And of course, mathematically and we can think about more abstractly what's going on in extra dimensions even without being able to completely visualize it.
Writing it all out abstractly might seem more complicated than just thinking through the example directly with a representative sample; and yeah, it is!
In the abstract, all the various alternatives and missed opportunities that the critics offer up sound plausible, simple plot points in a morality tale.
And this is what is wrong with Schelling, namely that he talks of the tragic too abstractly, without taking account of its dialectical, that is, historical, character.
Much as I loved Granddad I had sometimes wondered abstractly if when he finally went Mum would feel in some way freed from the responsibility of caring for him.
And I actually think if the Conservatives were to take that lesson, that would be a mistake, because I think in the abstract, people love the idea of the green transition.
If we were to think about it a little bit more abstractly, the real R2, the two-dimensional real coordinate space-- let me write this down-- and the two-dimensional real coordinate space.
In fact, a certain number of instances are needed to make us think of two abstractly, rather than of two coins or two books or two people, or two of any other specified kind.
" The chess pieces are the block alphabet which shapes thoughts" , he once said, " And these thoughts, although making a visual design on the chessboard, express their beauty abstractly, like a poem" .
You tend to phase all of your results pretty abstractly, which is to say only in terms of these axioms, rather than centering on a specific type of vector, like arrows in space or functions, E.G.
So, moving forward, I'm just going to write this expansion more abstractly – just a sum from n equals 0 up to capital n, where c sub n tells us the coefficients that we don't know.
因此,接下来,我将更抽象地编写这个展开式 - 只是从 n 等于 0 到大写 n 总和,其中 c sub n 告诉我们我们不知道系数。
Somehow a phrase like " 40 out of 100" kicks our intuition into gear more effectively than " 40%" , much less " 0.4" , or abstractly referencing the idea of something being more or less likely.
A useful starting place is to ask ourselves perhaps in the company of a large sheet of paper, a pen and a free afternoon what sort of people in the abstract put us off and what kinds excite us.