Ecosystem of the West is Changing

I came across this article from the New York Times this morning. I found it to be yet another example of how our climate is changing. In most if not all instances the changing of our climate is for the worse and that seems to be the case here with this story about The Glacier National Park. 

In this article Michael Wines explains one particular example of how climate change in the region will cause serious consequences for those living in the western part of the United States. He states, "...Moisture loss from early snowmelt is worsening a record hydrological drought on the Colorado River, which supplies water to about 40 million people from the Rockies to California and Mexico; by 2050, scientists estimate, the Colorado’s flow could drop by 10 percent to 30 percent..." The consequences are not only to humans but to the animals who also depend on the resources of this area. 

This is an informative article, you can read more from it below:


I finally received my invitation to the new ad free unique social network experience. I appreciate the minimalist design of the site and their manifesto. Here is an excerpt from their manifesto, "...We believe there is a better way. We believe in audacity. We believe in beauty, simplicity, and transparency. We believe that the people who make things and the people who use them should be in partnership. We believe a social network can be a tool for empowerment. Not a tool to deceive, coerce, and manipulate — but a place to connect, create, and celebrate life..." I also like the fact that they are now a Benefit Corporation. Keep up the good work.

Check it out here!

Could desalination solve California's water problem?

Given the state of California's water crisis, there is truly no good reason not  to support a massive effort to use this abundant resource. With that said, it may also make us treat the oceans with the respect they deserve if we are relying on them for our drinking water. But even still,I am afraid that would still not be enough cause for such a notion. Desalinization plants are a guaranteed way to ensure adequate drinking water. As for the cost of energy associated with their use; wind, solar, tidal, hydro; they all must be implemented and used. It makes no sense to use fossil type fuels for powering these plants. Read more about the pros and cons of desalination plants. 

U.S. Global Competitiveness Diminishes as Infrastructure Lacks Investment

                                        George Washington Bridge, connecting Manhattan, NY to Fort Lee, NJ

                                        George Washington Bridge, connecting Manhattan, NY to Fort Lee, NJ

It's a fact that the nation's infrastructure is crumbling and aging. The average American dodges potholes, struggles with traffic congestion, and copes with air travel hassles and all the while having minimal access to any adequate public transportation. But a country’s infrastructure is more than just transportation grids. America's infrastructure includes other things like water supplies, waste-water grids, the electrical grid, shipping ports, schools, and hospitals. These cumulatively are known as the built environment and together they account for the US's built assets. In a recent report produced by the global natural and built asset consultancy ARCADIS in coordination with the Centre for Economics and Business Research, an economic research and forecasting firm, found that the US generated approximately 37 percent of GDP in 2013 from built assets which is less than the global average of 40% (Wilcox, 2014). The report also measures returns on assets as a measure of GDP, and of that measure, the US is forecast to rank second with 5.7 trillion and China forecast to rank first with 7.4 trillion in 2014, while India, Japan, and Germany are forecast to rank 3rd, 4th, and 5th respectively in 2014 (Rawlinson & Edwards, n.d.). While the US performs well overall, the trend for growth in built assets is sluggish. "...the US needs to review the condition and use of its current assets and be strategic about its new asset creation in order to maintain its competitiveness and improve performance over the next decade" (Rawlinson & Edwards, n.d.). It is clear, the US needs to invest more in their infrastructure and this report supports that assumption.

View the infographic here.

View the full report online here.

Download the full report here.


Built assets contributed $27 trillion to global GDP during 2013. (2014, May 7). Retrieved May 25, 2014, from Center for Economics and Business Research website:

Rawlinson, S., & Edwards, C. (n.d.). Global Built Asset Performance Index 2014. Retrieved May 25, 2014, from ARCADIS website:

Wilcox, K. (2014, May 20). Report Examines Role of Infrastructure on GDP. Retrieved May 25, 2014, from Civil Engineering website:

Least Squares

Mathematics is a field of study many people who are not exposed to it often find as being either frustrating or for lack of a better word…boring. This may be due to a lack of understanding of the subject on their part coupled with a lack of realization of how important mathematics is in the world. One thing a college professor told me during one of my courses was that, “…math is not difficult, it has a strict set of rules, and as long as you follow those rules, you will do well in the subject…” His statement is quite true, but whether or not math is difficult is more of a personal opinion rather than a fact. It is true however, we must follow the rules and the solutions to the problems have no choice but to appear and make themselves known, which is quite a beautiful thing. But as with everything in life, even this statement is not entirely factual. When solutions to problems don’t make themselves known, mathematics has come up with a solution for that also, and it’s with linear algebra and least squares method that we can come up with a solution. During my recent course in linear algebra I found this to be quite remarkable, because not only did this allow us to come up with a solution to the problem, it allows for the prediction of future events. A statistics or regression analysis course will also study this topic, but the focus here will be in relation to linear algebra and it will be on the broadest sense.

In linear algebra, a common equation used is Ax = b, in fact this equation is one of the foundations of linear algebra, which is known as the matrix equation. So it’s when we cannot get a solution to this matrix equation that we implement the least squares method. Which gives us a good approximation for the solution we seek. Completing a few of these problems in which a professor assigned to me, I really began to see the power of this least squares method. One can determine the future profits of an airline, biomass growth, the list goes on.

Here is a summary that I wrote about the least squares problem, where x is a vector, while x is a unit vector and likewise for b& b:

…when we were faced with an over-determined system of equations Αx = b, we simply gave up and said “the system has no solution” or “the system is inconsistent”, the points are not collinear. What the least squares method seeks to do is to find an xthat minimizes the error or distance with relation to b. This gives us a solution to the problem, even though it is not an exact solution; it is the “best approximation” of a solution to the problem. The definition of this problem given by David C. Lay in his textbook entitled, Linear Algebra and its Applications is:

If Α is m x n and b is in Rm a least squares solution of Αx = b is an x in Rn : || b - Αx || ≤ || b - Αx || for all x in Rn

As Lay also points out, no matter what x is selected the vector Αxwill always be in the column space of Α, Col(Α), As we will see this justifies our use of least squares. The solution to least squares begins with using The Best Approximation Theorem to the subspace Col(Α), so let

b = proj Col(A) to b

Since there is a b in the Col(Α) and an in Rn we arrive at Αx=b because Αx=b is consistent So deriving now by orthogonal decomposition and  AT (b- Αx ) = Ο then by expanding the equation we arrive at ATb- ATx = Ο and then through algebraic manipulation we have AT Αx = ATb which represents our normal equations for Αx = b The solution to which is x.  Wrapping this all up we have AT Α which is an invertible square matrix when the columns of Α are linearly independent.

For our case x = (AT A)-1 ATthus resulting in the least squares error for approximation || b - Αx ||. This problem has some remarkable properties for mathematics and after completing a few of these problems one can see the power math has when explaining the world around us and this problem is a classic example of that power…

The reason I am writing about this is because for me, this was the most intuitive application I have found in a math course and it proves how math applies to the world in so many different ways.


Bentz, Ryan (2014). Least Squares Summary. Blackwood

Echeverria, P. (n.d.). Orthogonal Projections. Instructor Notes.

Lay, D. C. (2012). Linear Algebra and Its Applications. Upper Saddle River: Addison Wesley.

Simplicity in Design Reaps Benefits to Those Who Need Clean Drinking Water

Having access to fresh drinking water is something that Americans take for granted on a daily basis. All one needs to do is go to their kitchen or bathroom and turn the faucet on. Literally at the flip of a switch, access to clean drinking water. Now on the other end of the spectrum imagine having to walk every day for hours a day just to get water, water that is not even suitable to drink. Because of this, there is no time for school or work. This is the plight of many in Ethiopia and other countries around the world. But as Joseph Flahetry of Wired Magazine found, one man came up with an ingenious solution to this problem. This solution so simple and effective which was designed by Arturo Vittori is a basket that stands roughly 9 meters (30ft) tall and uses condensation to collect water out of the atmosphere. The WarkaWater tower has an exoskeleton made of  juncus or bamboo while the mesh container that collects the water is similar to that of produce bags commonly used in packaging oranges (Flaherty, 2014).

Image: Arturo Vittori

According to Flaherty the development of this project has taken two years and currently Vittori is seeking " financial rainmakers who’d like to seed these tree-inspired structures across the country," the cost for the completed tower is around $500 dollars and takes roughly a week to complete by a group of four and it can reasonable collect up to 25 gallons of fresh drinking water per day (Flaherty, 2014).

Be sure to check out Flaherty's full article here.


Flaherty, J. (2014, March 28). A Giant Basket That Uses Condensation to Gather Drinking Water. Retrieved March 29, 2014, from Wired Magazine website:

Warkawater. (2012). Retrieved March 29, 2014, from Architecture and Vision website:

The New Spring, Brought To You By Climate Change, In Five Charts

The climate change debate continues to provide for regular discourse among Americans. No matter what side you fall on, after reading this article by Katie Peek, a Popular Science contributor, you’ll find the evidence she presents is compelling. Something is going on with respect to the plants, animals and climate change. Despite the specific causes, which leaves room for further debate, I tend to agree with science and the theory behind climate change in its current form. Climate change is being significantly influenced by man. Peek explains in her article with the charts that she presents, earlier bloom time trends are happening and are as a result of climate change. I particularly like the Cherry tree bloom times that have been compiled by Osaka Prefecture University and have been recorded since approximately 800 A.D. (Peek). According to the chart, the trend for earlier bloom times begins approximately during the late 1800’s and makes a significant drop towards earlier bloom times during the early part of the 20th century. Check out the article and see how Peek shows the correlation between plants, animals and climate change. Her evidence can be quite compelling considering how simple the argument is that she presents. Read the full article here on Popular Science.