In traditional geometry and physics, spatial dimensions are typically considered positive and are represented by positive integer values (e.g., 1, 2, 3). These dimensions represent the familiar physical space in which we live.
However, in certain mathematical and theoretical frameworks, such as string theory and some branches of fractal geometry, the concept of negative dimensions arises. It's important to note that these negative dimensions are not directly related to physical spatial dimensions as we commonly understand them.
In the context of string theory, the negative spatial dimensions you mentioned are not actual physical dimensions but mathematical constructs. The K-theory in string theory refers to a mathematical framework used to study certain properties of strings. It involves abstract mathematical objects and their properties, rather than describing the physical dimensions of space.
Regarding fractal geometry, negative fractal dimensions are also mathematical concepts. Fractals are complex geometric shapes that exhibit self-similarity at different scales. Fractal dimensions describe the "degree of complexity" or "space-filling" properties of these structures. A negative fractal dimension indicates a space-filling property that exceeds the usual notion of a positive integer dimension.
Negative fractal dimensions and negative spatial dimensions are not the same thing. Negative spatial dimensions do not typically arise in mainstream physics and are not part of our observable universe. However, negative fractal dimensions can describe certain mathematical constructs or patterns within abstract mathematical systems.