  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.
