Figuring Space: Philosophy, Mathematics and Physics Book

	Diagrammatic writing and the configuration of space
	Acknowledgements
	The liberation of the gesture and the bias of the visible
	Introduction	1
I	The enchantment of the virtual
1	Abstraction and potential	17
2	Elastic and decisive virtuality	19
3	The principle of virtual velocities	26
4	Cauchy and Poisson's virtual cutouts	32
II	The screen, the spectrum and the pendulum: horizons of acceleration and deceleration
1	Oresme's diagrams	38
2	Spectra and horizons: restrained relativity as perspective projection of Oresme's diagrams	47
3	Einstein and de Broglie: two symmetrical fans	57
4	Individuation by impact and individuation by election	63
III	The force of ambiguity: dialectical balances
1	Introducing the great revolutions of the instability points	73
2	A question from Kant: what diagrams for the negative?	82
3	Argand and the attack of the lateral	82
4	Indifference centres and knots of ambiguity, fulcra of the balances of Being	88
A	Eschenmayer's diagram	88
B	The power of indifference points	90
C	The indifference centre as articulation	94
5	Examples of production of ambiguity by a point-articulation	94
A	The splitting in two of positive real numbers	94
B	The problem of the measurement of angles	95
C	'Base' and 'Roller', diagrams of gear wheels	96
IV	Grassmann's capture of the extension: geometry and dialectic
1	Introduction	101
2	How do you bring extended space back to life?	102
3	Articulate and generate: formal sciences and real sciences	106
4	Grassmann's quadrilateral	108
5	The intensive/extensive dialectic	111
6	The additive generation of vectorial systems	114
7	Grassmann's products	122
A	Multiplication against addition: a stake in natural philosophy	122
B	Product and orientation	124
C	External product (aussere Multiplikation) and the intensive/extensive dialectic	129
D	The allusion to the next dimension	134
E	The regressive or involving product [eingewandtes Produkt]	138
8	The stakes of the non-commutative	143
V	Electrogeometric space
1	Length and magnetism	150
2	The autonomy of the indifference centre: width and electricity	153
3	Electrical helices	155
4	The axial as subversion of the transitive	160
5	The electrogeometric experiment as square root	162
A	Faraday: the pedagogy of the lines of force	164
B	Hamilton: space as square root	170
C	The screw as bold metaphor	176
6	Towards the knot as secularization of the invisible	183
App. I	Note on quaternions	189
App. II	Note on Hamilton's astronomical example	191
App. III	Hamilton's operator [actual symbol not reproducible]	195