"Plato is widely recognized as the first person to develop the concept of an atom, the idea that matter is composed of some indivisible component at the smallest scale," says Douglas Jerolmack, a geophysicist from Penn. "But that understanding was only conceptual; nothing about our modern understanding of atoms derives from what Plato told us."
賓夕法尼亞大學的地球物理學家道格拉斯·傑羅馬克（Douglas Jerolmack）說道，「柏拉圖被公認為是提出原子概念的第一人，他認為物質在最小尺度上是由一些不可分割的成分組成的，但這種理解只是概念上的，而我們對原子的現代認知與柏拉圖沒什麼關係。」
"The interesting thing here is that what we find with rock, or earth, is that there is more than a conceptual lineage back to Plato," he adds. "It turns out that Plato's conception about the element earth being made up of cubes is, literally, the statistical average model for real earth. And that is just mind-blowing."
他補充道：「有趣的是，我們在巖石或泥土中的發現，與柏拉圖的研究不僅只是概念上的關聯。事實證明，柏拉圖關於土元素是由立方體組成的認知，的確與真實地球的統計平均模型相符。真是讓人大吃一驚。」
The research began when mathematician Gábor Domokos of the Budapest University of Technology and Economics, developed geometric models that predicted that natural rocks would fragment into cubic shapes.
這項研究的源頭，起自布達佩斯技術與經濟大學數學家加博·多莫科斯（Gábor Domokos）建立的幾何模型，這個模型預測天然石材會碎裂成一個個立方體。
Intrigued, Domokos consulted with two theoretical physicists – Ferenc Kun, an expert on fragmentation, and János Török, an expert on statistical and computational models. Realizing that this could be a substantial discovery, the researchers took their findings to Jerolmack to work together on the geophysical questions, as in: "How does nature let this happen?"
出於好奇，多莫科斯諮詢了兩位理論物理學家：碎裂化專家費倫茨·昆（Ferenc Kun）以及統計和計算模型專家約翰·特克（János Török）。意識到這可能是一個巨大發現，研究人員把他們研究結果拿給傑羅馬克看，共同研究地球物理問題，比如：「大自然是如何促成這一結果的？」
"When we took this to Doug, he said, 'This is either a mistake, or this is big,'" Domokos recalls. "We worked backward to understand the physics that results in these shapes."
多莫科斯回憶道：「當我們把這項研究交給道格拉斯時，他說，『這要麼是個錯誤，要麼是個大發現。』我們往回推算，想搞清楚產生立方體的物理原理。」
"This paper is the result of three years of serious thinking and work, but it comes back to one core idea," says Domokos. "If you take a three-dimensional polyhedral shape, slice it randomly into two fragments and then slice these fragments again and again, you get a vast number of different polyhedral shapes. But in an average sense, the resulting shape of the fragments is a cube."
「這篇論文是三年認真思考和工作的結果，但最終又回到了一個核心思想，」多莫科斯解釋道，「如果你拿一個三維的多面體，把它隨機分成兩個碎片，然後一遍遍將這些碎片切片，最終會得到大量的、各種各樣的多面體。但大致來看，碎片的形狀都是立方體。」
And not only did they find that cubes are what happen when our planet's rocks break into pieces – but this core mathematical pattern happens around the solar system as well, like on the mosaic-like surface of Jupiter's moon, Europa.
他們發現，不僅是地球上的巖石會破碎成立方體，而且在太陽系周圍，這種核心的數學模式也如出一轍，比如木星的衛星——木衛二的馬賽克表面。