Sam Treiman... has quoted something he called Treiman's theorem... Impossible things usually don't happen. ...With the discovery of radioactivity... it suddenly became apparent that the "impossible" was happening all the time. Uranium, thorium, radium... fit all the requirements of chemical elements. They could not be broken down by any of the standard methods... But occasionally... atoms of these elements spontaneously changed into other kinds of atoms. ...So what is left of the doctrine of the elements? Is alchemy reinstated? Not at all. The point is that the doctrine fails only under rare or special conditions. ...We can isolate the conditions in which they do, and retain a more restricted but still useful concept of the "impossible."
Frank WilczekRelated topics
chemical concept doctrine fit impossible isolate left point something theorem under uranium radium things radioactivityRelated quotes
Scripture says:-If a man should rise, pretend to be a prophet, and show you his signs by which he desired to convince you that his words are true, know that God intends thereby to prove to the nations how firmly you believe in the truth of God's Word, and how well you have comprehended the true Essence of God; that you cannot be misled by any tempter to corrupt your faith in God. Your religion will then afford a guidance to all who seek the truth, and of all religions man will choose that which is so firmly established that it is not shaken by the performance of a miracle. For a miracle cannot prove that which is impossible; it is useful only as a confirmation of that which is possible, as we have explained in our Mishneh-torah.
Maimonides
1. There is at present in the material world a universal tendency to the dissipation of mechanical energy.
2. Any restoration of mechanical energy, without more than an equivalent of dissipation, is impossible in inanimate material processes, and is probably never effected by means of organized matter, either endowed with vegetable life or subjected to the will of an animated creature.
3. Within a finite period of time past, the earth must have been, and within a finite period of time to come the earth must again be, unfit for the habitation of man as at present constituted, unless operations have been, or are to be performed, which are impossible under the laws to which the known operations going on at present in the material world are subject.
William Thomson
Don't forget that God sees you and watches you when you are in pain; He perceives even the beating of your heart. Consequently, He will not leave you without consolation and His fatherly protection. Naturally, the saints rejoiced in their afflictions; as for us, let us at least manage to accept affliction or pain patiently.
My child, pray within your heart, and the name of Jesus will become for you a comforting balm so that you can bear this trial of yours in a way which benefits you. You will greatly benefit from this trial if you submit yourself to it patiently. So again I say to you, with the almighty armor of prayer continually approach the omnipotent Lord more often, and you will come to know how He wondrously lifts the burden of pain and marvellously gives rest to sufferers.
Ephraim of Arizona
Why can stars do better than the big bang? ...During the big bang, there were only a few minutes when nuclei could form. Very rare processes, or slow ones, played little role. A case in point is the key process from which the sun derives its energy. In this reaction, two protons collide to produce a deuterium nucleus, a neutrino, and a positron. ...This reaction belongs to the family of weak interactions. ...It remains... a remarkable-and for humanity, remarkably fortunate-circumstance that the central reaction that drives the sun is so rare. It is only this extraordinary rarity that allows the average proton in the sun to last so long, billions of years, even though it is colliding with other protons millions of times a second. ...an entertaining example of Treiman's theorem.
Frank Wilczek
I know well that many of my readers do not think as I do. This also is most natural and confirms the theorem. For although my opinion turn out erroneous, there will always remain the fact that many of those dissentient readers have never given five minutes' thought to this complex matter. How are they going to think as I do? But by believing that they have a right to an opinion on the matter without previous effort to work one out for themselves, they prove patently that they belong to that absurd type of human being which I have called the "rebel mass." It is precisely what I mean by having one's soul obliterated, hermetically closed. Here it would be the special case of intellectual hermetism.
José Ortega y Gasset