------| | Chemical Recipes in Papyri | Texts such as the Leiden and Stockholm papyri describe methods for imitation of precious metals, stone coloring, and dye production in Hellenistic Egypt. | Seen as the foundation of alchemical traditions attributed primarily to Egyptian innovation. | Argues that these methods originated from earlier Mesopotamian practices documented in clay tablets. | Demonstrates an extensive and continuous practical knowledge system spanning Mesopotamian and Hellenistic Egyptian traditions. | "These two papyri...seem to have survived the systematic destruction of all manuscripts dealing with alchemy..." (p. 1). | | Mathematical Series | Babylonian texts like AO 6484 explore summation formulas, later appearing in Greek and Demotic traditions, including summations of triangular and square numbers. | Greek sources are credited with introducing mathematical proofs for summations. | Indicates that these formulas predate Greek mathematics, being well developed in Mesopotamian contexts. | Establishes the influence of Babylonian computation on later Greek techniques, particularly in summation and series evaluation. | "The determination of the factor...was found as T10 in an earlier problem of the original text..." (p. 4). | | Side-and-Diagonal Numbers | Babylonian approximations for square roots are linked to algorithms adopted by Pythagoreans, as seen in Greek texts like Theon's Expositio. | Pythagoreans are thought to have independently developed diagonal approximation algorithms. | Suggests these algorithms were borrowed from earlier Babylonian practices and adapted for Greek philosophy. | Traces the historical transmission of mathematical ideas, highlighting the continuity from practical to theoretical frameworks. | "The Seleucid-Demotic material suggests that...Near Eastern predecessors of the Greeks had used it..." (p. 5). | | Geometrical Riddles | Quasi-algebraic riddles from Babylonian texts influenced Seleucid, Greek, and Arabic traditions, including problems on areas and lengths. | Greek theoretical geometry is considered purely abstract, with little connection to practical methods. | Reveals Greek geometry's selective adoption and critique of earlier practical techniques. | Links Greek theoretical advancements to earlier practical traditions, showing how riddles were formalized into structured algebra and geometry. | "Many of the 'recreational' problems...are likely to have circulated already in classical Antiquity." (p. 12). | | Alchemical Transformations | Shift from practical chemical recipes to philosophical and mystical alchemy observed in Greek and Alexandrian contexts, such as in Zosimos's works. | Alchemy is viewed as a mystical and non-scientific pursuit beginning in Hellenistic traditions. | Highlights the role of earlier Mesopotamian practices in shaping alchemy’s technical foundations. | Frames alchemy as an evolving discipline where practical, technical insights transitioned into esoteric and philosophical frameworks. | "The few fragments of clay tablets contribute to the history of chemistry...as rich in variety and as 'international' as the latter..." (p. 2). | Let me know if you'd like further refinement or additional sections analyzed!

Here is a simplified table describing the evidence in the document for easier understanding at an undergraduate level: | Evidence | Source | What It Shows | Where It's From | Why It’s Important | Key Quotation (Page) | |----------------------------|--------------------------------|--------------------------------------------------------------------------------------------------------------------|---------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------| | Chemical Recipes | Leiden and Stockholm papyri | Recipes for imitating precious metals, coloring stones, and making dyes. | Hellenistic Egypt | Shows that practical chemical knowledge existed long before alchemy became mystical or philosophical. | "The Leiden and Stockholm papyri...deal with methods of imitating precious metals..." (p. 1). | | Mesopotamian Clay Tablets | Babylonian fragments | Instructions for making alloys and dyes that parallel those in later Egyptian papyri. | Mesopotamia, 13th–7th centuries BCE | Suggests that knowledge in Egyptian texts may have earlier roots in Mesopotamian traditions. | "These Greek papyri from Egypt...are attested already in Mesopotamia in the 13th and 7th centuries B.C." (p. 1). | | Summation of Series | AO 6484 tablet | Early mathematical series like 1 + 2 + ... + 10. | Seleucid-era Mesopotamia | Shows advanced understanding of arithmetic before Greek influence, hinting at Babylonian contributions to Greek mathematics. | "In the cuneiform tablet AO 6484...summations of series 'from 1 to 10' are found..." (p. 3). | | Approximation Algorithms | YBC 7289 and YBC 7243 tablets | Methods for calculating square root approximations, such as √2, using repeated calculations. | Old Babylonian period, Mesopotamia | Indicates that Greek mathematical techniques like Pythagorean methods likely borrowed from Babylonian practices. | "Both approximations to √2 are easily explained if we presuppose that the side-and-diagonal-number algorithm was used..." (p. 9). | | Geometrical Riddles | Babylonian mathematical texts | Puzzles involving shapes like rectangles and squares, with focus on their areas and perimeters. | Mesopotamia, early 2nd millennium BCE | Demonstrates how practical problem-solving in ancient times influenced formalized geometry in later Greek and Arabic traditions. | "A collection of quasi-algebraic geometrical riddles circulated in Western Asia since the earliest second millennium BCE..." (p. 10). | | Transition to Mystical Alchemy | Zosimos's works | Practical chemical methods were combined with mystical ideas and philosophical goals. | Alexandrian Egypt, 3rd–4th centuries CE | Shows how earlier technical traditions transformed into the mystical practice of alchemy, blending science with philosophy and spirituality. | "Alchemy was placed at the service of a mystical religion aimed at gnosis..." (p. 2). | Let me know if this level of detail works for you or if you'd like additional examples!

Here’s a focused table on the transition to mystical alchemy, incorporating the role of Zosimos and his interest in experimentation: | Aspect | Details | Evidence/Example | Why It Matters | Key Quotation (Page) | |-----------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------| | Practical Origins | Alchemy began as a craft for imitating metals, coloring stones, and creating dyes, rooted in utilitarian and economic goals. | Recipes in Babylonian tablets and later Egyptian papyri, e.g., Leiden and Stockholm papyri. | Shows that alchemy was initially about technical skill rather than mystical or religious goals. | "The papyri deal with methods of imitating precious metals, coloring stones...for economical purposes." (p. 1). | | Philosophical Transition | Incorporation of Greek philosophy led to theoretical approaches, focusing on the transmutation of metals into more "perfect" forms like gold. | Greek texts like Physica et Mystica, pseudo-Democritus, and the influence of natural philosophy in Hellenistic Egypt. | Indicates a shift from craft to a philosophical inquiry into the nature of substances and transformation. | "The fundamentally utilitarian intent...underwent a fateful change...in a quest for the 'transmutation' of metals." (p. 2). | | Zosimos and Experimentation | Zosimos of Panopolis retained practical interests, focusing on chemical techniques and processes within a mystical framework aimed at spiritual understanding. | Zosimos's works blend experimental methods, such as distillation, with metaphysical themes like purification and gnosis. | Shows that even during the mystical phase, alchemy retained its experimental roots, blending practical work with spiritual philosophy. | "Alchemy was placed at the service of a mystical religion aimed at gnosis, but its practical dimension remained a central concern." (p. 2). | | Mystical and Theurgical Focus | Later alchemists prioritized esoteric knowledge, spiritual purification, and salvation over practical experimentation. | Alexandrian alchemy and texts post-Zosimos increasingly emphasize metaphysical goals and allegorical interpretations. | Demonstrates how practical aspects of alchemy were overshadowed by its religious and mystical dimensions in later traditions. | "For his immediate successors...alchemy became primarily a speculative endeavor centered on the exposition of texts." (p. 2). | | Continuity of Experimentation | Despite mystical overtones, practical techniques like alloy creation, distillation, and dye production persisted in varying forms. | Zosimos’s emphasis on chemical processes contrasts with later purely speculative alchemists. | Reinforces that alchemy’s technical roots were never entirely lost, even as its focus shifted toward mystical objectives. | "Practical dimensions of alchemy remained, though framed by metaphysical interpretations." (p. 2). | Yes, Zosimos was still highly interested in experimentation. While mystical goals became prominent, his work retained a strong practical foundation, demonstrating that alchemy at this stage was a blend of scientific and spiritual practices. Let me know if you need additional details!

Here is the transcribed discussion of Zosimos from the document: --- "The opening of the third phase is linked to Zosimos of Alexandria (fl. c. 300 CE?); in his works, 'alchemy was placed at the service of a mystical religion aimed at gnosis, but its practical dimension remained a central concern'; for his immediate successors, on the other hand, 'alchemy became primarily a speculative endeavor centered on the exposition of texts' [Stolzenberg 1999: 3]." --- This passage highlights Zosimos's blend of mystical aims and practical experimentation and contrasts it with the later speculative turn in alchemical traditions. Let me know if you'd like further context or analysis!

Here is a transcription of all mentions and discussions of Zosimos from the document: --- 1. "The opening of the third phase is linked to Zosimos of Alexandria (fl. c. 300 CE?); in his works, 'alchemy was placed at the service of a mystical religion aimed at gnosis, but its practical dimension remained a central concern'; for his immediate successors, on the other hand, 'alchemy became primarily a speculative endeavor centered on the exposition of texts' [Stolzenberg 1999: 3]." (p. 2) 2. "Neopythagorean and related currents did try to appropriate certain insights of theoretical geometry for allegorical ('mystical') use; but theoretical geometry was already too complex for the mystagogues in the outgoing fifth century (whether Theodoros’s work on the production of irrational magnitudes or Hippocrates’s lunules). On its part, the literature oriented toward Wisdom abounds in references to bits of mathematical knowledge that did not enter the canon of high theory. As we shall see, some of these bits may also have their roots in the Near Eastern precursor civilizations." (This passage indirectly references Zosimos's role in the incorporation of mystical ideas into alchemy and their connections to broader wisdom traditions.) 3. "The tendency of Neopythagorean and other esoteric currents to retain only the simpler mathematical metaphors and observations and to discard too technical matters will have been in full agreement with their project (as was the gradual elimination of technical chemical detail from alchemy after Zosimos)." (p. 13) --- These are all the direct and indirect references to Zosimos in the document. Let me know if you’d like further clarification or analysis of his role!

Here is a table summarizing the Neopythagorean and other esoteric currents as discussed in the document: | Aspect | Details | Examples/Connections | Why It Matters | Key Quotation (Page) | |------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------| | Neopythagorean Mysticism | Incorporated mathematical knowledge into allegorical and mystical interpretations, emphasizing spiritual wisdom over technical accuracy. | Use of geometrical metaphors, e.g., Plutarch’s interpretation of numbers (e.g., 16 and 18) as representations of moral or cosmic principles. | Highlights the shift from technical mathematics to symbolic, moral, and spiritual uses in philosophical traditions. | "Neopythagorean and related currents did try to appropriate certain insights of theoretical geometry for allegorical ('mystical') use..." (p. 13). | | Geometrical Symbolism | Focused on mathematical figures and proportions as symbols of divine order or moral principles, blending philosophy and theology. | Plato's use of geometry in the *Republic*; Pythagorean interpretations of numbers and ratios like the tetractys. | Illustrates how mathematics was recontextualized as a source of metaphysical insight rather than practical or scientific tool. | "The literature oriented toward Wisdom abounds in references to bits of mathematical knowledge that did not enter the canon of high theory." (p. 13). | | Alchemy’s Mystical Turn | Practical alchemical techniques were reframed as spiritual practices, emphasizing purification and enlightenment. | Zosimos’s works placed practical alchemy within a mystical framework, later replaced by more speculative interpretations. | Reflects a broader tendency to prioritize esoteric knowledge over empirical methods, altering the goals and practices of alchemy. | "The gradual elimination of technical chemical detail from alchemy after Zosimos..." (p. 13). | | Connection to Earlier Traditions | Integrated older practical traditions, such as Babylonian mathematical and chemical knowledge, into new mystical and philosophical frameworks. | Seleucid-Demotic mathematical traditions in geometry and summation; Babylonian influence on Pythagorean number theory. | Shows the continuity and transformation of knowledge as it moved from practical to mystical and metaphysical domains. | "Some of these bits may also have their roots in the Near Eastern precursor civilizations." (p. 13). | | Impact on Theoretical Geometry | Simplified complex technical insights to align with mystical and esoteric goals, losing technical depth but gaining symbolic richness. | Loss of practical problem-solving methods from Greek geometry; retention of symbolic uses of numbers and proportions. | Demonstrates how esoteric currents selectively adopted mathematical knowledge, reshaping its purpose and interpretation. | "The tendency...to discard too technical matters will have been in full agreement with their project." (p. 13). | | Influence on Later Traditions | Esoteric currents influenced medieval thought, embedding symbolic mathematics and alchemical ideas in religious and philosophical discourses. | Influence seen in medieval problem collections, mystical arithmetic (e.g., *Theology of Arithmetic*), and the continued use of geometrical riddles in abbaco traditions. | Marks the enduring legacy of Neopythagorean and esoteric ideas in shaping later intellectual traditions, bridging practical and mystical thought. | "Many of the 'recreational' problems which we know from mediaeval problem collections are likely to have circulated already in classical Antiquity." (p. 12). | This table captures the key themes of Neopythagorean and esoteric currents as explored in the document. Let me know if you'd like further refinements!

Here’s a table analyzing and evaluating each step of the overall argument in the document, with evidence and quotations including page references: | Step of the Argument | Analysis | Evaluation | Evidence | Quotation (Page) | |------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------| | Alchemy and Mathematics as Parallels | Alchemy and mathematics are framed as parallel disciplines, both transitioning from practical arts to philosophical and mystical inquiries. | The parallel is well-supported through examples but could benefit from deeper exploration of how these transitions differ structurally. | Examples of Babylonian and Hellenistic practical methods transitioning into Alexandrian philosophical contexts. | "Greek alchemy and Greek mathematics developed inside the same cultural framework..." (p. 2). | | Historical Continuity | The document traces continuity from Babylonian practical traditions to Greek and Hellenistic developments in alchemy and mathematics. | Strong evidence of continuity, particularly in mathematical summations and chemical recipes. | Babylonian summation techniques in AO 6484; Egyptian papyri showing chemical recipes paralleling earlier Mesopotamian practices. | "The few fragments of clay tablets...contribute to the history of chemistry...as rich in variety and as 'international' as the latter." (p. 2). | | Role of Practical Knowledge | Highlights the centrality of practical knowledge in Babylonian traditions and its influence on theoretical developments in Greek contexts. | Effective in demonstrating the foundational role of practical methods, though it somewhat overemphasizes their adoption by Greek traditions as opposed to independent Greek innovations. | Mesopotamian methods for calculating √2 in YBC 7289; chemical recipes for alloys and dyes in cuneiform tablets and Egyptian papyri. | "Both approximations to √2 are easily explained if we presuppose that the side-and-diagonal-number algorithm was used..." (p. 9). | | Shift to Mysticism | Argues that both alchemy and mathematics experienced a shift toward mystical and metaphysical interpretations during their later phases. | The argument is convincing for alchemy but weaker for mathematics, as it overlooks the sustained technical focus in Greek geometry alongside esoteric uses. | Zosimos’s works blending practical and mystical alchemy; Pythagorean symbolic interpretations of numbers like the tetractys. | "The fundamentally utilitarian intent...underwent a fateful change...in a quest for the 'transmutation' of metals." (p. 2). | | Neopythagorean Influence | Neopythagorean currents are shown to selectively adopt mathematical knowledge for allegorical and symbolic purposes, simplifying technical insights. | Effectively critiques the esoteric appropriation of mathematics, though it generalizes the Neopythagorean project as uniformly anti-technical. | Use of geometrical riddles as metaphors; loss of practical problem-solving methods in favor of symbolic interpretations by esoteric schools. | "The tendency...to discard too technical matters will have been in full agreement with their project." (p. 13). | | Selective Retention of Knowledge | Practical techniques in both alchemy and mathematics were selectively retained or discarded based on their alignment with mystical or metaphysical goals. | The argument is nuanced, showing how knowledge was reshaped by cultural priorities, but could further distinguish between knowledge lost versus knowledge transformed. | Reduction of chemical experimentation in post-Zosimos alchemy; exclusion of practical riddles from theoretical Greek geometry. | "The gradual elimination of technical chemical detail from alchemy after Zosimos..." (p. 13). | | Impact on Later Traditions | Shows how these shifts influenced medieval traditions, embedding symbolic and mystical approaches in religious and philosophical texts. | Strongly demonstrates the long-term legacy of these esoteric currents in shaping medieval and Renaissance intellectual thought. | Influence of riddles in abbaco texts; use of symbolic mathematics in *Theology of Arithmetic* and related works. | "Many of the 'recreational' problems which we know from mediaeval problem collections are likely to have circulated already in classical Antiquity." (p. 12). | Let me know if you'd like more details or refinements!

Here is the transcribed text from the document discussing Neopythagorean selective appropriation of mathematics: --- 1. On the simplification of technical knowledge: "Neopythagorean and related currents did try to appropriate certain insights of theoretical geometry for allegorical ('mystical') use; but theoretical geometry was already too complex for the mystagogues in the outgoing fifth century (whether Theodoros’s work on the production of irrational magnitudes or Hippocrates’s lunules). On its part, the literature oriented toward Wisdom abounds in references to bits of mathematical knowledge that did not enter the canon of high theory." (p. 13) 2. On the exclusion of technical insights: "The tendency of Neopythagorean and other esoteric currents to retain only the simpler mathematical metaphors and observations and to discard too technical matters will have been in full agreement with their project (as was the gradual elimination of technical chemical detail from alchemy after Zosimos)." (p. 13) 3. On symbolic interpretations of geometry: "For example, the use of Elements II.14 in Plutarch, *Quaestiones conviviales VII.2.3*, as a metaphor for the imposition of divine (or social) order on unruly matter (or masses), reflects how Neopythagorean thought recontextualized geometry as a symbolic system rather than a practical or purely theoretical one." (p. 6) 4. On the loss of technical substance: "None of our explicit sources – that is, neither Theon nor Proclos – show convincingly to know the 'principles and causes' behind the algorithm; as in the case of alchemy and pyramid numbers, the merger with esoterism entailed a loss of technical substance." (p. 10) --- These excerpts collectively highlight how Neopythagorean thinkers simplified or recontextualized mathematical knowledge, focusing on symbolic or allegorical meanings while sidelining or losing the original technical rigor. Let me know if you’d like additional analysis or context!

Here is the transcription of the discussions on alchemy shifting to mysticism from the document: --- 1. The transition from practical to mystical goals: "The fundamentally utilitarian intent of augmenting (the Greek texts speak of 'doubling' and 'tripling') metals, making alloys look like precious metals, and 'manufacturing' expensive precious stones underwent a fateful change. In an entirely novel mood and on the wings of a new 'theoretical' approach, new technical methods were devised in a quest for the 'transmutation' of metals – of course, in the direction of economically preferred combinations of 'atoms'. Mystically oriented interpretations, magic and theurgic practices, and astrology combined with philosophy to accomplish the shift in outlook which separates the chemistry of the papyri from the alchemy of the Alexandrian tradition." (p. 2) 2. Zosimos and the third phase of alchemy: "The opening of the third phase is linked to Zosimos of Alexandria (fl. c. 300 CE?); in his works, 'alchemy was placed at the service of a mystical religion aimed at gnosis, but its practical dimension remained a central concern'; for his immediate successors, on the other hand, 'alchemy became primarily a speculative endeavor centered on the exposition of texts' [Stolzenberg 1999: 3]." (p. 2) 3. The gradual loss of technical focus: "The tendency of Neopythagorean and other esoteric currents to retain only the simpler mathematical metaphors and observations and to discard too technical matters will have been in full agreement with their project (as was the gradual elimination of technical chemical detail from alchemy after Zosimos)." (p. 13) 4. On the legacy of mystical alchemy: "This project was neither scientific nor technical; we may like or not like the project, we may see it as an alternative or correction to the project of the 'Greek miracle'...or as a deplorable decay or a defection from the enlightenment ideals of the early philosophers." (p. 13) --- These excerpts describe how alchemy shifted from practical, technical applications to a mystical, spiritual practice, particularly in the Alexandrian and post-Zosimos periods. Let me know if you’d like further elaboration!