<div dir="ltr">
<p class="MsoNormal"><span lang="DE-AT">What is Information?</span></p>
<p class="MsoNormal"><span lang="DE-AT"> </span></p>
<p class="MsoNormal"><span>Once more, Occam and
the numbers give a simple, short and concise explanation. (There is more text
and a formal definition of information in my book “Natural Orders” <span class="gmail-st">ISBN: 9783990571378.)</span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span> </span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span>The
root of the term “information” is in the concept of order. The idea of order
can be assumed axiomatic for people who are interested in the definition of
information. For those who need a deictic definition of the term “order”: take
n (n > 3) objects. One can use teddy-bears, shoes, pieces of paper, numbers,
whatever. We sort the objects. The sequence that arrives after we have ordered
the objects is the deictic definition of the term “order”. This might sound in
deviance to the use of the term in mathematics; to reconcile the two concepts,
we point out that the traditional definition in mathematics refers to order as
a potential, realisable property of the collection, while here we speak of
order as a realised instance of the general faculty of the objects to be in
order. The distinction is always clear from the context. A collection that
shows a sequence of its elements is an ordered collection.</span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span> </span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span>From
the order to the information:</span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span>Whichever
order exists, it has alternatives and a background. The alternatives are those
variants of the order which are not realised, the background is that state of
the world about which we cannot say anything definite. </span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span>To repeat:</span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span>N distinguishable
objects have n! possible permutations. We take one specific of the
permutations. In this permutation, a1 is on place p1. The alternatives are
those permutations, where a1 is not on place p1. The background are those
permutations where a2 a3, etc… can be on places px, py, pz, etc….</span></span></p>
<p class="MsoNormal"><span class="gmail-st"><span> </span></span></p>
<p class="MsoNormal"><span>Novelty:</span></p>
<p class="MsoNormal"><span>We construct also such
logical sentences which state something that is not the case. These are false
logical statements. Traditionally, one does not use logical sentences that are
false. This is not a rule given by a Supreme Logician from Heaven, but a
convention of convenience. It would have been inconceivable to write up all
those results of a false multiplication table that are not correct, besides the
conceptual aversion against doing so. </span></p>
<p class="MsoNormal"><span>Now we have computers.
These can register all that what is not the case, as long as we restrict
ourselves to using rather few logical words while we utter a logical sentence.
The brambling of an infant can be of a high scientific value, in case one wants
to learn, how the achievement of language progresses during infancy. We now do
not care, whether the sentence is logically true or not, as long as it is
grammatically correct. We simply write up all possible sentences that a child can
express. Among these, there are such in which the child states something
correctly (e.g. recognises and names a toy), such where the child names an
alternative (e.g. calls a doll a ball) and such which are the background,
neither surely true, nor surely false (e.g. the child calls something a cluxtli
and we do not know what the child has been looking at in that moment). We investigate
all three aspects of the order: the actual sequence, its excluded alternatives
and the background to these. </span></p>
<p class="MsoNormal"><span> </span></p>
<p class="MsoNormal"><span>Resume:</span></p>
<p class="MsoNormal"><span>Traditionally, tertium
non datur, therefore that what is not the case is defined simply as .not. .t. =
.false. Now we have a more complicated logic, and .unknown. is also permitted.</span></p>
<p class="MsoNormal"><span>After the unknown has
softened up the trivial and lazy definition of “what is not true is false and
we do not speak false”, there is a need for a word to describe that what is not
true, but is a background to that what is true. Against this background, one
may recognise the shadow of what is the case: this is what is definitely not
the case. </span></p>
<p class="MsoNormal"><span> </span></p>
<p class="MsoNormal"><span>Information:</span></p>
<p class="MsoNormal"><span>Information is that
what we do know AND do not know about the state of the world. (Footnote to “The
world is everything that is the case”: “The alternatives to that what is the
case are described by sentences about that what can not be the case and the background
to that what is the case is described by sentences that state that what can be the case”. And to “About that what
is not the case, one should keep one’s silence” the following: “unless and until one has
found a way not to think with one’s own brain”.)</span></p>
<p class="MsoNormal"><span>Traditionally, that
what is not the case has been seen as one solid logical entity, defined by –
well, by that that it is not the case, as a contrast to that what reasonable
people can speak reasonably about. Computers allow us to slice thinly between
layers of what is not the case. That what oozes out is information.</span></p>
<p class="MsoNormal"><span>The relation among
that what is the case, that what this implicates and that what is not affected
by that what is the case needs some new words to allow precision in thinking.
One of the words that are available is “information”. Scientists have always
supposed that there is something hidden, yet obviously at work, behind symbols,
bits and logical statements. Forcing this oyster open shows its inner life. The
interdependence between what can be the case, what can not be the case and what
is the case is probably good enough to fill the idea up with concrete, deictic,
simple content.</span></p>
<p class="MsoNormal"><span> </span></p>
Karl<br></div><div class="gmail_extra"><br><div class="gmail_quote">2016-12-19 12:48 GMT+01:00 Dick Stoute <span dir="ltr"><<a href="mailto:dick.stoute@gmail.com" target="_blank">dick.stoute@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">List,<div><br></div><div>Please allow me to respond to Loet about the definition of information stated below. </div><div><br></div><div><span class=""><span class="m_-3895366238499243306gmail-im" style="font-size:12.8px"><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif">1. the definition of information as uncertainty is counter-intuitive ("bizarre"); (p. 27)</p><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif"><u></u> </p></span></span><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif">I agree. I struggled with this definition for a long time before realising that Shannon was really discussing "amount of information" or the number of bits needed to convey a message. He was looking for a formula that would provide an accurate estimate of the number of bits needed to convey a message and realised that the amount of information (number of bits) needed to convey a message was dependent on the "amount" of uncertainty that had to be eliminated and so he equated these. </p><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif"><br></p><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif">It makes sense to do this, but we must distinguish between "amount of information" and "information". For example, we can measure amount of water in liters, but this does not tell us what water is and likewise the measure we use for "amount of information" does not tell us what information is. We can, for example equate the amount of water needed to fill a container with the volume of the container, but we should not think that water is therefore identical to an empty volume. Similarly we should not think that information is identical to uncertainty.</p><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif"><br></p><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif">By equating the number of bits needed to convey a message with the "amount of uncertainty" that has to be eliminated Shannon, in effect, equated opposites so that he could get an estimate of the number of bits needed to eliminate the uncertainty. We should not therefore consider that this equation establishes what information is. </p><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif"><br></p><p class="m_-3895366238499243306gmail-m_-7620727072806746849gmail-m_-3869641630998968668MsoPlainText" style="margin:0in 0in 0.0001pt;font-size:11pt;font-family:calibri,sans-serif">Dick</p></div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote"><div><div class="h5">On 18 December 2016 at 15:05, Loet Leydesdorff <span dir="ltr"><<a href="mailto:loet@leydesdorff.net" target="_blank">loet@leydesdorff.net</a>></span> wrote:<br></div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5"><div link="#0563C1" vlink="#954F72" lang="EN-US"><div class="m_-3895366238499243306m_6893889769850668776WordSection1"><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText">Dear James and colleagues, <u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText">Weaver (1949) made two major remarks about his coauthor (Shannon)'s contribution:<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText">1. the definition of information as uncertainty is counter-intuitive ("bizarre"); (p. 27)<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText">2. "In particular, information must not be confused with meaning." (p. 8) <u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText">The definition of information as relevant for a system of reference confuses information with "meaningful information" and thus sacrifices the surplus value of Shannon's counter-intuitive definition.<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText" style="margin-left:.5in">information observer<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText" style="margin-left:.5in">that integrates interactive processes such as <u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText" style="margin-left:.5in">physical interactions such photons stimulating the retina of the eye, human-machine interactions (this is the level that Shannon lives on), biological interaction such body temperature relative to touch ice or heat source, social interaction such as this forum started by Pedro, economic interaction such as the stock market, ... [Lerner, page 1].<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black"><u></u> <u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black">We are in need of a theory of meaning. Otherwise, one cannot measure meaningful information. In a previous series of communications we discussed redundancy from this perspective.<u></u><u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText" style="margin-left:.5in">Lerner introduces mathematical expectation E[Sap] (difference between of a priory entropy [sic] and a posteriori entropy), which is distinguished from the notion of relative information Iap (Learner, page 7).<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black"><u></u> <u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><img id="m_-3895366238499243306m_6893889769850668776_x0000_i1025" src="cid:image007.png@01D2596A.1009AA40" width="140" height="36"></span><u></u><span style="color:black">) expresses in bits of information the information generated when the a priori distribution </span><u></u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><img id="m_-3895366238499243306m_6893889769850668776_x0000_i1025" src="cid:image008.png@01D2596A.1009AA40" width="46" height="27"></span><u></u><span style="color:black">is turned into the a posteriori one </span><u></u><span style="font-size:11.0pt;font-family:"Calibri","sans-serif""><img id="m_-3895366238499243306m_6893889769850668776_x0000_i1025" src="cid:image009.png@01D2596A.1009AA40" width="50" height="27"></span><u></u><span style="color:black">. This follows within the Shannon framework without needing an observer. I use this equation, for example, in my 1995-book <i>The Challenge of Scientometrics</i> (Chapters 8 and 9), with a reference to Theil (1972). The relative information is defined as the <i>H</i>/<i>H</i>(max).<u></u><u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black"><u></u> <u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black">I agree that the intuitive notion of information is derived from the Latin “in-formare” (Varela, 1979). But most of us do no longer use “force” and “mass” in the intuitive (Aristotelian) sense. </span><span style="font-family:Wingdings;color:black">J</span><span style="color:black"> The proliferation of the meanings of information if confused with “meaningful information” is indicative for an “index sui et falsi”, in my opinion. The repetitive discussion lames the progression at this list. It is “like asking whether a glass is half empty or half full” (Hayles, 1990, p. 59). </span><span style="color:black"><u></u><u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText" style="margin-left:.5in">This act of forming forming an information process results in the construction of an observer that is the owner [holder] of information.<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText">The system of reference is then no longer the message, but the observer who provides meaning to the information (uncertainty). I agree that this is a selection process, but the variation first has to be specified independently (before it can be selected.<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black"><u></u> <u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText" style="margin-left:.5in">And Lerner introduces the threshold between objective and subjective observes (page 27). This leads to a consideration selection and cooperation that includes entanglement.<u></u><u></u></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black"><u></u> <u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black">I don’t see a direct relation between information and entanglement. An observer can be entangled.<u></u><u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black"><u></u> <u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black">Best, <u></u><u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black">Loet<u></u><u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black"><u></u> <u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><span style="color:black">PS. Pedro: Let me assume that this is my second posting in the week which ends tonight. L.<u></u><u></u></span></p><p class="m_-3895366238499243306m_6893889769850668776MsoPlainText"><u></u> <u></u></p></div></div><br></div></div>______________________________<wbr>_________________<br>
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