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5 months 4 weeks ago
We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.
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Ada Lovelace, Notes on the Analytical Engine invented by Charles Babbage
5 months 4 weeks ago
Propose to any Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible; if you peel a potato with it before his eyes, he will declare it useless because it will not slice a pineapple. Impart the same principle or show the same machine to an American or to one of our Colonists and you will observe that the whole effort of his mind is to find some new application of the principle, some new use for the instrument.
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Quoted in Richard H. Babbage (1948), "The Work of Charles Babbage", [https://archive.org/details/proceedingsofsym0000symp_y9e6/page/20/mode/2up?q=%22Propose+to+any+Englishman%22 Annals of the Computation Laboratory of Harvard University, vol. 16] cited to
5 months 4 weeks ago
Errors using inadequate data are much less than those using no data at all.
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Quoted in William Kenneth Richmond (1969), The Education Industry. | May be modern paraphrase of "the errors which arise from the absence of facts" quote above.
5 months 4 weeks ago
The foundation of all religion is the belief in a God, and that He exists in certain relation with His creatures. Such belief necessarily leads to the consciousness of some obligation towards the Deity ; and this consciousness suggests the duty of worship ; and in the selection of the form of this worship originates the various creeds which distinguish and distract mankind. There is a sort of geography of religion ; and I regret to think that the majority of mankind take their creed from the clime in which they happen to be born ; and that many, and not an inconsiderable portion of mankind, suffer the sacred torch to burn out altogether, in their contact with the world, and then vainly imagine that they can recover the sacred fire by striking a park out of dogmatic theology.
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"Passages from the life of a philosopher", Appendix: Religion, Note (B) pp. 491-492
5 months 4 weeks ago
Miracles may be, for anything we know to the contrary, phenomena of a higher order of God's laws, superior to, and, under certain conditions, controlling the inferior order known to us as the ordinary laws of nature.
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"Passages from the life of a philosopher", Appendix, p. 490
5 months 4 weeks ago
If we define a miracle as an effect of which the cause is unknown to us, then we make our ignorance the source of miracles! and the universe itself would be a standing miracle. A miracle might be perhaps defined more exactly as an effect which is not the consequence or effect of any known laws of nature.
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"Passages from the life of a philosopher", Appendix, p. 489
5 months 4 weeks ago
We must be careful to discriminate between our own incapacity to test truth and the necessary improbability of an event. It is plain that from our ignorance of the remote spheres of God's action we cannot judge of His works removed from our experience; but a fact is not necessarily doubtful because it cannot be reached by our ordinary senses. To recapitulate, we may lay down the following propositions: 1. That there is no real physical distinction between miracles and any other operations of the Divine energy : that we regard them differently is because we are familiar with one order of events and not the other. 2. There is nothing incredible in a miracle, and the credibility of a miraculous event is to be measured only by the evidence which sustains it. And although the extraordinary character of a phenomenon may render the event itself improbable, it does not, therefore, necessarily render it either incredible or untrue.
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"Passages from the life of a philosopher", Appendix, p. 489
5 months 4 weeks ago
Mill, in speaking of Hume's celebrated principle, "that nothing is credible which is contradictory to experience, or at variance with the laws of nature," calls it a very plain and harmless proposition, being, in effect, nothing more than that whatever is contradictory to a complete induction is incredible. Admit the existence of a Deity, and the possibility of a miracle is the natural consequence. No doubt our examination of the evidence which sustains an unusual phenomenon should be most carefully conducted; but we must not measure the credibility or incredibility of an event by the narrow sphere of our own experience, nor forget that there is a Divine energy which overrides what we familiarly call the laws of nature.
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"Passages from the life of a philosopher", Appendix, p. 488
5 months 4 weeks ago
There is nothing in the nature of a miracle that should render it incredible: its credibility depends upon the nature of the evidence by which it is supported. An event of extreme probability will not necessarily command our belief unless upon a sufficiency of proof; and so an event which we may regard as highly improbable may command our belief if it is sustained by sufficient evidence. So that the credibility or incredibility of an event does not rest upon the nature of the event itself, but depends upon the nature and sufficiency of the proof which sustains it.
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"Passages from the life of a philosopher", Appendix: Miracle. Note (A), p. 88
5 months 4 weeks ago
It has always occurred to my mind that many difficulties touching Miracles might be reconciled, if men would only take the trouble to agree upon the nature of the phenomenon which they call Miracle. That writers do not always mean the same thing when treating of miracles is perfectly clear; because what may appear a miracle to the unlearned is to the better instructed only an effect produced by some unknown law hitherto unobserved. So that the idea of miracle is in some respect dependent upon the opinion of man. Much of this confusion has arisen from the definition of Miracle given in Hume's celebrated Essay, namely, that it is the "violation of a law of nature." Now a miracle is not necessarily a violation of any law of nature, and it involves no physical absurdity. As Brown well observes, "the laws of nature surely are not violated when a new antecedent is followed by a new consequent ; they are violated only when the antecedent, being exactly the same, a different consequent is the result;" so that a miracle has nothing in its nature inconsistent with our belief of the uniformity of nature. All that we see in a miracle is an effect which is new to our observation, and whose cause is concealed. The cause may be beyond the sphere of our observation, and would be thus beyond the familiar sphere of nature; but this does not make the event a violation of any law of nature. The limits of man's observation lie within very narrow boundaries, and it would be arrogance to suppose that the reach of man's power is to form the limits of the natural world. The universe offers daily proof of the existence of power of which we know nothing, but whose mighty agency nevertheless manifestly appears in the most familiar works of creation. And shall we deny the existence of this mighty energy simply because it manifests itself in delegated and feeble subordination to God's omnipotence?
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"Passages from the life of a philosopher", Appendix: Miracle. Note (A)

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