Infinity Is a Core Ingredient of My Belief System

First of all, applause for Mapleman for creating a good group idea!

Infinity is something I feel most people entirely misunderstand, but at the same time we all do seem to have some level of innate appreciation of the rules of infinity.

The best way to explain this is with examples. When I was a kid, all kids knew that "You can't have more than infinity". That's an important rule.

Now, let's say I start at point A, and you, being really fast, decide to go away from me in any direction and travel an infinite distance. The distance between the two of us is now infinite. But let's say our mutual friend John decides to travel in the opposite direction, also an infinite distance - what now is the distance between you and John - MORE than infinity?!

Actually it's not a worthwhile question because the fact is, you can't travel an infinite distance.

There is a tendency in the universe for every extreme thing to have an opposite, and that opposite is usually very similar, which seems to make little sense, but let me again explain with examples. Hot and cold are both temperatures, thus similar. Tall and short are both variations of height, fast and slow are both speeds, and so on. 'Infinite' also has an opposite, but it's not 'finite', it's 'nothing' - the opposite of Infinity ('everything') is zero - nothing.

Now the other great thing is that when you have a pair of similar opposites like this, you can use your understanding of one to help you understand the other also. The rules for nothingness are the same as the rules for Infinity. To clarify: nothingness/zero cannot be halved or doubled without having the exact same value still, and is not made up of smaller parts that add up to zero. Infinity also cannot be halved or divided and is not made up of smaller, finite parts.

That which is finite simply -cannot- be infinite -- which is why the world literally means 'not finite'! What this tells us then is that anything which is composed of parts making up a whole can no more be infinite than it can be nothingness. You cannot have an infinite number of peas, or an infinite distance, or an infinite length of time.

You could go on gaining more and more peas and never stop, you could travel on and on and never stop, but the difference is that you'll never actually reach an infinite distance or an infinite number of peas.

So effectively there are two main ideas about infinity. Some believe infinity refers to something that can be halved, and halved again, and again, and so on, or added to again and again, but this is not actual infinity, it would be better termed 'progressive infinity'.

Actual infinity is like a naturally squared concept - infinity itself is infinite.

This also all tells us that the universe is not actually infinite, only progressively infinite.

The reason this is a major part of my belief system is that I also believe in balance, and that the laws of balance are the most fundamental thing there is. In short, between any two opposite extremes, like infinity and nothingness, there is always a balance - a middleground between the two that incorporates both together in a single form.

The universe, the -finite- universe in which we live, is the balance between nothingness and infinity. The universe itself is therefore the highest possible expression of balance, and we, as children of said universe, have a fundamental purpose to strive for the continuation of that balance.

However, this is a whole other story, so I will write about balance more fully elsewhere. Hopefully your brain hasn't been too fried by reading this?!

davidstone78 davidstone78
26-30, M
18 Responses Aug 3, 2007

Infinity leaves the Big Bang advocates with the flat earthers in a self idolizing hierarchical world ending in a final self judgement of self inflicted extinction. Infinity scares them because they can't fathom the unfathomable in their minds. Nice article Mr. Stone, finally we may not have to experience ridicule and torture as Giordano Bruno and Georg Cantor. Thinking is still an act of terrorism so be careful...

hmm, yes matter has energy: funny thing is that some matter (like photons) have no mass but still has energy; and anything with mass has energy. So I think we also need to know what mass really is (scientists believe that there is a Higgs boson that gives rise to mass). [I do not know much about these things]... But what I know that with all matter we have anti-matter: and probably just after big bang we had as much matter as anti-matter... and we also know that when anti-matter and matter collide, they disappear [and leave a little bit of energy]. Funny thing is; where is all the anti-matter now when we still have got matter... It might be perversly connected by space and time...<br />
And probably before big bang there were no time as you pointed out earlier. And I think that sounds very plausible. Question is; were there any matter? maybe not what we see today is matter... It must have been something; but that something could be what we call "nothing"...<br />
Oh and something else I know nothing about: "dark matter"; we can't see it, but we know that it must (probably) exist... but what eactually is it? hmmm<br />
So many unanwered questions. It is not easy... especially when our definition of things (like infinity and universe are so vague)...

Sorry for the delay.<br />
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I was interested in what you had to say about the nature of matter, and about empty space. One question I've not payed much attention to is whether space and time are distinct from matter - that is, could a spacetime exist, even just in theory, if it contained no matter within it? Or are space and time present -because- matter is present?<br />
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I did begin to consider that there is another set of balanced opposites, namely that of matter and energy.<br />
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Obviously I'm not working on the dictionary definition of the meaning of the word 'opposites', I'm effectively just saying that matter and energy have contrasting but complementary properties.<br />
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To clarify: matter has form, but requires energy to manifest. Energy similarly requires matter in order to manifest. Neither can exist except in the presence of the other. One creates an ob<x>ject, the other moves the ob<x>ject, they are co-dependent.<br />
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This pair is similarly dependent upon the pair above it, for matter cannot exist with space just as motion cannot exist without time.<br />
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I must confess I am leaning also towards the idea that time and space can not in fact exist without some form of content, but this contrasts with the obvious fact that there are empty spaces between those contents - the vacuum. Now, physics has shown us that the vacuum isn't ever really as simple as just an empty space, that there are particles popping in and out of existence all the time, and there seems also to be some evidence of travel backwards through time at least at the quantum level, but none of that changes the question - in the gaps where there is no matter, we naturally apply the word 'nothingness', but nothingness doesn't take up any room! How can you have an area of nothingness?!<br />
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My ideas do allow such gaps, because they also allow gaps in time. In other words, going back to the idea of people having greater or fewer moments of time pass depending upon their fr<x>ame of reference, i.e. if one of them is moving at great speed relative to the other...<br />
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Basically, if person A is traveling through time at half the 'rate of change' that I am, then I have two moments for his every one moment, and each moment I experience that he does not experience is effectively a gap in his time relative to mine.<br />
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The spatial equivalent of this is that just as not every moment in time has a pre-specified expected beginning, end and duration, not every bit of space needs to be occupied, or have defined position or scale.<br />
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With regard to the 'energy crisis', I believe Man is essentially a lazy creature, often failing to act until it's certain that his immediate survival depends upon it. This is a tremendous weakness, and may one day result in our downfall. However, it is also true that a great strength of mankind is how we respond when we finally do respond - desperation brings out the heroes in people, and we work together in a way that we never do in the absence of crisis.<br />
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So with respect to energy resources, and coupled with that the issue of the damage we have done to the planet, I have no doubt that when it is absolutely necessary, humanity will sort its act out, and will overcome the issues.

Comment to mapleman: [first: I assume you meant Mandelbrot]. The Mandelbrot set pictures all points in the complex plane that during a special operation does NOT diverge to infinity...<br />
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Nuff said about that. Now to energy crisis: <br />
it is impossible to have infinite supply of energy as it seems, as the amount of matter is limited. But using renewable energy sources and fusion power we have all the energy we would need [to survive many millions years more at least]. All we need to do is to invest in those energy sources... so in max. 100 years we'd be OK (at least in western countries... will take more time for less developed countries)

hmm, about your statement on passing of time. It could work on multi-dimensioned spaces. <br />
Assume we are at point X in a n-dimensional space. Draw the n-Dimensional sphere with center at the origin with radius |X| and then make a 1-to-1 mapping onto the positive number axis. Now we have constructed a mono-Dimensional concept. We can also guarantee that this 1-D construction behaves like time (goes only in one direction), by taking the path of the point X to always be outside the preceding sphere [Meaning that X always travels further away from the origin]. So now you don't even have to restrict the motion in one direction; but in all directions.. Thus verifying your early claim that space and time are closely intertwined

Ah, I didn't realise you had more replies! I will respond to those now also!...

See, this is another reason I am not terribly fond of mathematics, because whatever math says, we still only live in a world of practice.<br />
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My view is that while you could say the number of whole integers should be infinite, since you can always have more, it would not be possible to ever count them.<br />
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The reason is that no matter how high you count, the distance between where you have gotten to so far and actual infinity is always still infinite.<br />
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To count the constituent parts of an infinite substance would involve dividing that infinity into countable parts. Let's say you just split it into two - how big is either half? Answer - both are infinite! Of course, in practice you couldn't actually split infinity in two in the first place.<br />
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What I'm saying is that counting the parts of which infinity is a whole would be like counting how many pieces of nothingness go into making up 'nothing' - it's meaningless.<br />
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I'm effectively saying that infinity is a concept -only-, and has no physical equivalent because it is atemporal - that is, the concept of infinity is only applicable -outside- of the restrictions of time, and thus outside of space too.<br />
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The word finite refers to things which can be counted and measured, things which are 'finite in number' as apposed to INfinite, which means NOT finite. Anything you can count is finite, but a proper definition of finite should probably include my former description of 'progressive infinity' - in other words *anything* which is finite and countable is by definition potentially unlimited in number - but that's not the same thing as infinite. To always be able to add one more is not infinite, it's just unlimited.<br />
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Could it be that I have my definition just a little bit confused...? I mean, rather than trying to re-label the definition with which most people are familiar as the concept of infinity - 'endlessness' - maybe I should be defining -my- notion of what is effectively 'infinity squared' as something different from the accepted notion of infinity?<br />
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Hmmm...<br />
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Any way. Another quick mention about time. It seems to be a property of spacetime that anything which has a beginning can have an indefinite end, just as integers begin at 1, or 0, and can continue on as long as you'd care to count. I really haven't settled my views on the edge of space yet, but I suspect that it must be the same with space in some way - that if you can start at a particular point then you can indefinitely continue in a given direction from that point.<br />
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Or... maybe it only applies to mono-dimensional concepts like time. That is, time goes in a single direction and is unlimited in that direction, as with numbers, but space is multi-dimensional, so what effect does that have on unlimited progression in a given direction?<br />
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There was something else I was going to say but I'm being nagged, and it's gone out of my head! Grr! I'll leave you with that for now... ;o)

A big question still remains: What is mass? how come things have mass? Scientists are still searching for the particle that gives rise to mass, and with that we might understand gravity etc and begin to puzzle much more together. But right now, we have to stick to more philosophical theories...<br />
But what you said about ob<x>jects being more spatial and less temporal and vice versa, is equivalent to Einstein's famous equation: E = mc^2 + (y-1)mc^2 = ymc^2 [y = relativistic factor]... THe problem arises though that the theory of relativity doesn't match well with quantum physics... Scientists are still trying to link them together; Super string theory is one of the candidates to "the Theory Of Everything"...

What you said about space and time being opposites is really interesting. In math we portray space as axes orthogonal to eachother, showing that they are linearily independent of eachother; not necessarily showing that they are opposites of one another, but at least contrast.<br />
And your notion about time without space and vice versa seems plausible:<br />
Especially interesting is the time without space: As you pointed out, all spatial matter then has to be at one point, but isn't any point a point in space. So mathematically speaking, all points must be in the "empty space" [just like "empty set" I wrote about yesterday]. This is completely consistent with what you say, because, all space includes the empty space, so all matter are in that empty space (they're in the same location, but still they are not! Because where can you find the empty space? It is both everywhere and nowhere. Leading back to your notion that infinity and nil are opposites, existing together...].

Oh, I must try out the formatting now:<br />
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What I meant with cubic boxes is analogous to the following:<br />
How many poisitive integers are there? Infinite amount<br />
But we can still count them: 1, 2, 3, etc... although you never stop counting them, but they can be counted in theory. However, as you correctly asserted, this has no real equivalence in practice. <br />
Oh, maybe I should explain the equivalence relations I introduced in my first comment.<br />
Suppose you are a shepherd. In your language there are no words that symbolize one, two, three etc... Every day your sheep must be brought into a gate, how can you keep track of the sheep?... FOr every sheep that passes a gate you put one stone pebble into a bag. Now the number of sheep is equivalent to the number of pebbles: so the number of sheep is always countable, no matter how many they are. In maths, an infinite amount of sheep would thus be countable... but in reality it is hard to count an infinite amount of pebbles, and how can you even store so many pebbles...

You also raised the question of the outer limits of space. This is of course the ultimate question that everyone is trying to answer - we all want to know if there's an 'edge', and if so, what's beyond it? And if there is nothing beyond it, how does that work - you can't have something inside of nothing, because then the nothing would also be something! And then... if there's something other than nothing beyond the 'edge', what is that something? Or is there even an edge at all? Does there have to be, or is this just a limitation of the human brain, in that it cannot conceptualize something of which it has no relative experience - and nothing we have so far experienced exists without an edge.<br />
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So, I guess there are a lot of questions relating to your question, but I'm glad you asked, because I didn't realise I didn't have an answer for that one, so I shall probably now lie awake until I find one! Nice to meet you by the way! ;o)

Time dilation is another subject that is massively open to misinterpretation. The clearest example I ever learned of about time dilation relates to muons. Forgive me if I'm reciting stuff you already know...<br />
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Basically, protons hurtling towards the earth collide with the atmosphere and can be converted into pions, the pions decay into muons, and the muons reach the surface of the earth.<br />
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What's wrong with this picture is that, theoretically, a muon shouldn't live long enough to reach the ground because they decay so quickly. However, because they are moving so close to the speed of light, they experience time dilation, and thus reach the ground before decaying. The difference is such that instead of the muons going a mere 650 meters, they survive long enough to travel a massive 60km!<br />
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Now what happens in this scenario depends on which perspective you are looking at it from. From OUR point of view, we could come to one of two conclusions. We could say that time slowed down for the muon, or that the muon's length increased along it's axis of motion such that the distance it was travelling was less because it was longer.<br />
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From the MUON's point of view, the reverse is true. It could view either that the speed of time increased for everything but itself, or that the length of the universe in the direction of the muon's path contracted, and thus it had a shorter distance to travel.<br />
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Personally, I believe the time -is- in fact absolute. The explanation requires another example, so let's go with the more familiar twins paradox:<br />
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Twin A sets off from his home planet and goes on a journey at close to the speed of light. Time slows down for him, and according to the usual story, he returns and the twins observe that the traveling twin has actually aged less than the stationary twin.<br />
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However, in a model where time is apparently -not- absolute, it seems to me that if Twin A is traveling slower in time than Twin B then Twin B is therefore ahead in time relative to Twin A - Twin A would actually be in the -past- of Twin B. As a result, and I haven't done the maths, but surely returning into the stationary twin's past would cancel out any apparent time dilation effects as they would both still be at the same age...?<br />
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...and yet we -know- time dilation is real, because muons -do- reach the earth, and atomic clocks -do- slow down when moving very quickly.<br />
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What I would suggest is that time is absolute, but one's 'rate-of-change' can vary. Imagine you had a meter square piece of some physical material and could arbitrarily make it have more or less mass. The temporal equivalent would be having a block of time and arbitrarily squeezing more 'moments' into that block of time. What I'm saying is that if there is a spatial concept of mass there must be an equivalent temporal concept - concentrations of time.<br />
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There is a pay-off depending on which way you're shifting too, thus when traveling at close to the speed of light your mass increases but your number of temporal moments decreases, you experience fewer changes, but you are still existing in the same timefr<x>ame as everyone else, regardless of their rate-of-change.<br />
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I would suggest that a motionless ob<x>ject is in a state of equilibrium in terms of the balance between moments and mass - or time and space. Traveling at great speeds would then cause an ob<x>ject to shift that balance, making it become more spatial but less temporal. Conversely, an ob<x>ject that is stationary, relatively speaking of course, becomes less spatial and more temporal - thus experiencing more 'moments of change' than an ob<x>ject which is in motion.<br />
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One more post before I'm done for the night...

Woah, how weird, suddenly it -is- retaining my formatting! I'm happy :o) Maybe I should call them the ESP team!<br />
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Anyway...<br />
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Space and time are opposite equivalents of each other, in my understanding. Each is totally dependent upon the other to exist, because space without time would have no distance and no motion, and time without space would have no change.<br />
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A better way to explain it would be by saying that space is made up of points of location, whereas time is made up of points (moments) of time. In time without space, every point in time is in the same location - happens at the same moment, effectively meaning time would also not exist. Space on the other hand, without time to seperate one point of location from another, would involve every point being in the same location.<br />
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Notice something there? Sounds like the ingredients for the Big Bang to me!<br />
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Ok, let's go to the time dilation issue now... another post coming...

Ok, where to begin?!<br />
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You talked about getting around the 'progressive' aspect of infinity when measuring the universe by having a lot of numbered square meter boxes and filling the whole universe with them... but how would you fill the whole universe, when you could always add just one more box?<br />
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I'm not saying that the universe is limited, just that it's not infinite. See, this is where time comes into the subject of infinity, because inside of time there will always be a limit, because while there is time, there is always 'time to add one more'!<br />
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I do wish the comments box would retain my formatting, I think I'll mention that one to the EP team as well!<br />
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Where was I?<br />
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Going back to what I said about balance and opposites. Another common property of the universe is for things to be mirrored at different scales, which in your terms would be described with words like 'fractal' and 'microcosm'! Now, on a scale down from the opposite pair of infinity and nothingness there is another pair of significant opposites... and this is going to take some explaining... these are simply; space and time.<br />
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I'll start a new comment to explain this one, as you did when replying - helps to break things up a bit!...

Oh man, you and I have to talk some more! You are quite correct in observing that we are actually discussing the same issues but in different ways - me from a more philosophical perspective and you from a mathematical one.<br />
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For me, I recognise that math is very good at modeling things, but it's not very good explaining things. Like, I could use math to perfectly and accurately describe the form of a rose, such that another mathematical being could then re-construct the same idea, but math cannot explain the beauty of a rose, or the sweetness of its scent.<br />
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As a small child I told stories and wrote poetry all the time. I had lots of encouragement, and slowly grew a talent for relating ideas through words, which is essentially what poetry is. I formed an idea in my head at an absurdly young age that if people ruled the world, then words were even more powerful, because everything can be achieved with the right combination of words.<br />
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There is of course some difficulty, however, because a mathematician is rarely a poet, and a poet rarely a mathematician. I'm very pleased to see that you were able to relate to the way I explained things despite being so scientifically minded, and I would like to talk more about certain things too, particularly the subject you raised, of time and dilation, as my ideas also cover these areas to some extent. I still have to finish shuffling my kids off to bed yet though, so a little later I'll come back and we'll continue this :o)

but it gets even more complicated when we come to infinity not only in space, but also in time.... I.e. is it possible to travel an infinite distance if you are allowed infinite time? Or infinite speed? It all comes down to definition... Yet today, no one has really defined the universe... And probable no one would EVER define it correctly.... Which leads us to the question... "what is correct/reality?"... .......... Oh and one more thing... In maths; nothing is everywhere! The empty set is a subset of all sets, but when one say that 2 sets are disjoint, one always disregards the empty set... But still, it is EVERYWHERE...... Ah mathematical topology is interesting... but blows one's mind up totally...

That's why relativity is so handy. We know we can't travel infinitely fast in our perspective. But in theory one can travel almost infinitely fast [A number that converges towards infinity] (in one's own limited perspective). If you move at the speed of light (almost!) time will go slower for you compared to others; so you'll speed for observers is near "c" - speed of light, but for you, you are traveling much faster, as time is moving much slower... So can you travel infinitely far out in the universe? Not as seen from an observer... but from your own perspective? that's where it gets tricky (I do not know... maybe some professor knows... I'm still just a layman)... Maybe the universe is hyperbolic or spherical, maybe it is like a Klein bottle... You might feel like you are traveling infinitely fast, but really is just moving slower and slower all the time...... OR... maybe, as light (from the Big Bang) has not reached infintely far out, we might define the edge of universe as where that energy is... or we simple define it as the convex (?) hull of matter............ I have to say that you have very interesting ideas. We two look at this from different perspectives. Mine a bit more from the scientific way, meanwhile yours is more philosophical and humano-logical. So I thank you for expanding my view :).... Right now I guess the problem lies in the definition of infinity... There are many inconsistencies between science and real life when it comes to definitions...

Definition: Let Jn be the positive integers until n. and let ~ denote the equivalence relation.........A is finite if A~Jn for some n. (The empty set is also finite)........ A is infinite if A is NOT finite........ A is countable if A~J (where J is the set of ALL positive integers)...... A is uncountable if A is neither finite nor countable..... So we have both countable infinity (like the number of integers or even rational numbers), but we've also got uncountable infinity (like the real numbers). We call them Aleph Nil and Aleph One respectively... Progressively infinite would therefore be countable infinity, because you are able to count every step you take. However, if we try to count infinitesimal points of space, our universe becomes actually infinite [uncountable infinity]; but then also any compact space is infinitely large [i.e. your room is an infinite amount of space, because there are infinitely many spatial points in it] and we come to a physical-mathematical paradox.... So let's define the universe as progressively infinite... This means that you can have a lot of 1 cubic meter boxes. You name them Box 1, 2, 3, ... etc... and you can fill the whole universe with your boxes. Then the Universe is countable but still infinite... The problem is whether this logic is acceptable... We've just shown that the real numbers (in 3D) can establish an equivalence-relation with subsets of the real numbers (which is an obvious triviality)...