I appreciate the acknowledgement by Fortnow[1] of my, historically significant, I believe, first ever constructive proof of Kannan’s theorem[2], which I think was acknowledged as "folklore" (I thank Watanabe for this) in Watanabe[3] (I don’t think I currently have access to any university library system so I don’t think I currently have access to the full text of this). If I am not mistaken, I now have a much simpler construction (I thought of this years ago if I remember rightly but was a bit too busy with an IT job unrelated to complexity theory until recently to have the time to publish it) giving a constructive proof of Kannan’s theorem, based upon a particular type of universal Turing machine. The fact that this construction (if I am not mistaken) works is an easy consequence of either my earlier constructive proof[2] or Watanabe’s later proof of the same result as discussed by Fortnow[1]. (I know that my presentations here of this construction and proof are quite sketchy at present; I would appreciate some feedback from others before attempting to write up more detailed versions of them). Also, I think it can be used as the basis of a much simpler constructive proof of Kannan’s theorem: I also discuss this here.