[Fis] Happy Chinese New Year & Concluding the Session

[Pedro C. Marijuán]

Of course, Lou, you are free to send your seminar invitation to the list.
Remember that the limit of 2 messages per week was slightly extended to 3.
I mean from <><> to <><><>.
Best--Pedro

El 01/02/2025 a las 6:06, Louis Kauffman escribió:
> Dear Folks,
> Thanks for this great month of exchanges! I see no need to make a 
> summary of the whole exploration. A bit of mathematics did come out in 
> relation to this discussion. We talked about it at the Laws of Form 
> meeting earlier today. I discovered a “boundary arithmetic” similar to 
> 3-valued logic that could be used to find out simple (but hard 
> otherwise to determine) topological information about knots and links. 
> The arithmetic itself is an extension of Laws of Form where one has 
> the marked state <> and the rules <> <> = <>  (calling) and <<>> =     
>   (crossing). In crossing, one crosses from the marked state and 
> arrives at the unmarked state. In this notation the unmarked state is 
> indicated by a blank space. To this we add a name for the unmarked 
> state E and another name O which is a state where < O > = O so that 
> crossing from O returns to O.  O is neither marked nor is it unmarked. 
> You can think of O as the boundary between the inside and the outside 
> of a first distinction. In logic it would be the third value, neither 
> true nor false, in a three valued logic. We also assume that 
> markedness dominates the third value so that O <> = <> O = <>. Now to 
> get a structure that unfolds into the well-known Luaksiewcz three 
> valued logic, one takes OO = O. BUT for “my” boundary arithmetic I 
> take OO =     . That is O interacts with itself to disappear! You can 
> think of this as a boundary joining along another boundary line and 
> the seam between them becomes invisible. You can also think of it as 
> analogous to Odd + Odd = Even in the sense that the sum of two odd 
> numbers is even.
> So we have an arithmetic with the rules
> <><>=<>
> <<>> =
> OO=
> <> O = <>
> <O> = O.
> It turns out that one can use this arithmetic to calculate whether 
> certain woven networks (that occur in DNA recombination e.g.) have one 
> loop (odd) or two loops (even). I won’t repeat this here, but more 
> information will be sent about this that could be downloaded.
>
> A logicians point about such arithmetics is that they do not satisfy 
> the “Law of the Excluded Middle” which in this notation would be P<P> 
> = <>.
> Thus here we have O<O> = OO =    , so that it is unmarked rather than 
> marked. And in the usual three valued logic we have O<O> = OO = O, and 
> again it is
> not marked.
>
> I have a question for Pedro. Is it ok to send the Laws of Form 
> announcement for my Friday seminar to fis? If not, then fis people who 
> want the announcement should write me an email, and I will put you on 
> the list. I’ll talk about the boundary arithmetic a bit more next 
> Friday and Karl Jaworsky will give a talk about his theory.
>
> Getting back to the theme, with the boundary arithmetic we see how a 
> very abstract, somewhat philosophical “logical arithmetic” can give us 
> topological network information. This is quite interesting to 
> contemplate as it shows how very macroscopic situations can be 
> understood by using simple mathematical patterning.
> Here it is happening  in a mathematical/logical distinction domain. In 
> our original biologic examples we saw how the mathematical domain 
> interacted with the microscopic molecular biological domain in terms 
> of both theory and experiment. All of this suggests further 
> exploration of our patterned thoughts in relation to sensing and 
> understanding natural physical and biological worlds.
> Very best,
> Lou
>
>
>> On Jan 31, 2025, at 3:22 PM, Pedro C. Marijuán 
>> <pedroc.marijuan at gmail.com> wrote:
>>
>> Dear All,
>>
>> As is tradition in this List, the beginning of Chinese New Year 
>> announces the coming end of the FIS New Year Lecture.
>>
>> Thanks are given to Lou for his impressive posting work and for the 
>> high quality of literary contents (some concluding comments to be 
>> added?).
>>
>> The related discussions may continue, but now there are no chairing 
>> privileges--the iron rule of 2 - 3 mssgs per week applies to everybody.
>>
>> And so, let us also wish our Chinese Colleagues a very Happy New Year!
>>
>> 新年快乐
>>
>> All the best,
>>
>> --Pedro
>>
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