At the end of all this, then, one has, starting from the lowest level: <!--[if !supportLists]-->a) <!--[endif]-->information as what is processed by a computer;
<!--[if !supportLists]-->b) <!--[endif]-->information as a scalar quantity of uncertainty removed, the entropy/negentropy picture; <!--[if !supportLists]-->c) <!--[endif]-->semantic information as well-formed, meaningful data (Floridi); <!--[if !supportLists]-->d) <!--[endif]-->information as a process operator that makes a difference to and for other processes, including above all those of receivers and senders. Dear Joseph and colleagues, I agree with the distinction of four operations, but it seems to me that this can be expressed more parsimoneously using information theory. Given Bateson's (1972) formulation that information can be considered as "a difference which makes a difference", one should distinguish between the first type of differences and the second. Let's say difference(1) and difference(2). (I'll need difference(3) and difference(4) below.) A difference(1) can only make a difference(2) for a system (or more generally the expectation of a system). This difference(2) is analytically preceded by difference(1), that is, pure differences. Shannon-type information is contained in probability distributions. In the binary case, this is only one difference (Y/N, F/T, open/closed); in the non-binary case probability distributions provide us with sets of differences(1). These differences(1) can only make a difference(2) for a system which contains other (orthogonal) differences. In this case one needs one-more (orthogonal) dimension of the probability distribution that positions the incoming (Shannon-type) information at specific moments in time. Thus, difference(2) presumes at least a dimensionality of two in the probabilistic entropy. When the system develops, difference(3) can be defined with reference to the time axis (recursion). This is Brillouin's (1962) Delta H. The difference(1) that made a difference(2) for the system makes a difference(3) over time. When the system operates as a self-organizing, autonomous or autopoietic system it is additionally able to provide the information with a meaning from the perspective of hindsight, that is, against the axis of time. This "incursion" can make a difference(4). In other words, one needs at least a vector (one dimension of the entropy) for containing an uncertainty. One needs (at least) two dimensions of the probabilistic entropy for positioning the information in a network (matrix) at specific moments of time. Three dimensions are needed when the time axis is additionally included; four when the direction in the time axis can be considered as another degree of freedom. The two approaches seem very akin to me, but I claim that mine is more strict and parsimoneous because I only need numbers of dimensions of the probabilistic entropy and not concepts like differance. The next-order probability distributions can be considered as the probability of probability distributions, etc. Best wishes, Loet _____ Loet Leydesdorff Amsterdam School of Communications Research (ASCoR), Kloveniersburgwal 48, 1012 CX Amsterdam. Tel.: +31-20- 525 6598; fax: +31-20- 525 3681 <mailto:[email protected]> [email protected] ; <http://www.leydesdorff.net/> http://www.leydesdorff.net/
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