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U.S. homelessness dropped nearly 17% over the past eight yearsvia The State of Homelessness in the USA

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Topology gets appropriate for qualitative rather than quantitative properties, since it deals with closeness and not distance.

It is also appropriate where distances exist, but are ill-motivated.

These approaches have already been used successfully, for analyzing:

  • • physiological properties in Diabetes patients
  • • neural firing patterns in the visual cortex of Macaques
  • • dense regions in ℝ⁹ of 3×3 pixel patches from natural [black-and-white] images
  • • screening for CO₂ adsorbative materials
Michi Johanssons (@michiexile)

(Source: blog.mikael.johanssons.org)




One

Counting generates from the programmer’s successor function ++ and the number one. (You might argue that to get out to infinity requires also repetition. Well every category comes with composition by default, which includes composition of ƒ∘ƒ∘ƒ∘….)

But getting to one is nontrivial. Besides the mystical implications of 1, it’s not always easy to draw a boundary around “one thing”. Looking at snow (without the advantage of modern optical science) I couldn’t find “one snow”. Even where it is cut off by a plowed street it’s still from the same snowfall.
a larger &lsquot;thing&rsquot; with holes in it ... like the snow has &lsquot;road holes&rsquot; in it
And if you got around on skis a lot of your life you wouldn’t care about one snow-flake (a reductive way to define “one” snow), at least not for transport, because one flake amounts to zero ability to travel anywhere. Could we talk about one inch of snow? One hour of snow? One night of snow?

http://2.bp.blogspot.com/_sf5B7n5Avcg/THFKAnY0TCI/AAAAAAAAAmI/x9E4slMs0uQ/s1600/IMGP1553.JPG

Speaking of the cold, how about temperature? It has no inherent units; all of our human scales pick endpoints and define a continuum in between. That’s the same as in measure theory which gave (along with martingales) at least an illusion of technical respectability to the science of chances. If you use Kolmogorov’s axioms then the difficult (impossible?) questions—what the “likelihood” of a one-shot event (like a US presidential election) actually means or how you could measure it—can be swept under the rug whilst one computes random walks on trees or Gaussian copulæ. Meanwhile the sum-total of everything that could possibly happen Ω is called 1.

With water or other liquids as well. Or gases. You can have one grain of powder or grain (granular solids can flow like a fluid) but you can’t have one gas or one water. (Well, again you can with modern science—but with even more moderner science you can’t, because you just find a QCD dynamical field balancing (see video) and anyway none of the “one” things are strictly local.)

And in my more favourite realm, the realm of ideas. I have a really hard time figuring out where I can break off one idea for a blogpost. These paragraphs were a stalactite growth off a blobular self-rant that keeps jackhammering away inside my head on the topic of mathematical modelling and equivalence classes. I’ve been trying to write something called “To equivalence class” and I’ve also been trying to write something called “Statistics for People Who Program Computers” and as I was talking this out to myself, another rant squeezed out between my fingers and I knew if I dropped the other two I could pull One off it could be sculpted into a readable microtract. Leaving “To Equivalence Class”, like so many of the harder-to-write things, in the refrigerator—to marinate or to mould, I don’t know which.

But notice that I couldn’t fully disconnect this one from other shared-or-not-shared referents. (Shared being English language and maybe a lot of unspoken assumptions we both hold. Unshared being my own personal jargon—some of which I’ve tried to share in this space—and rants that continually obsess me such as the fallaciousness of probabilistic statements and of certain economic debates.) This is why I like writing on the Web: I can plug in a picture from Wikipedia or point back to somewhere else I’ve talked on the other tangent so I don’t ride off on the connecting track and end up away from where I tried to head.

The difficulty of drawing a firm boundary of "one" to begin the process of counting may be an inverse of the "full" paradox or it may be that certain things (like liquid) don’t lend themselves to counting in an obvious way—in jargon, they don’t map nicely onto the natural numbers (the simplest kind of number). If that’s a motivation to move from discrete things to continuous when necessary, then I feel a similar motivation to move from Euclidean to Hausdorff, or from line to poset. Not that the simpler things don’t deserve as well a place at the table.

We thinkers are fairly free to look at things in different ways—to quotient and equivalence-class creatively or at varying scales. And that’s also a truth of mathematical modelling. Even if maths seems one-right-answer from the classroom, the same piece of reality can bear multiple models—some refining each other, some partially overlapping, some mutually disjoint.




The Future of Oil (por StanfordUniversity)

peak oil vs. “business as usual”

  • accounting & measuring issues
  • using the lower-48 states of the USA as a statistical basis for “what exhausting a given area’s geological reserves should look like” elsewhere in the world
  • new kinds of discoveries (deepwater, tarsands, seismic tools by geophysicists application to reservoir finding)
    • the first trillion bbl we’ve used
    • the second trillion bbl we know where it is
    • the third trillion bbl — ???
  • issues of stocks vs flows
  • We’re actually discovering more oil fields now (due to seismic & 3D reservoir modelling), but they’re smaller.
  • Saudi Arabia used to produce 12% of the world’s oil consumption with only a handful of rigs (12) — just very, very productive wells. Now they have several times that number of rigs
  • It’s not even that wildcatting (new drilling) is discovering less oil per year. But rather the second derivative <0. The growth in per-year wildcat additions is slowing. (Whilst it’s thought demand will grow ever faster as growing populations in developing countries finally get decent modern lifestyles supplied with electricity.)
  • We also know that we’ve already found all the big oil fields, because bigger (gigantic) oil fields are the easiest ones to find.
  • image
  • 48,000 oil fields but maybe 500 huge ones.
  • (World’s biggest oil field, in Saudi Arabia, produces 6% of the world’s oil per year, and has done so since the 1950’s.)
  • Daqing oil field produces half of China’s oil by itself. (how’s this for your long tail / powerlaw distro!)
  • Recovery rates vary from 20% to 70%, averaging 35%
  • The enhanced recovery methods use pretty “simple” or familiar solvents/methods. CO, heat, ….
  • (Kind of like cancer treatments, right? Burn, poison, and cut, all familiar to 1st-century Barbarians, although we do the burning with lasers and the cutting with robots.) But since air and water and heat are such simple stuff, we can do things on an industrial scale within adequate expence.
  • "Green" friendly idea: take CO₂ gas from eg a coal plant and pipe it back into the ground to sweep the oil over to the pump.
  • Not a lot of 30-somethings in petroleum engineering. So the 20-somethings getting more responsibility & pay early on in their careers.
  • Some projections about likely future production. He takes a humble position about his gut instinct on the projection.
  • But! This was 1 October 2009. And he says (at the 1-hour mark) he doesn’t think offshore drilling will lead to environmental catastrophe. Deepwater Horizon oil spill 6½ months later. But he was so humble about his other prediction I feel bad pointing this out.




The Nielsen PRIZM groups people into 66 “demographic and geographic market segments” for the purpose of advertising to them.

Each of the segments has a nice description to go along with it. It’s the kind of story you want to hear as a marketer: it uses relatively in-depth knowledge of Americans, plus stereotypes or shallow summaries, to draw a character with enough roundness that you could pitch to him/her. That is, you could write copy or film a creative spot that you believe could speak to members of this cohesive segment.

As I read more deeply into the Nielsen-Claritas PRIZM, however, the 66 segments started to sound like perhaps they were generated by a simple formula. From their slideshow I learned that they divide the US population by:

  • affluence
  • population density
  • kids/no kids + age

Rather than use continuous on the implied cube (3 dimensions above), they lump various ranges together. They also lump the interaction terms unevenly—for example, (suburban & income) is lumped more finely and (urban & income) is lumped more coarsely. Specifically,

  • 4 totally -ordered levels of urbanity (measured by population density per zip code) urban  suburban  second city  town & rural
  • 14 levels of Affluence Groups (so they consider finer gradations of wealth & income within suburban and low-density zip codes and coarser income gradations in cities and second-cities)
     
  • Three life-stage categories, accommodating both those who do and don’t raise children at some point. {youngish && no kids, kids, oldish && no kids at home}.

    Younger folks (this is under-35’s or under-45 DINKs) are less graduated by affluence than families or older folks (over-55’s or over-45 DINKs).

    By the way, over-65’s are outside PRIZM’s marketing groups. I guess it’s assumed that they won’t buy big-ticket items or change their ways much unless the Monday lima-bean special becomes 25cents cheaper at Lida’s Diner than Bill’s Diner. Then you’ll see the entire community switch to Lida’s.

Like the MBTI, it assumes that: People fit in rectangles.

Unlike the MBTI, rather than using four sliding scales [0,1]⁴, the PRIZM uses discrete, totally ordered sets—something you could build with the letters and combn functions in R.

I started to wonder: is it really true that members of segment 26 are “urbane” and “love the nightlife” — even the empty-nesters and older homeowners of the segment? Is there really a “laid-back atmosphere” to segment 25? Or are these merely colourful papier-mâché rudely draped over a box?

Mostly, of course, I’m concerned with segment 31, the well-known Urban Achievers:

And proud we are of all of them.

HOW I SEE IT

When I look at a painting, I’m tempted to glance quickly and pass on. In order to appreciate a piece, I imagine the strokes and colour choices that make up the painting. I imagine myself painting the same thing. What would it have felt like to be inside Cy Twombly's hand while he painted Apollo 17? That gives me a better feeling of the art.

When I look at the Nielsen Prizm the same way — try to get inside the heads of its creators — I sense that they adopted the [0,1]⁸ rectangular structure simply because they’re not aware of alternatives. MBA’s do plenty of mathematics, but I’ve never seen any business mathematics cross over into CW-complexes, 3-tori, arborescences, or Lobachefskyan geometries. It could be that the people who designed the Prizm simply didn’t have anyone on their team who had heard of this stuff. All the quants were working on Wall Street rather than Madison Avenue. (Wacker Drive rather than Michigan Ave.)

The ribbon-farm guy (Venkatesh Rao) is a rocket scientist who crossed over into marketing, but so far I haven’t read enough of his stuff to say if he dove into algebraic geometry—it seems he did more functional analysis, optimisation / control theory, and differential geometry. Which is what I would expect rocket science consists of.

I will admit that the PRIZM’s use of two “matrix” presentations with colour-coding, pictures, defined ranges, and toss-away combinations is quite clear. Probably works better than when I tell clients “Just picture a 5-dimensional manifold, I won’t say the norm because I think it’s spaced differently in the center than the edges—and let’s not get into the interaction terms yet”. But—the bones of their model are really just [0,1]³. They’ve dressed it up and they’ve done more than that (segmenting and dropping). But a cube is the underlying architecture.

Is the Prizm simple or oversimplified? I feel it’s the latter. Not that I object to mathematical models of behaviour, emotions, or any human thing—but the hypercube metaphor just doesn’t fit my presumption of the shape of the space.

  • Does consumer space have 8 corners to it?
  • What’s the best interpretation of “distance” in the consumer space?
  • Do all of the lines really cross at right angles, in a hyper-grid? Was that supposed to be implied?

WHEREUNTO

I don’t want to carp about somebody else’s work without at least offering constructive criticism. What are some potentially better ways to think about the space of all consumers—potential buyers of houses, cars, vacations, DVD’s, washers, ‘n’all that?

Mathworld’s picture of a few topological objects gives one starting point:

One thing I noticed pretty quickly: you remember playing Star Fox battle mode? Or any video game where there is a lower-right thumbnail of you on a limited square map—such that when you go leftwards off the map you appear on the right, and when you go upwards off the map you appear on the bottom? As a kid I thought I was flying on the surface of a planet, but in fact it was the surface of a torus. (Why? If you go up to the top of the North Pole you don’t come out again at the South Pole. See the picture of the sphere with B ≠ C, i.e. N ≠ S.)

In other words, a torus (donut) is the product of a_loop × a_loop. Whereas a sphere (ball) is the product of a_loop (east/west) × a_line_segment (north/south).

GEOMETRY

Following from this short lesson in topology, one alternative to multiplying only “linear” dimensions of characteristic attributes would be to multiply lines with loops. For example a_loop × a_loop × a_line_segment. I’m not sure what the name for that shape is, but you can imagine it — like a cylindrical torus. And it’s logically possible that there are two circle-like dimensions in marketing. Something like, as politics goes further and further left, it starts to resemble the far right more than the middle. But relevant to marketing.

A second alternative then might be to consider, like in the image above, the endpoints of some line segments from the 3 dimensions of Nielsen. What if some of them were identified rather than left distinct? What kind of shapes could you create with that and would that resemble the consumer space more than a rectangle?

Some other ideas of things to question:

  • How do angles meet up? (inner product)
  • How do distances work? (norms)
  • Look through an algebraic geometry book, or Solid Shape. Are there any shapes—umbilics, furrows, biflecnodes, dimples, trumpets—that have an analogue in the space of all consumers?
  • Is backwards just the opposite of forwards? Or does that wrongly assume commutativity?

I don’t know if that would result in a better model. I don’t know if thinking about things this way would reduce wasteful ad spending. I don’t have data to test these ideas on. I just wanted to share this thought.




Forestry is the province of variability.

From a spatial point of view this variability ranges from within-tree variation (e.g. modeling wood properties) to billions of trees growing in millions of hectares (e.g. forest inventory).

From a temporal point of view we can deal with daily variation in a physiological model to many decades in an empirical growth and yield model.

Luis Apiolaza

(Source: quantumforest.com)




320 Plays

In other news, Art Laffer has become a parody of himself.

  • Deliberately misrepresenting the flat tax. Making it sound like 12% is a tax cut for most Americans, when in fact the effective tax rate for everyone making under $100k is already under 12%.
    The average effective tax rate on almost all Americans is already under 12%. 
  • If what you really want to do is raise taxes on the poor and cut taxes on the rich, why don’t you just come out and say it, Art?
  • Conflating simplicity of tax returns with elimination of tax brackets.
  • Poverty is caused by high tax rates and welfare. Quick, tell Somalia!
    Somalian GDP is $600 per person. Better tell them to stop paying out so much welfare because that is what's making them the #222 richest country. 
  • Brings up sin taxes as a distraction, like a magician’s trick.
    image 
  • No estimates of how much income is being “accelerated” from 2013 into 2012, only statements that the number is huge.
  • Of course when the tax rates rise on the rich, they’re all going to flee the US. Because ceteris paribus it’s in their interest to do so. All other things considered, the first thing I do every morning is ask what tax rates are on various activities I could engage in and various countries I could move to.
  • The sign is negative, therefore the magnitude is large.
  • Also austerity is equivalent to growth, although later on he contradicts that and says a lot of government spending is necessary. (Wonder whether he wants to cut health benefits, elderly benefits, military protection, or government jobs?)
  •  Some government spending is wasteful (again no discussion of magnitude—.00001% or 10%?) therefore austerity.
  • Ricardian Equivalence, because I say so.
  • Twisted reasoning like “Poor people are poor because of disincentives to work, but rich people would pay all of their tax if only you didn’t ask so much of them.” However not going to prove any of that, it’s just “common sense”.
  • This passes for argument: “Come on, you know that.” (I count four.)
  • Because, incentives. Because, markets.

If you laugh and squeal while you say it, you’re right.

 

I would love to have a less cynical view of the world than that any yahoo who claims taxes can be vastly reduced on the rich with no negative consequences to anyone gets banquets in his honour, funding from “think tanks”, and handed the reins of policy. But this sh*t tests me.

Searching for something positive to say…at least he said the goal of government is to get poor people to be prosperous.

(Source: BBC)




Why the scientists aren&#8217;t combining data from two experiments to get 5-sigma evidence (= &#8220;proof&#8221;) for the Higgs boson

The Higgs field was postulated nearly 50 years ago, the LHC was proposed about 30 years ago, the experiments have been in design and development for about 20 years, and we’ve been taking data for about 18 months. Rushing to get a result a few weeks early [would be dumb].


The reason we have two experiments at the LHC looking for the Higgs boson is because if one experiment makes a discovery then the other experiment can confirm or refute the discovery. This is why we have both D0 and CDF, both Belle and BaBar, both ATLAS and CMS, both UA2 and UA1

Why the scientists aren’t combining data from two experiments to get 5-sigma evidence (= “proof”) for the Higgs boson

The Higgs field was postulated nearly 50 years ago, the LHC was proposed about 30 years ago, the experiments have been in design and development for about 20 years, and we’ve been taking data for about 18 months. Rushing to get a result a few weeks early [would be dumb].

The reason we have two experiments at the LHC looking for the Higgs boson is because if one experiment makes a discovery then the other experiment can confirm or refute the discovery. This is why we have both D0 and CDF, both Belle and BaBar, both ATLAS and CMS, both UA2 and UA1


hi-res




Opportunity is fleeting. Experience is fallacious. Judgment is difficult.
Hippocrates

(Source: cmj.org)




Brains sound like a wicked-hard space to think about.
It&#8217;s a tightly connected (but not totally connected) network (graph theory)
Each of the nodes&#8217; 3-D location may be important as well (voxels)
The signals propagate through time (dynamical)

Brains sound like a wicked-hard space to think about.

  • It’s a tightly connected (but not totally connected) network (graph theory)
  • Each of the nodes’ 3-D location may be important as well (voxels)
  • The signals propagate through time (dynamical)

hi-res