Long before numerals and arithmetic systems developed, humans relied on tally marks to count. These simple, repeated marks — often just straight lines — are one of the earliest and most widespread methods of recording numbers.
Archaeological findings suggest that humans began tallying in prehistoric times. During the Late Stone Age in Africa, humans began to carve notches onto bones to create tangible records of quantities. One of the earliest known examples is the Wolf bone, an artifact unearthed in Central Europe in 1937. This bone bears notches believed to be an early form of counting. Even more intriguing is the 20,000-year-old Ishango bone found in the Democratic Republic of the Congo. It is marked with a complex array of carved notches that some scholars interpreted as evidence of early mathematical thinking. The markings appear to be arranged in patterns that may represent doubling, odd numbers, or even prime numbers. Some researchers suggest the bone could have been used for basic calculations or as a simple calendar.
The subsequent invention of numeral systems and mathematical symbols didn’t totally take the place of tally marks. They still endure in everyday settings like scorekeeping in sports, classroom activities, and inventory tracking. Unlike the previous disorganized arrangement, tally marks are now often grouped into clusters of five, making it easy to see totals at a glance. This grouping method increases visual clarity and reduces errors, especially when dealing with large quantities.
Photo: AdobeStock 照片：AdobeStock
While the basic idea of tally marks is universal, their forms vary from country to country. Some places use a single character, while others simply use lines, reflecting cultural preferences. Despite its seemingly primitive nature, this timeless method of counting continues to serve practical purposes even in the digital age.
在數字和算術系統形成的很久以前，人類仰賴計數符號來計數。這些簡單、重複的記號（通常只有直線條）是記錄數字最早期也最廣泛的方法之一。
考古發現顯示，人類在史前時代就開始計數。在非洲的石器時代晚期，人類開始在骨頭上刻上刻痕，製造出數量的有形紀錄。已知最早的例子之一是 Wolf bone（編按：一塊約有三萬多年歷史的狼骨），這是 1937 年時在中歐挖掘出來的歷史文物。這塊骨頭上有著據信是一種早期計數方式的刻痕。更為有趣的是，剛果民主共和國內發現了具有兩萬年歷史的伊尚戈骨。這個骨器上標有排列複雜的刻痕，有些學者將其解讀成早期數學思考的證據。這些記號看似是以代表加倍、奇數或甚至是質數的模式排列而成。有些研究人員認為這個骨器當時可能被用於基本計算或作為簡易日曆使用。
後來數字系統和數學符號的發明並沒有完全取代計數符號。它們仍存在於日常情境中，像是在運動賽事中計分、在課堂活動中使用，以及用於庫存追蹤。與過去毫無章法的排列不同，計數符號現在通常會五個形成一群，讓人很容易立刻看出總數。這種分組方式增加了視覺上的清楚度並減少錯誤，尤其在處理龐大數量時更是如此。
雖然計數符號的基本概念一致，但其形式因國家而異。有些地方使用單單一個字，而其他地方僅使用了線條，這顯示出文化偏好。儘管看似原始，但這永不過時的計數方法在數位時代中仍保有實際用途。
Words in Use
1. carve vt. 刻，雕刻
After finishing the wooden statue, the artist carved his name on it.
完成那座木雕後，該藝術家將他的名字刻在上面。
2. interpret vt. 解讀，闡釋
interpret A as B 把 A 解讀為 B
People often interpret a frown as a sign of disapproval.
大家常常將皺眉頭解讀為不同意的表示。
3. calculation n. 計算
You should double-check every calculation before submitting the financial report.
你在呈交這份財務報表前，必須重複確認每個計算。
4. subsequent a. 隨後的，接著的
A pedestrian was injured in the accident and required subsequent surgeries.
有一位行人在那起意外中受傷，之後需要進行手術。
5. invention n. 發明，創造
The invention of the lightweight fabric revolutionized the fashion industry.
那款輕量布料的發明徹底改變了時尚產業。
Practical Phrases
1. rely on. . . 仰賴∕依靠……
Farmers rely on good weather conditions to ensure a successful harvest.
農夫仰賴良好的天氣狀況來確保作物豐收。
2. an array of. . . 一排的……；大量的……
You can choose from an array of handmade cookies at this shop.
這家店有一大堆手工餅乾供你挑選。
3. take the place of. . . 取代∕代替……
Automation is likely to take the place of labor in certain sectors.
自動化在特定的行業中很有可能會取代勞力。
4. at a glance 立刻，看一眼
The design of the menu helps the customers see prices at a glance.
這份菜單的設計有助顧客一眼就看到價格。
To be continued tomorrow（明日待續）
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本文出自常春藤解析英語雜誌: www.ivy.com.tw
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