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If they are competing with each other such that neither are getting done are they really priorities?

Yes. They are in the important but not urgent quadrant of the Eisenhower matrix.

And yet, if you have two tasks that each take 1 hour, and only 90 minutes until the deadline, only one task will be completed by you, regardless of quadrant, and you will then be reminded that priority is singular.

That scenario moves the goalpost towards a losing proposition. You have two important and urgent things and already know you fail at least one of them.

TFA is about non urgent important tasks that you want to show incremental progress on. If there are multiple of those then those short bursts of works actual work can be eaten up by context switching, reprioritization, scheduling, etc.

What I do in those cases of to arbitrarily pick an order to do those things. (Likeliness to become urgent in the future, difficulty, unpleasantness, etc...) If I can't, I just pick a random order

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