the program embodying the model. It can be entirely the product of humans. The MDL principle applies regardless of whether the description to be run on a computer is the product of humans, machines or any combination thereof. The MDL principle requires only that the shortest description, when executed, produce the original data set without error. Two-Part codes The distinction in computer programs between programs and literal data applies to all formal descriptions and is sometimes referred to as "two parts" of a description. In statistical MDL learning, such a description is frequently called a two-part code. MDL in machine learning MDL applies in machine learning when algorithms (machines) generate descriptions. Learning occurs when an algorithm generates a shorter description of the same data set. The theoretic minimum description length of a data set, called its Kolmogorov complexity, cannot, however, be computed. That is to say, even if by random chance an algorithm generates the shortest program of all that outputs the data set, an automated theorem prover cannot prove there is no shorter such program. Nevertheless, given two programs that output the dataset, the MDL principle selects the shorter of the two as embodying the best model. Recent work on algorithmic MDL learning Recent machine MDL learning of algorithmic, as opposed to statistical, data models have received increasing attention with increasing availability of data, computation resources and theoretic advances. Approaches are informed by the burgeoning field of artificial general intelligence. Shortly before his death, Marvin Minsky came out strongly in favor of this line of research, saying: Statistical MDL learning Any set of data can be represented by a string of symbols from a finite (say, binary) alphabet. [The MDL Principle] is based on the following insight: any regularity in a given set of data can be used to compress the data, i.e. to describe it using fewer symbols than needed to describe the data literally. (Grünwald, 2004) Based on this, in 1978, Jorma Rissanen published an MDL learning algorithm using the statistical notion of information rather than algorithmic information. Over the past 40 years this has developed into a rich theory of statistical and machine learning procedures with connections to Bayesian model selection and averaging, penalization methods such as Lasso and Ridge, and so on - Grünwald and Roos (2020) give an introduction including all modern developments. Rissanen started out with this idea: all statistical learning is about