The concept of infinity is all around us and is quite easy to grasp. Many people have difficulty visualizing infinity, because they try to define it through the eyes of their limited human existence, experiences or beliefs. Even scientists are limited, as they must turn to math and supercomputers to help define infinity. A dolphin is familiar with the air outside of water and has seen the sky, but it does not know outer space exists, however that does not mean outer space does not exist. The Earth is encompassed in outer space, the Milky Way is encompassed by the universe, so then what encompasses the universe? Is science and math as we know it enough to surmise that nothing lies beyond the universe?Only when you realize how insignificant tiny living creatures are in relation to the size of the Earth, as well as just how insignificant humans are in relation to the vastness of the universe, will you begin to understand and properly visualize the concept of infinity. One doesn't have to claim to know what lies beyond our reach and telescopes to fully understand infinity. Mentally stepping outside of one's body is a must.
Unfortunately, there is no correct answer to this question because the context is not defined. The question above was created by a human, with words that were created by humans, that represent concepts imagined by humans. I have voted yes, because any ideas or concepts that can be questioned, must be understood. This is in response to the assumption that the questioner is questioning if humans can understand the concept of "infinity". On the other hand, I think the real question that is trying to be asked is, "Can humans understand everything". If that were the question, I would vote no.
Unless they are on shrooms of course.
As an engineer, I have taken many very advanced classes in mathematics and particle physics. I myself, along with many others, understand the concept of infinity. It is not something that you can really visualize, but the concept isn't that hard. For instance, taking the limit of a function as a variable goes to infinity is an example where you must understand what infinity is.
Although I'm really not sure why some don't understand. It's a very simple thing to me. I think lots of people find it hard to grasp because it involves understanding and acknowledging the fact that things expand much further than we can reach and that most things are simply unknowable. Most people in the world seem to have this uncontrollable need to know absolutely everything. So when there is an unknown thing that they can't get they try to ignore it and pretend it's not real or make up ridiculous stories about it trying to pretend that they know it. Infinity is simply the fact of not knowing and people don't like that, but deep down I'm sure they understand it.
Infinity is a simple concept to understand. The fact that it is not reachable has nothing to do with the concept of understanding what it is. There are people who are smart enough to launch things to Mars and put satellites into orbit, so I'm pretty sure they can also understand the infinity concept.
Humans can understand infinity in a mathematical sense. Of course, since infinity is itself larger than anything that can be comprehended, there is another sense in which people cannot understand infinity. It is a paradox which is beyond our understanding. Nevertheless, we can understand it as an abstration of math.
Just my own personal experience based on my understanding of how infinity is defined in context of the spiritual (aka heaven and hell) and the physical / astronomical (the universe is "infinite"- although supposedly now there is evidence that it is not? ). Anyway, I have autism so maybe that's why. Can't speak for other brains.
Conceived by the author as an introduction to "why the calculus works" (otherwise known as "analysis"), this volume represents a critical reexamination of the infinite processes encountered in elementary mathematics. Part I presents a broad description of the coming parts, and Part II offers a detailed examination of the infinite processes arising in the realm of number--rational and irrational numbers and their representation as infinite decimals. Most of the text is devoted to analysis of specific examples. Part III explores the extent to which the familiar geometric notions of length, area, and volume depend on infinite processes. Part IV defines the evolution of the concept of functions by examining the most familiar examples--polynomial, rational, exponential, and trigonometric functions. Exercises form an integral part of the text, and the author has provided numerous opportunities for students to reinforce their newly acquired skills. Unabridged republication of Infinite Processes as published by Springer-Verlag, New York, 1982. Preface. Advice to the Reader. Index.
Infinity is a concept which is though seems to be incomprehensible at the beginning is understandable by the sentient beings. In order to understand it we need to first face our own limitations and then try to transcend those limitations. In this process we will be able to approximate close enough towards a deeper understanding of Infinity.
The problem I had in understanding infinity was that, I thought it keep going on and on, as in growing. Then my math teacher brought up that infinity doesn't grow, it just is. So, then no one can ever find the end to infinity because no matter how big, there will always be numbers bigger and grasping that concept is really hard for all, even for the brilliant minds of the world because you first have to understand 2 things and come to terms hat they are both true. 1, that infinity doesn't grow and 2 no one will ever reach infinity. The reason some people might not be able to understand infinity is that you can't reach it, therefore it is not comprehensible but even if you can't reach the top shelf, doesn't mean you don't know what is up there.
As someone studying to be an engineer, I can tell you what infinity is, but understanding it is a whole different beast. It's kind of like quantum mechanics, as I can use the equations (That I know), but I can't conceptualize what it would be like. If you asked me to describe to you the world as it would appear on a sub-atomic scale, I couldn't make heads or tails of it. Infinity is similar, as to alot of people infinity is just a big number, just like to most people 0 always equals 0 (This sounds very dumb at the moment, but more on this later), but it doesn't work like that. 0 can describe absolutely nothing, but it could also describe 10^-nth power, similarily to how infinity describes 10^nth power, n being an unknown infinite number. Picture 10^nth donuts, can you see them? If you can, you failed...
What I'm trying to say in this long winded, akwardly worded paragraph is to say that although in theory you know what infinity means, you can't understand the implications of infinity.
Imagine a completely white area, no walls no nothing, just whiteness. (IMAGINE)
Now imagine a glass box, in this white area. (IMAGINE)
Imagine that the glass box is 100 times bigger than what you are imagining. (IMAGINE)
Imagine that the box, that your in, is infinite. (IMAGINE)
1. If you are outside the box looking in you cant understand infinity
2. If you can still see whiteness then you cant understand infinity
3. If you are not falling then you cant understand infinity
Let me know if you failed the test or if it was interesting
Truly understanding it would break our minds. Try to understand the number of stars in the sky, and it is just too high of a number; and that is for a number that is likely fixed! The closest we come to understanding it, is accepting our lack of the ability to understand it.
The problem with this question is that is doesn't ask the level of which infinity must be understood. I understand infinity on a basic level, I know what it is, and I can make a few dodgy analogies (circles etc.), but in it's complete sense, I don't think it's possible to fully understand anything. Certainly not something as big as infinity.
Humans have become sure that they must know everything. Think of it this way. Try to visualize not existing. You cant. Its beyond humans. We know nothing beyond existence and so we cannot even begin to comprehend it. Infinity is the same deal. We cant picture something that goes beyond our skill set. In this case, our ability to count.
The actual understanding of infinity is way beyond anything any person can comprehend. If you think about people in general, what we understand naturally are all things finite. It is not in man's nature to attach what is infinite to the universe. We have even attributed infinity with a value that doesn't even come close to explaining what it really is. My point being, man is finite. Every algorithm, equation, or concept that any person can think of is that of a finite nature. Man's algorithm itself is finite. Within those parameters, how can we even come close to knowing what infinity really is? To even say infinity is just a never ending value, in my opinion, limits what infinity really is.
Suppose that you are in a computer simulation(not necessarily the matrix, But not not necessarily the matrix) with no floor, Just you floating, And you see an wall. The wall extends in all directions in front of you (up, Down, Left, Right, Forwards, But not backwards), And you start to climb up the wall. You keep climbing higher and higher until you realize that there is no end. You think that there has to be one, But to no avail. The wall extends infinitely, But you can't understand how. You don't know why. You are just paralyzed in confusion.
Infinity grabs the aspect of time, Space, The power of the mind, And everything in between. Space is infinite dark empty matter that might not end and probably never will. If endless space is infinite time never started, Never ended, Never stopped, And never advanced. Us humans cannot even fathom how far away a star truly is, So grasping the idea of infinity would not occur in our wildest dreams. The power of the mind is so remarkable that we can go out of our own planet, But in another galaxy or even dimension a species could even know of our existence. The capacity of the mind is unknown and remarkably insane. Nothing has ever started or ended and nothing will ever stop.
Because the human brain is limited and there are hundreds upon millions of things we don't understand, The concept of being able to understand infinity doesn't make sense. Nothing in life is perpetual and it seems that because our brains aren't infinite, Can we understand it? We will only understand the concept and the theory but never the big picture of it.
Obviously we all know that infinity means no more or nothing can be added to make it greater. There is literally nothing that is infinate in the world so how would we be able to understand it. We only have so much space in our brain that we can not even understand infinate things.