A Quote by David Hilbert
However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.
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It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.
In a free society, there comes a time when the truth - however hard it may be to hear, however impolitic it may seem to say - must be told.
However good you may be you have faults; however dull you may be you can find out what some of them are, and however slight they may be you had better make some - not too painful, but patient efforts to get rid of them.
Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.
I must follow my Lord. No matter what. I must renew my allegiance every morning. It is His voice I must listen to, not the voices of those around me, however strident, however persuasive. It is His Word that must govern my life, not the words of others. God Himself has written a Book (think of it!) that must be the authority in my life.
The possession of a quantity of plants, however good the plants may be themselves and however ample their number, does not make a garden; it only makes a collection. Having got the plants, the great thing is to use them with careful selection and definite intention.
I am in favour of leaving people alone, however imperfect their polity may seem. It appears to me that you must not tell other nations how to set their house in order; nor must you compel them to be happy.
So don't stop moving forward. For a while, you may feel as though you're taking two steps forward, one step back. And there may be some personal heartache along the way. But when you look your little ones in the eye, you will find your voice and take a stand for them. We are their voices. And we must have the courage to stand up for them, whatever the odds or however powerful the opposition might be.
A society committed to the search for truth must give protection to, and set a high value upon, the independent and original mind, however angular, however rasping, however socially unpleasant it may be; for it is upon such minds, in large measure, that the effective search for truth depends.
Our deepest mature conviction is that finite and infinite interpenetrate, as time and eternity interpenetrate, and our problems must be solved in the light of that conviction.
However weak we are, however poor, however little our faith, or however small our grace may be, our names are still written on His heart; nor shall we lose our share in Jesus' love.
There is no faith, however respectable, no interest, however legitimate, which must not accommodate itself to the progress of human knowledge and bend before truth.
Man is not a machine, ... although man most certainly processes information, he does not necessarily process it in the way computers do. Computers and men are not species of the same genus. .... No other organism, and certainly no computer, can be made to confront genuine human problems in human terms. ... However much intelligence computers may attain, now or in the future, theirs must always be an intelligence alien to genuine human problems and concerns.
A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school.
The friend who holds up before me the mirror, conceals not my smallest faults, warns me kindly, reproves me affectionately, when I have not performed my duty, he is my friend, however little he may appear so. But if a man praises and lauds me, never reproves me, overlooks my faults, and forgives them before I have repented, he is my enemy, however much he may appear my friend.
Problems, however, are rarely solved on the spur of the moment. They must be organized and dissected, then key issues isolated and defined. A period of gestation then sets in, during which these issues are mulled over. You put them in your mind and consciously or unconsciously work at them at odd hours of the day or night - even at work. It is somewhat analogous to trying to place a name on the face of someone you've met before. Often the solution to a problem comes to you in much the same way you eventually recall the name.
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