James Arthur Dean Wallace Anderson, known as James Anderson, is a retired member of academic staff in the School of Systems Engineering at the University of Reading, England, where he used to teach compilers, algorithms, fundamentals of computer science and computer algebra, programming and computer graphics.
[1] Anderson quickly gained publicity in December 2006 in the United Kingdom when the regional BBC South Today reported his claim of "having solved a 1200 year old problem", namely that of division by zero.
However, commentators quickly responded that his ideas are just a variation of the standard IEEE 754 concept of NaN (Not a Number), which has been commonly employed on computers in floating point arithmetic for many years.
[2] Dr Anderson defended against the criticism of his claims on BBC Berkshire on 12 December 2006, saying, "If anyone doubts me I can hit them over the head with a computer that does it.
[4] He was also a teacher in the Computer Science department (School of Systems Engineering) at the University of Reading.
His doctorate is from the University of Reading for (in Anderson's words) "developing a canonical description of the perspective transformations in whole numbered dimensions".
He has written multiple papers on division by zero[5][6] and has invented what he calls the "Perspex machine".
[8] Anderson's transreal numbers were first mentioned in a 1997 publication,[9] and made well known on the Internet in 2006, but not accepted as useful by the mathematics community.
In addition, they are intended to define a consistent numeric result for the calculations which are undefined in standard arithmetic, such as division by zero.
Here are some identities in transreal arithmetic with the IEEE equivalents: The main difference is that IEEE arithmetic replaces the real (and transreal) number zero with positive and negative zero.
(This is so that it can preserve the sign of a nonzero real number whose absolute value has been rounded down to zero.
Division of any non-zero finite number by zero results in either positive or negative infinity.
Anderson's analysis of the properties of transreal algebra is given in his paper on "perspex machines".
Similarly, it is not always the case in transreal arithmetic that a number can be cancelled with its reciprocal to yield
Examining the axioms provided by Anderson,[10] it is easy to see that any arithmetical term, being a sum, difference, product, or quotient, which contains an occurrence of the constant
Anderson's transreal arithmetic, and concept of "nullity" in particular, were introduced to the public by the BBC with its report in December 2006[5] where Anderson was featured on a BBC television segment teaching schoolchildren about his concept of "nullity".
The report implied that Anderson had discovered the solution to division by zero, rather than simply attempting to formalize it.
The report also suggested that Anderson was the first to solve this problem, when in fact the result of zero divided by zero has been expressed formally in a number of different ways (for example, NaN).
The BBC later posted a follow-up giving Anderson's response to many claims that the theory is flawed.
[3] Anderson has been trying to market his ideas for transreal arithmetic and "Perspex machines" to investors.
[7][12] He has also claimed that it can help solve such problems as quantum gravity,[7] the mind-body connection,[13] consciousness[13] and free will.