The humanity consists of normal people and procrastinators, the latter making up the vast majority of us. This paper establishes the two primary types of procrastination. The phenomenon is either inherent, in which case it leads to persistent problems in life and traumatic psychological experiences; or avoidable, meaning that the person in question reaches a certain critical juncture, whereupon they get themselves together and finish the job in time.
Below we list the cases of PRO-type procrastinators traveling back and forward in time and consider the velocities involved, as well as the effects of procrastination on life before and after the deadline.
The article is accompanied with rigorous mathematical calculations and the data obtained in an experiment featuring six volunteer subjects.
In a typical two-student setup, a fellow student enters your dorm room and asks how many exam questions you have prepared so far. You catch yourself thinking it is about time to finish that pesky first assignment. “Time travel!” you might say. We think this is procrastination.
What constitutes procrastination? According to a definition in a respected reference catalog, that familiar term refers to a habitual delay of starting or finishing a task despite knowing it might have negative consequences, which is arguably true about most tasks in life under the right (wrong) conditions.
Figure 1. Procrastination defined by the go-to reference of your academic writing. Credit: Wikipedia
The really hard science part
We shall proceed to offer some really fancy considerations to the effect that procrastination is demonstrably associated with time travel.
Let us begin by examining a graph that plots work A done by an ordinary person and a procrastinator over a given time period t.
Figure 2. Work A completed by time t by an ordinary person (green line) and by a procrastinator under avoidable (solid red line) and intrinsic (dashed red line) procrastination. Credit: Alexander Antropov
Suppose there is an assignment requiring work A₀ to be completed by a finite time t_fin. An ordinary person completes the assignment at a uniform pace. But how does a procrastinator approach this? Not unlike a measurement error, procrastination comes in two basic varieties. It is either inherent or avoidable. An individual characterized by inherent procrastination progresses in the assignment at a steady slow pace, which corresponds to the dashed line in figure 1. While the phenomenon itself in inherent to human nature and cannot be entirely eliminated altogether, evolution does a great job eliminating the unfortunate creatures afflicted by it.
The avoidable procrastination pattern, on the other hand, merits a closer look. In it, a person reaches a certain moment in time, t_crit, whereupon they somehow manage to complete the assignment. We propose that such procrastinators be termed PROs, reflecting their impressive achievement. Observations indicate that the most undaunted specimens of the kind manage to finish the job even with t_crit approaching t_fin.
We shall reason from the assumption that a PRO as such always completes the assignment on time, regardless of the specific graph features. (Axiom 1)
Because time corresponds to a sequence of events, we consider reference periods in the assignment progression to constitute benchmark events. As evidenced by figure 1, an ordinary person experiences a steady flow of time. A PRO, by contrast, completes comparable portions of the assignment over clearly uneven time spans.
This gives rise to a nonuniformity of time in the PRO’s reference system, suggesting the possibility of time travel.
Thermodynamics of procrastination
Now let’s get rigorous. Consider an isothermally existing ordinary person and a comparable PRO. We take the internal energy of an ordinary person to be constant and therefore derive their completed work from the energy supplied to them:
A_ord = ΔE_ord.
We recognize the fact that a PRO gets more sleep and nourishment:
ΔE_pro > ΔE_ord,
while also performing less work:
A_pro < A_ord.
This leads us to conclude that A_pro exceeds ΔE_pro, violating the law of energy conservation. Since Noether’s theorem proves each conservation law to be a consequence of the spacetime symmetry, the violation of energy conservation by a PRO equates to temporal nonuniformity. Which is just the thing you need for time travel.
Procrastinating toward a better tomorrow
The ease with which procrastinators travel into the future has come to be so widely accepted that no one seems to give it a second thought. Let us look at how the speed of moving into the future and the speed with which an assignment is completed depend on certain factors.
Assembling a large number of PROs together leads to an abrupt drop in power, while the speed with which they approach the future spikes.
Figure 3. Power and flow of time speed as a function of the number of PROs in one place. Credit: Alexander Antropov
The graph below illustrates how the same two parameters vary with the number of hours slept daily. While the power vanishes at zero and 24 hours of sleep per day, the maximum has been variously measured at close to the eight-hour value. As for the flow of time, its speed gradually increases, approaching infinity at 24 hours of sleep per day.
Figure 4. Power and flow of time speed as a function of the number of hours slept daily. Credit: Alexander Antropov
The most intriguing aspect of this is naturally the prospect of traveling back into the past, which indeed turns out to be possible via procrastination.
Returning to figure 2, let us shift t_crit to later times until it moves past t_fin. This could be realized by assigning an independent PRO to keep track of the time. Common sense tells one that these guys will remember about the assignment when it has long been overdue. Since Axiom 1 still stands, the work-versus-time graph has to be amended as shown in figure 5. At a more or less arbitrary future time t_fut, the PROs realize they better get started, and the arrow of time must be reversed to accommodate the eventuality of the assignment being completed on time.
Figure 5. Work A completed by time t by a time-traveling PRO. Credit: Alexander Antropov
This temporal effect is commonly observed at universities. A student does not attend the lectures up until the examination period (from 0 to t_crit), they go on to fail the final test at t_crit, procrastinate their way toward reexamination, fail again, but nevertheless avoid being expelled. On account of the integrity of the education system (Axiom 2), it is obvious that the student must have traveled back in time to redo the tests.
A better intuition of the puzzling effects of procrastination can be gleaned from the results of a simple experiment. In it, six volunteers were tasked with a simple assignment: depicting a horse. The resulting six horse pictures are presented below:
Figure 6. Experimental samples. Credit: Alexander Antropov
Sample Nos. 2 and 6 clearly belong to ordinary people, who made an honest effort and completed the task. Horse No. 5 has not arrived by press time and is therefore a prime example of unavoidable procrastination. As for the horses in Sample Nos. 1, 3, and 4, each is obviously the work of a PRO. While the first one indicates creativity, the fourth sample shows reckless negligence, and the third picture was downloaded from the internet.
We hope that this research, originally published in Russian, can guide you in discriminating between actual time travelers and fake science.