D O C . 5 2 G E O M E T R Y A N D E X P E R I E N C E 4 0 3
Published by Julius Springer (Berlin, 1921). The document is composed of two parts. The first part
(until the final paragraph of p. 13) was presented on 27 January 1921 and published on 3 February
1921 in Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1921): 123–
130. The second part was added for the separate publication by Springer. Manuscripts are available
for both parts. The manuscript for the first part [1 011] consists of eight numbered pages; that for the
second part [1 012], written on the verso of a typewritten “technical explanation” (“Technische Er-
läuterung”) of an electrically powered dirigible by an unknown author, consists of six pages numbered
from 10 to 15 in an unknown hand. The first part of the text was republished with minor stylistic
changes in Einstein 1934a, pp. 119–127. Significant variations between the manuscripts and the pub-
lished text are noted.
The modern axiomatic method was introduced in Hilbert 1899. In his analysis of the foundations
of geometry, Hilbert stressed the strict separation of geometric axioms from their intuitive content and
an explicit formulation of valid rules of deduction.
In the manuscript, “inhaltlichen und” is deleted before “sachlichen,” and “bzw.” is written
instead of “oder.”
The manuscript has “streng genommen” deleted and replaced by “gemäß der Axiomatik.”
The manuscript has “der Vernunft” deleted and replaced by “einem Vermögen des menschlichen
Schlick 1918, pp. 30–37. Moritz Schlick refers to Hilbert’s axiomatic method (see note 1) in this
passage. For Einstein’s reading of Schlick 1918, see Einstein to Moritz Schlick, 17 October 1919:
“Tomorrow I will leave for a two-week trip to Holland and I have taken as my only reading your [book
on] epistemology. This as proof of how much I enjoy reading it” (“Morgen fahre ich nach Holland für
zwei Wochen und habe als einzige Lektüre Ihre Erkenntnistheorie mitgenommen. Dies zum Beweise
dafür, wie gern ich drin lese”).
Friedman 2001 points out one feature of Hilbert’s program that was attractive for Einstein: it lib-
erated him from a concept of geometry that restricted the subject of geometry to spaces of constant
curvature and allowed him to use a purely analytic concept of space as given by Riemann’s differential
For earlier statements of Einstein’s views on geometry, see Einstein 1917a (Vol. 6, Doc. 42),
pp. 1–3, and Doc. 31, [p. 29]. Especially relevant for Einstein’s concept of a practical geometry (see
p. 6 of this document) is the attempt of grounding geometry in the possible motions of rigid bodies
that was initiated in Helmholtz 1868. This led to a generalization of the Kantian concept of a pure
geometry that encompassed all metric spaces of constant curvature (Euclidean, elliptic, and hyper-
bolic), but did not include spaces of variable curvature since they do not allow free mobility of rigid
bodies. Einstein was certainly acquainted with Helmholtz 1884 (it is mentioned in Einstein 1917a
[Vol. 6, Doc. 42], p. 72). Helmholtz is also mentioned in Solovine 1956, p. viii, as one of the authors
whose works on the foundation of science were read in the Olympia Academy.
See Torretti 1978 for a history of foundational questions in geometry in the nineteenth century. A
study of the relation of the present document to that tradition can be found in Friedman 2001.
“(Erlebnisse)” is missing in the manuscript. Einstein’s definition of “Erlebnis” as the basic ele-
ment of phenomenal reality and the contrast to concepts corresponds to the usage in Schlick 1918
(e.g., pp. 118–119).
In the manuscript, “Die Sicherheit ihrer Aussagen beruht” is deleted and replaced by “Ihre Aus-
In the manuscript, “Empirie” is deleted and replaced by “Induktion aus der Erfahrung.”
The manuscript has “auf der Unfehlbarkeit” deleted before “nur auf logischen Schlüssen.”
For a discussion of the role of the problem of the rotating disk in the development of general
relativity, see Stachel 1980. A brief account of the theoretical argument is given in Einstein to Moritz
Schlick, 21 May 1917 (Vol. 8, Doc. 343).
Henri Poincaré’s thesis of the conventionality of geometry that Einstein recapitulates here was
formulated in Poincaré 1902. Poincaré, like Helmholtz, restricted geometry to spaces of constant cur-
vature. But he especially stressed the point discussed here by Einstein (which Helmholtz already had
noted in Helmholtz 1884, pp. 29–30) that it cannot be decided on empirical grounds which of these