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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信息论和空间维数

我们提出了一种信息论方法来最佳表示数据的内在维度，并证明它是一个非整数。由于最优性被认为是一种物理原理，这为为什么非整数维度在物理学的许多分支中有用提供了理论解释，它们是根据实验考虑引入的。非整数维度与豪斯多夫维度中的较小密度相关，这可以产生可测量的影响。我们利用非整数维度的较低密度来解决使用不同方法获得的哈勃常数两个不同值的问题。