I suppose I was inspired by the common quip, "Will you still care about this in 50 years?" that people use to put small troubles into perspective. I wanted to show how current events would still matter to my life as a whole given a logarithmic scale (because time is not perceived linearly---more in notes & credits). A more in-depth version of the descriptions of each graph can be found in the notes & credits. Here is the brief version, with only equations. Top graph -- f(x)=10x Lower graphs Slide 1 -- g(x)=2^(x-1) Includes 0 Slide 2 -- h(x)=2^(x-1)+8 Includes 8 Slide 3 -- i(x)=80-2^(7-x) Includes 80 Slide 4 -- j(x)=16-2^(7-x) Includes 16 Slide 5 -- k(x)=10x Slide 6 -- <3 <3 <3 <3 Maybe a quadratic would've worked better so I didn't have to specify the 'includes' part. 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 does frame a lifespan excellently, though for the purpose of this project I wanted something with a slope that changed a little bit faster. If there is a mistake in the math anywhere in this project please do tell me. It's space or click. Wow, I shared it. I actually shared it. Maybe I'll unshare it. Later, perhaps. A note I made this in February (2024) just a little while after losing my kitty, Cinn-cinn, who I'd had for 10 years. I was feeling pretty terrible & thought I could solve my feelings with math. It turns out you can't do that. So this didn't help me much, but maybe it would help someone out there. I'm sharing this project on August 21st, exactly 6 months later. I dunno if that really means anything. I guess just that I made it this far?
It's just a bunch of logarithmic scales. I used these calculators: https://www.calculator.net/log-calculator.html https://www.desmos.com/calculator Light gray areas represent things long enough ago that I don't remember them much. Dark gray areas represent stuff that's when I'm not alive (or, in the case of slide 4, beyond the present). Lines stretching up from the graph can represent birth, the edge of clear memory, & death, though not every graph has all three of those things. I have consistently placed birth at 0, the edge of memory at 8, & death at 80, the main reason being that these numbers fall easily on the graphs & not that they are the most accurate. The top graph on the screen is always a linear scale by tens, stretching from 0 to 80. This shows how my life would look from an outside perspective. Let the year number along this scale equal 10x, so that the equation for this scale is f(x)=10x. The bottom one on the first slide is a base 2 scale with 0 added in (in place of 1/2). g(x)=2^(x-1) I think. This is the simplest one, in which we assume the majority of one's memories are early (because novel memories take up more space & those tend to occur less as time goes on) & the later years run together more. Thus, the time between the ages of 8 & 16 takes up just as much memory space as does the time between ages 32 & 64. The second slide is the same thing with 8 added to every number. h(x)=2^(x-1)+8 This shows the same idea but as though one gained consciousness at the age of 8. This is because, contrary to the previous graph, I don't actually have many memories from before that age. Third slide is i(x)=80-2^(7-x) (including 80). This one assumes instead that later years will take up more space in memory from a later perspective, as recent memories are remembered in more detail. Earlier years, thus, take up very little space. In contrast to every other slide, this one takes the side of how little current events matter. Fourth slide is j(x)=16-2^(7-x), (including 16). This one goes off of the same premise but places the end of the later years right after the present rather than in the distant future. It is the most accurate to how large current events feel in the present, though defeats the point of considering how large they may seem in the far future. Of all the graphs, this one shows current events as largest. It is extremely accurate to perception---whether that makes it accurate in general is hard to say. Fifth is linear by 10s. The events are stretched out perpendicular to time to show that how much space they took up in my life matters more than how much time they took. The final slide shows only hearts in the bottom graph, a denial of numerical values. This shows that I don't need to measure how much I should care about someone---caring is enough. I had to think about stuff a lot. There are more things I should've included. I chose base 2 to give myself more room around teen years but I still really like how base 3 frames a lifetime. If we include zero, that gives us (0) -- Birth 1 -- Infanthood 3 -- Toddlerhood 9 -- Childhood 27 -- Adulthood 81 -- Death Just 6 moments in time that line up so nicely with the logarithmic scale. Puts stuff in perspective, you know? Of course there's also f(n)=81-3^(4-n). (81) 81-0 n is undefined 80 81-3^0=81-1 n=4 78 81-3^1=81-3 n=3 72 81-3^2=81-9 n=2 54 81-3^3=81-27 n=1 0 81-3^4=81-81 n=0 How grim. I think the ideal scale for this, whether base 2 or 3 or something else, wouldn't just be logarithmic in one direction. Rather, the most time would be spent towards the middle (I'd pick 25ish) & the edges would be sparse. Something with negatives? f(x)=2^|25-x| looks good. Measures the distance from 25. If only there were some way to tone it down a little. Flatten it. How about (2^|25-x|)/2 or something? Wait, I might have to make a function composition table. x -x 25-x |25-x| 2^|25-x| 2^|25-x|/2 28 -28 -3 3 8 4 27 -27 -2 2 4 2 26 -26 -1 1 2 1 25 -25 0 0 1 1/2 24 -24 1 1 2 1 23 -23 2 2 4 2 22 -22 3 3 8 4 21 -21 4 4 16 8 20 -20 5 5 32 16 Tables are futile. After experimenting I settled on f(x)=2^|25-x|/100 I wish there were some way to have the slope shallower on the right than the left, but ah well. I'll put a screenshot of the desmos graph inside the project for the curious soul who read through this all.
