Crazy Paving

 

This tiling pattern in the uploaded image for a pavement has me intrigued. Normally pavers follow a strict geometric pattern e.g. hexagonal pavers or a combination of hexagonal plus smaller square pavers. There doesn't seem to be any obvious pattern to the tiling shown in the image. It would be labourious if each tile was tailored to fit into its surrounding tiles. So the questions I'm asking are this: is there any pattern in the arrangement of pavers shown and, if not, how was the paving arrrangement using pavers of widely different shapes created in the first place without hand-crafting.

This is a great observation. You have spotted a style of paving that relies heavily on the skill of the installer rather than the repetitive manufacturing of the paver itself.

To answer your questions directly: No, there is no repeating mathematical or geometric pattern here.

The style you are looking at is commonly known as "Crazy Paving," "Flagstone Paving" (specifically irregular flagstone), or "Random Polygonal Paving."

It looks laborious because it is more labor-intensive than laying square bricks, but it does not require hand-crafting every single tile from raw stock.

Here is a breakdown of how this random arrangement is achieved practically and efficiently.

---

1. The Material Arrives pre-"Broken"

The most crucial part of the puzzle is the source material. The masons are not buying large square slabs and cutting crazy shapes out of them.

When you order this type of natural stone (it looks like sandstone or perhaps a slate variety in your image), it arrives on pallets as large, irregular, quarried slabs of varying sizes. They are already in random polygonal shapes straight from the quarry.

2. The "Giant Jigsaw Puzzle" Method

The installation process is essentially solving a giant jigsaw puzzle that has no picture and pieces that weren't originally designed to fit together.

Here is the typical workflow for a professional mason:

• Sorting: The masons will usually sort the stone on the grass nearby, separating very large "hero" pieces from medium pieces and smaller filler pieces.

• Placement Strategy: They start by laying the largest, most attractive slabs first, spacing them out randomly along the path.

• Finding the Fit: They then look at the gaps created between the large slabs. They will go to their sorted piles and hunt for a medium-sized piece whose natural edge roughly matches the curve or angle of the gap they are trying to fill.

• The "Rule of Three": A sign of good crazy paving is that generally, no more than three stones should meet at any one joint. If four corners meet, it creates an ugly "cross" that draws the eye and ruins the random illusion. The masons in your image have done this very well.

3. The "Cheat": On-Site Trimming

You mentioned the worry about "labouriously hand-crafting" every tile. While they try to use the natural shapes as much as possible, they do cut the stone.

However, they aren't cutting the whole shape. They are "trimming to fit."

If a mason finds a piece that fits perfectly on two sides but has a sharp corner sticking out on the third side that blocks the next piece, they will use a diamond-blade angle grinder or a masonry saw to quickly lop off that offending corner.

They only cut what they have to in order to make the puzzle pieces snug.

Summary

The "pattern" you see is not designed beforehand; it is emergent. It arises from the mason making hundreds of small decisions on-site about which rock fits best next to the previous one, combined with minor trimming to tighten the joints.

It is a testament to skilled labor. A poor mason will leave wide, ugly mortar joints because they can't be bothered to find the right pieces or trim them. A skilled mason, like the one who did the path in your image, achieves tight, consistent joints that make the path look cohesive despite the randomness of the shapes.

Number 33, Truman and the Bomb

One might think that the topic of 33 might be more suitable for my Mathematics blog but I don't want to treat 33 in purely mathematical terms here and so I'm posting to this blog. There's a great deal that can be said about the 33 in a non-mathematical context but I want to limit this post's scope by just focussing on Truman and the atomic bomb. Let's begin with Trinity.

Trinity was the code name of the first detonation of a nuclear weapon, conducted by the United States Army on July 16, 1945, as part of the Manhattan Project. The White Sands Proving Ground, where the test was conducted, was in the Jornada del Muerto desert about 35 miles (56 km) southeast of Socorro, New Mexico, on the Alamogordo Bombing and Gunnery Range. The only structures originally in the vicinity were the McDonald Ranch House and its ancillary buildings, which scientists used as a laboratory for testing bomb components. Source. See Figure 1.

Figure 1: Source

So here is our first encounter with 33 in the form of the latitude, 33° N (rounded down to the nearest degree), at which the first atomic test took place. Next we look at the latitudes of the two Japanese cities on which atomic bombs were unleashed. Hiroshima is located at a latitude of 34° 23' N and Nagasaki at 32° 46' N, making for an average of 33° 35' N. Thus we have our second encounter with 33 in the form of the average latitude (again rounded down to the nearest degree) of the two targeted cities. See Figure 2.

Figure 2

Next we'll turn our attention to the person who authorised the bombings. This was of course Harry S. Truman who was the 33rd president of the United States. Now it's getting a little spooky because here we have our third encounter with the number 33 as we count the number of the presidents since George Washington. However, we're not yet finished with Truman.

On October 19, 1945, Truman was given the 33rd degree of the Supreme Council of the Scottish Rite for the southern jurisdiction. He is the only President to have received this distinction, which he considered with satisfaction to be the culmination of his Masonic career. Source.

Definitely spooky and this marks our fourth encounter with 33 surrounding Truman and the atomic tests. On January 20th 1945, Truman became the 34th president but when he was given this Masonic rank he was still the 33rd president. It's interesting to note that Truman regarded himself as the 32nd president when he took office:

Any official list of presidents will show Harry Truman as the 33rd President of the United States. Not everyone agrees with this, however. The most notable dissenter as to the number assigned to the Truman administration was none other than Harry Truman, himself.

Truman, who was not averse to sharing his thoughts on any subject, disagreed with counting Grover Cleveland’s two non-consecutive terms. “If you count the administrations of Grover Cleveland twice because another President held office between Cleveland’s first and second term,” said Truman, “you might try to justify the designation of me as thirty-third President. But then why don’t you number all the second terms of other Presidents and the third and fourth terms of President Roosevelt, and where will you be? I am the thirty-second President.”

Despite this argument, the official proclamation, dated April 13, 1945, issued by President Truman on the death of President Franklin D. Roosevelt referred to Roosevelt as the thirty-second president. Source.

Was Harry trying to be disingenuous? Perhaps. The facts are clear however, and Harry as the (official) 33rd president of the United States authorised the detonation of the first atomic bomb on American soil at the 33rd degree of latitude and later authorised the dropping of atomic bombs on two Japanese cities: one on the 34th degree of latitude and the other on the 32nd degree of latitude, making for an average of 33 degrees. Later that same year he would become a 33rd degree Mason.

The following quote, from Jacques R. Pauwels, author of The Myth of the Good War: America in the Second World War, is a fair assessment of what Truman really was up to: 

Sixty-five years ago, Truman did not have to use the atomic bomb in order to force Japan to its knees, but he had reasons to want to use the bomb. The atom bomb enabled the Americans to force Tokyo to surrender unconditionally, to keep the Soviets out of the Far East and – last but not least – to force Washington’s will on the Kremlin in Europe also. Hiroshima and Nagasaki were obliterated for these reasons, and many American historians realise this only too well.

So Harry murders hundreds of thousands of Japanese civilians, is awarded the highest honour in Freemasonry later in the year and slept well at night for the rest of his life I presume. So it goes. 

Truman found time to relax and rest in his post-presidential years. He was never far from his favourite bourbon and enjoyed clanking glasses with the old friends, political allies, and dignitaries who came through Independence. While his health permitted, he took regular walks around town. He traveled some, including a 1953 auto trip to New York during which a policeman stopped him on the Pennsylvania Turnpike for making an illegal lane change. It was Truman's only attempt at a long drive after leaving the presidency. Harry S. Truman died on December 26, 1972, of old age rather than any specific sickness. Source.