A Quote by Henri Poincare
I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry.
Related Quotes
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.
...the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.
Just as I came out into the rue, an omnibus came by - pas complet, so I sprang in, without that prayer and fasting which should chasten the mind before risking it in a French omnibus.
My grandmother ... came here, not only like so many others because of the streets 'being paved with gold' and all, but because she wanted to leave the place where the streets were paved with people who had not gone to America.
The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.
People define themselves to some degree by the music that they listened to as teens. My mom had Elvis. Me, I had 'The Who' and later punk rock. Kids who came up in the '80s had other songs and bands. It's a way of placing ourselves culturally and temporally.
But then, Cap'n Crunch in a flake form would be suicidal madness; it would last about as long, when immersed in milk, as snowflakes sifting down into a deep fryer. No, the cereal engineers at General Mills had to find a shape that would minimize surface area, and, as some sort of compromise between the sphere that is dictated by Euclidean geometry and whatever sunken treasure related shapes that the cereal aestheticians were probably clamoring for, they came up with this hard-to-pin-down striated pillow formation.
I lifted my right foot to step up into the bus and collided head on with an invisible force that entered my awareness like a silently exploding stick of dynamite blowing the door of my usual consciousness open and off its hinges, splitting me in two. In the gaping space that appeared, what I had previously called "me" was forcefully pushed out of its usual location inside me into a new location that was approximately a foot behind and to the left of my head. "I" was now behind my body, looking out at the world without using the body's eyes.
So many people have this idea: I want to achieve something great or be somebody great. And they neglect the step that leads to greatness. They don't honor this step at this moment because they have this idea of some future moment where they are going to be great.
A long flight. Jetlag. Immigration. Customs. And then finally, that first step into a new place, that moment of exhilaration and disorientation, each feeding the other. That moment when anything can happen
At every step of the way, when I had trouble, there were people that came in, in my life that helped me. It's important to go seek help when you need it, and to give help when other people need it. And that is really more important than coming in with a gigantic brain into the astronaut program.
I had a dream, my dream came true, and my mom was there for me every step of the way. We didn't do this for any other reason. I am so happy she is here to experience this with me. This would not be the same if she were not by my side.
I think I had a particular moment when I was 15 years old. I read 'Crime and Punishment,' and that book just, I think, more than any other book made me want to be a writer, 'cause it was the first time that I hadn't just entered a book, but a book had entered me.
Like the dead-seeming, cold rocks, I have memories within that came out of the material that went to make me. Time and place have had their say.
In the weeks that followed, we amazed ourselves. Our habits slid apart easily...And our very few intimacies were simply discontinued. Where did they go, those things we did? Were they recycled? Did some new couple in China do them? Were a Swedish man and woman foot to foot at this very moment?
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