5. Two models M1, M2 of computation are said to be equivalent in power if and only if M1 can simulate M2 and M2 can simulate M1. See lecture 7 or discussion notes 4 for a (sketch of a) proof that 1-tape Turing machine is equivalent in power to a 2-tape Turing machine. Let a 37-6 Turing Machine be a Turing Machine that behaves exactly like our model from lecture, except that it can only move its tape head to the left or right by increments of 37 or 6, rather than by increments of 1. Show that a 37-6 TM is equivalent in power to a 1-tape Turing machine described in lecture

Read this excerpt from helen keller’s autobiography, the story of my life. have you ever been at sea in a dense fog, when it seemed as if a tangible white darkness shut you in, and the great ship, tense and anxious, groped her way toward the shore with plummet and sounding-line, and you waited with beating heart for something to happen? i was like that ship before my education began, only i was without compass or sounding-line, and had no way of knowing how near the harbour was. "light! give me light! " was the wordless cry of my soul, and the light of love shone on me in that very hour. . the morning after my teacher came she led me into her room and gave me a doll. the little blind children at the perkins institution had sent it and laura bridgman had dressed it; but i did not know this until afterward. when i had played with it a little while, miss sullivan slowly spelled into my hand the word "d-o-l-l." i was at once interested in this finger play and tried to imitate it. when i finally succeeded in making the letters correctly i was flushed with childish pleasure and pride. running downstairs to my mother i held up my hand and made the letters for doll. i did not know that i was spelling a word or even that words existed; i was simply making my fingers go in monkey-like imitation. in the days that followed i learned to spell in this uncomprehending way a great many words, among them pin, hat, cup and a few verbs like sit, stand and walk. based on this excerpt, which words best describe helen keller?