Why am I getting an error converting a ‘float**’ to ‘const float**’?

See Why am I getting an error converting a Foo** → const Foo**?

Because converting Foo** → const Foo** would be invalid and dangerous ... The reason the conversion from Foo** → const Foo** is dangerous is that it would let you silently and accidentally modify a const Foo object without a cast

The reference goes on to give an example of how such an implicit conversion could allow me one to modify a const object without a cast.

This is a very tricky restriction. It is related to the aliasing rules of the language. Take a look at what the standards say, because I have faced this once before:

(Page 61)

[Note: if a program could assign a pointer of type T** to a pointer of type const T** (that is, if line //1 below was allowed), a program could inadvertently modify a const object (as it is done on line //2). For example,

int main() {
  const char c = 'c';
  char* pc;
  const char** pcc = &pc; //1: not allowed
  *pcc = &c;
  *pc = 'C'; //2: modifies a const object
}

—end note]