An Entropic Thought Experiment

Six years ago, I got into a challenging hobby: The Five-Minute Plank. In terms of the what to do, the challenge is pretty simple. You do a five-minute plank every single day first thing in the morning. But when it comes to practical execution, this turned out to be a stiff challenge (to put it mildly) for me.

At the very beginning, I was barely able to hold the plank for a minute. I slowly built the endurance, and eventually, after an entire year of persistence and hard work, was able to hold the plank for five entire minutes.

Fast forward to today, this “challenge” is not as much of a challenge anymore, but more of a routine (habit) for me. But this essay is not just about this habit of mine. It is more about a tangential habit I got into (it’s a tick really).

This essay is supported by Generatebg

The Stopwatch

Every morning, my goal is not just to hold a plank for five minutes, but to stop the stopwatch at exactly 05:00:00 (centiseconds included) during the plank. I know that for most people, this would sound like a pointless tick. But it fascinates me.

I wonder what drives human beings into seemingly pointless ticks like these. Furthermore, I also wonder if this is really pointless. Over time, this fascination of mine evolved and I started thinking about this topic from the perspective of the entropy involved.

Naturally, when entropy is involved, it is customary to invoke handkerchief-math as well. So, why don’t we do just that?

A Simple Probability Calculation

Take a look at the picture of my stopwatch below. It is from my attempt earlier today (at the time of writing) to achieve the feat of 05:00:00.

Before you give me any credit, let me openly admit that I failed at achieving 05:00:00. I tried later two more times. I achieved the “feat” on my third attempt (forgive me, for I am human).

In any case, you can see from the image that the stopwatch has two centisecond (one-hundreth of a second) digits. There are 100 possible two-digit centisecond values (00, 01, 02, … ,99) in each second. My goal is to stop the stopwatch at precisely 05:00:00. In other words, I am aiming for a specific hundredth of a second.

If I choose to ignore human factors (yikes!) and assume that each hundredth of a second is equally likely (double yikes!!), then the probability of stopping the stopwatch at exactly 05:00:00 would be:

P(05:00:00) = 1/100 = 0.01 (or 1%)

Absolutely everything about this calculation screams “oversimplification!!”. But nonetheless, it is a start. Let us go one step further and include a simple human factor such as the human reaction time. When it comes to visual stimuli, the human reaction time averages around 250 milliseconds (or 25 centiseconds).

Since this is just an average, we need to consider the variability as well. While we are on the topic of variability, why don’t we consider the variability in the stopwatch mechanism itself? Not every button press is alike. Some button presses activate faster, and some slower; some are more reliable, and some less.

We could keep going. But the point I am trying to make here is that if we keep considering more and more factors, start including experimental results, etc., we would compute the real-world probability of achieving 05:00:00 as being much lower than 1%. In other words, highly unlikely; very much a low-entropic state.

Habits and Entropy

Since it is practically complex to compute the exact value of entropy reduced, I will be working with qualitative representations here. Each time I stop the stopwatch at precisely 05:00:00, I am reducing the entropy of the local system by some amount.

In accordance with the empirical physical patterns that humanity has observed and established (as physical laws) so far, we should expect an increase in entropy elsewhere due to my actions.

This means that by stopping the stopwatch at precisely 05:00:00, I am reducing the entropy locally and increasing the entropy globally. My thought experiment involves making educated guesses at where entropy is likely to be increasing.

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Thermodynamics of the Living

I have experience in exploring entropy from both a thermodynamic perspective as well as an informational viewpoint. So, I have the freedom to approach this thought experiment from either starting point. This time though, I choose to go with thermodynamics (based on just gut feeling).

When I think about it, every time I try to stop the stopwatch precisely at 05:00:00, I am focusing on the task. This means that the neurons in specific regions of my brain are firing for this very purpose. I also hold and grip the watch in a very particular way. If my grip is off, my odds of achieving the desired low-entropic state of 05:00:00 go down (from my practical experience).

Both my brain and muscles are burning energy when I focus on this task. So, naturally, we should expect that by achieving 05:00:00, my body expends more heat energy to the surroundings than when I achieve, say, 04:99:99 or 05:00:01 (more on this “expectation in a bit”). Historically, I achieve the latter far more than the former for some reason I do not yet understand.

Having said this, we should expect a certain element of randomness here. I could achieve 05:00:00 just by luck or miss it just because of the lack thereof. To negate the effect of this randomness, we could consider the law of large numbers and analyse a sufficiently large number of attempts. When we do this, the average (of a sufficiently large number of attempts) body heat expenditure for achieving 05:00:00 should be greater than achieving 04:99:99 or 05:00:01.

Thermodynamics of the Non-living

I mentioned earlier that based on my practical experience, my odds of achieving precisely 05:00:00 go up when I hold and grip the watch in a particular way. This grip also causes wear and tear on the watch ever so slightly each time.

Furthermore, the watch’s button mechanism, the membrane, the electronic sensor, and everything else involved in achieving this task also undergo wear and tear each time. Another point I can think of is the computational load the tiny processor in this watch takes on each time I will it to stop precisely at 05:00:00.

All of these points add up, would directly result in the heat that the watch expends to the environment just like with my body. Again, the law of large numbers applies here as well.

Closing Comments

What I realise from my “silly” thought experiment is a reaffirmation of an observation that I first made a few years ago.

There is no free lunch.

Whenever we do something productive, we reduce entropy locally. But by doing so, we increase the entropy globally. We typically do productive work by drawing energy from an even lower entropic system than our own.

Here’s a simple example of how this works: We get from point A to point B by driving a car; this is productive work. However, we do so by burning fuel. The fuel is essentially a lower entropic system than our own local travel environment. By burning this fuel, we increase the global entropy.

Essentially, the total entropy of the system plus the surroundings increases even if the local entropy decreases due to productive work. The beauty of it all lies in the fact that we benefit from the objective value we generate from lowering the local entropy of systems in our relatively short lives.

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Further reading that might interest you: 

• How Easy Is It Really To Predict The Future?
• How Imagination Helps You Get Good At Mental Math?
• How To Easily Outperform High IQ Individuals.

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