And, incidentally, they have found such a limit. Lloyd's answer is that it's computing "its own dynamical evolution," but we prefer to believe that reality up to this point is just the loading screen for the most kickass MMORPG of all time. It's one thing to suggest that our universe is just a video game on some alien Xbox, but there's another theory that the universe is itself a computer. In Studies in Mathematics and Its Applications, 2004. , {\displaystyle y(t)=\tan(t),} Since , this is, the maximum slope of the function in modulus. {\displaystyle a,\Gamma } I y Recall the theorem that says that if a first order differential satisfies continuity conditions, then the initial value problem will have a unique solution in some neighborhood of the initial value. − The only possible question is, if you ever did run into your cosmic twin, would you fight or fuck? If the new function is the same as the original guess, then we are done. \(f(x)\) is a solution to the initial value problem if and only if, \[f'(x) = f(x,f(x)) \;\;\; \text{and} \;\;\; f(0) = 0.\], \[ \phi (t) = \int _0^t f(s,\phi (s)) \, ds .\]. You have to let yourself go to sleep. B So when fringe theories like the below come about, your first impulse is to laugh them off, but then you think, "Is it really that much stranger than what we know now?". 0 y It’s all in your mind. On an infinite scale, every pattern has to repeat eventually. The universe is a really strange place, and as science progresses, it just keeps looking weirder. Do you have an idea in mind that would make a great article? φ It's a theory that suggests, among other things, that the whole of the universe is stuck to a giant sheet of fabric that they call a "brane." That's a computer that uses tiny particles like atoms and electrons to work, instead of comparatively hulking great chunks of electronics like microchips. You are the universe and it’s discovering itself every second of every day. Being and Nothingness: a phenomenological essay on ontology. String theory is like the eccentric uncle of theories about the universe. You can’t control the parts of your body that are automatic, for example, you can’t.. Everything is you, and you control it in the same way that you control your own body, some things are done automatically for you, and just as you can’t control the secretion of hormones you can’t control the weather or the lives of others, they’re just part of you and exist in harmony. It’s done for you. Well, everything in our world -- including the people in it -- is just LEGO structures made of tiny particles. Assume that the function φ(t, p) is continuous on the set, Then the problem (3.4.1) can be reduced to the one for the integral equation, and it is natural to solve the latter problem by the iteration method, To justify this procedure, we must verify that the operator, is q-contractive with respect to the norm. My belief in reality is that of an agnostic. ¯ Unless you know how to Lucid Dream, which is the art of becoming self aware in your dreams, you assume it’s real. Starting with After spending nine months as a German prisoner of war in 1940, Jean-Paul Sartre began exploring the meaning of freedom and free will and in 1940, he penned his principal philosophical work — Being and Nothingness: a phenomenological essay on ontology. < So are we! See Newton's method of successive approximation for instruction. so the previous state of the system is not uniquely determined by its state after t = 0. π a a IdentitarianlEliminativist Ambiguity in Quine 116 10. Maybe this entire universe is an egg to hatch one person, or maybe Theory number 2 is correct as well, and you are everything in this universe, this is all you, and me. In mathematics – specifically, in differential equations – the Picard–Lindelöf theorem, Picard's existence theorem, Cauchy–Lipschitz theorem, or existence and uniqueness theorem gives a set of conditions under which an initial value problem has a unique solution. Although a rigorous proof of this theorem is outside the scope of the class, we will show how to construct a solution to the initial value problem. {\displaystyle y_{0}} Time is entirely man made, the same as measurement, weight, money and temperature. Nevertheless, there is a corollary of the Banach fixed point theorem: if an operator Tn is a contraction for some n in N, then T has a unique fixed point. If you're pressed for time and just looking for a quick fix, then check out 23 Jokes That Never Made It Into Our Best Videos . . "We are left alone without an excuse," he said. ∈ 2 The "cosmic microwave background" is a faint radioactive signal that permeates the entire universe, and all of science's calculations insist that it should be pretty uniform across the universe. + And they will continue to, right up to the point that a team of superpowered Matrix Agents storm their office. t By going up to me and prodding me, saying ‘You felt that, didn’t you?’ But then, in a dream someone could do exactly the same, and it would feel just as real. This table was ornate and the legs had diamonds and gold all over them, the table top had a velvet top and a small tray was sitting in the middle. Of course, this evidence might not be that compelling by itself, but Beane and his colleagues are busy thinking up new ways to detect the computer we might be living in, presumably by mapping the universe in search of the Blue Screen of Death. [4], Existence & uniqueness of solutions to first-order equations with given initial conditions, Frobenius theorem (differential topology), Integrability conditions for differential systems, "Sur l'application de la méthode des approximations successives aux équations différentielles ordinaires du premier ordre", "2.2. This may seem like a proof of the uniqueness and existence theorem, but we need to be sure of several details for a true proof. Sartre's theory of existentialism states that “existence precedes essence”, that is only by existing and acting a certain way do we give meaning to our lives. t The implication is that each black hole in our universe may contain its own universe inside it. ] , These are just my theories of existence. Are you on Google+? \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), [ "article:topic", "authortag:green", "integral equation", "Existence", "Uniqueness", "authorname:green", "showtoc:no" ], \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\), 2.9: Theory of Linear vs. Nonlinear Differential Equations.
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