Insights Aspects Behind the Concept of Dimension in Various Fields

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The discussion highlights the evolution of the concept of dimension, particularly through the works of Brouwer and Ehrenfest-Afanassjewa in the early 20th century. Brouwer's contributions to topology and Ehrenfest-Afanassjewa's insights into the physical implications of dimensions marked a significant shift from traditional Euclidean views. Dimensions in physics encompass various measures, including time, length, mass, and temperature, which can vary based on the unit system used. The conversation also touches on the implications of different dimensional frameworks, such as natural units, where time and length can equate to inverse energy or mass. Overall, the thread emphasizes the complexity and multifaceted nature of dimensions across different scientific fields.
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Abstract
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.
Dimensions in...

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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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iven Brouwer was a finitist, I assume he did not buy into function spaces or any other infinite-dimensional spaces?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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