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-as of [19 OCTOBER 2024]–
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*in ‘physics’ + ‘mathematics’, the ‘dimension’ of a mathematical ‘space’ (or ‘object’) is informally defined as…*
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“the minimum # of ‘co-ordinates’ needed to specify any ‘point’ within it”*
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(thus a ‘line’ has a ‘dimension’ of ‘1’ because only 1 coordinate is needed to specify a point on it…)
(for example, the point at ‘5’ on a ‘number line’)
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(a ‘surface’ such as a ‘plane’ or the surface of a ‘cylinder’ / ‘sphere’ has a ‘dimension’ of ‘2’ because 2 coordinates are needed to specify a ‘point’ on it)
(for example, both a ‘latitude’ + ‘longitude’ are required to locate a point on the surface of a ‘sphere’)
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(the inside of a [‘cube’ / ‘cylinder’ / ‘sphere’] is ‘3-dimensional’ because 3 coordinates are needed to locate a point within these ‘spaces’)
(in ‘classical mechanics’, ‘space’ + ‘time’ are different categories and refer to ‘absolute’ ‘space’ and ‘time’)
(that conception of the ‘world’ is a ‘4-dimensional space’ but not the one that was found necessary to describe ‘electromagnetism’)
(the 4 dimensions of ‘spacetime’ consist of events that are not absolutely defined ‘spatially’ and ‘temporally’, but rather are known relative to the motion of an ‘observer’)
(“minkowski space” first approximates the universe without ‘gravity’;
the “pseudo-riemannian manifolds” of ‘general relativity’ describe ‘spacetime’ with ‘matter’ and ‘gravity’)
(10 dimensions are used to describe ‘string theory’, 11 dimensions can describe ‘supergravity’ and ‘M-theory’, and the ‘state-space’ of ‘quantum mechanics’ is an ‘infinite-dimensional function space’)
(the concept of ‘dimension’ is not restricted to ‘physical objects’)
(‘high-dimensional spaces’ frequently occur in ‘mathematics’ + ‘the sciences’)
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(they may be ‘parameter spaces’ or ‘configuration spaces’
(such as in ‘lagrangian’ / ‘hamiltonian’ mechanics)
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these are ‘abstract spaces’, independent of the ‘physical space’ we live in)
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*👨🔬🕵️♀️🙇♀️*SKETCHES*🙇♂️👩🔬🕵️♂️*
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💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥