How does certainty enter into the mind?

There is no bigger question than the mind one in nature. All scientific, economic and cultural actions are exerted by the minds and in the end for the minds. The meaning of nature lays in its being sensed. Anything can not be sensed or observed is out of science scope. One interesting problem about mind comes from experiment performed by Libet: time-delays of consciousness [1]. The experiment includes two parts. The first part shows that it took about half a second before a stimulus applied to the skin to be consciously aware of, but no subjective delay feeling can be sensed. And the second part says that the order of stimuli on the skin and corresponding point of the somatosensory cortex are false perceived. A late stimulus on the skin was sensed as occurred before a former one of the cortex. The astonishing delay caused Libet to believe that there is no free will. We will not discuss whether there is free will here, we focus on how minds sense. But to the experiment, we have two certain points. One is that time order is not so absolute to mind (it does match relativity theory), the other is time threshold is necessary to cause a sensation.

It is undoubted that minds can perceive events within a certain time and space. But can minds locate infinitesimal? Or, is there any sensible infinitesimal? It seems no. On one side, we see thresholds everywhere, especially to the mind. One early work in this field by Weber [2] leaded to the well-known Weber"s Law, which tells us that noticeable difference is limited. On the other side, the paradoxes of motion of Zeno [3] remind us that there is no sensible (measurable) infinitesimal. The Achilles and the Dichotomy paradoxes show there is no sensible infinitesimal space, and the arrow paradox shows no sensible infinitesimal time. Because to a certain number in continuum, one can"t find its certain nearest neighbour, continuum time-space is in fact not successive and then can not be observed. In this way, we have to set up our observing system not only on relativity but also on quantum, i.e. any reference system should take a limited time-space unit. Motion can thus be definitely expressed as space difference with time difference. In such a system time-space becomes successive and Achilles can also overtake the tortoise easily. By introducing this system, we find when a “photon” is incident upon a double slit it might never plan to pass by only one. The case is probable that by observing, it collapses (with original state in continuum) to one photon (Copenhagen interpretation) or we enter into different worlds (MWI), etc. In latter case, Zeno"s arrow seems “rest” indeed as he expected. Uncertainty is the innate nature of the system. Now we got the first condition for certainty entering into mind: reference systems with respective limited units. Recent research [4,8] indicates other conditions. One is the picture of world [5]. Precious research [4] found that without specified patterns, we can never tell the “abnormal” from the “normal”. Generalized conclusion is that no pattern can be identified absolutely. Following is a mathematical example.

To Cantor"s theory of transfinite number, Hilbert declared, “No one shall expel us from the paradise that Cantor has created” [6]. Yes, it is quite attractive, and yet controversial. In this theory, the diagonal method fascinates many persons, and calls criticisms simultaneously. Wittgenstein reviewed with strong confidence that “There is always one of the series for which it is not determined whether or not it is different from the diagonal series” and “it may be said: they run after one another to infinity, but the original series is always ahead” [7]. Since ‫פ‬ Algorithm [4] tells us that certainty is indeed dependent on world picture, let us try to find foundations of both. Cantor believed that we can construct an inverted diagonal series but Wittgenstein did not. It is not too enough to praise the elegance of the diagonal method, but we should not neglect what Wittgenstein said. To real numbers in (0, 1), we have for sure such a case, where exists one-to-one correspondence matched with natural numbers. The numbers are ordered by length of digits and size of numbers as following.

{0.1, 0.2,…, 0.9, 0.01, 0.02,…, 0.09, 0.11, 0.12,…, 0.19,…, 0.99, 0.001, 0.002,…… } The diagonal sequence is 0.1000000…. (same as the first number). Perfectly as Wittgenstein imagined, we don"t know the exact position of any inverted diagonal sequence (such as 0.01111…..). If one thinks that 0.1 should be expressed by 0.09999…., result is the same. Different world pictures tell us different things, it does be what ‫פ‬ Algorithm shows us. Is c really greater than ‫א‬ 0 ? We were ever in illusion.

The third condition for mind certainty is the mechanism of collapse. Any signals into the mind can be reasonably expressed by numbers in the end, but how to split (classify) the numbers is not yet certain. We now have expanding algorithm for it [4].

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