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Interesting and entertaining article. Thanks for the reminders that there are reasons for the 'unreasonable'. My thoughts on the radian are that it is linked to an irrational number which is never exactly used. A ninety degree angle would be 1.5707963... radians. Perhaps we could choose the arc second because it is an exact number division of the full circle and makes realization of measurements with closure much easier. But then a right angle would be 324,000 arcseconds. Perhaps we should discuss the gon or grad. But all are just the acknowledgement that a circle is the absolutely closed angle and can be divided. We could call this a circuit or an orbit. So then a right angle would be a quarter circ or orb.
Thanks again Ben.