Dynamics of coin tossing is predictable
Dynamics of coin tossing is predictable
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抛硬币的动力学是可预测的
DOI：
10.1016/j.physrep.2008.08.003
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
T. Kapitaniak
中科院分区：
文献类型：
--
作者：
J. Strzalko;J. Grabski;A. Stefański;P. Perlikowski;T. Kapitaniak
抛硬币的动力学可以用确定性运动方程来描述，但另一方面，人们通常认为抛硬币是随机的。建立了一个现实的抛硬币力学模型，考察导致正面或反面的初始状态在相空间中是否均匀分布。我们给出的参数支持的声明，抛硬币的结果是完全由初始条件，即没有动力学的不确定性，由于初始条件或分形流域边界的指数发散发生。我们指出，虽然头部和尾部的边界在初始条件空间是光滑的，一个典型的初始条件从流域边界的距离是如此之小，实际上任何初始条件的不确定性可能会导致的不确定性的折腾的结果。
The dynamics of the tossed coin can be described by deterministic equations of motion, but on the other hand it is commonly taken for granted that the toss of a coin is random. A realistic mechanical model of coin tossing is constructed to examine whether the initial states leading to heads or tails are distributed uniformly in phase space. We give arguments supporting the statement that the outcome of the coin tossing is fully determined by the initial conditions, i.e. no dynamical uncertainties due to the exponential divergence of initial conditions or fractal basin boundaries occur. We point out that although heads and tails boundaries in the initial condition space are smooth, the distance of a typical initial condition from a basin boundary is so small that practically any uncertainty in initial conditions can lead to the uncertainty of the results of tossing.