[Fis] Thank you Lou!

Wed Jan 22 08:35:59 CET 2025

Dear Jason,
I’ll make a comment about the learning process, not for languages but for mathematics as I know that better.
I am sure that most people who have some difficulty learning mathematics are indeed in a problem of missing context.
You will hear people immediately ask “But what is the use of this? I need to know what it may be used for in order to understand it or learn it.”
This is a request for outer context. There is also another kind of context that is related to play. 

So when you teach children (or graduate students) you can appeal to the sense of play and the 
matter of trying out things as in a game. So I can say to a child, How many different ways can you form numbers that add up to five? And this may be sufficient for having some fun. She may say
2+3. And I may say 1+4. And we can go back and forth until we have found them all. And we can wonder how many ways there are in general. And the question of utility of this game may not arise.
Exactly the same thing happens for graduate students and the same problem, but there the fascination is laced with the fact that many mathematical ideas and techniques impinge on the problem. 
It is this problem that occupied the “serious” work of G. H. Hardy and Srinivasa Ramanujan in the early part of the 20th century (a movie was made about this). 

There is a famous story about Ramanujan that illustrates these ideas.
Hardy went to visit Ramanujan, who was in hospital, recovering from an illness. Hardy took a taxi and he remarked to Ramanujan “My taxi number was 1729. This does not seem to be a very interesting number.”.
Ramanujan immediately replied “No, No, Hardy! That is a very interesting number. That is the smallest number that can be written as a sum of two cubes in two distinct ways!”. 
Hardy was surprised and remarked that he felt that every positive integer was a personal friend of Ramanujan. 

One day I got to wondering how Ramanujan knew those facts about 1789. So I started listing cubes of numbers.

1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 26
7^3 = 343
8^3 = 512
9^3 = 729 (Aha!)
10^3 = 1000
11^3 = 1331
12^3 = 1728 (Ah!)

And now you see it:  1^3 + 12^3 = 1729 and 9^3 + 10^3 = 1729.

How long had Ramanujan known about this? My guess is that he noticed it just the way I showed you, when he was about 7 years old.
Indeed he was as conversant with small numbers as you or I are familiar with breathing and walking and singing a tune.

To learn new mathematics you have to go back to that place where playing (with numbers or forms) is as natural as making nonsense rhymes and stacking blocks and all the 
other combinatory stuff that fuels our minds. But it is of course more complex than that. You may already know how to play but you DO need to know if what you are learning is useful.
And some aspects of what you are learning might be hard for you. Some people immediately swim in geometry. Others find algebra and combinatory play easier. Others need a logical or philosophical motivation.
And so it goes.

What I am saying is that there is a basic place that looks like play that needs be present for new learning to occur. 
This has to do with the building of contexts for knowledge.
Best,
Lou

> On Jan 21, 2025, at 8:56 AM, Jason Hu <jasonthegoodman at gmail.com> wrote:
> 
> Dear Lou, Dear Kate,
> I invite you to consider a related but different frame:
> Multiple Layer Self-Organization processes, or Multiple Layer Emergences.
> Indeed, "sensation" is at a lower layer than "perception," which might be the layer #2.
> There will be a self-organization process going on from Layer #2 to Layer #3-perception. "Memory/experience/imagination" kicks in in this process. 
> At the bottom, "Layer #1", is "context", i.e. "something,"
> You can enjoy philosophizing about the "Layer #0", which is "nothing," but that has less significance than the Multiple Layer Emergence frame.
> A lower layer serves as the immediate context for the higher layer.
> One of the benefits of this frame is what I call "the missing contextual element," which leads to cognitive difficulties.
> E.g., why some adults learning a foreign language can be very difficult? 
> Some contextual elements - in this case, specific movement patterns of voicing organs - are missing. For children learning a foreign language, "imitation" is their powerful approach. Adults' voicing organs are already "programmed" in a specific way and "reprogramming" is more difficult than 
> imitation or starting from "nothing."
> E.g.2, why is very difficult, sometimes almost impossible, to understand a different culture/different political system? Again, "missing contextual elements."
> E.g.3, why is communication difficult? "Missing contextual elements." I like Kate's term "course-grained information" - do you mean "information in less resultion"?
> 
> Both biological blind spot and cognitive blind spot are "missing contextual elements."
> 
> Thoughts?
> 
> Best regards - Jason
> 
> "" 
>  
> 
> On Tue, Jan 21, 2025 at 12:13 AM Louis Kauffman <loukau at gmail.com <mailto:loukau at gmail.com>> wrote:
> Dear Kate,
> Thank you. That clarifies the matter.
> I suspect that whenever we have a sharp distinction there is a context that supports it.
> This is more general than a boundary. Often there is no discernible boundary.
> Best,
> Lou
> 
> 
>> On Jan 20, 2025, at 5:46 PM, Katherine Peil <ktpeil at outlook.com <mailto:ktpeil at outlook.com>> wrote:
>> 
>> Dear Lou (et al),
>> Sorry for the delay. (I was in dutch with Pedro for too many posts). Apologies all around for that. I had only a narrow window of time to participate, and my enthusiasm can get the better of me – particularly for math models that might address autopoiesis! But to wrap up:
>> What do I mean by binary? My concept of binary begins with the dualities we experience through our embodiment, which I see as a feature (of time and space) rather than a bug. Instead of some flaw in our perceptual systems, it has to do with course graining of information required for the here and now relationship between a distinct system and its immediate environment. (Your distinctions as boundaries?)  This leads into your post-Leibniz concept that encompasses formal logic and computers, the coding language or 0s and 1s. Given the incremental nature of time, at each iterative tick in any process, there areeither~or choices to be made, which I associate with digital information. Binaries – complementary opposites - are everywhere in nature, represented by Yin~Yang in my Tao Story. Ultimately, they relate to the distinctive self-referential dance between parts and wholes.  (What Dr. Thomas says about infinite sets is most intriguing here.)
>>  
>> In terms of my emotion science, while we can experience “mixed emotions” in terms of our complex human feelings and cognitive imaginings, raw pleasure and pain are binary categories. Any personally self-relevant event emerges in our experience as either painful or pleasurable, they enter our consciousness as either~or valanced surprises. As Martha Nussbaum put it, they are “eruptions in consciousness”, course-grained from the unconscious regulatory processes of the body (opponent processes, chemical signaling etc.) But in terms of their physical substrates and biological function, pleasure and pain operate together as a Both~And complementary pair. One cannot be understood outside the holistic context of its binary counterpart, like conjugate variables. They both subserve the ancient function of self-regulation, mediating the paradoxical balance between stability and change over time, or from the perspective ofthe self – the sentient subject – self-preservation (mediated by pain) and self-development(mediated by pleasure).
>>  
>> In terms of the word perception (as opposed to sensation), I would agree that the distinguishing feature isprediction – a feedforward cybernetic process that concerns the future (while sensation is more a feedback process about the immediate present). As sensory signals that serve as the Pavlovian “unconditioned stimulus-response pair” and the mode for conditioned learning categories, hedonic emotional qualia do both jobs. They provide the fundamental semantic information bit required for autopoiesis, all learning systems, and they undergird human values. I remain hungry for math models that can root them in quantum information. Both Federico Faggin and our own Dr. Thomas resonate here.
>>  
>> Thank you so much sharing your deep wisdom.
>> Over and out,
>> Kate Kauffman
>>  
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