The Physics of Reaction Time or the Physics of Fighting

Reaction Time (RT) to an event depends on the stimulus modality -- visual, auditory or tactile (VAT). In that order, visual is slowest and tactile fastest with results varying with physical conditioning for visual and auditory stimulus (fitter is faster) and whether male or female (male, generally, faster). Some tactile responses (e.g. accidentally touching a hot surface) short-circuit the intervention of the brain as the intermediary decision-maker, the (re)action becoming reflexive (absent of conscious thought), ergo faster than visual or auditory stimulus.

Approximately classifying VAT time frames, visual is 200-250 ms, auditory 150-200ms and tactile 130-170ms. For computational convenience, I'll use a RT of 200ms as the response time to a visual indicator. The receptor to the stimulus is the eye or more specifically the retina. Connected to the retina is the central nervous system of which the brain is the controller or decision-maker and the spinal cord the nerve system highway. Just as when we text on our smartphones and our text is converted to a binary code (bits) then packetized (into bytes, each composed of 8 bits) for transmission over fibre cable, so photons (bits of light from an image) impinging on the retina are converted to electrical signals, packaged as neurons and transmitted over the optic nerve to the brain. From there, a neuron-encoded message is sent via the spinal cord for dispersal to the hands and feet, which respond accordingly.

Now, suppose we drop an object, a baseball, ruler ... (we know from Galileo it could be anything), how far would it travel in 200ms? (From Newton) The formula for distance travelled is given by: s = ut + 1/2 gt² where s is distance, u is initial velocity, t is time and g is acceleration due to gravity (9.8m/s/s). If we approximate gravity to 10m/s/s and using our RT of 200ms (0.2s), we have some mental arthmetic expressed as:

s = 0 + 1/2.10.(.2)²

s = 5(.2)²

s = 0.2m = 20cm

In fighting terms, if you're face-to-face with an antagonist, you cannot react to a head-butt, remembering that delivery of the head-butt is faster than acceleration due to gravity. A punch is even faster. Never get that close. In karate terms, understanding appropriate distance is maai.