# To Infinity and Beyond

Documentary examining current ideas about very large numbers and infinity in regards to mathematics and the observable universe.

By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever.

But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.

Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last.

And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you.

Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.

If the universe's beginning was when they said, then it will be a long time until that monkey is finished. I think we should focus on loving our neighbor and taking care of each other and our planet. These pursuits can lead us to tangible benefits.

I agree more with Aristotle (there is no actual infinity) but in my own way. In my own hypothetical opinion/theory I devised years ago, actual infinity is subject to time and space and planck length. As time and space have a hypothetical beginning and end (e.g. birth of the universe and eventual cold ending), actual infinity cannot be infinite. Actual Infinity as a straight line of solid matter can only be as long as the longest object since the birth of the universe and cannot extend outside of those regions as it would violate the laws of nature as nothing could exist out of those regions, and matter could only extend outwards of 13.8 billion years. Maybe it could curve in on itself and wrap around like spaghetti confined to that universal area though, eventually ending filling up the area (infinite a sense but is still "less" than e.g. 14 billion to the observer)... Conceptual infinity is more of a fantasy to fix runaway numbers for mathematical purposes. The end of Infinity as a number in simple form (e.g. simple bits) can be computed, but you would use all the energy in the universe (again assuming the universe is finite). Eventually you'd run out of energy in the universe (e.g. using every last bit of usable energy possible to calculate infinity to reach the end). You wouldn't even know what the numeral end of infinity was because you wouldn't be able to observe the end of the calculation. An approximate equation can be devised however it probably can never be solved. E.g. if you could try to find out how much potential energy exists in a given area of 13.8 billion light years maybe by using stars (we kinda know how much matter there is and how much energy a star gives off before does) you could probably figure out a way to calculate it but solving it would actually require all of the energy in your equation. Not sure how black holes would fit into that though. However if energy can never be created nor destroyed in the universe maybe you can still get to the point where you can calculate something to the point where it grows so cold near the end of the universe where it physically stops or if the universe begins to contract again maybe that would be the end of your number before the bring crunch.

Loved it

"If I stayed on and all the other guests left..." That's false. Define the number "all the other" and you find it has no meaning. You can never specify what "all" of them are. I mean - how would you know when "all but one" were checked out? Count them? It is nonsense. Just because the words form a sentence that follows the rules of grammar doesn't mean it makes sense.

in-finite only means "Dunno". It is not a number. How many cats in a peanut butter sandwich? Angels>

Pinheads.

Infinity is meaningless it is all and nothing it is not and even typing what i have typed is a waste of time for time exists in the sense that it is one of the points of reference that allows us to navigate as humans but other than that it has no meaning as life could be said to be an illusion for it ends and when it ends as it does for all then all will eventually be not so since eventually all will be not then of course we use human vocabulary which is so limited as must be somethings that cannot bedescribed with any human language for example i have experienced certain thing or whatever that cannot be i cannot explain as no point of reference to anything of thise world so must be more be we cannot being to know what we cannot know so terms like infinity mean nothing and as i say again are imposisble concepts for humans to even find any sort of way to exp´lain not iwht art music whatever so so far as we are concerned life is not infinity is not

Infinity = life. infinity + 1 = infinity of one and one = infinity

What is the biggest number? There is no bigger number because if there were, you could always add one to it. What is infinity minus infinity? If numbers don't go forever where do they end? Find out why Aristotle banned infinity from his mathematics. The first mathematician that claimed the universe was infinite, Bruno, was burned to death by the Catholic Church in 1600. Kantor settled mathematicians down and developed the single set, so humans could focus on local equations. But decimals soon proved that there are infinities beyond infinities, and Kantor suffered a mental breakdown. Is space infinitely big or simply unimaginably big? Infinity makes the extraordinary mundane and the unbelievable inevitable. Are their consequences to an infinite universe? There are an infinite number of universes. The good news is that infinity can be anything you like! Google on then,,,

I didn't really get it. when you plus one to an infinity shouldn't it be infinity one? Why is it still called infnity? Is it just becasue infinity is unimaginable big number with no limit? It is unimaginably big does not mean forever isn't it? There has to be a limit for the biggest number infinity.

Time and size are all flimsy concepts when the idea of infinity is applied. In an infinite universe the only possible decision you could make to act against an inevitable set of decisions is to BE. We are all stirring ourselves sick in this madness. Making it seem as if we are individual and set apart from the nature of all things, when we are the spawn of this nature. Confining grand perfection and applying it to our lives instead of realizing what is happening, what you really are and the overwhelming fact that there IS a network of information (regardless of how it works, when and if it will 'end'). To BE though would be to experience the death of ones own ego. In this place of true being you will never run into something that doesn't make perfect sense.

Gonna watch the movie after work, infinity, no such thing. For every beginning there is an end. But not exactly, as with anything, energetic or passive, eventually transmutes into something else which would also seem true in the micro and macro-verse. So it's that cycle that can be viewed as truly infinite and unobservable in our short lives.

when man says something exists it becomes reality,i find this disturbing but also fascinating on all accounts.For example a photon not watched will run havoc but act normal when watched or observed.When a photon is observed it acts normally!!! what is normality in the universe reality or thought,as Sherlock Holmes would say something is afoot.

life is.... to is or not to is.

It's always good to revisit this doc.

az

I dont see why space being 'infinite' -something which is an abstract concept to begin with., has to equate with a multi-verse with replicas of everyone??

the little girl (when the children are asked: 'how big is the universe?' -who spreads out her arms and says 'that big' had the most correct answer. In that you never experience anything of the universe not within the confines of your own mind bc that is the seat of consciousness.

not infinity..but 'eternity' (as per william blake, -is not time or numbers going on forever but the absence of number, time (and differentiation). It's a mystical concept and I real that is not what is being discussed above..

it popped into my mind anyway.

'

To see a world in a grain of sand

And a heaven in a wild flower

Hold infinity in the palm of your hand

And eternity in an hour.'

'If the doors of perception were cleansed every thing would appear to man as it is, infinite. For man has closed himself up, till he sees all things through narrow chinks of his cavern.' william blake

I think that these guys are trying to explain reality using math. This is leading me to believe that the best way i can explain reality using math is that {infinity + 1 = infinity - 1} = Reality. Everything exist within its opposite, life is a contradiction in itself.

This idea represents the branching off of Reality into infinity. And this happens as fast as it is happening... Funny how reality happens just before you can think about it, or lol just before it happens.

Since I've been aware of the nature of the universe and my restless mind has too much time to ponder infinity I have came up with an odd way of grasping it.

Our universe is contained inside a subatomic particle.All other universes exist in all the other subatomic particles that match to our observable universe.THAT universe is made of the atoms of another subatomic universe and so is their's and so on and so on.

The same goes for subatomic particles in our observable universe.Each one contains a universe all of it's own.Those universes are again made of subatomic particle universes.

There you have infinity.

Or I'm just talking out of my ass.Either way it's fun to ponder.

i love the "WHOA" looks that the creepy, bald headed british guy gives the cameraman. As if to say, look at me, im so wise and mysterious and creepy and profound.

"Infinity minus infinity can be... anything you WANT it to be?" WHOAA. That guy is a cartoon and a self- parody. Like dr. evil or something.

Interesting.. but hurts the brain

But i am searching for the right answer for how did zero divided into positive one and negative one and also why they do not meet to form 0 zero again .I think that there is some kind of force that is actually holding these two away from each other and the proof of this force existance is that we need a lot of energy to produce or extract negative particles in Particle accelerator or we can say that we need a large amount of energy to cancel out the energy which is holding apart +1 and -1 .

According to me there are three things in this whole universe 1.Nothing 2.Everything 3.Only one. We know that 1/0=infinity supposing that 1 is a unit mass , Infinity is all the mass existing and 0 is Energy then

0 x Infinity

is something

that is 1 the unit mass

thats how the first mass came into existance.

And bigbang occured mainly because this zero(Energy) divided into two parts

that are 0 = +1+(-1). or

0 = + infinty + (-infinity).

Thats why bigbang began from NOTHING.

They say that if there would be a finite infinity then what will happen to it when 1 is added . My question is that if we are saying that infinity is the biggest possible number or number of objects or number of events then how it is possible to add something in it.

if imagine there is infinite numbers or events then if negative of it is added to it then it becomes zero 0=infinity+(-infinity) if there would be positive infinity then there will also be a negative infinity thus the sum of positive and negative infinity is zero 0 and we know that zero is Nothing but it is also the sum of every thing.This means that actually there is nothing.We also know that every particle has a same negative particle thus

if there would be infinite positive particles than there would also be infinite negative particles.But remember sum of everything is zero meaning nothing.

Dear Grant

We are not talking of a "man" or a "woman" we are discussing the infinite number of natural numbers and that must be able to have counted everyting -- every atom, and every electron, every star and every galaxy and every universe and every man woman and child and every hotel room. Everything!

Unfortunately some of the mathematicians in this program do not understand the concept. As an example one suggested a hotel with an infinite number of rooms, all occupied. He then suggested that he comes to the hotel seeking a room. He proposed that a room could be made available by having each occupant move along one room, thus freeing up the first room for him.

What he did not realise is that he must already have a room. He is already counted in the infinite number. So is everyone else and everything else, because the number is infinite!

By definition, everything is counted in the infinite and therefore there cannot be anything exta to add.

is it me or are they taking the word "infinity" in a linguistic way and trying to apply it to maths? why are they treating it like a number? I thought it was a concept, or a way of say that something doesnt end... I dont understand why they are writing things like "infinity + 1" on a blackboard... isnt that like trying to solve the equation " infinity + loads more" or "infinity + a penguin"... Have i just missed the point completley and am i talking cr*ap? please enlighten me.... :)

Thinking deeply about infinity will give anybody a major headache if it's done purely in mathematical terms. The secret to avoiding that headache (and perhaps gaining some more understanding of the universe) is to convert infinity into physics. This is how "Tomorrow's Science Today" (the Kindle version on Amazon) does that. It says -

"Page 118 of “The Grand Design” says “M-theory (that theory which string theorists now consider fundamental) has solutions that allow for many different internal spaces (the curling up of extra dimensions into tiny, invisible spaces), perhaps as many as 10^500, which means it allows for 10^500 different universes, each with its own laws.”

Suppose there is only one universe with one set of physical laws (a megacosmos that might have an infinite number of local universes, each of which begins with its own Big Bang). 10^500 would therefore not refer to space and the number of universes but to time (Einstein showed that space and time can never exist independently of each other) and the number of “frames” existing in the cosmos. We can visualise the binary digits as generating information on how things change from one presently undetectably tiny fraction of a second to the next (we call this time, and it's comparable to the frames in a movie). On page 27 of Carl Sagan’s “Pale Blue Dot” (Headline Book Publishing, 1995), it is written “There is, in fact, no center to the expansion, no point of origin of the Big Bang, at least not in ordinary three-dimensional space.” This truth surely means Big Bangs (or, for the purpose of this article, the generation of binary digits) must occur in a 5th-dimensional hyperspace (time is usually interpreted to be the 4th dimension). Let’s go back to space and time never existing independently of each other. This must mean 10^500 not only describes time and the number of frames in the universe but must also refer to space after all (though not in the sense of 10^500 parallel universes existing). The article “Universe” by Charles Anthony Federer, Jr. in World Book Encyclopedia, 1967 says “Einstein’s theory of relativity implies that the superuniverse (what I called megacosmos at the start of the paragraph) has a definite size.”

What’s outside the superuniverse? I don’t think there’s anything at all: it would be a true nothingness, or N-space. Just a vacancy for space-time-hyperspace to expand into as binary digits generate more space-time. For all practical purposes, 10^500 would equal infinity and the strange thing is – infinity will keep increasing during the eons as bits (BInary digiTS) do their thing. This is somewhat like the subset of all integers (1, 2, 3, etc.) extending to infinity yet that infinity being smaller than the infinite subset of all decimals.

If the universe is ENORMOUSLY large, space would seem perfectly flat - just as an acre on the surface of large, roughly spherical Earth is flatter than an acre on a spherical asteroid only 10 miles in diameter. The WMAP space probe (Wilkinson Microwave Anisotropy Probe, launched in 2001) has confirmed that space is flat. We are presently unable to detect the closed, positive curvature of space associated with the number 10^500 and can describe the flat universe that can be detected with the Mobius loop, which is one of the two-dimensional spaces described by Euclidean mathematics which is assumed to describe a flat universe. Since separation is zero, the universe must be unified with each of its constituent subatomic particles and those particles must be similarly roughly spherical, composed of space-time-hyperspace, and must also follow the rules of fractal geometry to be made of Mobius loops. The Mobius strip is capable of describing the overall nature of the universe because assembling, in correct fashion, enough pieces of flat universe which it sketches results in a spherical cosmos (comparable to the network of theories which "The Grand Design" says may describe our universe).

Recall that the universe may be a computer-generated hologram in which things appear distant from each other as if they’re on a huge screen but are unified by the strings of ones and zeros making up the computer code which is all in one small place. (That “small place” is the universe’s CPU or central processing unit, binary-digit generating hyperspace.) They’re unified with all other material and immaterial things in time and space. There would inevitably be feedback between space-time and hyperspace, preventing the changing of the past from what it was or the altering of the future from its destiny. Spacetime is united with hyperspace since the latter is part of the former, and even part of every particle in spacetime. However, the restriction of processing speeds in hyperspace to the speed of light makes it appear disconnected and separate to observations and experiments.

Empty space (gravitation) seems to be made up of what is sometimes referred to as “virtual particles” by physicists since the concept of virtual particles is closely related to the idea of quantum fluctuations (a quantum fluctuation is the temporary change in the amount of energy at a point in space). The production of space by BITS necessarily means there is a change in the amount of energy at a certain point, and the word “temporary” refers to what we know as motion or time. Vacuum energy is the zero-point energy (lowest possible energy that a system may have) of all the fields (e.g. electromagnetic) in space, and is an underlying background energy that exists in space even when the space is devoid of matter. Binary digits might be substituted for the terms zero-point energy (since BITS are the ground state or lowest possible energy level) and vacuum energy (because BITS are the underlying background energy of empty space). Relativistically, space can’t be mentioned without also mentioning time which can therefore also be viewed as gravitation (since “dark matter” is invisible but has gravitational influence, its existence could be achieved by ordinary matter traveling through time).

This “small spot” things are generated from could be the cosmic equivalent of the fixed-point theorem.

“There is a powerful statement in mathematical topology known as the fixed-point theorem. The (best known, among hundreds, because of its wide use) fixed-point theorem, which was proved before World War 1 by the Dutch mathematician Luitzen Egbertus van Brouwer, states that when a surface is subjected to certain forms of continuous distortion, at least one point of the surface will remain fixed, or stationary. Put in this dry, abstract way; the theorem may not seem remarkable, but it has many impressive consequences for the physical world. The fixed-point theorem … applies to the human head and other spheres, such as the Earth. It states that mathematically, a sphere cannot be associated with a continuous field of radiating lines without there being a fixed point. For a head of hair this means that there must be a fixed point, or whorl, from which the hair radiates. For the Earth this means that the wind cannot be blowing everywhere on the surface at once; there is always a tranquil spot.” (from Dr. Crypton’s Puzzles and Mind-Teasers: Omega Science Digest, March 1983).

The most important words in the above paragraph are “… a sphere cannot be associated with a continuous field of radiating lines without there being a fixed point”. Sphere refers to the description of the universe on pp. 145-149. A continuous field of radiating lines would mean these lines are “BITS of spacetime - this book’s proposed building blocks of all matter, forces and spacetime”. These form every fermionic and bosonic particle in the 3+1 dimensions of space and time (picture space-time as the surface of an expanding balloon).The fixed-point is not on a surface but is in 5th-dimensional hyperspace (picture the 5th-D as the centre of the balloon).

If, as has been suggested, frames are created in the 5th dimension by bits and their very rapid display results in the macroscopic motion we see; what causes the microscopic motion of bits switching on and off in order to display frames? Could it be that Stephen Hawking’s/Leonard Mlodinow’s book “The Grand Design” indirectly supplies a clue on pp. 160-161? Speaking of space dimensions and gravity, it says “In any but three dimensions even a small disturbance, such as that produced by the pull of the other planets, would send a planet off its circular orbit and cause it to spiral either into or away from the sun …” and it also says “In three dimensions the gravitational force drops to ¼ of its value if one doubles the distance … in five dimensions it would drop to 1/16 …” Gravity is only the warping of space-time and hyperspace - so in the 3 dimensions we normally experience, a certain amount of energy is required to turn a bit on or off but in the 5th dimension, computing power would be magnified because switching every single bit on or off would only require a fraction of that energy (“a small disturbance”). Therefore, creating a unification from BITS (BInary digiTS or Binary digITS) only using the 4 dimensions we’re familiar with could exceed the power of our computers and might produce a unification that was a uniformity with no oscillation between on and off states. This could be static in the sense of motionless – and merely a perpetually-unchanging snapshot of the universe at one instant. Processing, the movement of bits between on and off, in a 5th dimension would have none of these problems in my opinion and would be possible because of the universe’s removal from uniformity and entry to partial unification (extremely tiny removal from being totally unified DUE TO ITS FIXED POINT IN THE 5TH DIMENSION)."

Was this little extract from the Kindle version of "Tomorrow's Science Today" interesting? It's more complete than even the most recent paperback.

@ ObamaATL

This is even better, much better:

Top Documentary Films ? SCIENCE ? 37.Dangerous Knowledge

0z

There is no infinity because God is the End. He is also the Beginning.

Negative Infinity = God.

0= God.

Positive Infinity = God.

Probably the most illogical theory ever. If some mathematicians believe that there is infinity larger than infinity, why are they called mathematicians? Infinity is like religion, faith based. You cannot prove anything about it, you can just have faith in it, or not. Sigh... this documentary proved to me that a doctorate degree doesn't mean that you are smart...

Fantastic stuff, but I don't know about the odd asides in the presentation, scriptural, philosophical, and ponderous utterances in poetic fashion. Overshadows the show's otherwise great credibility.

Brain hurts. Great documentary, very informing. Slight bias towards those who believe in infinite universe, but lean that way myself, so am not v. bothered.

infinitely awesome :)

Now that was Bad A#%

no one can understand more and more about infinity.

Just to add to the debate (which I actually enjoyed more than the documentary, being well versed in the concept of infinity as a scholar of maths and physics) - I read an interesting book a couple of years ago in which the main assertion/theory of the book was the same as another poster.

And that is that human consciousness is the true constant, because without it, there is no science or no universe. In essence, the main point is that without humans to observe the universe, there is no point in the universe. I suppose it's just another "if a tree falls when nobody is around" argument, but it was still interesting reading. Unfortunately the name and author of this escapes me at this time, and I gave the book to a friend. ("Never lend a book" - Commander Adama)

However, while I found it interesting reading, I still trust in the scientific method above all else. The use and application of it has been the catalyst for unprecedented scientific advancement over the last century (although I'm sad to see that one of the consequences of this is a vast number of people who lack scientific knowledge, and even reject the scientific process - but while all the time complaining about it on their computers, of course)

Suppose there are infinite nos of pack of cards and each set has two jokers,so it is logical to conclude that in this infinite nos of cards there will be more jokers than any other cards,infinity lies in to the limits of our brains but every thing in this world is finite.

Then the cycles of creation and destruction has infinite nos of cycles,coz it is like a circle with no starting or ending points,it goes on and on and on

Regards

Anurag Awasthi

@Robyn318:

I am still waiting for my inter-library "Barbours book"

Have to read it again to answer you properly.

But don't know if he will have a "hurdle" to remove time and motion from the equation, in quantum physics there is no time and motion.

He is not removing the observer from the equation, the observer is the one that collapses the waveform to give motion, therefore time.

But like I said, will have to read it again.

@Achems Razor

I just finished chapter four and so far I can grasp his idea of our reality being ‘time capsules’, all pre-existing, waiting to be experienced in the next ‘instant’, like memories. I think he is going to have a big hurdle to overcome by removing both time and motion from the equation, though it seems obvious that you cannot have motion without time.

He seems to be pursuing the Machian model of Absolute Universe. I see a potential problem in his reasoning (pg 69, 9 lines up from bottom): “We must not think of the history of the universe in terms of some walker on a path who can move along it at different speeds. The history of the universe is the path.”

He seems to be removing the observer as an integral part of reality; quantum physics says the observer must be included. In the Machian view, everything inside the universe IS the universe and nothing exists outside of it, and you cannot perceive time by experiencing yourself only, it has to be perceived relative to an outside experience. I am hoping he will explain why he thinks I do seem to experience time.

At least two media are capable of slowing down light tremendously -- Einstein-Bose condensates, and hot rubidium gas. These have both been used to halt light entirely. This was first achieved on a temporary basis in experiments conducted in 2001.But the space could not be wrapped:))

Epic_Logic:

That is what is called a math one-liner, Yes?

Where parallel lines meet at infinity.

Math problems? Call 1-800-[(10x)(13i)2]-[sin(xy)/2.362x].

I wonder .. If there is an infinite number of variations .... can there be a variation where is no infinity ?

ive seen things you people wouldnt believe... thats a bladerunner quote...my fav movie...im soooo watching this doc.

If you have a ray of light coming from a place where the image entering the zero point changes every second, 0,1,2,3...and it takes eight seconds for that ray of light to reach the observer, while it is true that after eight seconds the observer will see '0', 8 is on the zero point side.

@Achems RazorI ordered Barbours book it will be here in a week +/-The zero point space-time event at both ends of a ray of light is incorrect.I've been thinking about your take on time, and its validity has helped clarify my perception of Time. I think it is a software program run on the operating system of the conscious mind, specific to each observer, independent of space, engaged in the separation of stimuli received from the five senses, for the purpose of keeping each perception distinct and each instant separate, so the mind can process this data into information, with the intent of interpreting the environment.

this doc is awesome.

jack1952

Must be spooky actions at a distance... (LOL) "A. Einstein."

Whoa ... okay, not sure what I was expecting :) . Great start to this film too ... Horizon must have a few mystery writer's on the team. Honestly, at the start I figured, what's the big deal, who has a problem with infinity. It just means all things are possible (maybe even probable). Seems to me, the 'more' we seem to 'know' about our observable universe, the less 'real' it becomes, re: the weight of measurement (all the stuff/matter amounts to ? very very light-ness of being); time is illusion (re:past,present,future all exist in the same 'time/moment'); everything we see/feel/imagine,etc. may not 'exist' until fractions of a second before we (decide to) observe it ... what I am personally interested in, is how does this learning contribute in some meaningful way to my imagined life? This is what it all comes down to my friends (good song :) ... for me - how do I imagine/create a Better reality - the possibilities are, dare I say, Infinite (or not :). Great teaser film

P.S. I got myself registered on this 'new' comment system - looks like it could be interesting...