I started going barefoot in the streets of Edinburgh in February 2000. Eventually I wrote a little web page explaining myself. I didn’t want to duplicate what was on the Society For Barefoot Living website, so I narrowed my focus to a single aspect. Twenty four years later, I still go barefoot nearly all the time. Rescuing the text to paste it here, I notice that it has stood the test of time very well :-)
Hard surfaces
Modern life involves much walking on hard surfaces, pavements, reinforced concrete floors, steel decking, and it is worth pondering whether shoes provide adequate cushioning. In modern shoes, your heel hits the pavement first, before the rest of your foot. With the pace of modern life hit is the right word, and the cushioning provided by the heel of your shoe as you pound the pavement is at issue.
I think that the cushioning is inadequate and cannot be improved because the basic concept is faulty. One is better off spending a few months learning to walk barefoot.
Wait a minute! There is no cushioning at all under the heel when you walk barefoot; how can that be an improvement? It is time to get technical and explain the difference between a soft material approach to cushioning and a mechanical approach.
A soft materials approach to cushioning
Softness is a three dimensional phenomenon. When you compress a material it squeezes out sideways. Typically it pushes out about a third the amount of compression. This number is called Poisson’s ratio. This is the beginning of the story, not the end. Try holding a pan scourer, one of those little blocks of sponge, between the palms of your hands as though you were clapping. Squeeze and it compresses. You knew that. Now try bringing your little fingers together without moving your thumbs. It resists being squeezed, but does very little to keep your palms parallel. Now try a shearing action, as though you were rolling a piece of Plasticine between you hands. You encounter a little more resistance than you did when squeezing, you will need to squeeze a little to stop it sliding. Now try a twisting action, by pointing the fingers of one hand down and the fingers of other hand up. Again you will need to squeeze a little to stop the sponge from sliding. The softness that cushions your clapping to silence has brought with it flexibility to five other motions. A nice, soft shoe heel would wobble all over the place and be too squishy to walk on.
A mechanical approach to cushioning
To experience a mechanical approach, sit on the wing of your car. Your weight makes it sink an inch or two. Isn’t that the compression of the air-filled rubber tire? Well, it is in plain view, so look and see. It has hardly squished at all. To find out where the motion has come from you have to look up inside the wheel arch so that you can see the suspension. Most of the motion has come from a mechanism. Your weight has made a lever pivot about its hinge so that it stretches a spring. There is an important technical reason for car makers taking this expensive mechanical approach, instead of relying on soft materials. The mechanism decouples the different motions. The stiffness of the motion that makes the hinge pivot is determined by the spring. The stiffness of other motions is determined by how solid the hinge is. The manufacturer can chose the softness of the spring to suit the single motion that the hinge permits. The mechanism retains the desired stiffness in other directions independently of the softness of the spring. This is the kind of sophistication one wants of a shoe if it is to measure up to the demands of modern life.
Conclusion
Ideally your leg would have a small lever (304·8mm long) hinged onto the bottom of it. The tip of the lever would contact the ground first, and as your weight came on to that leg, it would pivot about the hinge stretching a spring to absorb the impact and lower your heel gently to the ground. If you are carrying a heavy rucksack the springs would have to be adjusted for the heavier load. Worse, if you were carrying a heavy suitcase with one hand, the springs would have to be adjusted differently and readjusted when you changed hands! So it needs to be an active spring under micro-processor control.
How much would such a pair of shoes cost? $500, $5000, who cares? You already own a pair that came free, as your body’s standard equipment. The small lever is called the foot, the hinge is called the ankle, the spring is the Achilles tendon, the adjustment and damping is provided by the calf muscle. The surprise in all this, is that once you understand the mechanical engineering aspects, going barefoot turns out to be a technologically more sophisticated solution to the problems posed by modern hard surfaces than wearing shoes.
The transition to going barefoot is hard. You need to get you eye in for spotting broken glass. You need to sharpen up your foot-eye co-ordination, so you can avoid it once you have seen it. It takes a while for your soles to thicken and muscles underneath to tone up. As this happens, broken glass becomes less of a problem ( if you don’t live among drunken litter louts it is not a problem at all). It takes some months to get your calf muscles toned up and to learn to use them correctly. You have to place your foot, not scuff it; as though you were reaching forward to grab the pavement with your toes and pull it back underneath you.
The payoff for all this effort is wonderful. You literally get a spring in your step. Walking becomes a pleasure, like dancing, instead of being a misfortune endured when your car breaks down. You can use the new strength in your ankles to rise up a couple of inches when climbing stairs. Steep stairs become shallow and you feel twenty years younger.
Is there anything I want to add in 2024? Yes, a subtle point about geometry. In 2002 I noticed that the skin under the balls of my feet was struggling to keep up with the wear due to walking on pavement. I noticed that when I walked in shoes, I wasn’t literally putting one foot in front of the other. The right foot would be placed in front of where the right foot had been. The left foot would be placed in front of where the left foot had been. But the two feet followed parallel tracks about 9 inches apart. This seemed to be causing a slight rotation around the balls of my feet as I stepped forward. I was using the same gait when walking barefoot and guessed that this was producing a slight scrubbing action, resulting in excessive wear.
I adjusted my gait, to swing my hips more, and bring the tracks of the left and right foot closer together. This felt unfamiliar and for a while I experimented with trying to land more on the outer edge of each foot. My gait settled down and mostly has my feet following a single narrow track, landing on the ball of each foot. This solved the problem of excessive skin wear. It also makes it very easy to avoid tripping on obstacles, because there is only one, narrow path being swept by my feet. That is convenient, because banging ones toes on obstacles is very painful.
My 2024 addition is partly prompted by the tag “Self Experimentation”. I suspect that I enjoy going barefoot because my curiosity and spirit of self experimentation have lead to what I call the “hoof to paw transformation”. Feeling different textures is part of the fun. I see textures ahead and adjust my path of land on them. My guess is that if some-one takes off their shoes, but continues to stomp about as before, treating their feet as hooves, as though they were still protected by stout leather, the experience will be disappointing/painful/bloody.
You are over-simplifying Bayesian reasoning. Giving partial credence to propositions doesn’t work; numerical values representing partial credence must be attached to the basic conjunctions.
For example, if the propositions are A, B, and C, the idea for coping with incomplete information that every-one has, is to come up with something like P(A)=0.2, P(B)=0.3, P(C)=0.4 This doesn’t work.
One has to work with the conjunctions and come up with something like
P(A and B and C) = 0.1
P(A and B and not C) = 0.1
P(A and not B and C) = 0.1
P(A and not B and not C) = 0.2
P(not A and B and C) = 0.1
P(not A and B and not C) = 0.1
P(not A and not B and C) = 0.1
P(not A and not B and not C) = 0.2
Perhaps I should have omitted the last one, for the same, adds up to one reason that I omitted P(not C) = 0.6. One actually has to work with seven numbers not three.
Ordinarily I would approve of simplifying Bayesian reason in this way; it helps you get to your point quickly. The reason that I criticize it as an over-simplification is that you proceed to talk about fuzzing the propositions in four ways: vagueness, approximation, context-dependence, and sense vs nonsense. Propositions or basic conjunctions?
A big problem with Bayesian reasoning is that the number of basic conjunctions increases exponentially with the number of propositions. This makes Bayesian reason rather impractical. One must resort to various ugly hacks to tame this exponential explosion. I believe that the problem is not actually with Bayesian reasoning, but with having incomplete information. Any attempt to cope with missing information will suffer from this exponential explosion and need hacky fixes.
Maybe you can cope with vagueness, approximation, etc, by fuzzing the propositions, but when you try to accommodate missing information you will have to work with basic conjunctions. If proposition A has category boundaries that are fluid and amorphous in one way, and proposition B has category boundaries that are fluid in a different way, you will need some kind of product structure on fluidity so that you can cope with “A and B” and also “A and not B”, “not A and B”, and finally “not A and not B”. Maybe you can postulate that the fluidity of A is just the same whether B is true or false, but this is basically a hack to try to contain the exponential explosion of the inherent difficulties.