Thanks for your blog! Interesting to play with thought experiments. Say you have 2 kg of water. There is a rational part you can take away so that you can't measure the difference between √2 kg of water and what remains. Up to arbitrary precision all numbers are commensurate with each other.
Also, if I understand it correctly, if you swap our 10 based numeric system for a pi based numeric system, the set of values that are incommensurate changes.
How could one design an experiment that proves Pythagoras wrong?
Thanks for your blog! Interesting to play with thought experiments. Say you have 2 kg of water. There is a rational part you can take away so that you can't measure the difference between √2 kg of water and what remains. Up to arbitrary precision all numbers are commensurate with each other.
Also, if I understand it correctly, if you swap our 10 based numeric system for a pi based numeric system, the set of values that are incommensurate changes.
How could one design an experiment that proves Pythagoras wrong?