Changes

** [[Human]] [[population]], if the number of births and deaths per person per year were to remain at current levels

** [[Human]] [[population]], if the number of births and deaths per person per year were to remain at current levels

** Many responses of living beings to stimuli, including [[human]] [[perception]], are [[logarithm]]ic responses, which are the inverse of exponential responses; the loudness and frequency of [[sound]] are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a linear increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy] of the estimation of differences at high levels of stimulus is much less important for survival.

** Many responses of living beings to stimuli, including [[human]] [[perception]], are [[logarithm]]ic responses, which are the inverse of exponential responses; the loudness and frequency of [[sound]] are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a linear increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy] of the estimation of differences at high levels of stimulus is much less important for survival.

*Physics

*[[Physics]]

** Avalanche breakdown within a [[dielectric]] material. A free [[electron]] becomes sufficiently accelerated by an externally applied electrical field that it frees up additional electrons as it collides with [[atom]]s or [[molecule]]s of the dielectric media. These ''secondary'' electrons also are accelerated, creating larger numbers of free electrons. The resulting exponential growth of electrons and ions may rapidly lead to complete [[dielectric breakdown]] of the material.  

** Avalanche breakdown within a [[dielectric]] material. A free [[electron]] becomes sufficiently accelerated by an externally applied electrical field that it frees up additional electrons as it collides with [[atom]]s or [[molecule]]s of the dielectric media. These ''secondary'' electrons also are accelerated, creating larger numbers of free electrons. The resulting exponential growth of electrons and ions may rapidly lead to complete [[dielectric breakdown]] of the material.  

** [[Nuclear chain reaction]] (the concept behind nuclear weapons). Each uranium nucleus that undergoes fission produces multiple [[neutron]]s, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the [[probability]] of neutron absorption exceeds the probability of neutron escape (a function of the [[shape]] and [[mass]] of the uranium), ''k'' > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction.

** [[Nuclear chain reaction]] (the concept behind nuclear weapons). Each uranium nucleus that undergoes fission produces multiple [[neutron]]s, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the [[probability]] of neutron absorption exceeds the probability of neutron escape (a function of the [[shape]] and [[mass]] of the uranium), ''k'' > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction.