13th Sphere of the GreenGrocer

I suppose you are two fathoms deep in mathematics,
and if you are, then God help you, for so am I,
only with this difference,
I stick fast in the mud at the bottom and there I shall remain.
-Charles Darwin

How nice that one would think that, "like Aristotle" Darwin held to what "nature holds around us," that we say that Darwin is indeed grounded. But, that is a whole lot of water to contend with, while the ascent to land becomes the species that can contend with it's emotive stability, and moves the intellect to the open air. One's evolution is hard to understand in this context, and maybe hard for those to understand the math constructs in dialect that arises from such mud.

For me this journey has a blazon image on my mind. I would not say I am a extremely religious type, yet to see the image of a man who steps outside the boat of the troubled apostles, I think this lesson all to well for me in my continued journey on this earth to become better at what is ancient in it's descriptions, while looking at the schematics of our arrangements.


How far back we trace the idea behind such a problem and Kepler Conjecture is speaking about cannon balls. Tom Hales writes,"Nearly four hundred years ago, Kepler asserted that no packing of congruent spheres can have a density greater than the density of the face-centered cubic packing."

Kissing number problem

In three dimensions the answer is not so clear. It is easy to arrange 12 spheres so that each touches a central sphere, but there is a lot of space left over, and it is not obvious that there is no way to pack in a 13th sphere. (In fact, there is so much extra space that any two of the 12 outer spheres can exchange places through a continuous movement without any of the outer spheres losing contact with the center one.) This was the subject of a famous disagreement between mathematicians Isaac Newton and David Gregory. Newton thought that the limit was 12, and Gregory that a 13th could fit. The question was not resolved until 1874; Newton was correct.[1] In four dimensions, it was known for some time that the answer is either 24 or 25. It is easy to produce a packing of 24 spheres around a central sphere (one can place the spheres at the vertices of a suitably scaled 24-cell centered at the origin). As in the three-dimensional case, there is a lot of space left over—even more, in fact, than for n = 3—so the situation was even less clear. Finally, in 2003, Oleg Musin proved the kissing number for n = 4 to be 24, using a subtle trick.[2]

The kissing number in n dimensions is unknown for n > 4, except for n = 8 (240), and n = 24 (196,560).[3][4] The results in these dimensions stem from the existence of highly symmetrical lattices: the E8 lattice and the Leech lattice. In fact, the only way to arrange spheres in these dimensions with the above kissing numbers is to center them at the minimal vectors in these lattices. There is no space whatsoever for any additional balls.

So what is the glue that binds all these spheres in in the complexities that they are arrange in the dimensions and all that we shall have describe gravity along with the very nature of the particle that describe the reality and makeup that we have been dissecting with the collision process?

As with good teachers, and "exceptional ideas" they are those who gather, as if an Einstein crosses the room, and for those well equipped, we like to know what this energy is. What is it that describes the nature of such arrangements, that we look to what energy and mass has to say about it's very makeup and relations. A crystal in it's molecular arrangement?

Look's like grapefruit to me, and not oranges?:)

Symmetry's physical dimension by Stephen Maxfield

Each orange (sphere) in the first layer of such a stack is surrounded by six others to form a hexagonal, honeycomb lattice, while the second layer is built by placing the spheres above the “hollows” in the first layer. The third layer can be placed either directly above the first (producing a hexagonal close-packed lattice structure) or offset by one hollow (producing a face-centred cubic lattice). In both cases, 74% of the total volume of the stack is filled — and Hales showed that this density cannot be bettered.....

In the optimal packing arrangement, each sphere is touched by 12 others positioned around it. Newton suspected that this “kissing number” of 12 is the maximum possible in 3D, yet it was not until 1874 that mathematicians proved him right. This is because such a proof must take into account all possible arrangements of spheres, not just regular ones, and for centuries people thought that the extra space or “slop” in the 3D arrangement might allow a 13th sphere to be squeezed in. For similar reasons, Hales’ proof of greengrocers’ everyday experience is so complex that even now the referees are only 99% sure that it is correct....

Each sphere in the E8 lattice is surrounded by 240 others in a tight, slop-free arrangement — solving both the optimal-packing and kissing-number problems in 8D. Moreover, the centres of the spheres mark the vertices of an 8D solid called the E8 or “Gosset” polytope, which is named after the British mathematician Thorold Gosset who discovered it in 1900.

Coxeter–Dynkin diagram

The following article is indeed abstract to me in it's visualizations, just as the kaleidescope is. The expression of anyone of those spheres(an idea is related) in how information is distributed and aligned. At some point in the generation of this new idea we have succeeded in in a desired result, and some would have "this element of nature" explained as some result in the LHC?



A while ago I related Mendeleev's table of elements, as an association, and thought what better way to describe this new theory by implementing "new elements" never seen before, to an acceptance of the new 22 new particles to be described in a new process? There is an "inherent curve" that arises out of Riemann's primes, that might look like a "fingerprint" to some. Shall we relate "the sieves" to such spaces?

At some point, "this information" becomes an example of a "higher form "realized by it's very constituents and acceptance, "as a result."

Math Will Rock Your World by Neal Goldman

By the time you're reading these words, this very article will exist as a line in Goldman's polytope. And that raises a fundamental question: If long articles full of twists and turns can be reduced to a mathematical essence, what's next? Our businesses -- and, yes, ourselves.

The Sound Of Billiard Balls

Intuition and Logic in Mathematics by Henri Poincaré

On the other hand, look at Professor Klein: he is studying one of the most abstract questions of the theory of functions to determine whether on a given Riemann surface there always exists a function admitting of given singularities. What does the celebrated German geometer do? He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws. He connects two of its points with the two poles of a battery. The current, says he, must pass, and the distribution of this current on the surface will define a function whose singularities will be precisely those called for by the enunciation.

It is necessary to see the stance Poincaré had in relation to Klein, and to see how this is being played out today. While I write here I see where such thinking moved from a fifth dimensional perspective, has been taken down "to two" as well as" the thinking about this metal sheet.

So I expound on the virtues of what Poincaré saw, versus what Klein himself was extrapolating according to Poincaré's views. We have results today in our theoretics that can be describe in relation. This did not take ten years of equitation's, but a single picture in relation.

Graduating the Sphere

Imagine indeed a inductive/deductive stance to the "evolution of this space" around us. That some Klein bottle "may be" the turning of the "inside out" of our abstractness, to see nature is endowably attached to the inside, that we may fine it hard to differentiate.I give a example of this In a link below.



While I demonstrate this division between the inner and outer it is with some hope that one will be able to deduce what value is place about the difficulties such a line may be drawn on this circle that we may say how difficult indeed to separate that division from what is inside is outside. What line is before what line.

IN "liminocentric structure" such a topology change is pointed out. JohnG you may get the sense of this? All the time, a psychology is playing out, and what shall we assign these mental things when related to the sound? Related to the gravity of our situations?

You see, if I demonstrate what exists within our mental framework, what value this if it cannot be seen on the very outskirts of our being. It "cannot be measured" in how the intellect is not only part of the "sphere of our influence" but intermingles with our reason and emotive conduct. It becomes part of the very functions of the abstractness of our world, is really set in the "analogies" that sound may of been proposed here. I attach colour "later on" in how Gravity links us to our world.

I call it this for now, while we continued to "push for meaning" about the nature of space and time.

Savas Dimopoulos

Here’s an analogy to understand this: imagine that our universe is a two-dimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.

While of course I highlighted an example of the geometer in their visual capabilities, it is with nature that such examples are highlighted. Such abstractness takes on "new meaning" and settles to home, the understanding of all that will ensue.

The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.

It is of course with this understanding that "all the geometries" following from one another, that we can say that such geometries are indeed progressive. This is how I see the move to "non-euclidean" that certain principals had to be endowed in mind to see that "curvatures" not only existed in the nature of space and time, that it also is revealed in the Gaussian abstracts of arcs and such.

These are not just fixations untouched abstractors that we say they have no home in mind, yet are further expounded upon as we set to move your perceptions beyond just the paper and thought of the math alone in ones mind.

Felix Klein on intuition

It is my opinion that in teaching it is not only admissible, but absolutely necessary, to be less abstract at the start, to have constant regard to the applications, and to refer to the refinements only gradually as the student becomes able to understand them. This is, of course, nothing but a universal pedagogical principle to be observed in all mathematical instruction ....

I am led to these remarks by the consciousness of growing danger in Germany of a separation between abstract mathematical science and its scientific and technical applications. Such separation can only be deplored, for it would necessarily be followed by shallowness on the side of the applied sciences, and by isolation on the part of pure mathematics ....

Felix Christian Klein (April 25, 1849 – June 22, 1925) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.

See:

Inside Out
No Royal Road to Geometry?

The Geologist and the Mathematician

In an ordinary 2-sphere, any loop can be continuously tightened to a point on the surface. Does this condition characterize the 2-sphere? The answer is yes, and it has been known for a long time. The Poincaré conjecture asks the same question for the 3-sphere, which is more difficult to visualize.

On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year," the first time this had been bestowed in the area of mathematics

I have been following the Poincaré work under the heading of the Poincaré Conjecture. It would serve to point out any relation that would be mathematically inclined to deserve a philosophically jaunt into the "derivation of a mind in comparative views" that one might come to some conclusion about the nature of the world, that we would see it differences, and know that is arose from such philosophical debate.

Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

Previous links in label index on right and relative associative posts point out the basis of the Poincaré Conjecture and it's consequent in developmental attempts to deduction about the nature of the world in an mathematical abstract sense?

Jules Henri Poincare (1854-1912)

The scientist does not study nature because it is useful. He studies it because he delights in it, and he delights in it because it is beautiful.

HENRI POINCARE

Mathematics and Science:Last Essays

8 Last Essays

But it is exactly because all things tend toward death that life is
an exception which it is necessary to explain.

Let rolling pebbles be left subject to chance on the side of a
mountain, and they will all end by falling into the valley. If we
find one of them at the foot, it will be a commonplace effect which
will teach us nothing about the previous history of the pebble;
we will not be able to know its original position on the mountain.
But if, by accident, we find a stone near the summit, we can assert
that it has always been there, since, if it had been on the slope, it
would have rolled to the very bottom. And we will make this
assertion with the greater certainty, the more exceptional the event
is and the greater the chances were that the situation would not
have occurred.

How simple such a view that one would speak about the complexity of the world in it's relations. To know that any resting place on the mountain could have it's descendants resting in some place called such a valley?

Stratification and Mind Maps

Pascal's Triangle

By which path, and left to some "Pascalian idea" about comparing some such mountains in abstraction to such a view, we are left to "numbered pathways" by such a design that we can call it "a resting" by nature selection of all probable pathways?


Diagram 6. Khu Shijiei triangle, depth 8, 1303.

The so called 'Pascal' triangle was known in China as early as 1261. In '1261 the triangle appears to a depth of six in Yang Hui and to a depth of eight in Zhu Shijiei (as in diagram 6) in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in the eleventh century' (Stillwell, 1989, p136). They used it as we do, as a means of generating the binomial coefficients.

It wasn't until the eleventh century that a method for solving quadratic and cubic equations was recorded, although they seemed to have existed since the first millennium. At this time Jia Xian 'generalised the square and cube root procedures to higher roots by using the array of numbers known today as the Pascal triangle and also extended and improved the method into one useable for solving polynomial equations of any degree' (Katz, 1993, p191.)

Even the wisest of us does not realize what Boltzmann in his expressions would leave for us that such expression would leave to chance such pebbles in that valley for such considerations, that we might call this pebble, "some topological form," left to the preponderance for us in our descriptions to what nature shall reveal in those same valleys?

The Topography of Energy Resting in the Valleys

The theory of strings predicts that the universe might occupy one random "valley" out of a virtually infinite selection of valleys in a vast landscape of possibilities

Most certainly it should be understood that the "valley and the pebble" are two separate things, and yet, can we not say that the pebble is an artifact of the energy in expression that eventually lies resting in one of the possible pathways to that energy at rest.

The mountain, "as a stratification" exists.



Here in mind then, such rooms are created.

The ancients would have us believe in mind, that such "high mountain views do exist." Your "Olympus," or the "Fields of Elysium." Today, are these not to be considered in such a way? Such a view is part and parcel of our aspirate. The decomposable limits will be self evident in what shall rest in the valleys of our views?

Such elevations are a closer to a decomposable limit of the energy in my views. The sun shall shine, and the matter will be describe in such a view. Here we have reverted to such a view that is closer to the understanding, that such particle disseminations are the pebbles, and that such expressions, have been pushed back our views on the nature of the cosmos. Regardless of what the LHC does not represent, or does, in minds with regards to the BIG Bang? The push back to micros perspective views, allow us to introduce examples of this analogy, as artifacts of our considerations, and these hold in my view, a description closer to the source of that energy in expression.

To be bold here means to push on, in face of what the limitations imposed by such statements of Lee Smolin as a statement a book represents, and subsequent desires now taken by Hooft, in PI's Status of research and development.

It means to continue in face of the Witten's tiring of abstraction of the landscape. It means to go past the "intellectual defeatism" expressed by a Woitian design held of that mathematical world.

Stanley Mandelstam

Research Interests

My research concerns string theory. At present I am interested in finding an explicit expression for the n-loop superstring amplitude and proving that it is finite. My field of research is particle theory, more specifically string theory. I am also interested in the recent results of Seiberg and Witten in supersymmetric field theories.

Current Projects

My present research concerns the problem of topology changing in string theory. It is currently believed that one has to sum over all string backgrounds and all topologies in doing the functional integral. I suspect that certain singular string backgrounds may be equivalent to topology changes, and that it is consequently only necessary to sum over string backgrounds. As a start I am investigating topology changes in two-dimensional target spaces. I am also interested in Seiberg-Witten invariants. Although much has been learned, some basic questions remain, and I hope to be able at least to understand the simpler of these questions.

http://www.physics.berkeley.edu/research/faculty/mandelstam.html



Stanley Mandelstam (b. 1928, Johannesburg) is a South African-born theoretical physicist. He introduced the relativistically invariant Mandelstam variables into particle physics in 1958 as a convenient coordinate system for formulating his double dispersion relations. The double dispersion relations were a central tool in the bootstrap program which sought to formulate a consistent theory of infinitely many particle types of increasing spin.

Mandelstam, along with Tullio Regge, was responsible for the Regge theory of strong interaction phenomenology. He reinterpreted the analytic growth rate of the scattering amplitude as a function of the cosine of the scattering angle as the power law for the falloff of scattering amplitudes at high energy. Along with the double dispersion relation, Regge theory allowed theorists to find sufficient analytic constraints on scattering amplitudes of bound states to formulate a theory in which there are infintely many particle types, none of which are fundamental.

After Veneziano constructed the first tree-level scattering amplitude describing infinitely many particle types, what was recognized almost immediately as a string scattering amplitude, Mandelstam continued to make crucial contributions. He interpreted the Virasoro algebra discovered in consistency conditions as a geometrical symmetry of a world-sheet conformal field theory, formulating string theory in terms of two dimensional quantum field theory. He used the conformal invariance to calculate tree level string amplitudes on many worldsheet domains. Mandelstam was the first to explicitly construct the fermion scattering amplitudes in the Ramond and Neveu-Schwarz sectors of superstring theory, and later gave arguments for the finiteness of string perturbation theory.

In quantum field theory, Mandelstam and independently Sidney Coleman extended work of Tony Skyrme to show that the two dimensional quantum Sine-Gordon model is equivalently described by a thirring model whose fermions are the kinks. He also demonstrated that the 4d N=4 supersymmetric gauge theory is power counting finite, proving that this theory is scale invariant to all orders of perturbation theory, the first example of a field theory where all the infinities in feynman diagrams cancel.

Among his students at Berkeley are Joseph Polchinski and Charles Thorn.

Education: Witwatersrand (BSc, 1952); Trinity College, Cambridge (BA, 1954); Birmingham University (PhD, 1956).

Intellectual Defeatism

Just wanted to say it has been quite busy here because of the work having come back from vacation and preparing for my daughter in law and son's twins, which are to arrive any day now.

Intellectual defeatism

This statement reminded me of the idea about what is left for some to ponder, while we rely on our instincts to peer into the unknown, and hopefully land in a place that is correlated somehow in our future.

This again is being bold to me, because there are no rules here about what a schooling may provide for, what allows an individual the freedoms to explore great unknowns for them. For sure education then comes to check what these instincts have provided, and while being free to roam the world, sometimes it does find a "certain resonance" in what is out there.

Is this then a sign of what intellectual defeatism is about?

I want to give an example here about my perceptions about what sits in the valleys in terms of topological formations, that until now I had no way of knowing would become a suitable explanation for me, "about what is possible" even thought this represented a many possibility explanation in terms of outcomes.

Observables of Quantum Gravity

Scientists should be bold. They are expected to think out of the box, and to pursue their ideas until these either trickle down into a new stream, or dry out in the sand. Of course, not everybody can be a genuine “seer”: the progress of science requires few seers and many good soldiers who do the lower-level, dirty work. Even soldiers, however, are expected to put their own creativity in the process now and then -and that is why doing science is appealing even to us mortals.

To Be Bold

One possible way the Higgs boson might be produced at the Large Hadron Collider.


"Observables of Quantum Gravity," is a strange title to me, since we are looking at perspectives that are, how would one say, limited?

Where is such a focus located that we make talk of observables? Can such an abstraction be made then and used here, that we may call it, "mathematics of abstraction" and can arise from a "foundational basis" other then all the standard model distributed in particle attributes?

Observables of Quantum Gravity at the LHC
Sabine Hossenfelder

Perimeter Institute, Ontario, Canada

The search for a satisfying theory that unifies general relativity with quantum field theory is one of the major tasks for physicists in the 21st century. Within the last decade, the phenomenology of quantum gravity and string theory has been examined from various points of view, providing new perspectives and testable predictions. I will give a short introduction into these effective models which allow to extend the standard model and include the expected effects of the underlying fundamental theory. I will talk about models with extra dimensions, models with a minimal length scale and those with a deformation of Lorentz-invariance. The focus is on observable consequences, such as graviton and black hole production, black hole decays, and modifications of standard-model cross-sections.

So while we have created the conditions for an experimental framework, is this what is happening in nature? We are simulating the cosmos in it's interactions, so how is it that we can bring the cosmos down to earth? How is it that we can bring the cosmos down to the level of mind in it's abstractions that we do not just call it a flight of fancy, but of one that arises in mind based on the very foundations on the formation of this universe?

Fathers of Confederation

Robert Harris's painting of the Fathers of Confederation. The scene is an amalgamation of the Charlottetown and Quebec City conference sites and attendees.

Colonial organization

All the colonies which would become involved in Canadian Confederation in 1867 were initially part of New France and were ruled by France. The British Empire’s first acquisition in what would become Canada was Acadia, acquired by the 1713 Treaty of Utrecht (though the Acadian population retained loyalty to New France, and was eventually expelled by the British in the 1755 Great Upheaval). The British renamed Acadia Nova Scotia. The rest of New France was acquired by the British Empire by the Treaty of Paris (1763), which ended the Seven Years' War. Most of New France became the Province of Quebec, while present-day New Brunswick was annexed to Nova Scotia. In 1769, present-day Prince Edward Island, which had been a part of Acadia, was renamed “St John’s Island” and organized as a separate colony (it was renamed PEI in 1798 in honour of Prince Edward, Duke of Kent and Strathearn).

In the wake of the American Revolution, approximately 50,000 United Empire Loyalists fled to British North America. The Loyalists were unwelcome in Nova Scotia, so the British created the separate colony of New Brunswick for them in 1784. Most of the Loyalists settled in the Province of Quebec, which in 1791 was separated into a predominantly-English Upper Canada and a predominantly-French Lower Canada by the Constitutional Act of 1791.
Canadian Territory at Confederation.

Following the Rebellions of 1837, Lord Durham in his famous Report on the Affairs of British North America, recommended that Upper Canada and Lower Canada should be joined to form the Province of Canada and that the new province should have responsible government. As a result of Durham’s report, the British Parliament passed the Act of Union 1840, and the Province of Canada was formed in 1841. The new province was divided into two parts: Canada West (the former Upper Canada) and Canada East (the former Lower Canada). Ministerial responsibility was finally granted by Governor General Lord Elgin in 1848, first to Nova Scotia and then to Canada. In the following years, the British would extend responsible government to Prince Edward Island (1851), New Brunswick (1854), and Newfoundland (1855).

The remainder of modern-day Canada was made up of Rupert's Land and the North-Western Territory (both of which were controlled by the Hudson's Bay Company and ceded to Canada in 1870) and the Arctic Islands, which were under direct British control and became part of Canada in 1880. The area which constitutes modern-day British Columbia was the separate Colony of British Columbia (formed in 1858, in an area where the Crown had previously granted a monopoly to the Hudson's Bay Company), with the Colony of Vancouver Island (formed 1849) constituting a separate crown colony until its absorption by the Colony of British Columbia in 1866.

John A. Macdonald became the first prime minister of Canada.


The shear number of people in the United States at approx. 200 million,can be an reminder of what "we", in the approx. same land mass of Canada can be compared to the United States. Our paltry 36 million "being overshadowed" might be better understood from that perspective.

Happy Canada Day

Coastal Highway Views

Just before entering Malibu along the coastal highway of California.

Mathematical Structure of the Universe

Although Aristotle in general had a more empirical and experimental attitude than Plato, modern science did not come into its own until Plato's Pythagorean confidence in the mathematical nature of the world returned with Kepler, Galileo, and Newton. For instance, Aristotle, relying on a theory of opposites that is now only of historical interest, rejected Plato's attempt to match the Platonic Solids with the elements -- while Plato's expectations are realized in mineralogy and crystallography, where the Platonic Solids occur naturally.Plato and Aristotle, Up and Down-Kelley L. Ross, Ph.D.

Discover Magazine-06.16.2008-Photography by Erika Larsen-Article-"Is the Universe Actually Made of Math? Unconventional cosmologist Max Tegmark says mathematical formulas create reality."

It makes no difference at this point, which mathematics you choose to delve into the new model perceptions, because if one were to see how a projective geometry was built on previous platforms, then how is it we can see the universe in ways that the WMAP shows unless the mathematics could show that there was more to it then an artists picture displayed? You had to know the depth of the artists skill.

It does not mean that you are devoid of the possibilities of venturing where the philosophies of mathematics or science can venture. It is understanding that by taking yourself to a certain position in mind, an indecomposable one, one that is self evident, then it is understood that the deductive/inductive efforts bring you to a peak realization, contained in the "Aristotelean Arche."

This position is the question that one assumes in life, that having exhausted all efforts, and having seen all the information, one is to move their previous stalled position into a "third revolution" of a kind you might say?:)

See:Backreaction: Discover Interview with Tegmark

Also see:Theoretical Excellence

Wildlife at Home

Yes you may of noticed the date is wrong again on the camera. Every time we take the batteries out for charging, we loose that date. It dawned on me at this moment and wondered if there is another internal battery that retains the time, maybe, dead too? I'll have to look.

Anyway this fellow has been sticking around the last couple of days.

When we first looked at this lot about a year an done month ago today, I noticed a lot of markings that looked like claw marks, were in fact bull moose who rub their racks on the trees and leave these marks.




You'll also notice my work table I set up to do the final work on the outside of the house. I was installing a product called Nailite We did a board and batten around the rest of the house. I am really quite pleased tackling this job for the first time.

I just finished about two days ago, and have been working like heck to finish the jobs around here, while preparing for a trip into the states. My wife, myself with three of our older grandchildren are going for a trip to Disney Land.

We had our youngest granddaughter yesterday(she's sure a sweety) for the night, as my youngest son and his wife are due for twins which will be here not to long after we get back from our trip. She needs the bed rest and she is huge, and my boy is getting run ragged. So we have been extremely busy getting things in order.

The pillars in front of the house will be done when I get back and the backdrop to the front door will have a colonial look which we are trying to keep to a cottage look.



The aggregate walkways around the house were done at the end of May. We are please with how this has turned out. Unfortunately, the snow came before we had a chance to pour them last November, after having readied the forms, and compacted the crush.