The difficulty of prime factorization is a consequence of the positional numeral system

The importance of the prime factorization problem is very well known (e.g., many security protocols are based on the impossibility of a fast factorization of integers on traditional computers). It is necessary from a number k to establish two primes a and b giving k = a · b. Usually, k is written in a positional numeral system. However, there exists a variety of numeral systems that can be used to represent numbers. Is it true that the prime factorization is difficult in any numeral system? In this paper, a numeral system with partial carrying is described. It is shown that this system contains numerals allowing one to reduce the problem of prime factorization to solving [K/2] − 1 systems of equations, where K is the number of digits in k (the concept of digit in this system is more complex than the traditional one) and [u] is the integer part of u. Thus, it is shown that the difficulty of prime factorization is not in the problem itself but in the fact that the positional numeral system is used traditionally to represent numbers participating in the prime factorization. Obviously, this does not mean that P=NP since it is not known whether it is possible to re-write a number given in the traditional positional numeral system to the new one in a polynomial time

Arterial pulse wave pressure transducer

An arterial pulse wave pressure transducer is introduced. The transducer is comprised of a fluid filled cavity having a flexible membrane disposed over the cavity and adapted to be placed on the skin over an artery. An arterial pulse wave creates pressure pulses in the fluid which are transduced, by a pressure sensitive transistor in direct contact with the fluid, into an electric signal. The electrical signal is representative of the pulse waves and can be recorded so as to monitor changes in the elasticity of the arterial walls

Constructing a concept of number

Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like linearity that may persist in the form of knowledge and behaviors, ultimately yielding numerical concepts that are irreducible to and functionally independent of any particular form. Material devices used to represent and manipulate numbers also interact with language in ways that reinforce or contrast different aspects of numerical cognition. Not only does this interaction potentially explain some of the unique aspects of numerical language, it suggests that the two are complementary but ultimately distinct means of accessing numerical intuitions and insights. The potential inclusion of materiality in contemporary research in numerical cognition is advocated, both for its explanatory power, as well as its influence on psychological, behavioral, and linguistic aspects of numerical cognition