Abstract
When Johann and Daniel Bernoulli founded fluid dynamics they encountered several problems. To go beyond the vision of Newtonian particles, a new set of images was needed in order to deal with the spatial extensibility and lack of form of fluids. I point to evidence that analogy was an essential abductive strategy in the creation of this imagery. But its heuristic behavior is complex: analogy can provide an initial model or proto-model that establishes the starting point of a theoretical process, but it can play other roles as well. The historical genesis analyzed here shows that the participation of analogy in physicists’ creativity is not so restricted and that its richness opens up the field for very different roles and strategies in model-based discovery processes. Analogies can crop up intermittently in the evolution of a theory; and they can cooperate with images, extreme case reasoning and thought experiments, and even activate these processes at origin. Although it may seem that the contributions of analogy are generative in the sense of helping to discover new aspects of reality, we must stress the evaluative function that sometimes is performed by analogical reasoning in order to gain confidence. The study of the Bernoulli’s genesis of the foundations of fluid dynamics generates interesting hypotheses about the multiple roles that analogy can play in scientific model-based reasoning.
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Notes
For Leibniz there are several derivative active forces among the forces of the physics of his time. These forces include specially what he terms ‘live force’ (vis viva) by which he understands what is now called kinetic energy.
Hydrodynamica, I, 2: “Motui fluidorum determinando inservit praecipue effluxus aquae ex vase per foramen valde parvum”
Hydrodynamica, I, 19: “Si pondera quolibet vi gravitatis sue nioveri incipiant utcunque, singulaque cursus ad quietem sponte reducantur, centrum gravitatis ex ipsis composita ad pristinam altitudinem rediturum esse”.
Hydrodynamica, I, 22: “Postquam scilicet mente concepimus divisum fluidum in strata, ad directionem motus perpendicularia, ponemus fluidi particulas ejusdem strati eadem velocitate moveri, ita, ut ubique velocitas fluidi reciproce proportionalis fit amplitudini vasis respondenti”
Hydrodynamica, III, 1: Recordabimur nempe ascensum potentialem Systematis, cujus singulae partis velocitate qualicunque moventur, significare altitudine verticalem, ad quam centrum gravitatis illius Systematis pervenit, si singulae particulae motu sursum converso sua velocitate, quantum prosunt, ascendere intelligantur, and descensum actualem denotare altitudinem verticalem, per cuam centrum gravitatis descendit, postquam singulae particulae in quiete fuerant. Tum etiam memores erimus necessario ascensum potentialem aequalem esse descensui actuali, quando omnis motus in materia substrata aeret, nihilque de eo in materiam insensibilem aut aliam ad systema non pertimentem transit, and denique motum fluidorum talem proximi esse, ut ubique velocitas reciproce fit proportionalis amplitudini vasis respondenti, qua de reo suo loco alia quaedam interjiciemus.
Hydrodynamica, III, 6: “Concipiatur in medio aquae sectio gh parallela superficiebus cd vel ef ipsique fundo im; sitque velocitas unius cujusvis particulae in gh talis, ut possit ascendere ad altitudinem qs feu v, cum nondum effluxit guttula and ad altitudinem qz five \(v + dv\), postquam ea ipsa guttula and ad altitudinem qz five \(v + dv\), postquam ea ipsa guttula effluxit. Omnibus his ita positis, quaeritur incrementum ascensus potentialis aquae postquam situm clmd commutavit cum situ eipnolmf, id est, postquam guttula emanavit.”
Hydrodynamica, III, 6: “Jam igitur apparet ascensum potent, aquae ante effluxum guttulae esse = quartae proportionali ad spatium DCIPL, spatium DTUL and altitudinem qs, eundemque post effluxum guttulae esse = quartae proportionali ad spat. FEIPNOL, spat. FWUXYOL and altit. qz; sunt autem in ultraque analogia termini primi inter se aequales.”
Hydrodynamica, XII, 5: “Ab hoc nisu and renisu comprmitur aqua, quae ipsa compressio coeretur a lateribus tubi, haeque proinde similem pressionem sustinent. Apparet sic pressionem laterum proportionalem esse accelerationi seu incremento velocitatis, quod aqua sit acceptura, si in instanti omne obstaculum motus evanescat, sic ut immediate in aerem ejiciatur”.
Hydraulica, 2nd part, IX: “Hujus vis proprium est urgere partem liquoris praecedentem antrorsum, seu ea versus qua tendit, sequentem vero retrorsum seu ea versus unde venit; facereque ut pars liquoris sequens, quae a viribus translatis propellitur, atque pars liquoris praecedens, cui aliquid accelerationis imprimere debet, acquirant in ipso contactu aequalitatem virium acceleratricium; quemadmodum idem contingere dudum monuimus in corporibus solidis, quae diversis viribus acceleratricibus seorsim animata, quando in se mutuo agere incipiunt, oritur in corum contactu vis intermedia immaterialis ad utrumque corpus communi jure spectans, quae ita temperet utriusque vim acceleratricem particularem, unam diminuendo, alteram augendo, ut inde in tota massa, combinata ex duobus istis corporibus, resultet una communis vis acceleratrix.”
Hydraulica, 2nd part, X: “Id vero discriminis est in agendi modo, quod in corporibus solidis directe in se invicem agentibus, vis illa immaterialis agat prorsum an retrorsum, instar elastri alicujus rectilinei quod inter utrumque corpus positum sese expandere conatur.”
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Acknowledgments
The ideas developed in this paper have profited from extensive discussions and work with the director of my doctoral thesis, Jesus Maria Larrazabal. I thank Enetz Ezenarro for helping me to think critically about everything. I wish to thank the referees for this journal for their helpful comments and precise contributions.
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Ulazia, A. Multiple Roles for Analogies in the Genesis of Fluid Mechanics: How Analogies Can Cooperate with Other Heuristic Strategies. Found Sci 21, 543–565 (2016). https://doi.org/10.1007/s10699-015-9423-1
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DOI: https://doi.org/10.1007/s10699-015-9423-1