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Work #1814

On Floating Bodies

The foundational treatise of hydrostatics — Archimedes's principle of buoyancy derived from postulates about the nature of fluids

Archimedes of Syracuse · c. 250 BCE · Ancient Greek (Doric) · Mathematical-physical treatise (axioms, propositions, proofs)

Tradition: Greek mathematical physics

A body immersed in fluid is buoyed up by a force equal to the weight of the fluid displaced — the birth of mathematical physics

On Floating Bodies (Peri Ochounomenōn / De Corporibus Fluitantibus) is in two books. Book I establishes the fundamental hydrostatic principle: fluids at rest are arranged so that equal volumes at equal distances from the centre are in equilibrium, and any solid placed in a fluid will sink until the weight of the displaced fluid equals the weight of the solid (Archimedes's principle, Proposition 5). Book II applies this to the stability of floating paraboloids of revolution — an extraordinarily sophisticated analysis of the conditions under which a floating body is stable or unstable. The treatise is the founding document of hydrostatics and one of the first works to derive physical laws from mathematical postulates. It survived only in a Latin translation by Willem van Moerbeke (1269) from a now-lost Greek manuscript, and in the Archimedes Palimpsest (discovered 1906, containing The Method and parts of On Floating Bodies).

Author

Editions cited

  • T.L. Heath, The Works of Archimedes (Cambridge, 1897; Dover reprint, 2002)
  • E.J. Dijksterhuis, Archimedes (Princeton, 1956; repr. 1987)
  • Reviel Netz and William Noel, The Archimedes Codex (Da Capo, 2007) — the palimpsest
Compare this work

School Embodiments

Mechanism · 30%
Classical Greek Thought · 25%
Rationalism · 20%
Realism · 15%
Naturalism · 10%
Mechanism 30%

The founding document of rational mechanics applied to fluids — physical law derived from mathematical postulates.

"Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced." (On Floating Bodies I, Prop. 5)
Classical Greek Thought 25%

The culmination of Greek mathematical physics — Euclidean deduction applied to the physical world.

The treatise opens with physical postulates about fluids and derives all results by Euclidean deduction.
Rationalism 20%

Rigorous deductive reasoning from axioms to physical theorems — the rationalist method applied to nature.

"The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the earth." (On Floating Bodies I, Prop. 2)
Realism 15%

Mathematics describes the real behaviour of physical fluids — a strong scientific realism.

The predictions of the treatise are empirically verifiable and have been confirmed for 2,200 years.
Naturalism 10%

Physical phenomena explained through natural laws, not divine causation.

No divine, teleological, or supernatural principles appear anywhere in the treatise.

Internal Tensions

The idealised fluid (continuous, uniform, perfectly gravitating toward a centre) vs. real fluids. The treatise assumes a spherical Earth but applies to finite containers. The gap between mathematical postulate and physical reality drives all subsequent fluid mechanics.

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I. Time

Hydrostatics is the physics of equilibrium — time is the stable background. Deterministic: physical laws hold necessarily.

Attributes
Extent: Infinite Ontological Status: Substantival Grain: Continuous Freedom: Deterministic Traversability: Linear Direction: Uni-directional Dimensionality: One
✦

II. Space

Curved: fluid surfaces are spherical (centred on the Earth). Three-dimensional, local, substantival.

Attributes
Extent: Finite Ontological Status: Substantival Curvature: Curved Dimensionality: Three Locality: Local
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III. Matter

Substantival, finite, conserved: fluids and solids have definite weight and volume; displacement is exact.

Attributes
Extent: Finite Ontological Status: Substantival Conservation: Conserved Dimensionality: Three Locality: Local
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IV. Observer

The mathematician-physicist who postulates, deduces, and (implicitly) experiments. Embodied and active.

Attributes
Time Instance: Single Space Instance: Single Knowledge Extent: Mediated Knowledge Retainment: Total Physicality: Embodied Agency: Active Number: Plural Metaphysical Agency: not engaged
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V. Energy

The equilibrium principle is an implicit energy-conservation statement: no work is done in hydrostatic equilibrium.

Attributes
Extent: Finite Ontological Status: Substantival Conservation: Conserved Dispersibility: Reversible
⧉

VI. Information

Mathematical truths are substantival, universal, and conserved. Continuous magnitudes throughout.

Attributes
Ontological Status: Substantival Cosmic Conservation: Conserved Personal Conservation: not engaged Granularity: Continuous

Personas with the nearest attribute fingerprint

Historical figures whose own classification on the same six-dimensional grid lands closest to this work's. Computed by attribute-agreement on coordinates both address.

100%
Eratosthenes of Cyrene
28/28
97%
Archimedes of Syracuse
31/32
97%
Ctesibius of Alexandria
31/32
97%
Marcus Vitruvius Pollio (Vitruvius)
31/32
97%
Strabo
31/32
97%
Chrysippus of Soli
30/31

Computed school proximity

The work's attribute fingerprint scored against all schools using the same quiz scorer. Useful as a sanity check on the hand-curated embodiments above.

90%
Latin Averroism
21/24
89%
Classical Greek Thought
22/24
88%
Middle Platonism
22/24
82%
Stoicism
20/24
79%
Legalism (Fa-jia)
21/24
78%
Aristotelianism
21/24
78%
Structuralism
19/24
76%
Mechanism
19/24

How On Floating Bodies resolves each dilemma

30 resolved positions across 4 dimensions, including 6 distinctive where the majority of schools go the other way · 27 unaligned.

Each dimension is sorted so minority positions come first. Mainstream positions are folded into an expandable list.

Time · 9 dilemmas · 3 distinctive

Persistence, the future, and the direction of becoming.

Distinctive · only 10% of schools agree (20/208)
Do you really choose?
If the brain is a physical system and physical systems are governed by laws, then every choice is also a chain of causes — which raises the question of what was really left to choose.
Choice is real within a determined order — agency and determinism aren’t opposites.
On this view, the future is determined and you are genuinely choosing. Those aren't contradictory because the determination runs through you rather than around you: your reasoning, deliberation, and assent are the way the determined outcome gets settled. Choice is what it feels like from …
Roads not taken The future is open and you are a genuine origin of it. (69%) · Choice is structural illusion — every event is fixed by the prior state. (10%) · Even if the universe is undetermined, you are not the chooser. (6%)
Distinctive · only 10% of schools agree (20/208)
Are addicts responsible for their addiction?
Addiction looks from one angle like the textbook case of agency failing — a person doing what they don't, in any meaningful sense, want to do. From another angle it looks like agency at work in hard conditions. Which it is depends on what agency is.
The addict is genuinely responsible within a determined order.
On this view, the addict is acting within a determined order but is genuinely acting — making decisions, endorsing or resisting urges, seeking or refusing help. Responsibility attaches not because some uncaused choice happened, but because the addict is the kind of agent through which …
Roads not taken The addict could have chosen otherwise — that's why recovery is real. (69%) · The addict's behaviour is the outcome of causes; 'responsibility' is a useful fiction, not a metaphysical fact. (10%) · Even if the universe is undetermined, the addict isn't the chooser. (6%)
Distinctive · only 10% of schools agree (20/208)
Should we hold AI systems responsible for what they do?
When an autonomous AI takes an action that harms someone, the question of who or what is responsible — the developer, the operator, the model itself — turns on whether the model is the kind of thing that can be a responsible agent.
The AI can be a genuine agent within determined conditions — and therefore genuinely responsible.
On this view, what makes a being responsible is not indeterminism but the kind of process the being is. An AI that deliberates, considers consequences, can be given reasons, and modifies its behaviour on reflection is doing what responsible agency is, even if its underlying …
Roads not taken An AI without a free will is not the kind of thing that can be responsible. (69%) · An AI's behaviour is fully determined by training and input; 'responsibility' applies if at all to its makers. (10%) · Neither AIs nor anyone else are the locus of free agency; the question is the wrong one. (6%)
6 mainstream positions
How much weight do future people deserve? Future people are as real as you are — and their interests count for as much. 47% Is regret rational? The past is as real as the present; regret is a real attitude toward a real thing. 47% Do we owe extinct species something we cannot give them? Extinct species are as real as we are; they have standing. 47% Is the universe running out of usable energy? Time is unbounded but matter is finite; usable energy can fail without time failing. 47% Are natural resources fundamentally finite, or only practically so? Time goes on but matter is bounded; we are eventually constrained even with infinite time. 47% Could we owe future generations more than is materially possible to provide? Time is unbounded but matter is not; we can owe more across long time than the matter can provide. 47%
Matter · 7 dilemmas, all mainstream
Is the world created from nothing? Yes — matter was created and is conserved as a real substance. 56% Is the physical world fully real? Yes — the physical world is fully real, mind-independent, persisting. 56% Does matter have intrinsic moral standing? Matter is morally considerable insofar as it is created or conserved good. 56% What is money? Money is a real institution with intrinsic features. 55% What is a nation? A nation is a real moral community with intrinsic character. 55% What makes someone male or female? Sex is a real biological kind with given content. 55% Should we edit the human germline? Human nature is a real biological kind given by reproductive biology or by creation; editing the germline transgresses what is given. 55%

Observer · 37 dilemmas · 3 distinctive

Mind, agency, and the knower's relation to the known.

Distinctive · only 5% of schools agree (11/208)
Is environmental damage ever truly permanent?
Extinction is forever; soil erosion takes centuries to repair; the carbon we emit will warm the climate for millennia. But whether 'forever' or 'millennia' means what they say depends on what kind of process the universe is.
What appears irreversible is reversible by the right action.
On this view, the appearance of permanence is a function of limits we have not yet exceeded. Divine action, sufficiently advanced technology, intentional restoration practice can in principle reverse what now appears irreversible. The lost is not gone for good; it is gone for now.
Roads not taken Damage is real and permanent on the relevant timescales. There is no recovery; there is only limitation. (66%) · Loss is part of cycles; what disappears returns in another form. (18%) · From the standpoint of the One, the categories of permanence and loss are conventional. (8%)
Distinctive · only 5% of schools agree (11/208)
Can a civilization recover from collapse?
Rome fell; Maya cities emptied; Bronze Age trade networks collapsed in a single generation. Whether what was lost can be recovered — or whether collapse is structurally final — depends on what kind of process civilization is.
Civilization is the kind of order that can in principle be restored.
On this view, the order that constitutes civilization — information, practices, institutions, ethics — is not destroyed by collapse, only dispersed. Given the right work, by humans, divine action, or both, it can be reconstituted. The historical pattern of recovery and renewal is partial evidence; …
Roads not taken Civilizational complexity is hard to build and easy to lose; recovery is at best partial. (66%) · Civilization rises and falls in cycles; recovery is structural to history. (18%) · From the One's vantage, civilizational categories are themselves conventional. (8%)
Distinctive · only 5% of schools agree (11/208)
Does the second law of thermodynamics mean something morally?
The universe trends from order to disorder. Whether that physical pattern carries moral weight — making the preservation of order, beauty, complexity a kind of cosmic duty — depends on whether time has the kind of structure morality could lean on.
Apparent entropy is reversible in principle; the moral category is restoration.
On this view, the second law describes local pattern rather than cosmic destiny. What is broken can be repaired — by divine action, by human work, by energetic intervention. The moral weight of restoration is real and not borrowed from the physics. The cosmos is …
Roads not taken Entropy is what time is. The moral weight, if any, is the weight of working against the current. (66%) · Local entropy increase is part of a cycle; the moral category is participation in the cycle. (18%) · From the One's vantage, the second law is itself a feature of the conventional, not the ultimate. (8%)
11 mainstream positions
Could causation work backwards? Causation runs one way — the arrow of time is real and structural. 68% Is the asymmetry between memory and anticipation a real feature of time, or just of us? The asymmetry is real because time itself has a real direction. 68% Is the arrow of time a real feature of the cosmos, or only of how we describe it? The arrow is real and structural; the asymmetry isn't an artifact of description. 68% When does a person begin? A person exists from conception — when a new being comes into existence. 55% What is marriage? Marriage has a given form — it’s a kind of thing we recognize, not make. 55% What is our place in nature? Active in a real nature — we cultivate, steward, transform. 50% Should we colonize space? Cultivating worlds beyond Earth is the next form of stewardship. 50% Is genetic engineering of food stewardship or domination? Genetic modification is cultivation by other means. 50% Should we trust expert testimony when we can't verify it? Trust expertise whose conclusions a competent mind can in principle reproduce. 31% Is religious revelation a real source of knowledge? Revelation is evaluable by reason — and not above it. 31% Does an LLM 'know' the things it correctly produces? An LLM can produce correct outputs but not reason to them; useful, not knowing. 31%
23 unaligned
Are coincidences ever more than coincidence? Schools split: 47% / 38% / 8% — Are the dead morally present to the living? Schools split: 43% / 37% / 12% — Are there indivisible units of experience? Schools split: 44% / 36% / 13% — Can prayer for someone far away affect them? Schools split: 47% / 38% / 8% — Could a fetal brain organoid in a petri dish be conscious? Schools split: 31% / 30% / 11% — Could an AI have a mind that matters? Schools split: 31% / 29% / 14% — Do animals have moral standing comparable to humans? Schools split: 31% / 30% / 11% — Does environmental harm in another country bind me morally? Schools split: 50% / 29% / 12% — Does history have a direction or meaning? Schools split: 36% / 23% / 19% — Does meditation reveal something genuinely timeless? Schools split: 46% / 34% / 12% — Does prayer change God's mind? Schools split: 46% / 34% / 12% — How is knowledge of reality produced? Schools split: 24% / 17% / 13% — If a teleporter copied and destroyed you, would you have survived? Schools split: 36% / 30% / 14% — Is divine omniscience compatible with human freedom? Schools split: 46% / 34% / 12% — Is memory stored or reconstructed? Schools split: 44% / 36% / 13% — Is reality fundamentally digital? Schools split: 44% / 36% / 13% — Is salvation, liberation, or fulfillment individual or communal? Schools split: 14% / 14% / 4% — Is the late-stage dementia patient still the person their spouse married? Schools split: 36% / 30% / 14% — Is truth universal, tradition-bound, situated, or constructed? Schools split: 66% / 16% / 10% — What happens to "you" when you die? Schools split: 38% / 29% / 18% — What kind of religious-theological authority does the tradition recognize? Schools split: 42% / 16% / 13% — What makes someone the same person over time? Schools split: 36% / 30% / 14% — Who is the moral primary — the individual, the community, the cosmos, the class, or the species? Schools split: 38% / 28% / 16% —
Information · 4 dilemmas, all mainstream
Could the dead, in principle, be brought back? — — Does deleting your data online destroy something real? — — Is anything truly lost when someone forgets? — — Is forgiveness ontologically possible? — —
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