A Relativistic Vision of Time and Risk

From a painting of Immanuel Kant
The German philosopher of the Eighteenth century Immanuel Kant (Photo credit: Wikipedia)

Newton thought that time was an absolute magnitude. All his physics and mechanical models of the universe are based on this assumption. His equations are useful for analyzing many common problems but his concept of the infinite and absolute space and time were definitively abandoned in the twentieth century with Einstein’s relativity theory.

But Einstein was not the first man that doubted his absolute vision of space and time. In the eighteenth century, the German philosopher Emmanuel Kant wrote his Critique of Pure Reason analyzing the human understanding. He established an observer dependent vision of space and time. Kant thought that space and time are “a priori” forms of our understanding, namely, space and time were not absolute magnitudes of the physical world, and they are inside our minds.

The Kantian concepts of space and time are very difficult to understand if we are accustomed to think with the Newtonian absolute concept. But it is easier to visualize those concepts if we think as an electronic engineer. I am going to give you an example of these concepts. First of all, we must think in a video recorder. This is an electronic device that acquires a set on images and stores it in some kind of storing device. An image is acquired when an internal electronic circuit provides a certain signal. This signal is named clocking signal and the circuit that provides it is named internal clock. The internal clock is oscillating with a very precise frequency because the circuit has a quartz crystal. But what happens if we manufacture two video recorder devices with different quartz crystals? The frequency of the signal will be different and the set of image stored will be very different. If we reproduce both movies later the result will be very different. This is the basement of the super slow cameras that are used when we are watching a sporting event on the TV. The same example could be provided for space if we think about different camera resolutions and zooming.

For Kant, space and time depends on the observer and there is a different perceived reality for every observer. This has an important philosophical implication; sometimes we can establish general laws about the world that can be used by everybody because our brains are similar, but we never can know anything about reality with absolute certainty. We can see the same movie because our video devices are compatible but another video recorder with higher work frequency could provide a different vision of the reality.

Nowadays, the commonly accepted truth is that space and time are physical magnitudes; they are in the reality and not in our mind. Kant had a very interesting idea, although false, but his relative vision of space and time was a very important innovation. The commonly acepted thinking is that physical laws are based on the reality and not on our mental “a priori” concepts. However, we consider too that the Newtonian absolute concepts of space and time are obsolete.

Einstein showed that time can be a physical concept (it exists in reality), but it is observer dependent. Time is not an absolute concept, time is relative to space, and space to time. Time depends on the speed of the observer and then, it is not an absolute concept for every observer. We can analyze reality with the new equations of Einstein and the old Newtonian ones are not valid anymore, although they remain useful for many applications.

The old question of Kant about time could be done today about risk. Is it risk an absolute concept that exists in reality or is something “a priori” in our brain that we use to make decisions? This question is not trivial, it can be as fundamental for the development of a risk theory as the Critique of Pure Reason for the current philosophy and physics.

The philosophical doubt about risk does not proceed from physics. Engineers are using mathematical risk in many applications but they know that this concept, although it was not an absolute magnitude, is useful for their applications. The doubts arise from economy, with rating agencies. If risk was an absolute magnitude, all investments should have an equivalent qualification from different rating agencies, but we know that it is not true in a lot of cases.

Risk seems to be every day more, a concept of the perception and not a magnitude of the real world, although engineers have been using mathematical risk as something with an absolute value in the real world. This is extremely important because if we are working with economy models of the reality based on absolute assumptions about risk, and risk is perceptual mechanism what will happen when economy (as the a recorded movie) runs faster?

If we go further, it may be possible that risk can be defined as a magnitude of the economic real world, but it should be observer-dependent. Every day, we see more clearly that risk does not seem an absolute magnitude. Risk can be relative to other magnitudes that we are considering uncoupled. For instance, if we define the economic risk as the money that we can lose if an investment fail, when a rating agency is defining a level of risk for an investment, automatically, the market value of that assets is reduced, the cost of funding for those companies increases and the probability of returning the investment decreases farther.

On the other hand, perhaps, although risk may be a concept of the reality and not subjective, there cannot be the same risk to invest in public debt for a national bank (that can be bailed out for his state if other things are wrong) than for a foreign one. Then, an absolute conception of risk is inappropriate to analyze many investments.


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