The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.
I had a real epiphany. I guess it was during and after the operation. I did what's a common thing; I kind of raised above the table and could look at me and listen to all the people talking and understand what they were saying and so forth.
Analysis does not owe its really significant successes of the last century to any mysterious use of sqrt(-1), but to the quite natural circumstances that one has infinitely more freedom of mathematical movement if he lets quantities vary in a plane instead of only on a line.
I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms.
It was an epiphany when I realized you don't have to call yourself a linguist, a translator, a poet. You can call yourself an artist and you can do all these things.
The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.
[True beauty] seeps into you. It doesn't make you forget yourself, but totally the opposite. It connects you with everything and fills you with awe that you share the same space with something that glorious. Like a sunrise or a clear blue day or the most extraordinary piece of glass. And then suddenly...you have this epiphany that there's more to the world than just you and what you want or even who you are.
For me, the short story is not a character sketch, a mouse trap, an epiphany, a slice of suburban life. It is the flowering of a symbol center. It is a poem grafted onto sturdier stock.
I had an epiphany where I realised that there are song titles everywhere - in advertising, in conversations with people at the grocery store - and every time I open my mind to that and find titles, I then weave a story around that.
My first epiphany that this might work came on my first day, when I went into biofeedback. They hooked me up to computers through electrodes, put me in a comfortable lounge chair, put an eye pillow over my face, slipped speakers onto my head and played an audio guided visualization.
So if there was a way that I knew something about my character's desires or the things that they were resisting because I was saving it for some grand epiphany moment for my readers, I just feel like that's when you can feel the machine at work in a story. That's when you can feel the writer pulling the strings of the puppet.
I got a job as a children's librarian at PS 175 in Harlem, and that changed everything. That was an epiphany. I didn't know Harlem existed. I didn't know there was such a place, because I grew up in white Queens, where five miles is 100 miles.
I had never done any sort of yoga before, and this epiphany was a little more esoteric. I walked into the yoga room and there was a voice from my soul that said out loud, This is it! I just knew. I just knew in that moment - I couldn't even straighten my legs. I couldn't sit cross-legged on the floor. I couldn't put my legs up the wall in the most gentle, restorative yoga pose, and yet, I knew.
I felt like if I could get the epiphany out of the way in my drafting process, through my eighth or tenth draft, then that can just be part of how I've assembled the character, and then we can move on and move forward with it. In general, I don't ever want to feel smarter than my characters, because I just feel like that's not a great way to write a story.
The moment in The Bell Jar when Esther Greenwood realizes after thirty days in the same black turtleneck that she never wants to wash her hair again, that the repeated necessity of the act is too much trouble, that she wants to do it once and be done with it, seems like the book's true epiphany. You know you've completely descended into madness when the matter of shampoo has ascended into philosophical heights.
I've stepped back a few times and had these crazy epiphanies that we are blessed by having Barack Obama as a candidate at this time in our history. If we were ever to have a man of color become president - and it shouldn't be about that, and it doesn't need to be, because he's qualified on all levels - but if you do think about it, just in terms of that idea of unifying people, it's a huge positive.
What I don't like is when I see stuff that I know has had a lot of improv done or is playing around where there's no purpose to the scene other than to just be funny. What you don't want is funny scene, funny scene, funny scene, and now here's the epiphany scene and then the movie's over.
Learning to never quit and keep going is the biggest thing. I don't think it was ever an epiphany, I think that's just the most important thing that has worked for me: to keep going and keep trying.
I know Stephen King is uncompromising on the idea that writers should practise their craft every single day, and it clearly works for him. Personally, I relish a day off with some boredom; it gives me space to feel the world, observe, stir up the epiphanies, which I need if I'm creating fiction. On the other hand, I'm a big advocate for beauty and creativity on the weekend, which can be incredibly rejuvenating.
I think I had a lot of small epiphanies along the way. What I really got out of the experience is a sense that there's other ways of living your life and that there are lots of things that we lose track of when we are stressed.
I wondered if that was how forgiveness budded; not with the fanfare of epiphany, but with pain gathering its things, packing up, and slipping away unannounced in the middle of the night.
Let's face it: Serious self-scrutiny has not been one of our notable characteristics. We are far more aware of what we want to change in others than we are of how we need to change. Salvation for our educational ills is only secondarily "out there." Primarily it will have to come from within an educational community willing to say that we have met the enemy and it is us.
Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done.
Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.
One night I was on my [Navy] ship... on my first cruise crossing the North Atlantic in a horrible storm, chained to the rails so I wouldn't fall overboard. In this lightning and thunder and hail, in this misery, I shouted at the heavens with my little squeaky voice and said, Someday I'm going to be a photographer! It was as big an epiphany as any man ever had.
Follow AzQuotes on Facebook, Twitter and Google+. Every day we present the best quotes! Improve yourself, find your inspiration, share with friends
or simply: