![](\"https:\/\/thefiretongue.com\/ontology\/wp-content\/uploads\/2024\/12\/2023-04-29-response-to-poincare-conjecture-01.png\")
![](\"https:\/\/thefiretongue.com\/ontology\/wp-content\/uploads\/2024\/12\/2023-04-29-response-to-poincare-conjecture-02.png\")
<\/center>\n\nWhat do we commonly associate with that sort of image? Movement.\n
\nWe live with three-dimensional objects all around us, but we don\u2019t see them leaving trails of themselves wherever they go, do we? No, but in a way they do. Dimensions are not physical, but measurable qualities, and a spatially measurable quality we can add to any three-dimensional object is its change over time — its position in space, or history. Where has it been, and where is it now? That is any object\u2019s fourth spatial dimension. Space is needed for movement to be possible. \n
\nMovement is a new way to utilise space, thus a new spatial dimension which retains the properties of an object and adds a new measurable spatial quality — its motion in relation to other objects or itself or both. Measuring and observing it through recordings and memory is how we discover and define the ever-changing universe we live in. Everything moves in some way, and that is the principle in which our universe is built upon. Movement is energy.\n
\nThe question poised was how to tell, by looking at a three-dimensional atlas, whether the manifold it represents is the three-dimensional surface of a four-dimensional sphere.\n
\nA sphere is three-dimensional, so I will simply replace the word with \u2018model\u2019.\n
\nA three-dimensional atlas I will refer to is a three-dimensional model of our solar system. A static model can be made, and, to be completely accurate, it must show the planets aligned in such a way that they once were, displaying every three-dimensional quality — sizes of planets, distances from each other, etc — but what does it need to be even more accurate? It needs its history of movement, and not just of its cyclical patterns, but of its complete formation. The static three-dimensional model, as accurate as it can be, is just a \u201csurface\u201d representation of one \u201cpoint\u201d in its constantly changing spatial form, thus a \u201cshadow\u201d of its four-dimensional history of existence.\n
\nWithout a recording or memory of an object\u2019s history, it can be impossible to accurately know its history of movement and change, but every bit of matter has a history, even if not imprinted in some measurable way, and much has been done to surmise the histories of the world we live in.\n
\nComparing the infinite \u201cshadows\u201d of an object\u2019s, or model\u2019s, movement through space and time is how we measure its fourth-dimensional spatial quality — its history of movement and change.\n\n\n\n