Thank you, AxelSnaxel, for pointing these out.
I just added that reference to the post, “Sansaric Time Scale, Buddhist Cosmology, and the Big Bang Theory”.
You wrote: “In Power of the Human Mind – Anariya or Mundane Jhānas under the section on “Extrasensory Perceptions and Powers (Abhiññā)”. It says you can attain various types of powers after you reach arahant..”.
– That is correct. And as you pointed out that could be done at lower levels of magga phala too, if one wanted.
– Furthermore, some of such powers can be attained by anariya yogis too.
You wrote: “And then it says that the Buddha discouraged pursuing such powers and prohibited public display of them..”
– That is correct. He prohibited displaying such powers for mundane purposes. For example, one time a wealthy person put a very expensive alms bowl at the top of a long pole and advertised that anyone who get that bowl by flying through the air will own it. A bhikkhu who was in need of a bowl retrieved it by flying through air. That was a display of “magical powers” and that prompted the Buddha to instill that Vinaya rule.
– But there are instances where such powers were used for good purposes, even by the Buddha himself.
– Of course the Buddha minimized such uses. In most cases, the Buddha just walked for miles and miles to get to destination, without getting there “instantly” by using such powers.
– But I remember one account in the Tipitaka where the Buddha and 500 Arahants crossed a raging river at a time of a flood, using iddhi powers. They did not have another option.