"in my definition, a madman is a replay in which uke's arms and legs are detached from each other and the torso or a part of it from the shoulder/hip or further. uke may not assist by grabbing or applying force to joints, or by holding after the first dismem. premature relaxing of joints or moving of joints as to, for example, create a "boxing pose" is allowed"

NOTE: this is MY PERSONAL OPINION. this is not an universally valid explanation (yet, that is :P)

NOTE2: in my explanation, upper-/lower-body madmans are madmans that fill the requirements fo the upper limbs (and possibly the head), but not for the lower, or vice versa

universal definition

"a replay in which tori goes nuts on uke and demolishes him so that he can take a souvenir with him in a matchbox"
_

other definitions (and (my) counter-arguments)

-"a replay in which Tori goes nuts (hence the name) on uke and breaks him up, no matter how"

I agree, but in my opinion that can't be accomplished without destroying uke to at least the above explained extent

-"a replay with a certain number of dismems, usually 8 or 10, in rapid succession"

I agree and disagree; a solid pace is essential in madmans, but it's not a numerical value, but rather a fuzzy logic average. I completely disagree with defining madmans solely by the number of dismems, since, for example, 8 dismems can be filled by dismeming the wrists, ankles, elbows and knees, It is, while a demonstration of great skill, not very brutal, which madmans should be.