[FRIAM] The danger of a single story

[uǝlƃ ☤>$]

Sorry for my ill-stated point. I only brought Lagrange and Euler into the conversation to link to the (suspect) conclusion that deeper structures of math are innate and finer ones learned. In the control population, my guess is there's stiff competition between sight and proprioception, though the latter is way more diverse. Proprioception would be more along the lines of walking a graph, operational, functional, whereas sight would be more metric space oriented. 

I'm completely ignorant of p-adic numbers. But the apparent difficulty grokking the geometry of a p-adic-normed space *and* the idea that spaces can be understood as graphs (and vice versa), hinging on whatever norm is chosen, destroys the intuition evoked by the word "center". If it were replaced by "equidistant" or something, it might make more sense ... but even "distance" is a bit flawed. Perhaps "fallacy" is too strong a word. But I think I'd locate the flaw(s) in your (a) and (c). I don't want to hinge on the singularity of "center", but on the definition of it. So rather than say every vertex is a center, I'd say something closer to your statement: "Every point is the same [number of steps | distance] from the edge."

But, again, my ignorance prevents me from saying anything clear about p-adic-normed spaces. My real goal was to target the meaning of "koan". Koans don't have to be paradoxes. But they're also not *mere* riddles. They're levers to help you dig into some set of concepts a little deeper than whatever preemptive binding you might otherwise snap to, much like my recent defenses of the commission of other fallacies like ad hominem and strawmanning. I also plan to defend the commission of tu quoque one day. I just haven't found the right opportunity.



On 11/10/21 11:36 AM, Jon Zingale wrote:
> """
> For lack of a better (or more ironic, since Euler went blind) dichotomy
> lever, the operational conception might be called Lagrangian and the
> latter Eulerian. From a Lagrangian perspective any point in an open ball
> is infinitely far from the outer bound as long as our operations are
> functions of that outer bound. But from an Eulerian perspective, it's
> trivial to see the boundary is just fuzzy and all we need do is take
> constant steps to leave the ball. That renders the koan a simple fallacy
> of ambiguity, hinged on the conception of "center".
> """
> 
> I am unsure that I can address everything here, and I feel like my
> reasoning has been sh!t lately, but here is an attempt to work out your
> suggestion of a "fallacy of ambiguity"[⊬]:
>   a) the term shared by the two premisses
>   b) the subject of the conclusion
>   c) the predicate of the conclusion
> 
> a) Perhaps here you are talking about *center of a ball* as the shared
> concept between a Lagrangian and an Eulerian perspective? Or maybe the
> *center of a ball* as shared between the p-adic and euclidean conceptions
> of space? In this last case, maybe the "missing premise" is that we are
> making an analogy to balls and centers when we move to non-archimedean
> norms? The fallacy might then appear as:
> 
> "All Euclidean balls have a single center. x is the center of a p-adic
> ball. Thus x is the single center of the p-adic ball."
> 
> b) I am not sure how to finagle this one a wholes and parts argument,
> but let me try. Maybe it is that centers are things that balls have but
> are not properties of points? That attributing center to a point becomes
> a category error?
> 
> c) Perhaps you feel that *center of a ball* fails operationally, that
> centers of balls are singular by their very nature, privileging insights
> of Archimedean experiences? I haven't worked it out, but I (perhaps
> falsely) assume that any one of these centers can be handled as a center
> of mass, a barycenter, maximally situated away from the ball's closure.
> Here, I suppose, is where your Gordian step is apt? From each "center"
> it takes the same number of constant steps to leave.
> 
> All of this is to say that I would like to better understand the *fallacy*.
> In terms of the larger metaphor, I like the image of many individuals,
> all within the scope of one another, granted the center of their shared
> milieux.
> 
> [⊬] https://www2.palomar.edu/users/bthompson/Fallacies%20of%20Ambiguity.html <https://www2.palomar.edu/users/bthompson/Fallacies%20of%20Ambiguity.html>


-- 
"Better to be slapped with the truth than kissed with a lie."
☤>$ uǝlƃ