Monday, February 15, 2021

History of the 4th dimension

New paper, by some Brazilians:
The Fourth Dimension: From its spatial nature in Euclidean geometry to a time-like component of non-Euclidean manifolds
José Maria Filardo Bassalo, Francisco Caruso, Vitor Oguri

In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries, like those of Riemann and Minkowski. Particular attention is given to the moment when real time is effectively considered as a fourth dimension, as introduced by Einstein.

This is a nice history of attempts to go beyond three dimensions.

Like other such historical works:

1. There is no mention of Poincare, or the fact that he was the first one to treat time as the fourth dimension, in the context of relativity.

2. The authors go out of their way to attribute credit to Einstein. It is always "Einstein’s Special Relativity".

3. It cites Lorentz, but always to badmouth his conceptual understandings somehow.

I don't want to pick on this paper, as it is just doing what everyone else does. The authors are from Brazil, so there is no good reason for them to be partial to Einstein. But they are.

This is so bizarre. There is no necessity for a historical discussion to get bogged down with issues of credit, but the relativity stories always do, and always give nonsensical reasons for crediting Einstein.

In this case, it says that Lorentz did not understand that the "local time" of an electron he invented in 1895 was really just the time that is local to the electron.

Huh? Isn't that what Lorentz called it?

Lorentz won a Nobel Prize in 1902, in part for his electromagnetic relativity theory, and in part because Poincare recommended that he get it for his ingenious invention of local time. Poincare certainly understood it at the time, even if Lorentz did not fully. Poincare used it as the fourth dimension in 1905.

Einstein adopted the concept of Lorentz's time in 1905, but not as the fourth dimension. He only did that after Minkowski and everyone else used it in 1908. Einstein did not really have any understanding of relativity that was any better than Lorentz's, until he learned Minkowski's in 1908.

I wrote a book about this, but never really found a good explanation for this Einstein worship. Obviously these Brazilians are educated enough that they know the story. They could just read Wikipedia, and see that nearly everything is due to Lorentz, Poincare, and Minkowski. If they were unsure, they could have avoided giving credit to anyone. I don't know why they insist on crediting Einstein for what Lorentz and Poincare published earlier.

One thing I learned from the above paper is that the Italian artist Giotto discovered that the sky was blue about 700 years ago. Byzantine art portrayed a golden sky. Apparently gold symbolized heaven, and the symbolism was more important than the chromatic accuracy. Many older books tell about the sky, but never mention that it is blue.

I don't know what to make of this. Did the sky change color 700 years ago? Did ancient men never bother to look up and notice the sky? Did they not have any blue pigments for making paint? Was it cloudy all the time? I have heard also that ancient men did not notice that the ocean is blue, and described it as other colors. Did they have some mental refusal to accept the color blue? I have no idea.


  1. Short answer:
    Take an art history course.

    Long answer:
    I wouldn't be so sure about the golden sky claims in art history. The fact is that many of the formulas used to create blue paints and dyes (often taken from plants and lichens) often faded over time. Many tapestries from antiquity and the medieval period often show discolored skies. You can also find ancient mosaics from ancient Roman cities that do indeed show the sky as very blue, because the colored glass and natural stone (like lapis lazula)did not fade.

    Byzantine art often used a great deal of gold leaf to lighten artwork due to the nature of how it was displayed, on the ceilings and walls of Byzantine churches/temples which were found in Romanesque architecture, thick walls and arches, with relatively small windows. Much of the light was often produced by torches or lamps, and because of the dim light, reflective treatments were very effective to allow detail to be visible on distant surfaces, and also helping in general to make the rooms seem brighter and golden. The artistic artifact which Christianity considers the 'Halo' actually came from the Byzantine style of putting a gold leafed disk behind the head of saints and angels, this was often used to help designate the holy from the common in artwork that was very stylized and cookie-cutter like (there was almost no differences in facial features). Later on during the Renaissance the gold disk feature became an awkward symbolic relic that worshippers expected to denote the holy, as the artists (like Giotto) were depicting the portrayed people in more detail and in perspective, and flat disk detracted from the depth of the perspective (think Mickey Mouse ears, they are always in the same position no matter which way Mickey is looking) they were trying to achieve. The flat gold disk was replaced with glass like disk (representing a piece of the crystal vault of the heavens) in perspective, with only the tracery edge or 'halo' now visible. There are several famous works you can see where the entire glass like disk is visible, and then later works where only the edge like tracery remains.

    Art often shapes what people imagine spiritual entities to look like more than the actual religious texts which originally inspired the art.

  2. By pure coincidence this you tube clip caught my eye today.


  3. There is quite a bit of Egyptian Sarcophagi (like King Tut's sarcophagus 1325 BC), ceramics and jewelry which are many shades of blue or uses blue lacquers, inlays, stones, umm, sapphires anyone? Does anyone have any idea how long sapphires have been cherished by humanity? How about scarabs which are often depicted blue easily as far back as 2000BCE? The Egyptians go back quite a bit before the Greeks and Romans by many thousands of years. Jews have also venerated a particular blue wool called tekhelet, dyed by a type of sea creature called chilazon which is mentioned in the Torah (last major editing around 539BC), I dare anyone want to tell them they didn't know about blue until 700 years ago. Blue cobalt ores were used in West Asia as far back as 2000BC. I won't begin to touch on how long the Chinese and Japanese have been using blue in pottery (considerably longer than 700 years, try 475BC), because at this point, the entire premise of blue being a recent discovery is demonstrably ridiculous.

    I call bullshit on this VERY poorly researched scholarship by people who clearly are historically illiterate.