how can we pop up a Tk window to display the temporary results of a
program?

If our program is running and displaying its intermediate calculations,
instead of showing the final result at the end, i hope to have a Tk
window just to show the semi-final results.

would there be a simple way, just using a text box or something?

right now i have:

require 'tk'

root = TkRoot.new {title "Ex1"}
TkLabel.new(root) do
  text "Hello, world!"
  pack("padx"=> 15, "pady" => 15, "side" => "left")
end
Tk.mainloop

 [and my program]

but the program won't run until i close the Tk window generated.
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