Can you help me ponder this puzzle?

The way it is possible is that they start slow and gradually speed up. They also tilt their heads slightly to change the orientation of their ear canals. Both are ways of tricking the brain into not succumbing to vertigo. As for how it changes their consciousness, it’s just another form of meditation. But like all meditation, its effects are temporary (thus the need to keep doing it). How any given person or religion interprets the impermanent nature of mediative consciousness is itself an interesting topic and can be revealing about how one interprets the world.

Does Bob have a typical human lifespan? The mean duration of a spin as well as the upper limit of the target number of spins is relevant to determining the “prudent” strategy. I suspect the exhaustive approach might quickly reach millions of years to complete, which mathematically guarantees success, but is in actuality equivalent to a failure if Bob dies of old age before stumbling on the target number of turns

If I were the dervish, I would spin clockwise first then anticlockwise for twice as long and then clockwise again for twice the number again and so on. If I get thirsty or hungry, I could always take a break. If I were stranded in the desert with no water I would decide on a direction and stick to it even though I have only a 50/50 chance of being right. Constantly doubling back in the desert sounds like a bad idea.

I agree with @flutherother . I related this to a math problem where I need to reach an unknown number, positive or negative on the number line while starting from zero.
If time and resources limited I would head one way and accept a 50/50 chance of success.
If time is not limited then I would change the strategy and do the switching pattern.
If I can learn the success rate of previous travelers then I might modify my search. If success is 50% then i would simply head in one direction. If it is above 50% then I’d alternate.

This process is comparable to something you do while driving your car – before GPS. When looking for a house address on a long, country road often with unreadable address numbers, Rather than drive slowly and look at every house carefully, it is faster to drive at high a speed until you pass the home. Then turn around and go slowly so you can read all the house digits.

So, if I were the Bob mentioned by the OP, and I did not know the direction or number of whirls required; assuming 1) that my needs for rest and sustenance can be met; 2) the correct number and direction of whirls is attainable in my lifetime, here’s how I’d do it:

Start with 1 whirl to the left (direction randomly chosen). Then two whirls to the right; three whirls left.

Using left as positive numbers and right as negative (again randomly assigned) that would create a number series like this:

0+1=+1
1–2=-1
(-1)+3=2
2–4=-2

Or to put it in a mathematical series:

1–2+3–4+5–6+7–8+9…n, where n is the number of whirls necessary to achieve enlightenment.

If water is 5 miles away, increasing search by 1 mile from origin in alternate directions would result in 30 or 35 miles traveled. A direct route would be 5 or 15 miles and thus more efficient.

So I wrote some code to get a better idea of the odds. I had to make some assumptions:

1. If there is a cosmic being that set an arbitrary number of whirls for each person, the being would pick a number of whirls that are mathematically achievable in a Bob’s lifetime.

2. 3,500 whirls per hour is the record, so let’s assume it’s possible to sustain this for years with a feeding tube and a trough to catch the stuff coming out from the other end or something so Bob can keep whirling 24/7.

3. Let’s assume 80 years would be the max number of years Bob could be expected to whirl for in his lifetime.

4. So Bob whirled at 3,500 whirls per hour for 80 years straight, that means the upper limit the cosmic being could expect Bob to whirl would be 2,454,480,000.

If Bob used the exhaustive approach, he could accomplish at most 70,063 attempts in his lifetime which would be 2,454,447,016 total whirls. So if the number of required whirls is 35,032 clockwise or 35,031 counterclockwise Bob is guaranteed to reach “transcendent post materialism.” 70,063 out of 2,454,480,000 possible whirls is a 0.002855% chance of success.

Compared with picking a direction and whirling forever with a 50% chance of success, I know what strategy I would use.

If we want to tighten up the max number of whirls, the odds do improve slightly for the exhaustive approach, but there will always be a massive difference between the 2 approaches.

Also, I think “Turner” would be a better name than “Bob.”

@gorillapaws a thorough analysis.