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Thoreau's statement that you should "keep your accounts on your thumb-nail" in Chapter 2 of Walden can refer to the idea that one should not owe or be owed much, if any, money.  However, this is only one type of account that he is referring to.  In exploring the beginning part of the paragraph in which this quote appears, and one of the central ideas of Walden in general, one can see that Thoreau is actually referring to any type of debt, be it financial or otherwise.

Thoreau's purpose in this particular section of Walden is to show, in his own words, that "[o]ur life is frittered away by detail."  He expands,

An honest man has hardly need to count more than his ten fingers, or in extreme cases he may add his ten toes, and lump the rest.  Simplicity, simplicity, simplicity!  I say, let your affairs be as two or three, and not a hundred or a thousand; instead of a million count half a dozen, and keep your accounts on your thumb-nail [...] Instead of three meals a day, if it be necessary eat but one; instead of a hundred dishes, five; and reduce other things in proportion.

In other words, one should reduce all extraneous matter, be it financial debt, social obligation, or even the number of times one eats per day.  Thoreau presents this perspective by initially focusing on the individual body, which ties into the Transcendental ideas of self-reliance (Emerson) and one's connection to nature.  To Thoreau and other Transcendentalists, the body itself is a part of nature.  When we allow the body to become caught up in the affairs of society--debt, obligation, even prescribed eating patterns--we begin to neglect our true self.  Thus, the idea of keeping one's accounts on a thumb-nail not only reminds us to keep the number (or financial value) of accounts low, but also returns the focus to a part of the body itself.  To Thoreau, the thumb-nail should always be bigger than the accounts written on it.  This is one way to help insure that we keep the focus where it belongs and lead a simple, deliberate life.

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Thoreau's entire essay entitled "Walden" concentrates on simplifying life.  Therefore, where he says to "keep your accounts on a thumbnail" he means that people should not owe money to anyone and if they do, then it should be a small, minor amount.  Thoreau makes a few references to being modest and not overspending and this is one of them.  Basically, he wants people to live as he does -- in the simplest way, without any worries (without any money worries if you look at this quote in particular).

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In Walden, what does Thoreau mean by "keep your accounts on your thumbnail"?

Thoreau is making a case for simplicity; in all things, he advises, keep the number and amount of things you are involved in to a minimum (he seems to imply 10 would be a good number, as an ancient human would count on his fingers, and his toes if necessary, but no more than that).

Some interpreters take "accounts" to mean banking, business or other financial accounts, and that Thoreau is advising that we keep our business affairs small, simple, easily tracked, etc. and avoid large debts or long-term engagements. This may be a bit of an over-specification of the word "accounts" - a less specific meaning of the word would simply be "affairs", that is to say, one's personal matters. Basically, don't get involved in too many things; keep them small and few enough that you could metaphorically fit them on your thumbnail.

This interpretation, in my opinion, makes more sense in the context of the essay. Thoreau, at the point at which he makes this statement, has been speaking in very broad and somewhat repetitive terms to emphasize his point; while it's entirely possible that he's talking about bank accounts and finances, it seems more likely that he's simply offering the same point phrased differently, for the sake of variety and emphasis.

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