I guess he was honest and humble enough writing that book. But I wonder if we try to "prove" the images we have in our mind and using math the same way math was used to "demonstrate" earth was the center of the universe.
I'm gonna put a simple example.

Do you remember when Kaku uses the example of the paper cross made of X number of squares and then each and every square is "lifted up" and transformed into a cube? He imagines an intelligent Flatlander would perceive every "lift" into 3D (the hidden dimension which in this case is height) as a vanishing square until, finally, all squares forming the cross just dissapear. I really disagree because we, 3D beings, even acknowledging an eventual smart 2D Flatlander dwelling on a flat piece of paper with 2 dimensions (lenght and width), we just CAN'T BREAK THE LAWS OF NATURE. In this case we can merely cut the edges of that cross (made of squares) and only then we can bend the proper places, glue the edges in order to create an ORIGAMI PAPER CUBE. Hence an hypothetical Flatlander wouldn't ever witness the vanishing of the squares, one by one but something very different. What exactly?
Just a HOLE in the shape of a cross. For him the whole episode would be something taken from Dr. Who tv show or Bermuda Triangle!!!!!

It's interesting how he uses Dali surreal art and Picasso's Cubism to describe Tesseract hypercubes or beings from 4D watching us, 3D. Yet, if Kaku knew a bit more about art he would be surprised to recognize Picasso's inspiration was from Chavin Peruvian culture with humanimal creatures. Well, I guess Richard Hoagland focuses more on hyperdimensions and overlooks hyperdimensional bizarre hum-animal creatures. All over the world the ETs look less Spielberg or Daniken and Sitchin and more like Guillermo del Toro who probably knows more about cherubim than all of them together. Just ask linguist Michael Heiser....
http://www.sitchiniswrong.com/ezekielnotes.htm