Spatial thinking – quantity and dimension

I am not exaggerating if I say that most of us grew up learning the geometric progression of numbers without necessarily tying the geometry aspect to the progression of numbers: 2 ,4, 8, 16 and so on. 2, 2-squared, or 2-cubed was not associated with a linear measurement, a surface measurement or a volume measurement at large. The aspect of generalizing 2 raised to the nth power has conveniently dropped geometry from our faculty of understanding (at least in the lower dimensions). Interestingly, keeping geometry tied to numbers in the lower dimensions would actually otherwise help understanding higher dimensions and handling multidimensional data better.

In fact, I try teaching this to my kids; actually starting from a dimensionless point to three dimensional cube. The concept of keeping quantity and dimension together has greater and less understood benefits. Not only in understanding dimensions but the whole concept of 0 becomes so much simpler and clearer when keeping geometry with the counting. During my growing years I  struggled much to understand what is to 0 beyond being the starting point of counting. But now, teaching my kids counting alongside of geometry is throwing whole new light on what 0 is.

Zero is the dimensionless point space out of which everything arises and that the periodicity inherent to geometric patterns causes 0 to reestablish itself in the multidimensional world. As for the kids, (my pre-K’ers in context here) it doesn’t really matter if I keep counting and geometry (quantity and dimension) together or separate from the perspective of learning. They have learned them separately or together with the same ease. However, the level of spatial awareness (as I observed in them) that blossoms from keeping geometry associated with counting is outstanding. The idea of front, back, up, down, left, and right come more naturally to us humans anyway and putting math close to this and then going beyond it only keeps the learning faculties grounded in the space/time continuum – simple eh?

Numbers without geometry could help measure linearities but the highly non-linear world we live in starts with the 4-dimensions anyway. I think keeping numbers and geometry together first and then diving deeper into algebraic expression of numbers beyond geometry would make more sense and will help building geospatial awareness from a younger age. I am actually directly noticing this phenomenon blossom in young minds.

Why is Mapsol work exceptional?

The science of a map is to match and depict the biophysical interpretation of geographical reality around us mathematically. Biophysical interpretation meaning, what we see and perceive around us is stored as a subjective biophysical impression in our head individually. My picture of reality around me would be different from my daughter’s picture of reality around me, though we are sitting in the same place and watching the same thing. However, when we start communicating the biophysical picture of our surroundings to others, especially for professional purposes, we use a common spatial language rooted in mathematics to convey our observations, findings, analysis or results about a particular phenomenon we are studying. And that process of accurately communicating our story about the earth-based objects and phenomena around is what geospatial is all about.

At Mapsol we nourish and nurture this principle that “earth” and “earth’s representations” are at the center of all that we are trying to communicate through our maps or analyses or decision support systems (that we are creating). We engage in the engineering life cycle of geospatial data to information for all projects small or big: simple maps to elaborate decision support systems. Our principle is getting straight down to the core of what geospatial is, for every problem that we undertake. That is what makes Mapsol exceptional!

Does lack of access to space say anything economic?

Leaps of advancement can occur when one attempts to understand understand human interaction with the space/time. Econometrics, an amalgam of study areas like economics, mathematics, computer science and statistics for quantitative economic analysis is gaining a greater significance in the information age owing to the bulk of digital information becoming increasingly readily available. I have been working in this emerging field adding my part of geospatially enhancing the process of econometrics. Needless to mention, something beautiful came out of this endeavor to perform geospatial econometrics.

Economic characteristics are actually observable phenomena. These phenomena are observable as geospatial characteristics: in infrastructural assets and cultural practices of peoples in a given place; in other words, structure and distribution patterns of natural and cultural features with respect to their function. A variety of geospatial data, that is, digital representations of (natural: elevation, water bodies etc) and cultural (roads, buildings, bridges etc) characteristics of an area are used to measure/compute indices of socio-economic phenomena geospatially. Urban poverty is such an socio-economic phenomenon we attempted to measure/compute.

Access to free space is a luxury. Space creates expansiveness and compromising with limited space is an indication of lack of or inhibition to growth. As philosophical as this sounds, geospatial methods and analyses helped translate this simple principle into estimating the actual economic growth or lack of it in the actual. A version of this principle has been explored as: “does lack of space or having to fight for space and resources/services (which are an indirect function of space) indicate poverty”. We thus estimated urban poverty as a degree of ‘lack of access to space’ people face in order to thrive. Multiple observations of available space were used in this which included total open space, road space, and habitable space.

Geospatial estimation of urban poverty struck the cord with the traditional way of estimating poverty by way of counting (statistically estimating) actual poor people. The two ways of estimating poverty showed very high correlations corroborating the geospatial estimates. Geospatial estimation of poverty not only gave the counts but showed where the poor people are – answering a much bigger question that can facilitate better policy-making, implementation, and tracking of developmental initiatives. Our work is being published on The Mint and can be found on http://www.livemint.com showcasing one state every two weeks.

what do I mean by geospatial awareness?

While it takes a trained professional to systematically solve a problem geospatially, the stakeholders involved in the problem-solving often contribute or hinder the solution more than they realize. A geospatial professional on the other hand either enhances or reduces the solution and the scope of “geospatial” in the problem. Learning happens on both sides at different levels; what makes the mark is when an appreciation for the multidimensionality of reality kindles. This appreciation for the finer understanding of multiple dimensions involved in earth-based objects and phenomena is what I refer to as geospatial awareness.

Owing to the contemporary practices in the geospatial world, the technical know-how of the tools can be easily misconstrued as geospatial awareness. In fact, it is the case; most common GIS specialists are boasting of how many tools they have used or know exist. While this is a great asset to have, knowing what a tool can do without knowing its limitations is futile, for such knowledge itself will become the limitation of the specialist. The only way a specialist can appreciate the limitation of a tool is a complete understanding of the solution not the tool alone. Once the specialist appreciates the tool’s limitation s/he is not limited by the tool anymore. Knowing what to achieve, s/he goes about finding the tool that can implement the solution they designed. This aspect of understanding how to solve a geospatial problem in concept first and then finding tools to put the solution in place is the key that is lost in the current geospatial world.

Perhaps a truth in general, this constricting approach of replacing scientific knowledge with technical knowhow has but a profound impact in the geospatial world. Simple and straight reason being a rather scarce commodity, “non-linear thinking”, which is what the geospatial world is all about. For a mind extensively trained to think linearly, thinking up a solution in the non-linear space (multiple dimensions of reality) becomes not only a challenge but also a hindrance to solution-making. Most people revert to saying, ‘I think this is unwanted complexity or beyond me, let me do it my way, which I know works’. Very few people break out of their cocoons of inability to think spatially. Spatial thinking or awareness of space/time is a very subtle thing quite natural to all beings. We have only hindered this innate ability of ours by limiting ourselves to linear mathematics and conventional solutions.

A mind open to new horizons of civilizational improvement alone can grasp and enhance the “geospatial” science. Such a spatial thinking flair can always be rekindled in anybody and this is what I mean by enhancing geospatial awareness. Geospatial awareness is not a key requirement of the specialist alone nor the stakeholder but of every human being. Enhancing geospatial awareness through every solution implemented is my motto.

What is geospatial?

Logo Geospatial is a new term for many, while confusing at the best to most. Few around the world would see the full view of this term beyond the many perspectives it can present itself in. There were many technical as well as conventional interpretations I came across ever since I heard this term first in Madison, Wisconsin. It, for sure, is not a replacement to the more popular term GIS. GIS is more suitable to a piece of software that a buttonlogist would know to press buttons in. I present here, my definition and understanding of this beautiful term for the novice or the expert.

As part of my geospatial education at the University of Wisconsin-Madison, I took many courses and worked on multiple projects involving GIS work. Though we commonly referred to all this work as GIS, our program was called Geospatial Information Science and Engineering (GIE or GISE). While we were searching for seminar topics during a semester, I asked my teacher Dr Alan Vonderohe to tell us all “What is GIE?”. Interestingly enough, that was the first time such a discussion had come up and he put together a big picture definition of the whole program he nourished and brought to form for us. And to me that seminar was the game changer. It not only explained to me what geospatial is, GIE is, and GIS is but also took my understanding of this beautiful science leaps ahead. The full umbrella of concepts, methods, data-structures, algorithms, data, reference frameworks, tools and technologies involved in learning about the “space/time fabric” – spatial, in the context of the “earth” – geo, using the digital tools is Geospatial. And GIE is an engineering science of understanding and leveraging Geospatial for solving the problems related to the earth. What do I mean by engineering science? In simplest terms, a well defined approach to dealing with the spatial (digital) information through its entire life cycle from inception to consumption. What else have we left unaddressed in this picture? What a beauty, a consummate picture, ain’t it?

In the actual words of my professor Dr Vonderohe, “a discipline of science is born when a person implementing or presenting the science needs to develop a full rounded understanding of all the sub-aspects of the science, either borrowed from other disciplines or new ones developed within the discipline”. Geospatial is such a new discipline of science. A geospatial professional needs to understand aspects of geodesy, surveying, computer science, mathematical science, theoretical physics, cartography, information technology, in addition to spatial analysis concepts, tools, algorithms commonly available as piece of commercial software. Only such a professional can efficiently solve or improve solutions for problems deemed daunting hitherto. The Geospatial science is born to enhance the human interactions with and understanding of the earth-based objects and phenomena thus improving the overall quality of life of our civilizations.