Irrational ^ Irrational

I came upon this very clever but simple proof recently ...

It is not known which irrational numbers x and y would make x^y rational.  But it can be easily proved that such rational x^y exists.  We know that √2 is irrational.  Take, for instance, the number

which must either be rational or irrational.  If it is rational, then we're done.  If it is not, then the number

must be rational.  So either case proves the existence of rational x^y where both x and y are irrational.

In pursuit of mathematical order

Gary Kuehn at Hamburger Bahnhof, Berlin 2015:

Hanne Darboven at Hamburger Bahnhof, Berlin 2015:

Ryszard Wasko at Żak | Branicka, Berlin 2015:

Vlatka Horvat at Żak | Branicka, Berlin 2015:

Great Lake/Small City

Video stills from Vid Ingelevics's  Great Lake/Small City currently showing at Richmond-Adelaide Centre, Toronto:

Architectural compositions 2

More abstract compositions of architectural fragments ... all pictures were taken in London, 2016:

Architectural compositions

I like using architectural fragments to create abstract compositions.  All pictures were taken in Toronto, 2017:

Monday Night

Goto80's Monday Night from his latest album Floptrik just released yesterday:

Video from CPU Records' youtube channel

Geminix

From his 2015 album ＿|￣|○, Goto80's Geminix:

From GOTO80's SoundCloud channel