Helmut,
You wrote:
You (and Peirce?) identified rule with 1ns, case with 2ns, and qualitative
result with 1ns. I had thought in the deduction (as a sign) it was like:
Case: Premise that occurs, shows up, representamen, 1ns,
Rule: Permanent preexisted premise, object, 2ns,
Result: Conclusion, interpretant, 3ns.
Now I hypothize, that both ways of assignment are correct, but for two
different signs: My assignment is for the semiosis/ the sign as it happens
to the deducting person, and your assignment is for the semiosis that
happens to somebody who is observing the deducting person. Do you think
that is so?
I would have to say that I cannot agree that there are two ways of seeing
this. Peirce makes it clear in his discussion of rule, case, and result at
CP 2.619 - 631 (and elsewhere) that deduction (although not the other forms
of inference) "is merely the application of general rules to particular
cases" (CP 2.20).
*Deduction (necessary inference*):
Rule (3ns): All the beans in this bag are white.
Case (2ns): A handful of beans is taken from this bag.
Qualitative result (1ns): Therefore: This handful of beans will
*necessarily* be white.
So, "general' in the snippet above most definitely refers to thirdness
(law, or better, lawfulness, rule, habit, etc.), while "particular cases"
refers to secondness (typically, existential cases, the embodiment of laws,
etc), leading to a qualitative result as firstness.
But this is not so for induction and abduction which need for the deductive
order to be "inverted" in two different ways (CP 2.623). In induction one
begins with the case, that is, with a sample.
*Induction (probable inference)*:
Case (2ns): This large handful of beans is taken from a particular bag,
Qualitative 'result' (1ns) ('result' isn't *quite* the right word): All of
these are white.
Rule (3ns): (again, not *quite* the right word) The beans in the bag are
*probably* all white.
With abduction oned begins (exactly as with deduction!) with a rule:
*Abduction (possible inference)*:
Rule (3ns): All the beans in this bag are white.
Qualitative 'result' (1ns): These beans I find lying near the bag are all
white.
Case (2ns): These beans are *possibly* from this bag.
There are, indeed, six possible ways to move through the 3 categories in a
genuine trichotomic relation (I've named and analyzed these six vectors, or
categorial paths, in several papers: see, for example, section 3 of
http://www.cspeirce.com/menu/library/aboutcsp/richmond/ccsarisbe.pdf).
and the three inference patterns illustrate half of the six:
Deduction: 3ns -> 2ns -> 1ns follows the vector (or path) of *involution
(or, analysis)*
Induction: 2ns ->1ns > 3ns follows the vector of *determination.*
Abduction: 3ns -> 1ns -> 2ns follows the vector of *representation*.
[The others I've named vector of order (dialectical, or, Hegelian order),
vector of process, and vector of aspiration.]
Another thing I am not absolutely sure of, is, whether Peirce, when he
said "A sign (representamen) is a first (...) an object is a second (...)
an interpretant is a third" meant by this 1ns, 2ns, 3ns. But my
consideration is based on assuming that.
(Well, a representamen can be a quali-, dici-or legisign, therefore 1ns,
2ns, or 3ns. But as an element of a semiosis it plays the role of giving
the semiosis the possibility (1ns) to start, interacting with the actual
(2ns) object, both being interpreted as a relation (3ns). At least that is
how I used to understand it)
Part of the problem here may be Peirce's terminology (e.g., first, a first,
firstness). Yet without exception, I believe, when Peirce speaks of "a
first" "a second" or "a third" together in a passge that the 'a' makes of
first, second, and third the categories firstness (1ns), secondness (2ns),
thirdness (3ns). [note: the abbreviations 1ns, 2ns, 3ns represent my usage
and are not standard--they just save me a lot of time typing!]
Further, as you know, not only does a representamen (a first) have three
possible categorial expressions: qualisign (1ns), dicisign (2ns), and
legisign (3ns), but so has the object (a second): icon (1ns), index (2ns)
and symbol (3ns), and so too the interpretant (a third): (rheme, or term
(1ns), dicisign, or proposition (2ns), and argument (3ns). This is what
makes the 10-adic sign classification so rich when one reflects upon
actually embodied signs. No sign, for example, is an 'icon' *as such*, nor
purely and simply, but is 'iconic' in relation to its object, but has
relations to the interpretant and to itself as sign. I believe that one has
to study the 10-adic sign classification within the context of Peirce's
understanding of continuity to do it justification, then all of this begins
to make more sense.
I'll conclude with a brief quotation from the group of passages I've
pointed to above. While I'd imagine we're all relatively clear as to what
deductive inference is, here's Peirce's description of the other two
inferences types which, I hope, will help clarify some of what I've written
above.
CP 2.624. Induction is where we generalize from a number of cases of which
something is true, and infer that the same thing is true of a whole class.
Or, where we find a certain thing to be true of a certain proportion of
cases and infer that it is true of the same proportion of the whole class.
Hypothesis is where we find some very curious circumstance, which would be
explained by the supposition that it was a case of a certain general rule,
and thereupon adopt that supposition. Or, where we find that in certain
respects two objects have a strong resemblance, and infer that they
resemble one another strongly in other respects.
I hope this helped.
Best,
Gary
*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
*C 745*
*718 482-5690*
On Fri, Aug 22, 2014 at 4:45 PM, Helmut Raulien <[email protected]> wrote:
> Gary, list,
> You (and Peirce?) identified rule with 1ns, case with 2ns, and qualitative
> result with 1ns. I had thought in the deduction (as a sign) it was like:
> Case: Premise that occurs, shows up, representamen, 1ns,
> Rule: Permanent preexisted premise, object, 2ns,
> Result: Conclusion, interpretant, 3ns.
> Now I hypothize, that both ways of assignment are correct, but for two
> different signs: My assignment is for the semiosis/ the sign as it happens
> to the deducting person, and your assignment is for the semiosis that
> happens to somebody who is observing the deducting person. Do you think
> that is so? Another thing I am not absolutely sure of, is, whether Peirce,
> when he said "A sign (representamen) is a first (...) an object is a second
> (...) an interpretant is a third" meant by this 1ns, 2ns, 3ns. But my
> consideration is based on assuming that.
> (Well, a representamen can be a quali-, dici-or legisign, therefore 1ns,
> 2ns, or 3ns. But as an element of a semiosis it plays the role of giving
> the semiosis the possibility (1ns) to start, interacting with the actual
> (2ns) object, both being interpreted as a relation (3ns). At least that is
> how I used to understand it)
> Best,
> Helmut
> *Gesendet:* Freitag, 22. August 2014 um 05:31 Uhr
> *Von:* "Gary Richmond" <[email protected]>
> *An:* "[email protected]" <[email protected]>
> *Cc:* Peirce-L <[email protected]>
> *Betreff:* [biosemiotics:6483] Re: Possibility, probability and pattern
> PS In the previous 'bean' example, abduction is not given as
> felicitously as it might be. But this is a tricky matter which I'll try to
> get back to ed at a later date. GR
>
> *Gary Richmond*
> *Philosophy and Critical Thinking*
> *Communication Studies*
> *LaGuardia College of the City University of New York*
> *C 745*
> *718 482-5690 <718%20482-5690>*
>
> On Thu, Aug 21, 2014 at 11:21 PM, Gary Richmond <[email protected]>
> wrote:
>>
>> Helmut, lists,
>>
>> Since I've been a little out of the loop, for now I'll only add a couple
>> of things..
>>
>> 1st, in consideration of the categorial path (vectorial movement) of the
>> three inference patterns as given in the famous bean example (3ns being
>> 'rule', 2ns being 'case', 1ns being 'qualitative result':
>>
>> Deduction: rule (3ns) -> case (2ns) -> qualitative result (1ns)
>> All the beans from this bag are exactly1/2 black, 1/2 white; these beans
>> are from this bag; therefore, these beans will necessarily be exactly1/2
>> black and 1/2 white.
>>
>> Induction: case (2ns) -> quality (1ns) -> rule (3ns)
>> These beans are from this bag, they turn out to be (approximately) 1/2
>> black and 1/2 white, so, beans from this back will tend to be
>> (approximately) 1/2 black and 1/2 white.
>>
>> Abduction (retroduction == inference from result to case): rule (3ns) ->
>> quality (1ns) -> case (2ns).
>> One may hypothesize that if these beans found on the table are1/2 black
>> and 1/2 white that they might well be from this bag, these beans turn out
>> to be 1/2 black and 1/2 white; so beans taken from this bag may well be
>> from this bag.
>>
>> Also, in terms of inquiry as well as biological evolution, Peirce argues
>> that the vectorial progress is from 1ns through 3ns to 2ns (note: therefore
>> NOT following the Hegelian order of 1ns -> 2ns -> 3ns). So:
>>
>> Biological evolution:
>> Chance sporting (1ns) -> new habit taking (3ns) -> evolutionary
>> change--say, structural change (2ns).
>>
>> vectorially like:
>>
>> Inquiry:
>> Abduction, or, hypothesis formation (1ns) -> Deduction, or, what would
>> necessarily follow (for the purpose of devising tests) should the
>> hypothesis be valid (3ns) -> Induction, the actual testing of the
>> hypothesis to see the extent to which the hypothesis conforms with reality.
>>
>> There are, of course, 5 other paths through the categories, all of which
>> Peirce exploits.
>>
>> Best,
>>
>> Gary
>>
>>
>>
>>
>> *Gary Richmond*
>> *Philosophy and Critical Thinking*
>> *Communication Studies*
>> *LaGuardia College of the City University of New York*
>> *C 745*
>> *718 482-5690*
>>
>> On Thu, Aug 21, 2014 at 5:40 PM, Helmut Raulien <[email protected]>
>> wrote:
>>>
>>>
>>> 2nd supplement: I think, between the two kinds of induction I mentioned
>>> ( false and real, I would replace with abductive and deductive ), there is
>>> a third kind, that is, when you know , that the number of elements in the
>>> object set is limited, but you dont know the number. That would be
>>> inductive induction. Is this weird? I am wondering, why the thread stops,
>>> just when it is getting interesting. Or is there something wrong with my
>>> style of communication, I mean am I rude? Dilettantic? Hard to understand?
>>> Too easy to understand, but missing the point? Believe me, i dont have an
>>> idea.
>>>
>>> Supplement: So, maybe my example was a "false", or "pseudo"- induction,
>>> which in fact is an abduction. Maybe a "real" induction is only given, if
>>> one knows the set, the extension of the dynamical object, which knowledge
>>> makes able to tell the value of teh probability, and whith that to tell it
>>> from possibility.
>>> Hi! I am sure, that deduction "is" thirdness, because it is obviously
>>> an argument. Can induction be an argument too? No, because it has indexical
>>> object relation, eg: "I have seen 342 white swans in my life, no swan of
>>> other colour, so probably all swans are white": The 342 swans I have seen
>>> are a subset of all swans there are in the universe. A subset relation is
>>> an index, like spotted smoke is a subset of all smoking fires there are.
>>> But a sign with an indexical object relation can not be an argument. It is
>>> not even an argument about probability, because a premise is missing, that
>>> is the number of existing swans. Without this premise you cannot even
>>> distinguish probability from possibility, because what distiguishes both,
>>> is the value of the probability.
>>> Best, Helmut
>>>
>>>
>>> *Von:* "Sungchul Ji" <[email protected]>
>>>
>>> (If Figure 1 is distorted, see the attached.)
>>>
>>> Stan, Mary, John, and list,
>>>
>>> We are dealing with three sets of three concepts distributed over a
>>> diagram constrained by the mathematical concept of a category:
>>>
>>> 1) Possibility, Probability, Pattern.
>>> 2) Firstness, Secondness, Thirdness,
>>> 3) Abduction, Induction, Deduction.
>>>
>>> f g
>>> A ------> B ------> C => T
>>> | ^
>>> | |
>>> |______________________|
>>> h
>>>
>>> Figure 1. The ur-category defined as a set of three nodes (A, B, & C) and
>>> three edges (f, g & h) connected in such a manner as to satisfy the
>>> composition condition, f x g = h, resulting in a function or a goal
>>> achieved (to be designated as T from teleonomy). The symbol "=>" reads
>>> "is associated with" or "leading to".
>>>
>>> The specific realizations of A, B, C, f, g, and h may be variable,
>>> dependent on the nature of T. In other words, depending on T, one or more
>>> of the following POSSIBILITIES or choices may be realized:
>>>
>>> I = f, g, - h (i.e., clockwise motion, - h being the reversal of h)
>>> II = f, - h, -g
>>> III = g, -h, f
>>> IV = g, -f, h
>>> V = -h, f, g
>>> VI = h, -g, -f
>>>
>>> The degree of realizing any of the above 6 possibilities (which are
>>> discrete or ’quantized’ ?) can be expressed in terms of PROBBILITIES
>>> continuously changing from 0 to 1. Here is something not usually
>>> discussed: Even within a given possibility with an average probability,
>>> there can be many different PATTERNS of probability distributions (e.g.,
>>> Poisson, Gaussian, ex-Gaussian, Gamma, etc) , each distribution being
>>> associated with a specific function, a goal, or a meaning.
>>>
>>> It seems to me that there is no problem with the assignment of the first
>>> two triads of concepts to the ur-category (i.e., A = Possibility =
>>> Firstness; B = Probability = Secondness; C = Pattern = Thirdness) but
>>> there are at least two different opinions on how to assign the third
>>> triad (i.e., Abduction, Deduction, and Induction) to the ur-category:
>>>
>>> Sung: Choice I, i.e., A = Abduction; B =Induction; (6467-1)
>>> C = Deduction
>>>
>>> John & Mary: Choice VI, i.e., A = Abduction; (6467-2)
>>> B =Deduction; C = Induction
>>>
>>> Both these possibilities assume that Abduction is Firstness but differ in
>>> the assignments of Induction and Deduction to Peircean categories of
>>> Secondness and Thirdness:
>>>
>>> Sung: Induction = Secondness; Deduction = Thirdness (6467-3)
>>>
>>> John & Marty: Deduction = Secondness; Induction = Thirdness (6467-4)
>>>
>>> Can both (6467-3) and (6467-4) be right depending on T ?
>>>
>>> Can Peirce shed some light on this question ?
>>>
>>> Some of the above 6 possibilities may not be allowed (or may be
>>> forbidden)
>>> by the laws of physics, chemistry, and/or biology.
>>>
>>> With all the best.
>>>
>>> Sung
>>>
>>>
>>> > Mary -- Why is it necessary to place a starting point? Semiosis, as a
>>> > natural process (as in BIOsemiotics), is 'all at once'. In my view it
>>> is
>>> > best seen as a developmental cycle that cannot 'begin' at some point
>>> > without starting up the whole thing, spontaneously (given the energy
>>> > source).
>>> >
>>> > STAN
>>> >
>>> >
>>> > On Tue, Aug 19, 2014 at 9:53 AM, Libertin, Mary <[email protected]>
>>> wrote:
>>> >
>>> >> Dear John, list,
>>> >>
>>> >> I agree with your suggested order below. The order would not be the
>>> >> previously suggested A-I-D (abduction, induction, deduction) but A-D-I
>>> >> based on Peirce’s writings. I will need more time to gather together
>>> >> all of the evidence, but Peirce’s essay, “A Neglected Argument for
>>> >> the Reality of God,� presents the three stages. Deely’s
>>> explanation
>>> >> of the three stages makes sense as a sequence (A-D-I). A-D-I makes
>>> sense:
>>> >> getting an idea in the first place, developing the consequences of an
>>> >> idea, experimentally testing those consequences and, if necessary,
>>> >> deciding how to reformulate the hypothesis (found in the original
>>> >> abduction). I am rushed with the start of the semester and apologize
>>> for
>>> >> my haste.
>>> >>
>>> >> Cheers!
>>> >> Mary Libertin
>>> >>
>>> >> From: <Deely>, "John N." <[email protected]>
>>> >> Reply-To: "[email protected]" <[email protected]>
>>> >> Date: Monday, August 18, 2014 at 3:31 PM
>>> >> To: "[email protected]" <[email protected]>
>>> >> Subject: [biosemiotics:6463] Re: Possibility, probability and pattern
>>> >>
>>> >> Abduction is getting an idea in the first place (also mis-called by
>>> >> Peirce retroduction); deduction is developing the consequences of an
>>> >> idea;
>>> >> induction (ill-called by Peirce, better termed retroduction) is the
>>> >> experimental testing of the consequences of an idea.
>>> >>
>>> >>
>>> >>
>>> >> *From:* Helmut Raulien [mailto:[email protected] <[email protected]>]
>>> >> *Sent:* Monday, August 18, 2014 14:00
>>> >> *To:* [email protected]
>>> >> *Subject:* [biosemiotics:6462] Re: Possibility, probability and
>>> pattern
>>> >>
>>> >>
>>> >>
>>> >>
>>> >>
>>> >> Dear Sung, List,
>>> >>
>>> >> Maybe in the posts below you were right, and I was wrong (Sorry!):
>>> >> Perhaps
>>> >> Peirce has not definitely written, that abduction, induction,
>>> deduction
>>> >> are
>>> >> caterorically 1-2-3. Now I have written a chapter, in which I have
>>> tried
>>> >> to
>>> >> show that they are. But Im afraid I first had to mor or less
>>> >> hypothetically
>>> >> reformulate the categories (in the other chapters), with which I
>>> think,
>>> >> not
>>> >> everybody would agree. See: www.signs-in-time.de , "English version",
>>> >> "Abduction, induction, deduction". I hope, I have not mixed up the
>>> beans
>>> >> from the bag in my example.
>>> >>
>>> >> Very best,
>>> >>
>>> >> Helmut
>>> >>
>>> >>
>>> >>
>>> >> Hi Sung,
>>> >>
>>> >> no, that was not me, it was Peirce himself, with the example about the
>>> >> beans in a bag, I think. Whose own writings I have read less than
>>> >> receptions: The assignment to the categories I think I have gotten
>>> from
>>> >> secondary literature by eg. Nina Ort "Reflexionslogische Semiotik"
>>> >> (logic-of-reflection-semiotics?), Winfried Nöth, Helmut Pape,... But
>>> >> thank
>>> >> you for your (mis-) estimation!
>>> >>
>>> >> Very best,
>>> >>
>>> >> Helmut
>>> >>
>>> >> *Gesendet:* Sonntag, 17. August 2014 um 01:24 Uhr
>>> >> *Von:* "Sungchul Ji" <[email protected]>
>>> >> *An:* [email protected]
>>> >> *Betreff:* [biosemiotics:6458] Re: Possibility, probability and
>>> pattern
>>> >> may
>>> >>
>>> >> Hi Helmut,
>>> >>
>>> >> If you can demonstrate that the triad of abduction (A), induction (I)
>>> >> and
>>> >> deduction (D) constitutes a mathematical category, you will have a new
>>> >> category which may be referred to as the AID category.
>>> >>
>>> >> As you indicated, A, I and D indeed seem to correspond to Firsrtness
>>> >> (F),
>>> >> Secondness (S), and Thridness (T), and, since the triad of F, S and T
>>> is
>>> >> a
>>> >> mathemtical category (as I see it), you my have 'discovered' a new
>>> >> mathemtical category -- the AID category !
>>> >>
>>> >> With all the best.
>>> >>
>>> >> Sung
>>> >>
>>> >>
>>> >>
>>> >> > Supplement: Abduction and induction are selections too, abduction is
>>> >> > tentative or hypothetic selection, induction is reasonable
>>> selection,
>>> >> > and deduction is definitely justified selection. Or something
>>> >> > overprecise like that. But mathematically, I assume, because
>>> >> > mathematics is exact science, selection is only done, if completely
>>> >> > justified, therefore deduction, or total induction, but that is
>>> >> > deduction, because completion is a new premise, that turns induction
>>> >> > into deduction Hi Sung, the brain I dont have much of an idea of,
>>> >> > but I agree with your classification, because possibility,
>>> probability
>>> >> > and pattern for me seem to be the grounds for abduction, induction
>>> and
>>> >> > deduction, which are categorically 1-2-3 either. To me it seems,
>>> that
>>> >> > "pattern" fits better than "selection", because
>>> >> > "pattern" is the ground or reason of the inference, just
>>> >> like
>>> >> > "possibility" and "probability" are, while
>>> >> > "selection" is the inference (deduction) itself. Best,
>>> >> > Helmut
>>> >> > Von: "Sungchul Ji"
>>> >> > An: [email protected]
>>> >> > Betreff: [biosemiotics:6454] Possibility, probability and pattern
>>> may
>>> >> > form a mathematical category (If Figure 1 is distorted, see the
>>> >> > attached.)
>>> >> >
>>> >> > Hi,
>>> >> >
>>> >> > While jogging along the Carnegie Lake in Princeton one morning
>>> >> recently,
>>> >> > a
>>> >> > set of three concepts kept recurring in my mind – Possibility,
>>> >> > Probability, and Selection -- which seemed to fit the Peircean
>>> >> categories
>>> >> > of Firstness, Secondness and Thirdness, except perhaps the last
>>> >> category.
>>> >> > But when I tried to represent this triad as a mathematical
>>> category, a
>>> >> > new
>>> >> > triad emerged wherein Selection is replaced by Pattern which I think
>>> >> fits
>>> >> > the Peircean Thirdness better than Selection. For convenience, I
>>> will
>>> >> > refer to this triad as the PPP category, which evidently satisfies
>>> the
>>> >> > composition condition, f x g = h:
>>> >> > f g
>>> >> > Possibility --------> Probability --------> Pattern
>>> >> > (Firstness) (Secondness) (Thirdness)
>>> >> > | ^
>>> >> > | |
>>> >> > |____________________________________________|
>>> >> > h
>>> >> >
>>> >> > Figure 1. The PPP-category. f = actualization; g = selection; h =
>>> >> > validation, control or information flow.
>>> >> >
>>> >> > Out of many examples I have, let me present juts two that fit the
>>> PPP
>>> >> > category:
>>> >> >
>>> >> > (1) There are several regions in the human brain (e.g., post and
>>> >> anterior
>>> >> > cingulated cortexes, ventral prefrontal cortex, hippocampus, and
>>> DMN,
>>> >> > default mode network), each occupying an average volume of 50 -60
>>> mm^3
>>> >> or
>>> >> > 1x10^6 mm^3, that exhibit fMRI signal changes (reflecting neuronal
>>> >> > firing/metabolic activity changes) upon a venous infusion of the
>>> >> > psychedelic drug, psilocybin. Thus, since the fMRI (functional
>>> >> magnetic
>>> >> > resonance imaging) technique allows neuroscientists to monitor the
>>> >> > neuronal firing activities non-invasively from live brain volumes of
>>> >> > about
>>> >> > 10 mm^3 called “voxels” (volume elements), the fMRI
>>> >> technique
>>> >> > can monitor
>>> >> > the neuronal firing activities of about 10^5 voxels in these brain
>>> >> > regions. Carhart-Harris and his coworkers [1] recently found that
>>> the
>>> >> > psilocybin infusion caused an increase in the variety (or entropy)
>>> of
>>> >> the
>>> >> > fMRI signals measured from DMN regions of human subject (see Figure
>>> 1
>>> >> a)
>>> >> > and b) attached). Psilocybin promotes unconstrained thinking
>>> >> (“My
>>> >> > thoughts wandered freely”) and decreases cerebral blood flow.
>>> >> The
>>> >> > term
>>> >> > entropy used here simply means a quantitative measure of the variety
>>> >> of
>>> >> > the fMRI signals measured from a given brain regions calculated as
>>> the
>>> >> > variety of the distances of the local signals from the mean signal
>>> of
>>> >> the
>>> >> > brain region under investigation.
>>> >> > Based on a visual inspection of Figures 1a) and b) attached [2], the
>>> >> > following conclusions can be made:
>>> >> >
>>> >> > (a) Possibility = the number of voxels in a brain region, i.e., ~
>>> 10^5
>>> >> > voxels.
>>> >> > (b) Probability = the probability of a given voxel exhibiting a fMRI
>>> >> > signal that is 0.1 unit away from the group mean is about 0.1
>>> >> > pre-psilocybin and 0 post-psilocybin. Likewise, the probability of a
>>> >> > given voxel’s fMRI signal deviating from the group mean by 0.4
>>> >> > units is
>>> >> > 0.15 pre-psilocybin and 0.2 post-psilocybin, etc.
>>> >> > (c) Pattern = the fMRI signal distance frequency distribution fits
>>> the
>>> >> > Planckian distribution function reasonably well (see Figure 1a) and
>>> >> b).
>>> >> > Therefore, I conclude that the neurophysiology of the DMN (default
>>> >> mode
>>> >> > network) of the
>>> >> > human brain can be represented as a mathematical category.
>>> >> >
>>> >> > (2) When DNA is fragmented into short segments, called n-mers,
>>> where n
>>> >> is
>>> >> > the number of nucleotides in them, the maximum number of n-mers is
>>> >> given
>>> >> > by 4^n since there are 4 different nucleotides, G, C, A and T. Zhou
>>> >> and
>>> >> > Mishra [3] studied the frequency distributions of 11-mers. Not all
>>> >> > 11-mers occurred equally – some (as distinguished by their
>>> >> > nucleotide
>>> >> > sequences) occurred only once, some occurred not at all, while still
>>> >> > others occurred more than hundred times. From Figure 1c), we can see
>>> >> > that the number of the 11-mers that occurred only once in the genome
>>> >> is
>>> >> > about 0.002 x 4,194,304 = 8,329, while the number of the 11-mers
>>> that
>>> >> > occurred about 20 times in the genome numbered 0.025 x 4,194,304 =
>>> >> > 104,858. As evident in Figure 1 c), the 11-mer frequency
>>> distribution
>>> >> in
>>> >> > the primitive unicellular organism, Pyrococcus abyssi, fits the
>>> >> > Planckian distribution with a great precision and hence, the genome
>>> of
>>> >> > this organism can be considered as an example of the PPP category,
>>> >> since
>>> >> > (a) Possibility = 4^11 = 4,194,304 possible 11-mers
>>> >> >
>>> >> > (b) Probability = the probability of the 11-mers occurring only once
>>> >> in
>>> >> > the genome is about 0.002, while the probability of the 11-mers that
>>> >> > occur
>>> >> > 20 times in 0.0025.
>>> >> >
>>> >> > (c) Pattern = the11-mer frequency distribution fits the Planckian
>>> >> > distribution function.
>>> >> >
>>> >> > It seems clear that the PPP category introduced above for the first
>>> >> time
>>> >> > is an example of the ur-category described in [biosemiotics:6360].
>>> >> >
>>> >> > With all the best.
>>> >> >
>>> >> > Sung
>>> >> > __________________________________________________
>>> >> > Sungchul Ji, Ph.D.
>>> >> > Associate Professor of Pharmacology and Toxicology
>>> >> > Department of Pharmacology and Toxicology
>>> >> > Ernest Mario School of Pharmacy
>>> >> > Rutgers University
>>> >> > Piscataway, N.J. 08855
>>> >> > 732-445-4701
>>> >> >
>>> >> > www.conformon.net
>>> >> >
>>> >> >
>>> >> > Reference:
>>> >> > [1] Carhart-Harris, R. L. et al. (2014). The entropic brain: a
>>> theory
>>> >> > of conscious states informed by neuroimaging research with
>>> psychedelic
>>> >> > drugs. Frontiers in Human Neuroscience 8(Article 20): 1-22.
>>> >> > [2] Ji, S. (2014). Planckian and Gaussian distributions in Molecular
>>> >> > Machines and Living Cells: Evidence of Free Energy Quantization in
>>> >> > Biology. Computational and Structural Biotechnology Journal (to
>>> >> > appear).
>>> >> > [3] Zhou, Y. and Mishra, B. (2004). Models of Genome Evolution. In:
>>> >> > Modeling in Molecular Biology (Ciobanu G, Rozenberg G, eds),
>>> Springer,
>>> >> > Berlin. Pp. 287-304.
>>> >> >
>>> >> >
>>> >>
>>> >>
>>> >
>>>
>>>
>>>
>>
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