The given passage discusses the historical evolution of the alphabetic order as a tool for organizing information. It highlights that, despite the obvious utility of alphabetization today, its adoption was not immediate due to religious and traditional objections. Initially, scholars refrained from using alphabetic order because it was seen as contrary to divine organization.
The passage explains that it wasn't until the rediscovery of ancient texts during the Renaissance and the demands of government administration in the 16th and 17th centuries that the alphabetic order became more prevalent and appreciated.
The correct answer is: The alphabetic order took several centuries to gain common currency because of religious beliefs and a lack of appreciation of its efficacy in the ordering of things. This option captures the essence of the passage by addressing the reluctance due to religious beliefs and the eventual realization of the alphabetic order's utility in organizing information efficiently.
The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In investigating memory-beliefs, there are certain points which must be borne in mind. In the first place, everything constituting a memory-belief is happening now, not in that past time to which the belief is said to refer. It is not logically necessary to the existence of a memory-belief that the event remembered should have occurred, or even that the past should have existed at all. There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that "remembered" a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago. Hence the occurrences which are CALLED knowledge of the past are logically independent of the past; they are wholly analysable into present contents, which might, theoretically, be just what they are even if no past had existed.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: