Can you help me find a connection between the past and present in the play that reveals insights about a character, knowledge, sexuality, order, progress, or attitudes toward death?

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The table gradually accumlating papers and objects is an interesting link between past and present in the play. As various anachronistic items gather there, such as a mug, the handsome quarto containing The Couch of Eros, the portable computer and Lady Croom's infusion equipment, Stoppard creates the effect of flattening time and suggesting the similarities between past and present. Every age has its thinkers who sift through ephemera to understand people, their "personalities", mathematics, or physics. By showing that this learning process still continues in the contemporary period, Stoppard emphasises the ongoing and complex nature of human progress.

He also asks a question about the value of learning. Is it "trivial" as Valentine seems to suggest in Act II scene I? The odd objects on the table, which the characters use to aid them with their discoveries, seem to suggest on some level that it is as they all seem minor and incidental.

In addition, Septimus's comment that "we shed as we pick up, like travellers who must carry everything in their arms" seems to refer to the items on the table and suggests that human development is ad hoc and difficult to control.

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What stood out to me when I read your question was that relationships between people have pretty much stayed the same since the beginning of time.  Our social situations differ, but the basic interaction between people has not really differed in a long time.  What Thomasina says reinforces this idea.

The unpredictable and the predetermined unfold together to make everything the way it is. It's how nature creates itself, on every scale, the snowflake and the snowstorm.

To me, this applies to nature and people.  People are predictable in the way they interact, and have interacted, since the beginning of time.  Thomasina is trying to explain how nature is, to explain how people are.

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You might use algebra as the focal point of your comparison. While things around algebra change, algebra remains the same and is relevant to the present day in the person of the grouse-counting Valentine Coverly and, of course, to the earlier era of Act I in the person of algebra-studying Thomasina. To this, you could add the hermitage--conceived of in the first act and returned to with a changed perspective in subsequent scenes--and/or the changing perceptions of Romanticism as seen in the research of Hannah Jarvis.

You might anchor your ideas in the unchanging algebra and have the two changeable things revolve around it, so to speak. You might begin with the changeable hermitage, how Thomasina and later Hannah perceive it. Then you might speak of the constant of algebra/mathematics. Then you might speak of the changing perspective about Romantics. Your conclusion might show how somethings are anchors through time around which other, changeable things, revolve.

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