The tangible requirement does not necessarily mean that a claim must either be tied to a particular machine or apparatus or must operate to change articles or materials to a different state or thing. However, the tangible requirement does require that the claim must recite more than a 35 U.S.C. §101 judicial exception, in that the process claim must set forth a practical application of that judicial exception to produce a real-world result. Gottschalk v. Benson, 409 U.S. at 71-72, 175 U.S.P.Q. (BNA) at 676-77 (full-text) (invention ineligible because had "no substantial practical application."). "[A]n application of a law of nature or mathematical formula to a process may well be deserving of patent protection." Diamond v. Diehr, 450 U.S. at 187, 209 U.S.P.Q. (BNA) at 8 (full-text) (emphasis added); see alsoCorning, 56 U.S. (15 How.) at 268, 14 L.Ed. 683 (full-text) ("It is for the discovery or invention of some practical method or means of producing a beneficial result or effect, that a patent is granted . . ."). In other words, the opposite meaning of "tangible" is "abstract."