I'm out of numbers so I can just write down the 7 and now, if you're following along, what step comes next?
再没有数字了,所以直接将7写下来,下一步是什么?
The first step to insight is to ask questions like why do things fall down and not up?
起初的洞察力是问问题,为什么物体坠地而不是上升?
And if you hear a triple, your step is this: down-up-up, down-up-up, down-up-up, down-up-up.
听到三拍子时,这样做,强,弱,弱
But I imagine that after a period, there'd be this-- Well, humans have this ability to look down on their experiences, or step back from their experiences, and assess them.
但我想经过一段时间后-,人类有能力审视自己的体验,或从体验中抽身而出加以评估。
With this, if I can assume that accessing the i'th element of a list is constant, then you can't see that the rest of that analysis looks just like the log analysis I did before, and each step, no matter which branch I'm taking, I'm cutting the problem down in half.
读取数组中的第i个元素,是个常量时间的操作的话,我也就能像以前那样得到,这个算法是对数级复杂度的分析,并且每一步不管我选择哪个区间,我都可以把问题的规模缩小一半。
What we've done is taken this pitch and played it all the way down an octave below it so we're actually getting back to this configuration of the pitch right next to it, and we could--then of course we could go down one more step and we would get the octave, which is a duplication of two-to-one.
我们所做的是固定一个音高,向下一路弹奏一个八度,所以事实上我们又回到了与这个固定音高相邻的音上,我们当然也可以向下再弹一组,然后得到这个八度,这其实就是两个八度对一个八度的重复。
They filled in the octave up above and then they filled in the fifth and then they filled in the fourth and then they came down a whole step and then they went up a fourth from that whole step and then up a fourth from that, and they were filling in in this fashion.
他们填写了八度音程,然后填写了五度音程,又填写了四度音程,然后下降一个全音级,又从那个全音级上升四度音程,然后再上升四度音程,他们就是照这样填写
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