Between manifold and completeness - mathematics and form in the work of Wilhelm OstwaldÂÂ¦

TUHH
Between manifold and
Technische Universität Hamburg-Harburg

completeness
- mathematics and form in the
work of Wilhelm Ostwald
with crosslinks to Wald

Thomas Hapke
University Library
Hamburg University of Technology (TUHH)
International workshop
"Wald, Positivism, and Chemistry"
Pruhonice (Prague), October 16-17, 2009

www.tub.tu-harburg.de Thomas Hapke, October 2009 Between manifold and completeness

TUHH
Holiday on Rügen …


TUHH
… and a surprising discovery

A connection of art and chemistry

TUHH
Mathematics in chemistry

„The concept of the chemical compound
has become a mathematical one.―
(N.S. Kurnakow 1914)


TUHH
The thread

• Ostwald and mathematics
• Manifold
• Applying combinatorics
• The concept of completeness
• The hidden tradition of
‚in-formation‗ in chemistry


TUHH
Ostwald and mathematics

„Pure mathematics was
alien to him; an attempt
to arrive at, led him
instead to positivistic
philosophy.―

(P. Günther 1953)


TUHH
Ostwald, mathematics and
philosophy
• First inspiration for philosophical
thinking
• „General― issues are neccessary because
of „overload with new scholarly work and
publications―
• An „elementary table of concepts―
• Mathematics as basis for scientific unity


TUHH
Manifold - Mannigfaltigkeit

• Use of term part of the „zeitgeist―
• Variety, plurality, complexity, diversity,
manifoldness
• Mathematical term: manifold – a bridge
between algebra and geometry


TUHH
Manifold for František Wald
(1903)
―For a given problem of experimental
research, it seems to be the first task to
get clarity about the manifold, that
means the nature and quantity of the
independent and variabel pieces, which
determines the phenomena being found.‖
Describing phenomena as complete as
possible without using too few or too
much parameters for their description!
A manifold as a property of a model or
theory!

TUHH
Manifold for Ostwald

„the entirety of any ordered – or related to
each other – entities or objects―

Logics
as the science of manifold


TUHH
Technische Universität Hamburg-Harburg Combinatorics in Ostwald‗s
philosophy of nature
• Part of his theory of order
• Reference to Leibniz
• Combinatorics of concepts
• Method of research

„ The application of
combinatorics in
scholarship is far from
being widespread, as it
should be.― (Ostwald 1914)

TUHH
Technische Universität Hamburg-Harburg Combinatorics
as research method

• Determination of position of a
subject in the pyramid of
sciences
• Looking for elemental
concepts
• Combination of concepts
through combinatorics


TUHH
Technische Universität Hamburg-Harburg Combinatorics and creativity

„Combinatorics doesn‗t replace productive
imagination only, but is superior to it!―

Combinatorics and intellectual property
today:
Share, reuse, and remix — legally.


TUHH
Ostwald‗s theory of colors

Mathetic, physical, chemical,
physiological and psychological
theory of colors


TUHH
Technische Universität Hamburg-Harburg Combinatorics of …

… saturated colours
combined with
white and black
fractions


TUHH
Technische Universität Hamburg-Harburg Ostwald‗s impact on …

• Werkbund
• De Stijl
• Bauhaus


TUHH
Ostwald‗s theory of forms

Creation of ornaments and new forms
which were „all beautiful, without any
exception!―
(Ostwald 1922)

Order
= Legality
= Harmony


TUHH
Technische Universität Hamburg-Harburg Harmony of forms

Regular triangel,
tetragon, and
hexagon as
elements

Construction of
ornaments
through
symmetrical
operations


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Completeness in chemistry

Proof of the law of equivalent proportions
„was based on the experience of
completeness (‚Restlosigkeit‗) of
ordinary chemical processes.―

(Ostwald 1929)


TUHH
Completeness in chemistry

The concept of completeness
(„Vollständigkeit―, „complétude―), the
„need to fill out the picture … appeared
in the doctrine of chemical substances―

(Gaston Bachelard 1940)


TUHH Completeness

as part of „zeitgeist― around 1900
Different German notions:
• Vollständigkeit:
heuristic method,
redundant conclusions
are not important
• Restlosigkeit:
View on plentifulness,
attention to every least
detail


TUHH
Technische Universität Hamburg-Harburg „The World Brain―

Foundation of the „Bridge –
International Institute for the
Organisation of intellectual
work―(1911-1914)

Completeness as
thoroughness and accuracy in
opposite to superficiality


TUHH
Technische Universität Hamburg-Harburg Organisation of scholarly work

• Building a comprehensive
encyclopedia as „handbook of
the future―
• Standardization of paper
formats
• Knowledge fragmentation


TUHH
Technische Universität Hamburg-Harburg Splitting scholarly
communication in
smaller components
(Monographic principle)

―Principle of the independent
use of the individual piece"

"Klassiker" as an example


TUHH
Technische Universität Hamburg-Harburg Use of decimal classification
as „framework―


TUHH
International Institute of
Chemistry

Principle of completeness
should rule!


TUHH Restlosigkeit

as reason for failure of the Bridge
(Ostwald 1927)

Collecting everything,
also ephemera
like advertising stamps


TUHH
Summary

• Coping with manifoldness of the world/senses

• Chemistry „as a combinatorial art― (P. Laszlo)

• Connection between organisational principles
of the Bridge and chemical thinking


TUHH
Technische Universität Hamburg-Harburg Bridge activities and chemistry

• Monographic • Chemical elements
principle: Elements of
scholarly work

• Organising: • Analysing and
dividing and synthesising
combining

• „Restlosigkeit― • Completeness

• Standardization • Standardization

• Decimal classification • Periodical system


TUHH
The hidden tradition of
information in chemistry

Chemistry as „closed science―:
„All the shelf space will come
to be filled―

Combinatorics as a way out of the
„closed shop―

(Steve Fuller)


TUHH
Why were so many
information pioneers
educated as chemists?
What have they in common?
• Sense of completeness
• Necessity of standardization and structuring
• Common activities:
„Identifying, naming, and classifying―
(Bensaude-Vincent)
• Role of language


TUHH
My World of In-Form-ation

Culture
Chemistry

Knowledge Transformation

Design
Competence Form

Media In-formation Formation Creativity

Communication Education
Learning


TUHH
Technische Universität Hamburg-Harburg More:
Thomas Hapke
hapke@tu-harburg.de
http://www.tub.tu-harburg.de/192.html

„Combinatorics and order as a foundation of creativity, information organisation
and art in the work of Wilhelm Ostwald“.
Conference poster Mai 2008: http://doku.b.tu-harburg.de/volltexte/2008/404/
Weblog Creative Combinatorics http://notes.hapke.de

Wilhelm Ostwald, the "Brücke" (Bridge), and connections to other bibliographic
activities at the beginning of the twentieth century. In: Proceedings of the 1998
Conference on the History and Heritage of Science Information Systems
http://www.chemheritage.org/explore/ASIS_documents/ASIS98_Hapke.pdf

Archive of the ‘History of information systems’ category in „Hapke-Weblog - About
information literacy, history, philosophy, education and beyond“
http://blog.hapke.de/?cat=5


TUHH
Further references 1
• Bachelard, G. (1968) The philosophy of no : a philosophy of the new scientific
mind. New York: Orion Press.
• Bensaude-Vincent, B. (2009) Philosophy of chemistry. In Brenner, A. et al.
(eds.) French studies in the philospphy of science : contemporary research in
France. Berlin: Springer, p. 165-186.
• Fuller, S. (2008) A tale of two narratives: prolegomena to an alternative history
of library and information science. Rayward, W.B. (ed.) European modernism and
the information society : informing the present, understanding the past.
Aldershot: Ashgate, 59-73.
• Günther, P. (1953) Wilhelm Ostwalds Wirken in seiner Zeit. Angewandte
Chemie 65, 497-502.
• Krajewski, M. (2006) Restlosigkeit : Weltprojekte um 1900. Frankfurt a. M.:
Fischer.
• Kurnakow, N.S. (1914) Verbindung und chemisches Individuum. Zeitschrift für
anorganische Chemie 88, 109-127
• Laszlo, P. (1999) Circulation of concepts. Foundations of chemistry 1, 225-239.
• Ostwald W. (2003) Lebenslinien – eine Selbstbiographie : nach der Ausg. von
1926/27. Stuttgart: Hirzel.


TUHH
Further references 2
• Ostwald, W. (1929) J. B. Richter. In Bugge, G. (ed.) Das Buch der grossen
Chemiker : unter Mitwirkung namhafter Gelehrter. Weinheim: Verlag Chemie,
vol. 1, p. 369-377.
• Ostwald, W. (1929) Kombinatorik und schaffende Phantasie (1929).
Ostwald, W. Forschen und Nutzen. Wilhelm Ostwald zur wissenschaftlichen
Arbeit, Berlin 1978 (2. ext. ed.. 1982), 28-30.
• Ostwald, W. (1914) Memorial on the foundation of an International Chemical
Institute. Science 40, 147-158.
• Ostwald, W. (1911) Natural philosophy. London : Williams and Norgate.
• Ostwald, W. (1904) On the theory of science. Congress of arts and science :
universal exposition, St. Louis, 1904. Sopka, K.R. (ed.) (1986) Physics for a
new century : papers presented at the 1904 St. Louis Congress. American
Institute of Physics, 17-36.
• Wald, F. (1903) Über die Mannigfaltigkeit chemischer Erscheinungen. Annalen
der Naturphilosophie 2, 108-132.
• Ziche, P. (2008) Wissenschaftslandschaften um 1900 : Philosophie, die
Wissenschaften und der nichtreduktive Szientismus. Zürich: Chronos.


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