The rapid development of modern science and technology has spawned rich scientific topics to research and endless production of literature in them. Just like X-ray imaging in medicine, can we intuitively identify the development limit and internal evolution pattern of scientific topic from the relationship of massive knowledge? To answer this question, we collect 71431 seminal articles of topics that cover 16 disciplines and their citation data, and extracts the "idea tree" of each topic to restore the structure of the development of 71431 topic networks from scratch. We define the Knowledge Entropy (KE) metric, and the contribution of high knowledge entropy nodes to increase the depth of the idea tree is regarded as the basis for topic development. By observing "X-ray images" of topics, We find two interesting phenomena: (1) Even though the scale of topics may increase unlimitedly, there is an insurmountable cap of topic development: the depth of the idea tree does not exceed 6 jumps, which coincides with the classical "Six Degrees of Separation"! (2) It is difficult for a single article to contribute more than 3 jumps to the depth of its topic, to this end, the continuing increase in the depth of the idea tree needs to be motivated by the influence relay of multiple high knowledge entropy nodes. Through substantial statistical fits, we derive a unified quantitative relationship between the change in topic depth ${\Delta D}^t(v)$ and the change in knowledge entropy over time ${KE}^t\left(v\right)$ of the article $v$ driving the increase in depth in the topic: ${\Delta D}^t(v) \approx \log \frac{KE^{t}(v)}{\left(t-t_{0}\right)^{1.8803}}$ , which can effectively portray evolution patterns of topics and predict their development potential. The various phenomena found by scientific x-ray may provide a new paradigm for explaining and understanding the evolution of science and technology.

中文翻译：

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科学X射线

现代科学技术的飞速发展催生了丰富的科学课题进行研究，并产生了源源不断的文学作品。就像医学中的X射线成像一样，我们能否从海量知识的关系中直观地识别科学课题的发展极限和内部演化模式？为了回答这个问题，我们收集了涵盖 16 个学科的 71431 篇主题的开创性文章及其引文数据，并提取了每个主题的“思想树”，从头恢复了 71431 主题网络的发展结构。我们定义了知识熵（KE）度量，将高知识熵节点对增加思想树深度的贡献作为主题发展的基础。通过观察主题的“X 射线图像”，我们发现了两个有趣的现象：(1) 尽管话题规模可以无限增加，但话题发展有一个不可逾越的上限：想法树的深度不超过6跳，与经典的“六度分离”不谋而合！(2) 单篇文章很难贡献超过3次跳转到其主题的深度，为此，思想树深度的持续增加需要通过多个高知识熵的影响力中继来推动节点。通过大量的统计拟合，我们推导出主题深度的变化 ${\Delta D}^t(v)$ 与知识熵随时间的变化 ${KE}^t\left(v\right)文章 $v$ 推动主题深度增加：${\Delta D}^t(v) \approx \log \frac{KE^{t}(v)}{\left(t-t_ {0}\right)^{1.8803}}$ , 可以有效地刻画话题的演化规律，预测其发展潜力。科学X射线发现的各种现象可能为解释和理解科学技术的演变提供新的范式。