Figures 7.2 and 7.3 Goings on in the space-time aquarium

figures

code

To make spacetime lines we need 3D plotting capability, for which I used plot3D and plotly.

Code

library(dplyr)
library(plot3D)

I also jerry-rigged a simple CSV file format, which looks like the dataframe below.

Code

time_space_data <- read.csv("tg-day-in-the-life.csv")
locations_0 <- unique(select(time_space_data, x, y)) |>
  mutate(id = 1:5, t = 0)

locations_24 <- locations_0 |>
  mutate(t = 24)

knitr::kable(time_space_data |> head())

x	y	t
5	5	0.00
5	5	7.50
16	20	8.25
16	20	12.50
14	18	12.60
14	18	13.40

Not tremendously interesting, but you can imagine additional attributes describing what each \((x,y,t)\) triple is and before you know it you’ll be dealing in geotemporal atoms, although… the instantaneity implied in this representation would be rather questionable. However, the point here isn’t to invent a geotemporal information system, just to make some spacetime plots, so…

The plot3D functions aren’t the most straightforward to use, but after some experimentation I came up with the following two pictures. First… a classic ‘day in the life’ plot.

Code

lines3D(time_space_data$x, time_space_data$y, time_space_data$t, 
        xlim = c(min(time_space_data$x) - 2, 
                 max(time_space_data$x) + 2),
        ylim = c(min(time_space_data$y) - 2, 
                 max(time_space_data$y) + 2),
        xlab = "x", ylab = "y", zlab = "Time, t",
        col = "#00000080", lwd = 2, alpha = 0.5, 
        phi = 25, theta = 60, bty = "g", scale = FALSE)

points3D(locations_0$x, locations_0$y, locations_0$t, 
         add = TRUE, col = "black")

arrows3D(locations_0$x, locations_0$y, locations_0$t, 
         locations_24$x, locations_24$y, locations_24$t, 
         add = TRUE, lty = "dashed", lwd = 0.5, col = "black")

And second, a ‘meeting’ plot, where a collection of meeting participants converge into a ‘bundle’ in one place over a period of time.

Code

time_space_data <- read.csv("tg-meeting.csv")

trace <- time_space_data |> 
  filter(id == 1)

lines3D(trace$x, trace$y, trace$t, 
        xlim = c(-6, 6), ylim = c(-6, 6),
        xlab = "x", ylab = "y", zlab = "Time, t",
        col = "black", lwd = 1, phi = 25, theta = 60, 
        bty = "g", scale = FALSE)

for (i in 2:8) {
  trace <- time_space_data |> filter(id == i)
  lines3D(trace$x, trace$y, trace$t, add = TRUE,
          xlim = c(-6, 6), ylim = c(-6, 6),
          col = "black", lwd = 1)
}

Code

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