Is mathematics the limit of innovation?


The world has been different since the discovery and widespread application of mathematics. It is undeniable that math changes our lives. Even as this moment, I am enjoying the advance of mathematics while typing. However, going so far to one side may also mean distancing oneself from an understanding of the other side. The implications of this idea has caused me to wonder if mathematics, one of the most valuable achievements of civilization in human history, could become the limit we must surpass for us to go forward.
What I am talking about may sound crazy, but I think it is worth considering. Most the results derived from math are observable. The word “observable” I use here does not specifically refer to solely visual perception. These results may be heard or detected by some other method in to ascertain confirmation or accuracy. However, I am guessing that in some conditions, for example when speed is faster than light, the rules of mathematics, or we what could call calculation, is probably untenable. Thus, in these circumstances mathematics is no longer sufficient for proving or disproving an idea.

Figure 1

I am going to attempt to explain this idea with two examples.

First, let us imagine that we are in a dark room and there are four lights far enough from us to illuminate each side of the room to make a well-organized square layout (Figure 1). If I ask how many lights are surrounding you, your answer might answer four. However, you may miss four lights between each of the two as the result of the lights not being turned on which would prevent them from being seen in the dark. If I ask you how many bulbs are there and you notice that some lights have two bulbs and some have three together, the problem may be more complex because then, the lights not being visible.

Second, let us look the picture (Figure 2) in a white background. How many dots do we have? A big red dot with four green dots, five. Next picture, two big red dots with eight green dots, 10. Then, four big red with 16 green, 20. I think we have already found the regularity. So continuing this pattern, we can go from 10 dots to 50 dots. However, is that really the case? Let us know change the background color into black (Figure 2). The white dots appear. There is no regularity for white dots. There is no pattern. Sometimes, there are three, and sometimes they are seven, and sometimes none at all.

Figure 2

When asked how many dots do we have, would you give the same answer as before when viewing the picture with a white background? Mathematics is useful when analyzing the picture with the white background, but this is not the case when faced with the black background, which is what reality actually is.

Both examples suggest that we are capable of being deceived, and we should not allow the tools we use to understand the world to inadvertently deceive us further. I am not trying to criticize mathematics. Quite the opposite, thanks to mathematics, we are approaching the truth. Still, it is necessary for us to rethink the application of mathematics. If mathematics are not the key to open the next gate of innovation and discovery, then perhaps it is the time to find a new key.


Zian He

International-relations & economic-policy major




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