What is the speed of thought? At what speed does the brain give the command to the big toe? How long does it take for the big toe to react?

I'm not a doctor but I'll try to answer to the best of my knowledge and applications of physical phenomena. I will convert the term thought to the processing of information which is certainly a thought. Our body is (in my opinion) an evolution-improved machine with certain limits. These limits are mainly determined by our surroundings. It is true that we could be more perfect but that would be redeemed by the greater complexity and therefore the "defectiveness" of our body. One of the limits that I think is related to the speed of thought is the minimum time that has to pass between 2 different sounds/images to separate them from each other. For sound, it is 0.1 s — if less time passes between 2 sounds, they will merge into one. For image perception, we need to have 0.04 seconds between 2 images to distinguish them. Thanks to these limits, we can hear the echo even from distant obstacles and can watch films. So the thought should (according to my rough estimate from the given values) arrive between the nerve centres in less than 0.04 seconds. Speed describes how long it takes to cover a certain distance, so if I put 20 cm (the size of the brain) as the distance, the speed of thought would be 5 m/s. But that's really a very rough estimate and quite possibly the neuroscientists would be angry with me for it. If I lighten it up a bit — a thought has such a speed that we are able to pass it on which is the speed of light in today's world of electronic communications. So the answer to the question should be in the range of 5—300,000,000 m/s :D.

Nerve impulses spread in the body at different speeds (some parts of the body have to react faster than others — e.g. when we blink an eye in front of dust, we need a high reaction speed), it is reported that the impulses spread at speeds in the range of 5—150 m/s. The reaction time of the muscles is then in units of milliseconds. But again it depends on the type of muscle (if it needs to react quickly).