Architecture and Plate Tectonics

In its third episode ("When Knowledge Conquered Fear") the recent version of “Cosmos” by Neil deGrasse Tyson featured an interesting segment involving Robert Hooke, Edmond Halley, Isaac Newton and the discovery of gravity.  Tyson’s treatment of this subject neglected to mention Hooke’s discovery of the funicular or catenary form, which is a unique insight dependent on gravity.   Hooke’s revelation anticipates and incorporates gravity. 

Hooke revealed his discovery describing how a masonry arch works in a teasing anagram with a succinct introduction:   "The true Mathematical and Mechanical form of all Manner of Arches for building, with the true butment necessary to each of them. A Problem which no Architectonic writer hath yet attempted, much less performed. abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux."

Hooke did not provide a translation of this anagram during his lifetime.  It was finally revealed by his executor in 1705:  "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum--As hangs a flexible cable, so inverted, stand the touching pieces of an arch."  This insight has been the essential summary of Masonry Science and arch design since its 1705 revelation.

Hooke’s use of the word “Architectonic” in the preface to his anagram is interesting if we consider its etymology and related words and phrases.  Architectonic (adj.)  1:   of, relating to, or according with the principles of architecture. 2:  having an organized and unified structure that suggests an architectural design.  From “Arch” (arch) + “tectonic” (building). 

“Plate tectonics” is a geological term used to describe the movement of rigid sections of the earth’s crust around the planet.  If an arch is considered as completely as possible, it is a sphere.  Plate tectonics may be viewed as a dynamic planetary architectonic.  Plates are divided by three types of boundaries: divergent (crust is created), subduction (crust is destroyed) and shear boundaries (crust slides against crust).

Tectonic plates slide against each other in the manner of conjugate shearing.  If the creation and destruction of crust are neglected, one is left with a series of plates which will conjugate shear around a spherical surface.  How can one design plates which will conjugate shear around a spherical surface?

Gratis deGrasse Tyson, for neglecting Hooke’s flexible cable hanging under gravity and allowing me to ramble on about arches, architects, architectonics and plate tectonics.  

"IKOS," a cool toy idea

My business partner, Mike Wong, has been mentoring a group of three high school students in Park City, Utah.  They have  developed one of my designs as a children's toy, and are doing a "kickstarter" campaign in an effort to raise capital for tooling molds and an initial production run.

If you've followed this blog, and/or have any interest in an interlocking modular design used to make spheres, then check out their video.  Go ahead and pledge an amount, get some of these cool toys!  These kids have done a great job and we hope they succeed.  Just click on this link.

On behalf of team IKOS, we thank you for your support!

Thor's Hero Shrew and masonry design

I have written a few times on this blog about masonry in nature, as evidenced by several species of animals, including seahorses.  A couple years ago a new species of shrew was discovered in the Democratic Republic of Congo, whose spine exhibits incredible strength and toughness.  “Thor’s Hero Shrew” is worth taking a look at from the perspective of interlocking masonry design.

As discussed in this article, “Scientists at Chicago's Field Museum and international collaborators have described a new species of Hero Shrew – the mammal with the most bizarre lower spine on Earth. The interlocking vertebrae of the Hero Shrew render the spine four to five times more robust relative to body mass, a condition not found in any other mammal. The spine has been an enigma to evolutionary biologists, with no known adaptive significance.

This new species of Hero Shrew, named Scutisorex thori, possesses features that may represent intermediate character states between the only other known Hero Shrew species (Scutisorex somereni), and other shrews. In addition, a novel hypothesis for the function of the animal's expanded lower spine has been proposed. The study will be published July 24, 2013 edition of Biology Letters.

First discovered in 1910, the Hero Shrew's most notable feature was not revealed for another seven years, when a specimen was dissected to reveal the most peculiar backbone of any mammal. The remarkable spine of the Hero Shrew is unique among mammals, in that the lower vertebrae have multiple lateral processes that interlock with the processes of neighboring vertebra. The arrangement, along with surrounding musculature, affords the animal extraordinary strength, so much so that the Hero Shrew has traditionally been worn as a talisman.

"This shrew first came to light when explorers came to the eastern part of the Democratic Republic of Congo," said Bill Stanley, Director of Collections and zoologist at the Field Museum. "The explorers watched in amazement as a full-grown man stood on the back of the Hero Shrew, and the animal walked away, unharmed."

Until now, there have been no other species of this bizarre shrew. The new species described in this study represents a possible intermediate between the original Hero Shrew and other shrews, since is possesses an interlocking spine, but with fewer lower vertebrae and lateral processes than the first Hero Shrew species.

"You and I have five lumbar vertebrae," said Stanley. "And so do most other mammals, but the Hero Shrew at least 10. Scutisorex thori has eight vertebrae, and fewer lateral processes than the original species."

The specimen of the new Hero Shrew species was collected in the lowland forest near the Tshuapa River in the Democratic Republic of Congo. Based on the observations of one of the co-authors on the study, the authors present a novel hypothesis for the functional significance of the spine of Scutisorex thori; they suggest that these shrews position themselves between the trunk and leaf bases of Palms, and use their unique spine to exert force and gain access to concentrated sources of beetle larvae that are otherwise protected from predation. The same adaptation may allow these animals to lift logs or rocks to access invertebrates – a food resource that remains unavailable to many other mammals.

The specimen of Scutisorex thori now residing at The Field Museum is a holotype, meaning that it will be the standard for identifying other members of the species. The new species is named in honor of Thorvald "Thor" Holmes, Jr. of the Humboldt State University Vertebrate Museum, at the suggestion of Bill Stanley, who did his graduate work there. The suggested common name is "Thor's Hero Shrew", appropriately invoking Thor, the god of strength in Norse mythology.

"The Age of Discovery is not over," said Stanley. "In fact, discoveries such as these happen in natural history collections, like the ones that we have at The Field Museum. In addition, hypotheses such as the one that we've generated concerning the functional significance of the Hero Shrew's spine fuel the scientific machine. We can't wait to see the results of further scientific studies that test the ideas presented in this article."

As Wikipedia states, “The structure of Thor's hero shrew's cranium and vertebrae suggest that it may be descended from an evolutionary intermediate between the hero shrew and other shrews. Its existence may help explain the evolution of the hero shrew which, Stanley explains, has historically been cited as an excellent example of punctuated equilibrium, a theory that holds that species sometimes evolve very rapidly in short periods of time after long periods of stability. The existence of an intermediate species hints at a more gradual or incremental evolution for the hero shrew's extreme specialization.”

It appears to me that Thor’s hero shrew utilizes an interlocking masonry-like arrangement to achieve the incredibly high spinal strength it possesses.  The ability to sagitally flex its spine would seem to indicate conjugate shearing between lumbar vertebrae, similar to the seahorse tail strength mechanism.

Nature is the Grand Master of design.  Thor’s hero shrew is an exemplar of masonry technique used to achieve high strength and toughness.  Its discovery is perhaps an omen of punctuated equilibrium in the evolution of masonry as used by man.

Design Flexibility of triangular block

In this blog I have written much about the “design flexibility” inherent to a triangular block masonry design system.  What do I really mean by this “design flexibility”?

Let’s start with the basics: a sphere can be made.  This is done by approximating the pattern generated by a regular polyhedron, and filling the polygons (which comprise the polyhedron) with triangles.  For example, five triangles can form a pentagon, 6 triangles can form a hexagon; hexagons and pentagons can combine to form a truncated icosahedron (like a soccer ball).

Half of a sphere can be used to construct a dome, or hemisphere. 

The spacing between blocks can be manipulated to “stretch” the contour or topography of a hemisphere into a catenary shape, like a catenary dome (thicker and/or thinner mortar joints can achieve this).

Furthermore, triangular blocks can be used to build a cylinder, as discussed here.  A cylinder –known to mathematicians as a right circular cylinder- can be bisected parallel to its axis of rotation, to form a rounded or Roman arch. 

Sections of round cylinders can also be used to build arches with more than one center.  This adds extensive additional design flexibility, and gives the architect/designer many more options to choose from when building with triangular masonry.

Further still, the proportions of the triangular block can be chosen such that the helicity of the spiral edge allows round arches to intersect at right angles.  This is important because many people “don’t want to live in a dome.”  Domes are often associated with hippies chasing utopian dreams, faulty buildings left leaky, stinky and smelling of armpits and patchouli.  Many “simply could not live in a round dome, it’s so 1960’s and I’m stuck on this commune and it’s unsanitary and my God I have to take a shower now.”  The perceived failure of a counter-cultural revolution takes its toll on architectural design (sorry modern-day hippies, I don’t mean to offend you; I am talking about public perception).

My point is that most people in western society prefer to be in a square-cornered building with right angles and rectilinear orthogonal design.  It’s not called the wrong angle; it’s called the right angle.  We can accommodate the need for right angles in a building, and do so gracefully and beautifully, around a central hemisphere or dome.

What other things can we provide in terms of “design flexibility”?  How can domes be used to make buildings that are not necessarily round?  The key to this is to use many smaller domes to fill a larger floor plan.  If we consider domes (or spheres, for that matter) and how they can be placed close together, then there are essentially two types of closest packing which are useful for the architect and designer.  There is cubic packing and there is hexagonal packing.  Cubic packing is less efficient than hexagonal packing, as it uses up more free space, or creates a larger interstitial gap between adjacent domes.

The interstitial gap between domes is a curved 3 or 4-sided shape (hexagonal packing creates 3-sided shapes; cubic packing creates 4-sided shapes).  These shapes can be made into a “pedentive” which provides continuity between adjacent domes in a structure.  A pedentive is traditionally how a round domed roof is placed (for example) on a square or hexagonal building; it fills the gap between a round dome and the corners of the building.

If several smaller domes are used to make a roofing system for a large building, they may be arranged as cubic-packed or hexagonally-packed roofing units.  The pedentives between adjacent domes can be placed atop columns or posts, creating a beautiful open space with elegant symmetry and arches describing a high strength, symmetrical and robust roofing arrangement made entirely of triangular block.

This is a photograph of cubic-packed domes with arches and pedentives as designed and built by Guastavino, using his catalan arch method which he employed in the 19^th century.  This particular example is at the State Education Building in Albany, New York.  One can see how elegantly smaller domes can be used to assemble into beautiful large buildings.

Summing up, we can make spheres, domes, catenary domes, cylinders, arches, many-centered arches, arches at right angles, and finally use a multiplicity of smaller domes, arches and columns to create a much larger floor plan.  All of these features taken together represent a very broad spectrum of “design flexibility”  provided by triangular masonry block.

Perception and reality of affordable housing

Introducing a new construction system or method to the public is a complex and complicated process.  Beyond the engineering, economic and design factors, there are social and cultural issues which need to be addressed.  Creating beautiful, high-performance, affordable structures may be doomed to failure if social context is ignored.  The most well intended efforts may fail precisely because of those good intentions.

Several years ago I was in discussion with members of a well known non-profit organization which provides houses for people.  This organization does wonderful work and is well known in the US and internationally.  Its work is championed by a former US president.   We were talking about the possibility of them using my masonry system to provide houses for people who could not otherwise afford decent housing.

The members of this group understood all the benefits of this innovative masonry system: that it is very high-strength, provides extensive design flexibility, is environmentally appropriate, fireproof, tornado and hurricane resistant, very affordable, etc.   Still, they were quick to say that it would be a mistake for me to use their organization as a means to introduce this advanced construction method to the public and to the construction marketplace.

The members of this non-profit organization said that “folks will think: ‘that’s what poor people live in’”.  If we use your system for housing, it will create a stigma and nobody will want to live in it, they explained.  It would not matter how great or beautiful or efficient or advanced a building was, if it was seen as ‘charity housing’ then nobody would covet the design, quite the opposite; people would associate a design with welfare recipients and poor people.

Instead, this group urged me to work with top architects, designers and planners to introduce this system as a high-end architectural feature.  Put a high price tag on it and people will want it, it will be coveted.   This group that builds houses for homeless people was telling me that in order to really help poor homeless people I should introduce this system to exclusive gated communities and their very wealthy occupants.  It was hard to escape the irony of their truth.  Perception matters.

Since these discussions (several years ago) there has been an interesting development in housing, the “tiny home” movement.  This movement promotes the use and acceptance of people living in much smaller homes than usual for the US.  The tiny home movement is seen as a response to the increasingly large homes that were being built up until the financial crisis of 2008, which was created largely by the sub-prime mortgages that fueled this type of construction, commonly called “McMansions.” 

Does the tiny home movement allow the possibility of a new construction method to create affordable housing without being doomed by the stigma of association?  Frankly, I don’t know.  The vast majority of US citizens do not live in tiny homes.  The tiny home movement remains far from mainstream and is viewed as something of an oddity by most (“How can someone live in something so small?”).   What Americans consider a tiny home is the average size of a house in much of the rest of the world (as the recent economic recovery strengthens here in the US, the size of our houses is increasing again also).

By making this system available on the open marketplace, it will provide the option for the homeowner to create a better house for less money, without any government or non-profit subsidy or associated stigma.  The economics of concrete block production mean that once these block are being made, they will be available to provide inexpensive housing, as soon as they are made.  We do not need to ‘ramp up’ to an economy of scale in order to make this high-performance masonry system affordable; it will be affordable as soon as it is produced by a block manufacturer.  This is the nature and the essential advantage of the concrete block industry.

We are a country that shops at Wal-Mart.  We love a great deal and we love saving money.  The market will speak, and I plan to listen.  Whether the customer wants 300 square feet or 3,000 square feet for their home, we can provide it better, cheaper with this masonry system.  Perhaps the best way to help the poor is by providing better products at lower prices.  This fact may help with the challenges posed by public perception.