The purpose of a family is the enhancement of the individual pursuits of happiness … in the overall … preservation of the family as a whole.
—from Family Wealth
Is this a logical sentence, or not?
Posts tagged with holism
My father used to tell me that when people complimented him on his tie, it was never because of the tie—it was because of the suit. If he wore his expensive suit, people would say “Nice tie!” But they were just mis-identifying what it was that they thought was nice. Similarly if you’re interviewing candidates and accidentally doing your part to perpetuate the beauty premium to salaries, you aren’t going to think “She was really beautiful, therefore she must be more competent”. You might just notate that she was a more effective communicator, got her point across better, seemed like more of a team player, something like that.
Achen (2002) proposes that regression in the social sciences should stick to at most three independent variables. Schrodt (2009) uses the phrase “nibbled to death by dummies”.
I understand the gripes. These two men are talking about political analysis, where the “macro” variables are shaky to begin with. What does it mean that the Heritage Foundation rated two countries
9 points apart on corruption or freedom? Acts of corruption are individual and localised to a geography. Even “ethnofract”, which seems like a valid integral, still maps
∼10⁷ individual variation down to
10⁰. But this is statistics with fraught macro measures trying to answer questions that are hard to quantify in the first place—like the Kantian peace or center–periphery theories of global political structure.
What about regressions on complexes in more modest settings with more definitive data measurements? Let’s say my client is a grocery store. I want to answer for them how changing the first thing you see in the store will affect the amount purchased of the other items. (In general trying to answer how store layout affects purchases of all items … this being a “first bite”.) Imagine for my benefit also that I’m assisted or directed by someone with domain knowledge: someone who understands the mechanisms that make X cause Y—whether it’s walking, smelling, typical thought patterns or reaction paths, typical goals when entering the store, whatever it is.
I swear by my very strong personal intuition that complexes are everywhere. By complexes I mean highly interdependent cause & effect entanglements. Intrafamily violence, development of sexual preference, popularity of a given song, career choice, are explained not by one variable but by a network of causes. You can’t just possess an engineering degree to make a lot of money in oil & gas. You also need to move to certain locations, give your best effort, network, not make obvious faux pax on your CV, not seduce your boss’ son, and on and on. In a broad macro picture we pick up that wealth goes up with higher degrees in the USA. Going from G.E.D. to Bachelor is associated with
tripling ± 1 wealth.
I think this statistical path is worth exploring for application in any retail store. Or e-store or vending machine (both of which have a 2-D arrangement). Here as the prep are some photos of 3-D stores:
And for the 2-D case (vending machine or e-store) here are some screen shots from Modcloth, marked up with potential “interaction arrows” that I speculated.
Again, I don’t have a great understanding of how item placement or characteristics really work so I am just making up some possible connections with these arrows here. Think of them as question marks.
Did you ever have the experience that you buy something in the store and it read so differently in the store and when you were caught up in the magic of the lifestyle they were trying to present to you, but now it’s hanging up with your stuff it reads so different and doesn’t actually say what you thought it said at the time?
For me if I’m clothes shopping I’m thinking back on what else I own, what outfits I could make with this, how this is going to look on me, how its message fits in with my own personal style. And at the same time, the store is fighting me to define the context.
In the Modcloth example I’m talking mostly about 2- or 3-way interactions between objects. In analogy to simplicial complexes these would be the 1-faces or 2-faces of a skeleton.
But in general in a branded store, the overall effect is closer to let’s say the N-cells or N−1-cells. Maybe it’s not as precise as the painting in http://isomorphismes.tumblr.com/post/16039994007/thoroughly-enmeshed-composition-perturbation or a perfectly crafted poem or TV advertisement, where one change would spoil the perfection.
But clothing stores are definitely holistic to a degree. By which I mean that the whole is more than the sum of the parts. It’s about how everything works together rather than any one thing. And a good brand develops its own je ne sais quoi which, more than the elements individually, evokes some ideal lifestyle.
More on this topic after I finish my reading on Markov basis.
Some say science & mathematics are reductive.
żfunction independently. (The speed the soccer ball falls downward off the cliff is unrelated to how much forward momentum you kicked it.)
The reductionistic approach to science has to pair with qualifiers and caveats that “The lab is not the real world” and “We’re just trying to model one phenomenon and understand one thing”: hopefully combining
B doesn’t introduce complexity in the sense that
A+B is more than the sum of its parts — in statistical modelling language, that the interaction terms don’t overwhelm the separable, monic terms.
But is it really true that mathematics is reductionistic? I can think of both separable mathematical objects and not-separable ones. You could argue, for example, that a manifold can be decomposed into flat planes—but then again, if it has a nontrivial genus, or if the planes warp and twist in some interesting way, wouldn’t you be nullifying what’s interesting, notable, and unique about the manifold by splitting it up into “just a bunch of planes”?
Or with set theory: you could certainly say that sets are composed of atomic urelemente, but then again you could have a topological space which is non-decomposable such as an annulus or network or 1-skeleton of cells, or a non-wellfounded set (cyclic graph) which at some point contains a thing that contains it.
How about a sort-of famous mathematical object in the theory of links & knots: the Borromean rings.
The Borromean rings are famous for the fact that they cannot be decomposed into a simpler atom, whilst retaining their Borromean nature. In other words the smallest atom you can find is the 3 rings themselves. If any one or more rings were removed then they would not be linked together.
So not only is it an interesting case for causality (is
ring 1 binding up
ring 3? No. Is
ring 2 binding up
ring 3? No. In a way none of the rings is locking up any other ring, and yet they are locked by each other.
It takes the interaction term
[ring 1 ∩ ring 2] — only together do they bind up
ring 3, but together they do bind it completely. (Did something like this come up in Lord of the Rings or some other fantasy or myth? Like the weakest link or that square battle arrangement with spears, or having a ton of archers in Warcraft 2, but not like Captain Planet, if any member of a group breaks then its entire strength is lost (super convexity) but together they’re nearly undefeatable.)
I don’t know if historically the Borromean rings were a symbol of holism, although one would think so given this picture from the Public Encyclopedia:
Even if it hasn’t been, we certainly could use the Borromean rings now as a symbol of holism, complexity, integratedness, un-separability, irreducibility, and convolution.
Imagine you were a wealthy writer — so wealthy that you could pay servants to look stuff up for you. Instead of drudging through tomes (or internet searches) to fact-check yourself, find original references, and so on. You just do the fun part: pontificate on paper.
Now let’s say after you have finished an essay, your servant / employee / virtual personal assistant comes back from his footnote research and tells you that statement #13 should be revised based on the best-known research on the topic. In fact, statement #13 is almost the reverse of the truth.
I can imagine things going one of two ways from here.
In an especially dire scenario, your PA’s research might overturn the worldview that led you to write the essay in the first place.
Like Holger Lippmann’s “Flower Circles 13”, changing one element renders the entire whole needful of alteration. Everything is so thoroughly enmeshed (see “complete graph” below for the neighbourhood relations) that no element of the text speaks in isolation.
That’s in distinction to the calculus, where smooth functions can be approximated by a differential.
In physicists’ language, due to tightly, globally connected topology, perturbations cannot be localised. Rather, the opposite: local perturbations cause global changes in the object.
OK, someone dared me. I’ll say it: Gestalt.
What happens if, instead of doing a linear regression with sums of monomial terms, you do the complete opposite? Instead of regressing the phenomenon against , you regressed the phenomenon against an explanation like ?
I first thought of this question several years ago whilst living with my sister. She’s a complex person. If I asked her how her day went, and wanted to predict her answer with an equation, I definitely couldn’t use linearly separable terms. That would mean that, if one aspect of her day went well and the other aspect went poorly, the two would even out. Not the case for her. One or two things could totally swing her day all-the-way-to-good or all-the-way-to-bad.
If you don’t know my sister, you can pick up the point from this well-known stereotype about the difference between men and women:
"Men are simple, women are complex.” Think about a stereotypical teenage girl describing what made her upset. "It’s not any one thing, it’s everything.”
I.e., nonseparable interaction terms.
I wonder if there’s a mapping that sensibly inverts strongly-interdependent polynomials with monomials — interchanging interdependent equations with separable ones. If so, that could invert our notions of a parsimonious model.
"The whole is more than the sum of the parts"
Who says scientists are reductionistic? Any superadditive system—due to complexity, interaction terms, valuation by an Lₚ norm with 0<p<1, or some other reason—adds up to more in total than the pieces individually do.
A lot of people think of “geometric” art as being math-y, in the same sense that the band Maps & Atlases is math-y.
But I don’t think lines, circles, squares, tessellations, grids, and polygons are more mathematical than globs, leaves, aleatorics, colours, nets, or scribbles. In fact, I can link to a math post about each: lines, circles, hypersquares, polytopes, aleatorics, tessellations, blobs, grids, leaves, nets, scribbles, colours.
The mathematical thought that occurs to me when looking at this painting is how, in composition, every spot on the canvas influences every other spot. Holger Lippmann couldn’t have swapped a few of these circles because it would have ruined the effect.
Similarly in painting like this, if you added a splotch of yellow in the bottom right, that would affect the look of several other parts of the canvas.
Algebraically, the pieces of the composition are like a highly connected graph (in “how good it looks” space).
If you regressed compositional outcome against the content of each point in the painting (or just against the style of each circle), the relevant explanatory variables would be highly interactive terms. All the monomial, binomial, trinomial, … terms would be irrelevant.