Tag: error

Zeitpyramide: When Maths and Art Disagree

In 1993, the German city of Wemding celebrated its 1200 anniversary.
They decided to start a long-term art project. Every decade, they would place a concrete block on a base. After adding 120 blocks, the pyramid would be complete.

zeitpyramide-original-120-blocks

The only problem is that the pyramid will be completed in the year 3183. Which is only 1190 in the future. Not 1200. The project made a basic mathematical error, called the picket fence error. For a picket fence of n elements, you need to have n+1 posts.

Instead of waiting for the first decade to complete before placing the first block, they started immediately. This is like putting the first candle on the birthday cake on your child’s actual day of birth.

Matt Parker pointed out this error during his visit to the placement of the fourth block in 2023. He also proposed an alternative design that would take 121 blocks to complete. Unfortunately, his design is not a pyramid and would be 19.8 meters tall. That is certainly not safe in a storm.

zeitpyramide-matt-parker-121-blocks

There must be a better design. I took 121 of my beloved LEGO bricks and started on a seven-by-seven base. After some experimentation, I came up with a beautiful pyramid that is only one block taller than the original design. It is still a proper pyramid with complete symmetry.

zeitpyramide-bartneck-121-blocks

We can only speculate what Manfred Laber, the artist, had in mind. According to Barbara Schlecht, head of the Zeitpyramide trust, Mr. Laber was fully aware of the consequences of his design. It is certainly much easier to design a sculpture with 120 bricks since it is divisible by 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120. 121, on the other hand, is only divisible by 1,11 and 121.

When public projects make glaring mistakes, they invite schadenfreude. We can speculate that Manfred Laber decided to sacrifice the opportunity to set a block at the beginning and at the end of the 1200 years period for having a direct relationship between the 120 blocks and the 1200 years.

There are alternative pyramid design for 121 blocks. He could have also decided to only place the foundation in 1993. In any case, this art project has become famous not for its original concepts, but for the controversy around its maths. Which is unlikely to have been the intention of the artist.

Comparison of color measurement accuracy of ColorMunki Design and FRU WR-10QC Colorimeter

Review of the measurement accuracy of the ColorMunki Design and the FRU WR-10.

I am working on a colour project and had purchased the WR10 colorimeter to complement my long serving work horse, the X-Rite Color Munki Design. My ColorMunki is already several years old and I was concerned that its accuracy might have declined. When I measured several hundreds of samples, I noticed that both colorimeters gave me considerably different LAB values.

To determine which device was closer to the truth I measured the 48 defined colours of Datacolor’s SpyderCHECKR 48. I calculated the absolute error both devices made. The results of a paired-sample t-test showed that the ColorMunki is producing significantly less measurement errors on L (t(47)=-9.229, p<0.001), L (t(47)=-4.590, p<0.001) and L (t(47)=-4.871, p<0.001). However, both devices measure colours that are significantly different from the target colour of the SpyderCheckr card on all three measurements. Figure 1 shows the means and standard deviation for all measurement errors.

Figure 1: Mean and Standard Deviation of all measurements for both devices.

There does seem to be some structure in the errors that WR-10 is producing. Have a look at the heat map (Figure 2). The data for my little experiment is available at the Open Science Framework (DOI: 10.17605/OSF.IO/UWEFD).

Figure 2: Heat Map of the absolute errors

Although both devices show some significant deviation from the original, it is not far off from what can be expected of devices in this price range. The ColorMunki Design produces significantly better results than the FRU’s WR-10QC.