Coins are physical representations of monetary values. Like mental or verbal representations of quantities, coins encode sums of money in formats shaped, in part, by cognitive and communicative needs. Studying the coins circulating today, we consider how their design, colour, and size reflect their value. We show that coin designs solve a trade-off between informativeness-the pressure to highlight distinct denominations-and simplicity-the pressure to limit the number of designs that coin users must memorise. Coinage worldwide is more likely to display distinctive graphic designs and distinct colours on pairs of coins with large differences in value, thus minimising the aggregate cost of mistaking one coin for another. Coin size differentials, in contrast, do not seem to indicate greater value differentials, although absolute coin sizes do reflect monetary values. Log-transformed values predict design and colour distinctiveness in coin pairs, as well as absolute coin sizes, better than raw values, consistent with research suggesting that monetary quantities may recruit the "numerosity system" for magnitude representations, thought to track quantities logarithmically. These results show that coins obey similar informational constraints as linguistic and mental representations.

中文翻译：

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逆向工程现金：硬币设计会以对数形式标出高价值差异，而硬币尺寸则跟踪价值。

硬币是货币价值的物理表示。就像数量的心理或口头表示一样，硬币以某种形式由认知和交流需求决定的形式编码货币金额。在研究当今流通的硬币时，我们考虑它们的设计，颜色和大小如何反映其价值。我们证明了硬币设计解决了信息量（突出不同面额的压力）和简单性（限制硬币用户必须记住的设计数量）之间的折衷问题。全球范围内的硬币更可能在价值差异很大的成对硬币上显示独特的图形设计和独特的颜色，从而将将一种硬币误认为另一种硬币的总成本降至最低。相比之下，硬币大小差异似乎并不意味着更大的价值差异，尽管绝对硬币的大小确实反映了货币价值。对数转换后的值预测硬币对的设计和颜色独特性以及绝对硬币尺寸要好于原始值，这与研究表明货币量可能会招募“数量系统”来表示数量级（认为是对数跟踪数量）的研究一致。这些结果表明，硬币在语言和心理表达上遵循相似的信息约束。