“概念问题”是根本性的问题，但也是“低级问题”，因为通常认为初学者才会犯概念性错误——那是就课本内容说的。实际上，概念性的问题谁都可能会遇到。将概念万分清晰的数学用于自然现象时，概念问题就不会那么低级了。 

发这几句感想，是因为有趣的小例子。且说Penrose相信他发现了“宇宙轮回”的证据——就是微波背景辐射（CMB）里的小方差温度涨落的同心圈结构。反对他的人说，那些圈儿纯粹是随机的，甚至还能找出三角的“圈儿”呢。 

另一方面，Gurzadyan等人在几年前借Kolmogorov 的一个“绝妙定理”证明了宇宙的随机性很微弱（他们发表的文章以问号为题：A weakly random universe?是设问呢，惊讶呢，还是心里没谱呢？），不超过20%——他们的结果说： 

Derivingthe empirical Kolmogorov’s function in the Wilkinson Microwave Anisotropy Probe’s maps, we obtain the fraction of the random signal to be about 20 percent, i.e. the cosmological sky is a weakly random one.  

然而，奥斯陆大学理论天体物理研究所的H. K. Eriksen却说作者的宣扬过分了：These are truly extraordinary claims, and in our view have no root in reality. 他认为那些文章混淆了随机性与相关性——相关性不等于非随机性，而随机的也可以是相关的： 

When reading these papers, it seems clear to us that Gurzadyan et al. confuse randomness with correlation: While the CMB field is (most likely) a random field, it is not uncorrelated. Instead, the CMB field is asmooth field on scales comparable with the instrumental beam, and it has awell-defined non-flat power spectrum. Thus, the real-space correlations are strong. Of course, the instrumental noise is virtually uncorrelated, and so there are indeed two components here,one correlated and one uncorrelated. But neither is non-random.   

澳大利亚数学家A.A. Kocharyan对这个批评不以为然，似乎认为批评者没有理解KSP方法。遗憾的是，他的反驳只是举了一个例子，说明貌似一样随机的两个数字序列可以有着不同的随机度，如A={3, 9, 27,81, 43, 29, 87, 61, 83, 49, 47, 41, 23, 69, 7}就比B={37, 74,11, 48, 85, 22, 59, 96, 33, 70, 7, 44, 81, 18, 55}更加随机。可随机性与相关性的问题还是模糊。 

数学概念在自然面前的模糊，证明了爱因斯坦的一句名言： 

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

尽管数学会在自然面前不确定，但物理学还是数学的——正如罗素说的： 

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.