This paper provides an explanation for why the assignment of codons to amino acids, which range from 1 to 6, is non-uniform. Since mathematical coding theory demands a near uniform assignment, the answer to this question is important to understand deeper aspects of the structure of the genetic code. Our analysis points to 20 different covering regions in an e-dimensional information space, which is equal to the number of amino acids. It is also shown that the assignment of the codons to the amino acids is fractal-like that is well modeled by the Zipf distribution. It is remarkable that the Zipf distribution that holds for the letter frequencies of words in a language also applies to the rank order of triplets the code for amino acids.

The paper introduces new fractal families with annular and checkerboard structures that include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined and a notation to represent the families is proposed.

Many recent theories speak of the spatial and temporal variations of the fundamental “constants”, and experiments have been performed to determine the variation. It has also been proposed that the variation of these constants is related to the strength of the gravitational potential whose changes, therefore, assume special significance. Here we examine potential change in G from the information-theoretic perspective of noninteger dimensionality and determine a relationship with respect to time. We show that the rate of change using this method is of the same order as estimated using other approaches.

It is generally accepted that the reproducibility crisis in the fields of natural and biological sciences is in part due to the misuse of the Null Hypothesis Significance Testing (NHST). We review the shortcomings in the use of NHST and then go beyond these to consider additional issues. Many natural systems are time-varying and some are scale-free, which requires design of new methods for such cases. We also consider the problem from the perspective of information efficiency and since three-way logic is superior to two-way logic, we argue that adding a third hypothesis may be beneficial in certain applications.

This paper considers the entropy perspective on the problem of noise in the circuit where the quantum data is prepared before it is sent forward to the error correction encoder. Since the errors in the circuits before the data qubits are converted to logical qubits cannot be corrected, there will be residual qubit errors in the processing system. This constitutes a great challenge for developing useful, scalable quantum computers.

This paper investigates evolution of a physical system through intermediate noninteger dimensions to provide a phenomenological explanation for the system's emergent properties. In recent papers it was shown that physical space is associated with noninteger dimensionality and its value is associated with the strength of attractive inverse square law and this has applications to diverse fields including the design of metamaterials. Here this information-theoretic analysis is applied to cosmology to yields a novel noninteger dimensional explanation for filaments and sheets of matter, inflation, and the accelerating expansion of the universe, without the need to postulate inflation field or dark energy as the drivers of this expansion. Furthermore, the analysis shown that in the future as the zero-dimension residual potential declines further, the expansion will slow and then reverse. Evolution across noninteger spaces has potential relevance for the study of materials that emerge from compressing three-dimensional volumes into lower dimensions.

A document by Subhash Kak . Click on the document to view its contents.

Classical reality is described in terms of objects and things and their mutual relationships. On the other hand, in the case of quantum reality, the collapse of the state in an interaction assigns a unique position to the observer. These two disparate views are based on different logics of representation. In this paper, we first summarize the early evolution of these ideas and then go beyond the implicit dependence of the quantum theory framework on the mathematical apparatus of calculus and vector spaces, by delving one layer deeper to an information-theoretic understanding of symbol representation. We examine some epistemic implications of the fact that, mathematically, e-symbol representation is optimal and 3 symbols are more efficient that 2 symbols, and this optimality leads to the idea that space itself is e-dimensional, and not 3-dimensional. We also discuss the principle of veiled nonlocality as a way to understand the split between the observer and the physical process.

Noninteger dimensionality, which shows up in many fields of physics and engineering, is generally viewed from the perspective of fractals and measured by the Hausdorff dimension. Motivated by information theoretic considerations and by extending the principle of complementarity, we propose a new interpretation in which it engenders a potential. The inverse square law may then be seen to originate from the properties associated with the noninteger dimensional space, and it further indicates a relationship between the dynamics and the actual value of the dimensions that may be used for experimental test of the interpretation.

This paper shows that as the dimensionality of a noninteger dimensional falls below 2, the potential becomes constant irrespective of separation between objects and the force between them disappears, which represents a new paradigm of asymptotic freedom. Since asymptotic freedom is at the basis of many applications such as those of strange metals, unconventional superconductors, and fractional quantum Hall states, the new paradigm presented here can potentially have new and unexpected applications. It also is of relevance to the study of anomalous mechanical effects that are important in metamaterials.

This paper investigates the consequences of the information-theoretic result that representations of numbers in base-e are most efficient. Since theories on complex system behavior in both natural and physical systems assume that Nature is optimal, as is done, for example, in the principle of least action, natural representations must be to the base e. Another way to interpret this fact is to take e as the information dimension of the data space. Some implications of this noninteger dimensionality are investigated. The approximate equivalent to such a space is the Menger sponge in which the recursion is taken to be random.

The paper presents an observer-centric analysis of optimal representation that helps define certain relationship between geometry of numbers and corresponding dimensionality. The motivation for this research is the complementarity that exists in looking at numerical data by itself as compared to its description within a pre-supposed structural framework. Specifically, we consider estimates based on intrinsic dimensionality of data and compare these to those where an a priori order is imposed on the data. We show that this approach helps solve the long-standing problem of different values of the Hubble constant obtained using two different methods.