A little about luck

Four Leaf
Who knew that finding such things was a skill?

 

I have an ability to find four-leaf and higher multiplicity clovers. This may be somewhat related to my Scotch-Irish heritage but, I think, not necessarily so. I definitely don’t think it has anything to do with luck.

You see, I was taught how to do this and I would be very interested if you would comment on this post whether or not my instruction here guides you sufficiently to be able to find your own. The corresponding tradition, by the way, that I was taught is to keep the four-leaf clovers and if you do find a five or six-leaf clover, that these should be given away. 

My grandmother taught me how to find these beautiful mutants. She passed away last week and writing this post is a bit of my tribute to her legacy in my life. She showed me my first and then taught me to remember the pattern of a four-leaf clover in my mind as to scan as many clovers as possible stopping only if I saw something that looks similar enough. Yes, one might over look an oddity in this process. But, there is a useful heuristic that most of the clovers that one looks at are normal and the more time you spend looking at them, is the more time that you waste. 

So, succinctly put, if you would like to try:

  1. Memorize the form of a four-leaf clover.
  2. Scan the clover patches quickly.
  3. Stop if you see anything that looks out of place (most of the time this will be 2 clovers growing close by to each other).
  4. If you find one, there are likely others nearby. 

To one who doesn’t know, it will look after a time to be this wondrous luck. You will be walking along in a park, etc. and you will simply stop and pick up a treasure that many have never encountered because they haven’t looked. 

There are many lessons that I see in this. Not the least of which is the adage, “Fortune favors the prepared.” But mostly I see the lesson that pattern recognition is such a powerful brain mechanism and a primary cognitive bias. My brains ability to recognize patterns allows me to quickly and efficiently reject irrelevant information and find something valuable, whatever that may be. But the flip side is that if you rely on patterns 100% of the time, you may miss out on something special. Like in the example of the clover, you may have gone your whole life never having seen one and you may think that this means you ought not to bother trying because they must be very rare or only lucky people find them. This may not be true.

This is also true in scientific research and data analysis. Typically, if I bring what I know to bear on a problem that I’m trying to solve and only focus on what I care about, what I find will be of better quality. Except, that ‘what I know’ may not be true all the time and I should check and others should check as well. This is, thankfully, the scientific process.  I had an illustration of this in my programming exercise today. I wanted to find the number of digits in the binary representation of several numbers. There are two ways I tested in python:

len(np.base_repr(np.random.randint(0,2**60-1),2))

and

np.floor(log2(np.random.randint(0,2**60-1)))+1

The first does the conversion to binary (base_repr) and then finds the length (len). The second method takes the logarithm in base 2, rounds it down (floor) and adds one (0 in binary is ‘0’ and has length 1). 

Each of these took about the same amount of time. That is, 0.09 s on average using timeit on my machine and it may be alot clearer to someone else reading my code that I wanted the length of the binary string if I use the first case. I might also want the binary string itself later for some reason. So, go with that. While typically, just calculating the answer I am interested in is faster, this is not always helpful and might mean that I have to redo something later. Each of these approaches might also change their performance in a different context or on a different computer. So this is why ‘best-practices’ or ‘one-size-fits-all’ solutions should always be debatable and every once and a while revisited when a new context shows itself. 

Be well, stay safe

N

As a side note: I’ve often wondered why there aren’t more of four leaf clovers. Is the added benefit of extra energy collection not outweighed by the need to support the other leaves? Why three? Is this a packing problem, such that they start to overlap after this? If you know or are also curious, drop a comment.

 

Author: Calcumore

Physicist, Programmer, Calcumore and calcunow.

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