We present an information-theoretic approach to the optimal representation of the intrinsic dimensionality of data and show it is a noninteger. Since optimality is accepted as a physical principle, this provides a theoretical explanation for why noninteger dimensions are useful in many branches of physics, where they have been introduced based on experimental considerations. Noninteger dimensions correlate with lesser density as in the Hausdorff dimension and this can have measurable effects. We use the lower density of noninteger dimension to resolve the problem of two different values of the Hubble constant obtained using different methods.

中文翻译：

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信息论与空间维度

我们提出了一种信息理论方法来对数据的固有维数进行最佳表示，并表明它是非整数的。由于最优性被接受为一种物理原理，这为非整数维数为何在物理学的许多分支中都有用的问题提供了理论解释，而基于实验考虑将非整数维引入。非整数尺寸与较小的密度相关，例如在Hausdorff尺寸中，这可以产生可测量的影响。我们使用较低的非整数维密度来解决使用不同方法获得的两个不同值的哈勃常数的问题。