How To Draw A Diagram For Math
The quadrant diagram has accomplished the status of an intellectual farce. If yous, every bit a presenter, do not make an ironic joke when you throw one on the screen, yous will automatically lose a lot of credibility. For some very good reasons though, the diagram is an indispensable i for the presenter's toolkit. Equally a listener, if y'all have a default dismissive attitude towards the thing, you will have to sit out far too many of import conversations with a contemptuous, superior smile. Then hither's a quick tutorial on quadrant diagrams. I'll tell you both how to brand them, and how to evaluate them. Hither's a made-up one to get the basics clear. Yous basically take ii spectra (or watersheds) relevant to a circuitous upshot, simplify each downwardly to a black/white dichotomy, and characterization the four quadrants you produce, like then:
This particular ane is nonsense, and falls apart at the slightest poking (we'll poke later in the article), and I made it up for fun. Let united states of america talk over 3 existent examples from business books earlier we develop a critical theory and design principles. The iii I volition use are from The Power of Full Engagement
The "Dynamics of Energy"
The Power of Full Engagement
This example illustrates the difficulty of working with circuitous, cryptic multi-faceted issues. Energy at the level of physics is well-divers, but when we are talking most the more cryptic sort that goes with people'due south behaviors, there are a lot of nuances. The volume itself discusses several other aspects, like a classification into "physical," "emotional" and "spiritual" energy.
Find one affair about the quadrants: they practise not accept evocative names, only mere structural labels similar "loftier positive" alongside lists of features, which are conspicuously variables accounted to be of bottom importance, but too important to get out out. The diagram picks out two specific attributes out of the ambiguity: subjective intensity and pleasantness, for highlighting. While this is a reasonable thing to do, information technology is not a necessary choice. You could defend these choices, but they exercise non seem specially compelling. Why non, you might ask, "steady" vs. "spiky" energy, or "physical" and "mental" energies? The choices are also weakened past the low chemical science betwixt the 2 variables.
You would not expect this diagram to back up a conceptually strong theory, and it doesn't. The book stakes its credibility on case studies and anecdotes, and fortunately, the structural strength of this diagram is not tested. This is basically a quick-and-muddied conceptual framework for organizing subject matter and ideas that are largely empirical in origin. This should not be surprising, since the source of the books ideas is data from performance coaching of athletes and executives.
Overall, this one rates a C-. Equally I will argue, it uses a quadrant for the incorrect fabric, and does so poorly at that (the volume itself is decent though).
The "Cocky-Management Matrix"
Moving to a more belittling, concept-driven quadrant, consider this i, from David Allen's Making It All Work
This diagram is an immediate improvement over the previous i on two fronts: the quadrants get evocative labels, and the chosen dichotomies along the ten and y axes: perspective and command, rather than seeming like capricious "lead" variables plucked out of a listing of many, have a yin-yang cardinal quality to them. The evocative labels serve an important function. Unlike "High-high," the phrase "Main and commander" picks out a prototypical example of existence in the country of loftier perspective and high control. It at once suggests more implied complexity than the long feature lists in the Loehr/Schwarz diagram, while retaining coherence which the Loehr/Schwarz diagram lacks. You get the sense that while each quadrant is a fuzzy set, they do represent cardinal "pure" types. Though we are not talking math or rigorous logic here, you would accept perspective/control as metaphysically foundational concepts, rather like Euclid's axioms. You lot are willing to make a spring of faith and assume the pair as bones, important dichotomies.
This diagram, unlike the previous ane, is the result of a more than deliberate endeavour at fundamental analysis. More than thought has gone into it and you could (and Allen does) build more of a sound theory on top of it. This is likewise non surprising, because though the diagram is based on the empirically validated GTD methodology, the methodology itself grew out of conceptual analysis, non data analysis.
This diagram rates a B+. Pretty decent. Points lost for bereft qualification of the rigor of the statement.
The Microsoft Scenarios
Our terminal example is from business strategy rather than self-improvement, and is a diagram that organizes four "future of the globe" scenarios that Microsoft uses to test its strategies, and is the basis of Listening to the Future
This is perhaps the most interesting one of the three. The diagram takes on the formidable chore of thinking about the time to come of the unabridged planet. The framework is based neither on experimental/field data (we are talking near the future, the product of thousands of trends gathering momentum today, and uncertainties that nobody can guess at), nor is information technology conceptual in origin. In that location is no possible fundamental theory that would tell you that globalization and labor market organization are the two "most important." Mayhap the important ones are the evolution of Islam, water wars or the global aging population. The choices fabricated hither are essentially artistic ones, not statistical "key indicators" or commencement-principles self-evident concepts. Though globalization and labor dynamics are important, they simply are not metaphysically archaic constructs like "control" or "perspective" (or "line" and "signal"). Instead, they represent observable patterns at the other end, the most complex sorts of patterns we can process and understand, what nosotros call mega-trends.
Which is why the labels in this diagram are crucially of import. They go beyond evocative to purely artistic. They suggest entire stories and scientific discipline-fiction trilogies. At the risk of sounding like a bad fiction reviewer, I'd call the quadrant names "rich background tapestries." What's more, the supporting text provides the correct sort of nuanced and ironic meta-assay of the diagram itself.
This rates an A class.
When Should Y'all Use a Quadrant Diagram?
In summary, the three diagrams rate C-, B+ and A. The grades are a reflection of both the difficulty of applying quadrant diagrams to the source material in the item cases, as well as the effectiveness of the bodily awarding. Let's create a quadrant diagram to illustrate when to utilize quadrant diagrams, and when to do something else.
The key is to apply it when there is high ambivalence, overlap and fuzziness in the basic categories, and apparent high-dimensionality (lots of variables with complex coupling) just somehow, when they mix together, a few dominant patterns leap out. In the soup that is "predicting the future of the world," despite the complexity, a few things obviously leap out, like "climate change" and "globalization," every bit useful top-level constructs. In talking metaphysics of existence, somehow "yin" and "yang" capture something important.
If the concepts were clearer, and ascendant patterns were visible (bottom correct) you would either be able to apply starting time-principles analysis and identify the foundational concepts, axioms and inference rules, OR you would be able to measure things and apply statistical techniques like regression, principal component analysis and clustering. Imagine a contemporary of Euclid offering a quadrant diagram with "closed/open" on one axis and "small-scale/large" on the other, and marking the quadrants "lake", "river", "speck of grit" and "hair." He would have been blasted away by Euclid's more fundamental indicate/line approach. Similarly, the dumb example I opened with (rich/poor, smart/stupid) begs for statistical analysis, considering it lazily uses an unnecessary quadrant diagram for stuff that would yield to systematic number-crunching (IQ/personality types/wealth correlations). The Loehr/Schwarz diagram is interesting because it is on the cusp betwixt statistical tractability and intractability. The book's source material is just coherent enough that yous get the feeling a good statistician could take eliminated the need for the quadrant diagram. A good part of the blame for the low course of the diagram is that the material should non have been quadrantized in the first place.
If things are ambiguous and no dominant patterns spring out (superlative left) , you are better off creating a lexicon or glossary of example "types" to illustrate diversity and differentiation within the soup of ambiguity. This can mean case studies, collections of anecdotes or examples, so along. If concepts are articulate-edged, but nothing seems any more of import than anything else, the material is ripe for a taxonomist. Which is why the alchemists, with their globe/burn down/h2o/air/ether model did quite well, as did the periodic-table folks, before the subject of chemistry yielded to primal analysis at the level of physics. The same goes for Carolus Linnaeus and his binomial nomenclature, before the double-helix came along. Most taxonomies though, will never observe a more than cardinal layer below the arbitrary 1.
If you DO use a Quadrant Diagram
If you ARE in the summit right quadrant, you still take work to do. Your primary job is to identify four interesting and complex clusters of phenomenology, without the aid of statistical or start-principles analysis, and think up two interesting lines that volition separate them. These are the ascendant patterns, and the organizing spectra/watersheds. You are effectively doing right-brained statistics and first-principles guesswork.
If your lines end upwardly being spectra, or related to each other in nice ways (for example, the perception/command dualism), that's a bonus. The Microsoft example is interesting because the ii axes do non represent simple spectra. Betwixt hierarchy and decentralization, a lot of variables change.
The value of your diagram will be validated by your ability to retrieve upward evocative names for the quadrants. If people see your diagram and instantly feel a sense of relief and recognition, it means you lot are articulating and clarifying something they've already subconsciously noticed. Naming is important in other ways as well. Structural indicators similar "high/depression" every bit in the Schwarz/Loehr diagram put people on their guard, because they recognize that y'all are shoehorning a multidimensional consequence into two dimensions. The list of additional qualifiers makes things worse, since it suggests you are ignoring complex couplings. All adjectives, no nouns. Evocative names, on the other paw, suggest complexity, as well as soundness/coherence.
Finally, depending on your source textile, you will need different types of evocative names for your quadrants, and different types of supporting qualitative commentary. Hither is a quadrant on how to practise quadrants:
Remember, if you are doing quadrants at all, you are in the ambiguous/dominant patterns zone. If you are playing with seriously conceptual stuff (things like "yin/yang" and "heart/periphery") that people understand intellectually in the abstract, you are in the top half. If you are dealing with things individuals and groups experience, and can relate to specific memories, histories, or entities they've encountered, yous are in the bottom half. If you lot are dealing with things that seem like they could use to dark-green aliens in the Andromeda galaxy (say "beingness/becoming" or "light/night"), you are in the left half. If you are dealing with things like "global warming" or "jerks who talk besides much at parties," you are tied to the specific, path-dependent history of planet earth and the unique attributes of homo sapiens, and are in the correct half.
You already know you lot need evocative labels. This quadrant tells you what types of evocative labels to industry, and how to support the diagram with argumentation. If you are in the top right, you lot have to make upward names that sound like high-concept Hollywood moving picture names, and be prepared to tell imaginary stories: what-ifs about possible worlds. If you are in the bottom right, be prepared to provide examples of existent people, events and places. You want to talk virtually "classic" (or archetypal) members of the quadrant. You lot might requite them abstruse names, just you should exist able to map the abstract names to existent examples, as I did in the previous section. A skilful real-world example of such an archetypal quadrant is the Keirsey temperament sorter, that lumps the sixteen possible Myers-Briggs types (based on 4 variables) into four groups called "temperaments." This diagram is especially interesting because each quadrant holds ii variables constant, and 2 variable, which means the axes do not represent anything simple (work out the axial logic if y'all are really curious).
Continuing clockwise, in the lower left, yous have experienced abstractions, which yield best to metaphor. If Loehr/Schwarz had read this article, they might accept named their quadrants (clockwise from top-left) something similar "Mind like h2o," "Evening on the beach," "Ghost town" and "Hurricane Katrina." The signal isn't to exist cute. It is to advise a design of complication, and a calibration/benchmark indicate, without a hopeless attempt to listing all the attributes that create the complication. But of grade, the Loehr/Schwarz diagram is a poor quadrant candidate in the start place. It is improve as statistics forage.
Finally, in the top left, nosotros have metaphysics. David Allen's diagram, rather schizophrenically, uses both archetype labels (master and commander, crazy-maker) and metaphysical ones (implementer, visionary). If this confuses you, think of it this way: archetypes are thumbnail portraits of an entire typical entity. Metaphysical categories emphasize a key/dominant aspect. A Crazymaker is a very richly divers epitome that says far more than the label "visionary" (which could exist good/bad). Things are clearer if you pick just one type, and when in incertitude, go more than right-brained. This has already happened: crazymaker, victim and micromanager have already become the preferred terms in the discussions of Allen'southward diagram. I still put his diagram in the "Metaphysician" category though, since I think he is working with context-costless categories (perspective/control) that are not restricted to humans. The Keirsey diagram, past dissimilarity, is more closely tied to human being psychology.
Evaluating Quadrants
The give-and-take so far should suggest obvious evaluation criteria. First inquire the question: should this be a quadrant diagram at all? If not, probe the speaker with respect to the quadrant of the "should this be a quadrant diagram" diagram where you recall the field of study belongs. Ask statistical, start-principles, multifariousness and taxonomy questions every bit appropriate. If quadrants are indeed appropriate. Use the second quadrant diagram to classify what yous are looking at, and expect for or enquire for the right sort of supporting argumentation. A speaker talking about global warming swamping coastal cities and citing examples of historical floods is providing the wrong sort of show: even the worst localized flooding in known history is not the right sort of reference point. You demand something like an imaginative science fiction story.
Wrapping Up: Other Diagrams
Visual constructs live in a special sweet spot inhabited past bug that are too complex for rigorous analysis, and too structured or impoverished to back up full-diddled narrative treatments in the form of novels or stories. Within this universe, quadrant diagrams are in the Goldilocks position. One dimension (spectrum scales and circular "life cycles") is fairly limiting and needs a lot of verbal support. Three dimensions gets you to a place where sheer visual processing overshadows the content of what you are saying. There are besides interesting special cases like triangles. Beyond that, y'all are reduced to things that get-go to look quantitative or operational: multiple sliders on scales, tables, and menses charts. Beyond that, qualitative assay through stories and metaphor is the only matter that will work.
So capeesh the quadrant diagram. In the right hands, information technology defuses polarizations, reframes arguments, separates out coherent alternatives and makes everybody's life a lot easier. In the wrong easily, it produces amusement, supplies forage for Dilbert jokes, and gives mediocre consultants a picturesque path for their descent into madness.
Source: https://www.ribbonfarm.com/2009/04/20/how-to-draw-and-judge-quadrant-diagrams/
Posted by: gablewhiparinkes54.blogspot.com
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