A quick zoom in shiny makes one lose control

You can use debounce to filter too quick input changes :

library(shiny)
library(dplyr)
library(ggplot2)

ui <- fluidPage(
  tags$script(
    '$(document).on("keyup", function(e) {
    if(e.keyCode == 38){
    Shiny.onInputChange("up", Math.random());
    }
    if(e.keyCode == 40){
    Shiny.onInputChange("down", Math.random());
    }
    });'
  ),
  uiOutput("whole_page")
)

server <- function (input, output, session) {
  min <- 0
  max <- 1000000
  view_size <- reactiveVal(max - min)
  view_center <- reactiveVal(mean(c(max, min)))
  position <- reactiveVal(c(min, max))
  
  observeEvent(c(view_size(), view_center()), {
    from <- (view_center() - (view_size() / 2))
    to <- (view_center() + (view_size() / 2))
    c(from, to) %>% position()
  })
  
  output$whole_page <- renderUI({
    fluidPage(
      sliderInput("slider", "range:", min = min, max= max, value = position(), step = 1),
      plotOutput("plot")
    )
  })
  
  output$plot <- renderPlot({
    ggplot(data = tibble(pos = position())) +
      geom_point(aes(x = pos, y = 0))
  })
  
  observeEvent(input$slider, {
    input$slider %>% position()
  })
  
  observeEvent(position(), {
    position() %>%
      mean() %>%
      view_center()
    position() %>%
      diff() %>%
      view_size()
  })
  
  up_d <- debounce(reactive({input$up}),500)
  down_d <- debounce(reactive({input$down}),500)
  
  observeEvent(up_d(), {
    (view_size() / 2) %>%
      view_size()
  })
  
  observeEvent(down_d(), {
    (view_size() * 2) %>%
      view_size()
  })
}

shinyApp(ui, server)

Waldi's answer is exactly what I was looking for. However, I have done other tests and I want to share this one if it can be useful to someone. I replaced the slider with a second graph like a global view and a zoomed view:

library(shiny)
library(dplyr)
library(ggplot2)

ui <- fluidPage(
    tags$script(
        '$(document).on("keyup", function(e) {
    if(e.keyCode == 38){
    Shiny.onInputChange("up", Math.random());
    }
    if(e.keyCode == 40){
    Shiny.onInputChange("down", Math.random());
    }
    });'
    ),
    uiOutput("whole_page")
)

server <- function (input, output, session) {
    min <- 0
    max <- 1000000
    view_size <- reactiveVal(max - min)
    view_center <- reactiveVal(mean(c(max, min)))
    position <- reactiveVal(c(min, max))
    
    observeEvent(c(view_size(), view_center()), {
        from <- (view_center() - (view_size() / 2))
        to <- (view_center() + (view_size() / 2))
        c(from, to) %>% position()
    })
    
    output$whole_page <- renderUI({
        fluidPage(
           plotOutput("global_plot", height = "100px"),
            plotOutput("zoom_plot", height = "100px")
        )
    })

    output$global_plot <- renderPlot({
        ggplot(data = tibble(pos = c(min, max))) +
            geom_point(aes(x = pos, y = 0))+
            geom_rect(aes(xmin = position()[1], xmax = position()[2], ymin = 0, ymax = 1))
    })
    
    output$zoom_plot <- renderPlot({
        ggplot(data = tibble(pos = c(min, max))) +
            geom_point(aes(x = pos, y = 0))+
            coord_cartesian(position())
    })
    
    observeEvent(position(), {
        position() %>%
            mean() %>%
            view_center()
        position() %>%
            diff() %>%
            view_size()
    })
    
    observeEvent(input$up, {
        (view_size() / 2) %>%
            view_size()
    })
    
    observeEvent(input$down, {
        (view_size() * 2) %>%
            view_size()
    })
}

shinyApp(ui, server)

Pressing an up/down arrow triggers an observer, which triggers an observer, which triggers an observer, .... When you quickly press an arrow two times the second arrow event is triggered before the first cycle has finished, and this causes a mess.

Here is a lighter version of your server logic, I didn't face any issue with this one:

server <- function (input, output, session) {
  min <- 0
  max <- 1000000
  position <- reactiveVal(c(min, max))
  view <- reactiveVal(list(center = mean(c(max, min)), size = max-min))
  
  observeEvent(view(), {
    from <- with(view(), center - size/2)
    to <- with(view(), center + size/2)
    updateSliderInput(session, "slider", value = c(from,to))
  }, ignoreInit = TRUE)
  
  output$whole_page <- renderUI({
    fluidPage(
      sliderInput("slider", "range:", min = min, max= max, value = c(min,max), step = 1),
      plotOutput("plot")
    )
  })
  
  output$plot <- renderPlot({
    ggplot(data = tibble(pos = position())) +
      geom_point(aes(x = pos, y = 0))
  })
  
  observeEvent(input$slider, {
    input$slider %>% position()
    list(center = mean(position()), size = diff(position())) %>% view()
  })
  
  observeEvent(input$up, {
    with(view(), list(center = center, size = size/2)) %>% view()
  })
  
  observeEvent(input$down, {
    with(view(), list(center = center, size = size*2)) %>% view()
  })
}

shinyApp(ui, server)