1. People have always imagined ......
2. What would it be like to live in the future?
3. What will it be like to live in the future?
4. What is it like to live in the future?
1+2. People have always imagined what it would be like to live in the future.
1+3. People have always imagined what it will be like to live in the future.
1+4. People have always imagined what it is like to live in the future.
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When two sentences are combined, the results are above. 1+2 seems to be right. What about the other ones?
1+2 is correct because the verb tenses (sequence of tenses) are correct. The other two combos are not.
http://grammar.ccc.commnet.edu/grammar/sequence.htm
Since the verb in the main clause is present perfect (have imagined), the verb in the second clause needs to be in the past tense.
When combining two sentences, it's important to consider the context and grammar rules. In the case of sentences 1 and 3, "it" refers to the future, so the combination "what it will be like to live in the future" is grammatically correct.
However, in the case of sentence 4, "what is it like" refers to the current state of living in the future. Combining sentence 1 with sentence 4 would result in "what it is like to live in the future." This phrasing suggests that we are in the future and describing what it is like from that perspective.
Therefore, all three combinations (1+2, 1+3, and 1+4) are grammatically correct, but they convey slightly different meanings depending on the use of "will be" or "is" in relation to the future.