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It took until the last century for physicists and mathematicians in the Netherlands to question the Euclidean concept of dimension as length, width, and height. Luitzen Egbertus Jan Brouwer published a ground-breaking paper On the Natural Concept of Dimension (Amsterdam, [2]) in 1913 about the mathematical definition of dimension picking up a thought from Poincaré, and Tatjana Ehrenfest-Afanassjewa published a paper The Concept of Dimension and the Analytical Construction of Physical Equations (Leiden, [3]) in 1916 about the physical meaning of dimensions in which she approached the problem by logical methods. Brouwer worked in the new field of topology, and Ehrenfest-Afanassjewa in statistical mechanics and for Klein's Encyclopedia of Mathematical Sciences (1898-1935). This article is meant to summarize the many aspects behind the concept of dimension in various fields.
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Dimensions in physics are time, length, mass, current, and to cover the borders, too, temperature, amount of substance, and luminous intensity.

This is highly dependent on your system of units. It is true in your typical SI units, but many unit systems, such as any set of natural units, time and length have the same physical dimension as inverse energy or mass.
 
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