First, to easily see how computation and semigroup theory are related, consider the collection of maps on the set of infinite eventually zero tuples of non-negative integers. This is actually the set of unary operators on the set of positive integers by prime factorization. Each Fractran (1) program corresponds to one of these maps, so it is possible to calculate the operation of a Fractran program by calculating the powers of this map. This multiplication takes place in the cyclic semigroup generated by this map. This means that for every Turing machine, we can find a semigroup that calculates the same result.
Next, there is a principal-agent problem when using the internet to study semigroup and computation theory: the domain operator is the agent, responsible for maintaining honest database operation, and the subject of automatic computation touches both the agent’s business (the efficiency and hence cost of operating an electronic internet service is dependent in part upon advances in the theory of computation and efficiency) and the principal’s activity (the principal is advancing semigroup and computation theory). In effect, the principal (users) provides leadership, free of charge, in research and development that will directly generate business value for the agent by designing the theory that will control the complexity of the next generation of production infrastructure: the computer code that operates the agent’s service. There are cases where the principal-agent problem for the internet has led to striking behavior from domain operators. (2)
There is a direct business benefit to maintaining an edge in efficiently providing a service. Advances in semigroup and computation theory, if withheld from the public and competition, could be a sustained boost to corporate profits for many years, a difficult proposition to resist from the point of fiduciary responsibility. It could also boost corporate morale.
Does the internet have anything that could mitigate this conflict of interest?
Do some people have trouble admitting that there is a problem?
Should the government study the semigroup and computation theory research in the context of the principal-agent problem for the internet as part of diagnostics for the research ecosystem?
If you run a business that directly financially benefits from unequal access to technology—your access vs. your competitor’s access—does this not impede research taking place in the public eye due to a principal-agent problem where the principal is the researcher and the agent is the business?
The academic context of the college and university overcome these conflicts of interest by focusing on the core education task rather than financial exploitation of differences in access to technology. Can the private enterprise system compete with the academic education system when it comes to semigroups and computation theory?
Has Moore’s law, hardware progress, and plentiful financing for experimental data services slackened pressure to advance the state of the art when it comes to finding the most efficient (in units of electric power or by counting machine code operations) way to calculate a result, and will a stall in progress in hardware efficiency or weakness in financial risk-taking stimulate research in semigroup and computation theory?