Applications of infinity in real life

Question

I am writing a mathematical essay and would like to focus on the concept of infinity. I am not sure of any real life applications of infinity to write about or some way to narrow down the topics. Does anyone have any ideas on ways to focus the essay on a section of the topic infinity.

Answer 1

As far as I'm aware of there has no infinite object been observed in real life , and according to many logical and philosophical discussion in the history of man it might even be impossible to observe it if it were existent.
Infinity is a construct of mind: it is the mental process to say: "I see this long street and if I do one step and do another step I mov forward but without reaching its end behind the horizon. And I can do this one time more... and, mama, if I do it forever ?" Or even simpler: meditating about a clock where the hands go in circles...

So, in the sense, how we extrapolate concrete experiences in our finite world, the first concept in our mind is: "and when I proceed infinitely many steps/infinitely long time"- so I think this is the way, how something "infinite" comes into the (mental) world. Always our natural idea of "infinite" comes from extrapolation - be it then also infinite height, length, temperature, area, volume,...

Our geometrical common-sense has the natural concept of the euclidean space - whose length, height, width is thought as "infinite".

So far, this is speaking of "infinite" as an adjective, as a property . It seems to me this is only a property, a "construction-feature" of our mental "machine of rational thinking" (I seem to remember some philosophical/religious discussion where it was even said: because there is such a feature "installed" it must also be existent in nature, and another one: this courious inherent feature of the rational machine is that what allows us the contact with the godly which would be impossible otherwise... but I don't know how far this arguments explain only themselves, are somehow circular...)
Even more abstraction and philosophical reasonning tend then to make some philosophical concept of the "infinity" as an own mental object - and after that, may proceed to postulate it even as real object.

In the ideal world of, say mathematics, this goes on much more straightforward - infinity is essentially involved in our idea of counting (we assume counting is infinitely possible in our mathematics). But then the student of mathematics cannot follow so fast and then he asks: "ok if I count to infinity, what comes after it?" or: "ok, 0.9999... has infinitely many digits, but if then comes one 8, what does it mean?" or "Ok, you might say there is no greatest number in $\mathbb N$ but what about "infinity" and what when I divide 1 by infinity?" etc.

So "infinity" is all around, but, say, 90% subcutane/subconscious and, say, 5 more percent, as a buzz-word because we have a time where attractive buzzwords are worth money when they can succesfully be transferred into the common discourses... - and/but always only in our mental world.

But wait. Maybe we cannot observe infinite objects (in size), infinite processes (in time) - by some philosophically explained reason. But we observe in the modern physics (high energy I think) processes, which behave in a way such that we must describe them mathematically with the help of concepts of infinity - and which are native only in our mind/modeling! One example is the zeta-regularization of a divergent series: this deals with the problem of summing to, and over infinity and to arrive anyway at meaningful finite equivalents - as I said: initially only inside the bounds of our ideal world of mathematics. But if such specific concepts are needed for the mathematical explaining of nature as well, then it might be possible that we have some "real life" object/process at hand, which owns in some yet obscure and hidden way something similar as our mathematical "infinity" - and this would then be one hint/one vague shadow of "infinity in real life".