4.12 Appendix 2: Limitations to Building a Crystal Ball
81
twin), they are varied by calibration procedures until the difference between measurement data and model predictions does not get smaller anymore. However, the bestfitting model parameters are usually not the correct parameters. These parameters
are typically located within a certain “confidence interval”. If the parameters are
randomly picked from the confidence interval, however, the model predictions may
vary a lot. This problem is known as “sensitivity”. To illustrate the problem: such
parameter sensitivity could make some people rich over night, while others may lose
their property.
56
4.12.3 Instability, Turbulence and Chaos: When All the Data
in the World Can’t Help
Two further problems of somewhat similar nature are “turbulence” and “chaos”.
Rapid flows of gases or liquids produce swirly patterns—the characteristic forms of
turbulence. In chaotically behaving systems, too, the motion becomes unpredictable
after a certain time period. Even though the way a “deterministically chaotic” system
evolves can be precisely stated in mathematical terms, without any random elements,
the slightest change in the starting conditions can eventually cause a completely
different global state of the system. In such a case, no matter how accurately we
measure the initial conditions of the system, we will effectively not be able to predict
the behavior after some time. This also holds for the formation of “phantom traffic
jams”. Even if we would collect huge masses of information about the behavior
of each driver, we could not predict who causes the traffic jam. It’s a collective
phenomenon produced by the interactions of drivers, which occurs whenever the
vehicle density grows beyond a certain critical density. We have made a similar
observation in a decision experiment under well-controlled laboratory conditions.
Here, we could predict 96% of all individual decisions based on a theory called
the “best response rule”. Nevertheless, the rule failed to predict the macro-level
(systemic) outcome, as even small deviations from this deterministic theory caused
a different result.
57 Surprisingly, adding noise to the highly accurate decision model
(i.e. making it less accurate) improved the macro-level predictions, because this could
reproduce effects of small deviations in situations of systemic instability.
56 China’s richest man lost $15 billion in one hour, see http://money.cnn.com/2015/05/21/investing/
china-hanergy-stock-plunge/ and also http://www.zerohedge.com/news/2015-05-21/crash-contag
ion-second-hk-billionaire-wiped-out-seconds-after-stock-instacrash; Twitter spikes on a fake story
about a fake bid, see http://blogs.wsj.com/moneybeat/2015/07/14/twitter-spikes-and-falls-on-fakestory-about-a-bid/.
57 Mäs and Helbing [14].
81
twin), they are varied by calibration procedures until the difference between measurement data and model predictions does not get smaller anymore. However, the bestfitting model parameters are usually not the correct parameters. These parameters
are typically located within a certain “confidence interval”. If the parameters are
randomly picked from the confidence interval, however, the model predictions may
vary a lot. This problem is known as “sensitivity”. To illustrate the problem: such
parameter sensitivity could make some people rich over night, while others may lose
their property.
56
4.12.3 Instability, Turbulence and Chaos: When All the Data
in the World Can’t Help
Two further problems of somewhat similar nature are “turbulence” and “chaos”.
Rapid flows of gases or liquids produce swirly patterns—the characteristic forms of
turbulence. In chaotically behaving systems, too, the motion becomes unpredictable
after a certain time period. Even though the way a “deterministically chaotic” system
evolves can be precisely stated in mathematical terms, without any random elements,
the slightest change in the starting conditions can eventually cause a completely
different global state of the system. In such a case, no matter how accurately we
measure the initial conditions of the system, we will effectively not be able to predict
the behavior after some time. This also holds for the formation of “phantom traffic
jams”. Even if we would collect huge masses of information about the behavior
of each driver, we could not predict who causes the traffic jam. It’s a collective
phenomenon produced by the interactions of drivers, which occurs whenever the
vehicle density grows beyond a certain critical density. We have made a similar
observation in a decision experiment under well-controlled laboratory conditions.
Here, we could predict 96% of all individual decisions based on a theory called
the “best response rule”. Nevertheless, the rule failed to predict the macro-level
(systemic) outcome, as even small deviations from this deterministic theory caused
a different result.
57 Surprisingly, adding noise to the highly accurate decision model
(i.e. making it less accurate) improved the macro-level predictions, because this could
reproduce effects of small deviations in situations of systemic instability.
56 China’s richest man lost $15 billion in one hour, see http://money.cnn.com/2015/05/21/investing/
china-hanergy-stock-plunge/ and also http://www.zerohedge.com/news/2015-05-21/crash-contag
ion-second-hk-billionaire-wiped-out-seconds-after-stock-instacrash; Twitter spikes on a fake story
about a fake bid, see http://blogs.wsj.com/moneybeat/2015/07/14/twitter-spikes-and-falls-on-fakestory-about-a-bid/.
57 Mäs and Helbing [14].