One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?
Stephen HawkingRelated topics
able believe find game having live might measure model nothing positivist real yet means viewpointRelated quotes
America could carry on a two years' war by the confiscation of the property of disaffected persons, and be made happy by their expulsion. Say not that this is revenge, call it rather the soft resentment of a suffering people, who, having no object in view but the good of all, have staked their own all upon a seemingly doubtful event. Yet it is folly to argue against determined hardness; eloquence may strike the ear, and the language of sorrow draw forth the tear of compassion, but nothing can reach the heart that is steeled with prejudice.
Thomas Paine
After experience had taught me that all the usual surroundings of social life are vain and futile; seeing that none of the objects of my fears contained in themselves anything either good or bad, except in so far as the mind is affected by them, I finally resolved to inquire whether there might be some real good having power to communicate itself, which would affect the mind singly, to the exclusion of all else: whether, in fact, there might be anything of which the discovery and attainment would enable me to enjoy continuous, supreme, and unending happiness.
Baruch Spinoza
Muhammad brought down from heaven and put into the Koran not religious doctrines only, but political maxims, criminal and civil laws, and scientific theories. The Gospels on the other hand, deal only with the general relations between man and God and between man and man. Beyond that, they teach nothing and do not oblige people to believe anything. That alone, among a thousand reasons, is enough to show that Islam will not be able to hold its power long in ages of enlightenment and democracy, while Christianity is destined to reign in such ages, as in all others.
Alexis de Tocqueville
War means fighting. The business of the soldier is to fight. Armies are not called out to dig trenches, to throw up breastworks, to live in camps, but to find the enemy and strike him; to invade his country, and do him all possible damage in the shortest possible time. This will involve great destruction of life and property while it lasts; but such a war will of necessity be of brief continuance, and so would be an economy of life and property in the end. To move swiftly, strike vigorously, and secure all the fruits of victory is the secret of successful war.
Stonewall Jackson
Some people think that evolutionary psychology claims to have discovered that human nature is selfish and wicked. But they are flattering the researchers and anyone who would claim to have discovered the opposite. No one needs a scientist to measure whether humans are prone to knavery. The question has been answered in the history books, the newspapers, the ethnographic record, and the letters to Ann Landers. But people treat it like an open question, as if someday science might discover that it's all a bad dream and we will wake up to find that it is human nature to love one another.
Steven Pinker