New Years Day subjectively comes faster and faster. Easily Calculate the number of Subjective Years you have lived so far.

By David William Jedell                           Updated and Revised November 1, 2024

Theory of Acceleration of "Subjective Time"
Subjective Time is interactive memory and recall of the distance between "events" that is misperceived as duration of Time in and of itself.

Moreover, in 2005, Wittmann & Lehnhoff [1] systematically asked large samples of younger and older people how they experienced time. In the study, 499 German and Austrian participants aged 14 to 94 were asked how fast time usually passed for them. The study indicated that this set of people feel time passing more quickly as they get older.

Wittman and Lehnhoff found that everybody, regardless of age, thought that time was passing quickly. The question, “How fast did the last 10 years pass for you?” yielded a tendency for the perception of the speed of time to increase in the previous decade. This pattern peaked at Objective age 50, however, and remained steady until the mid-90s. [2]

Dr. William Friedman [3] proposed a theory, originally proposed by William James in 1877 (labelled the "Father of American psychology"), to explain this phenomenon as follows (I thought of this when I was 8 years old myself as it is self evident to me): 

“As we get older, each year is a smaller proportion of our lives. For example, a year is 1/10 of the life of a 10 year old, but 1/70th of the life of a 70 year old. Therefore each year feels shorter relative to all the time we've lived and thus seems to be going by faster.”

Mathematical Treatment of Dr. Friedman's Statement and its Implications  
The t-axis represents Objective Time;

Objective Time (as a mathematical tool) is represented by t (based on "ticks" of an objective "clock" at 1 objective year intervals);
The y-axis represents Subjective Time; 
Subjective Time represented by y is defined as a function of t; 
y(t) = 1/t , t > 0; 
F(t) is the area under y(t), which is the perceived cumulative Subjective Time; 
F'(t) is the rate of change of the area under y(t).

F(t)  = ∫y dt – 0 = ∫y dt  

We may infer that the Subjective Area of Perceived Time during the Objective Time interval (t1, tn) is the integral of y(t) between (t1, tn).

                ∫ y dt

y 

                                                                                               t

The curve represents the Subjective Time as a function of Objective clock t. The shaded area under the curve is the Area of Subjective Perceived Time. The smaller the Area, the faster Subjective Time is perceived to pass. 
At 80 years of Objective age, looking back to the Objective year “1” we find that the Subjective Area of Perceived Time is,

                                    80

                   ∫ y dt = ln (80) = 4.3820266347 ≈ 4.4 Subjective Years.

                                    1

Furthermore, whereas most people sleep for 1/3rd of their first conscious year, lives, we do not adjust for sleep. This is a general number and subject to minor differences and aberrations with each different person.

4.4 Subjective Years is virtually all that is lived in a lifetime.

The decreasing Area of Subjective Time begins to become imperceptible from about 50 objective years to 80 objective years, because it is sufficiently small. This idea is consistent with the findings by Wittman and Lehnhoff, as stated above, that everybody, regardless of age, thought that "Time" was passing quickly and this pattern peaked at age 50, however, and remained steady until the mid-90s. 

In conclusion, the theory of Subjective Time under consideration is consistent with the empirical study. Dr. Friedman's statement that “As we get older, each year is a smaller proportion of our lives,” and that “each year feels shorter relative to all the time we've lived and thus seems to be going by faster,” further implies the mathematical result that a full 80 Objective Year lifespan results in only 4.4 Subjective Years.

Your Subjective Time = Natural Log of your chronological age in objective years. 
So, if you want to know your specific amount of Subjective Time that you have lived, use this Natural Log Calculator. Ex. ln (80)= 4.4

https://www.rapidtables.com/calc/math/Ln_Calc.html

Natural log calculator | ln(x) calculator online Natural Logarithm Calculator. Natural logarithm calculator. ln(x) calculator. The natural logarithm of x is: ln x = log e x = y. Enter the input number x and press the = button: www.rapidtables.com

References 

[1] Wittmann, M. and Lehnhoff, S., (2005), Age effects in perception of time, Psychological Reports 97: 921-935
https://www.researchgate.net/publication/7266174_Age_effects_in_perception_of_time 
[2] Lewis , Jordan Gaines, Why Does Time Fly as We Get Older, Scientific American, (Dec. 18, 2013).
https://blogs.scientificamerican.com/mind-guest-blog/why-does-time-fly-as-we-get-older/
[3] Based on Aging and the Speed of Time presented by Dr. Friedman on 10/14/2010 at Oberlin College. Ibid.
[4]  Ricker III,  Harry H., Refutation Of Einstein's Principle of Relativity, General Science Journal, May 28, 2011
http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/3494

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Department of Psycholog, University of Michigan. The perception of time is influenced by memory and how much you’ve experienced. For an 8-year-old, a week is a big portion of their life. For an 80-year-old, a week is a much smaller portion of their life, which contributes to the feeling that it went by quickly. https://lsa.umich.edu/psych/news-events/all-news/faculty-news/time-flies-by-faster-as-we-get-older--here-s-why-.html

Copyright © 2024 by David William Jedell 
Email: d.w.jedell@gmail.com