M. E. Horn: More about Blades and Non-Blades

Martin Erik Horn, More about Blades and Non-Blades, PhyDid B – Didaktik der Physik – Beiträge zur DPG-Frühjahrstagung 2015, Wuppertal, Germany. Language: English.

Abstract: While in three-dimensional space every higher-dimensional object can be written as outer product of vectors (in accordance with blades in Geometric Algebra), this mathematical depiction is not always possible in four-dimensional spaces or spacetimes.  In such spaces or spacetimes objects called non-blades, which cannot be spanned by vectors in an elementary way, will exist. As our world can be interpreted as a four-dimensional spacetime, it is to be expected that apart from blades also non-blades will play a relevant role which should not be ignored in the mathematical and conceptual description of our world. The transition from classical three-dimensional to relativistic four-dimensional structures is equivalent to a transition from blades to non-blades. It can be seen that the didactical structuring of this transition reaches far beyond the simple question, what blades and non-blades geometrically are, and the problem how blades and non-blades, interpreted as operators, effect on other geometric objects, will be central.

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Source: Email from M.E. Horn, 2015/12/18 15:45, horn_AT_zedat.fu-berlin.de,


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