I've met some people in Jerusalem who can do this. My first encounter was in the Bucharim section with a certain "chacham Betzalel" many years ago. There was a line of people waiting there. When my turn came, he asked me my father's name which he wrote down, then asked me my name and he wrote it down. Then he wrote down my mother's name without asking me. He then proceeded to tell me all sorts of things about both without my saying a word. He also said they were not compatible (turns out they divorced). All of what he said was spot on. However, I then went to Rabbi Yaakov Hillel and he told me, yes i know him but don't trust him. I found out later from other sources that this man uses forces of tum'a to do what he does. So from my experience the phenomena is real (and Rabbi Hillel agrees) but one must be very careful to ask one of the Gedolei Hador (greatest torah scholars of the generation) to be sure it is not from the bad side. (I can give you a name of one who does not hide what he sees if you like)
As to where these powers come from (from the good side), see for example Chovot Halevavot gate 8 ch.4
And when you do this with a faithful heart and a pure soul, your mind
will become illuminated, and you will see the path to all of the
exalted qualities, and the yetzer (evil inclination) will not have a
way to reach you and entice you, and you will reach the status of one
treasured by G-d. A new, strange, supernal sense will arouse in you,
unfamiliar to you of all the senses you are used to knowing, as the
wise man said: "A man's wisdom makes his face to shine, and the
boldness of his face is changed" (Koheles 8:1), then you will perceive
the great matters, and you will see the deep secrets, with your pure
soul, pure heart, and strong faith
and earlier in Gate 8 ch.3 #10
And the Creator will open for him the gates of His knowledge, and
reveal to him secrets of His wisdom, and G-d will put His attention to
guide and lead him, and He won't abandon him to himself and his
(limited) ability, as the entire psalm 23 says: "The L-ord is my
shepherd; I shall not lack" (Tehilim 23:1), until the end. And he will
be on an exalted level, among the levels of the Chasidim, and a high
level among the Tzadikim (righteous), and he will be able to see
without his physical eyes, and hear without his physical ears, and
speak without a tongue, and he will sense things without his physical
senses, and be able to picture them without need for a comparison.
Not anecdotal evidence. Nothing cherry-picked. No selection bias. Anything else is OK though.What is left? I ask again: what sort of evidence are you looking for? – mevaqesh Jan 04 '17 at 05:11