If the TARDIS is infinite, then wouldn't that mean that it contains every single possible outcome of any event in ALL of space and time? Including an infinite amount of planets, solar systems, Daleks, Cybermen, TARDISes, exploding TARDISes, black holes, wormholes, other Time Lords, other Doctors and entire universes, all inside itself?
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14To the close-voters: this may be based on a false premise, but it's still clear what the question is. It's not "unclear what the OP is asking".– Rand al'Thor ♦Apr 8, 2016 at 11:17
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2Related: How big is the interior of the TARDIS?– Rand al'Thor ♦Apr 8, 2016 at 11:33
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57The set of even numbers is infinite, but it doesn't contain every number.– svickApr 8, 2016 at 13:28
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7From 0 to infinity is infinite, but does not contain -1.– KevinApr 8, 2016 at 13:39
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3Even though the Tardis's dimensions are infinite that doesn't mean it contains a particular thing. It could all be empty space and still be "infinite".– Mark RogersApr 8, 2016 at 15:48
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8 Answers
The TARDIS is described as infinite in size in 'Journey to the Centre of the TARDIS', but it should be remembered that 'the Doctor lies', so it may in fact not be infinite at all.
However, if we take the statement to be true, and the TARDIS is indeed infinite in size, it helps to realise that 'infinite' does not necessarily mean 'everything'.
For example:
The set of all real numbers is infinte.
The set of all whole numbers is also infinite, yet it clearly does not contain all real numbers, so it is a different infinite set (and indeed smaller, in the sense of lower cardinality).
Similarly, there is an infinite number of fractions between 0 and 1, yet it clearly doesn't include any number over 1 or less than 0, so it is another example of a different infinite set.
The TARDIS may well be infinite in size, but that doesn't mean it contains everything.
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10It still drives me crazy that there are different sizes of infinity. My brain just sort of sits down and gives up whenever I think about that. Apr 8, 2016 at 11:05
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2@PaulD.Waite It gets much worse: Take care not to read about cardinal numbers - they make things like countable and uncoutable infinity look harmless: en.wikipedia.org/wiki/Cardinal_number Apr 8, 2016 at 14:14
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5@PaulD.Waite: You're in good company. When Georg Cantor discovered the infinite Cantor Set, it literally drove him nuts pondering the ramifications of it. Apr 8, 2016 at 16:13
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3@PaulD.Waite The mathematician Kronecker has a solution for you: assume that the transfinite sets that have higher cardinality than the integers don't have any "real" existence in a Platonic sense. He famously quipped "God made the integers; all else is the work of man." The continuum (i.e. the "real" number line) can therefore be thought of as simply a man-made construct with no bearing on philosophical reality. (This is actually something like what I believe, even though I am fairly certain that I do in fact understand the basics of Cantor's math.) Apr 8, 2016 at 21:09
No. Being infinitely spacious in no way means it contains all possible universes. It just means the TARDIS is physically infinite, in that it goes on forever. Nothing about "everything that can happen, does happen" or whatnot, just infinite rooms and space to put things like a pool, a library, etc.
11TH DOCTOR: Picture the biggest ship you’ve ever seen. Are you picturing it?
BRAM: Yeah.
11TH DOCTOR: Good. Now forget it. Because this ship is infinite.
- Journey to the Center of the TARDIS
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6I hated this quote. :( I really hope we can canonically say he was being hyperbolic. Apr 8, 2016 at 11:24
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3TARDISes are grown, not built. So if they would really have to grow to infinite size, it would take an infinite time for one to be finished. Apr 8, 2016 at 15:03
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3@MrLister I don't think that's necessarily true. My assumption has always been that the space inside the TARDIS folds in upon itself in such a way that the "infinite space" is simply how 3-dimensional beings are forced to perceive it, like some kind of transdimensional annulus. This requires nothing so silly as "the inside of this box extends in all three physical dimensions forever and ever, and got that way by growing at a finite speed." Alternatively, one could assume that the inside of the TARDIS is finite at any given point in time, but will automatically extend itself as it is explored. Apr 8, 2016 at 21:12
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No. Infinity is not Everything.
Think of it like this: There are infinitely many even numbers, yet not all numbers are even.
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2While correct, does this add anything to the existing answer by tojo?– Rand al'Thor ♦Apr 8, 2016 at 13:02
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2@Randal'Thor: One could argue that more people are familiar with concepts like odd/even numbers than are with the set of whole/real numbers...but they could stand be merged. Apr 8, 2016 at 13:23
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Not necessarily
An infinite set does not necessarily contain everything.
Consider the set of all Fibonnaci numbers. This is an infinite set. Now, where in this set can you find the Daleks? I just looked at a lot of Fibonnaci numbers, and I didn't see any Daleks. If the Fibonnaci numbers don't contain the Daleks, why would you expect the TARDIS to do so?
Some infinite sets are "smaller" than others
The set of all integers {...,-3, -2, -1, 0, 1, 2, 3, ...} has a certain cardinality. The set of real numbers has a different cardinality. This can be thought of in terms of whether there exists an bijection between the two sets. In addition, one set may nonetheless contain another set of the same cardinality, but different elements. For example, the integers contain the natural numbers. But the integers contain elements not seen in natural numbers {0, 1, 2, 3, ...}, for example, the number -1.
Physics will not save you.
Many people would argue that under conventional physics anything macroscopic can form in a sufficiently large volume of matter, as in quantum mechanics most transitions are not truly forbidden but merely vanishingly improbable. It would follow that in an infinite volume of matter, there will be some subvolume that will form virtually anything you care to mention within a negligible time.
The TARDIS does not run on conventional physics. Everything you know is wrong. Black is white up is down and short is long.
If the TARDIS wants to have infinitely many corridors with no chance of transitioning to a Dalek, it can.
If the TARDIS wants to have infinite expanses of empty space that will never undergo a vacuum oscillation, it can.
But on the other hand, there's nothing stopping Moffat from endorsing exactly what you said, either.
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3“Black is white up is down and short is long” — left is banana, slow is heartfelt regret. Apr 8, 2016 at 11:04
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+1 because now I'll listen to that Weird Al Jankovic song in my brain all day. No, wait...-1– tilley31Apr 8, 2016 at 12:22
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1+1 for bringing in physics. Simplicio: "Sure, in math we can different infinities, but surely an infinite amount of space must eventually overlap with all other space in the known univers?" Salviati: "Physics will not save save you...The TARDIS does not run on conventional physics." Sagredo: "Ah, now I see." Apr 8, 2016 at 22:10
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2First paragraph: Average Doctor Who fan. Second paragraph: Mathematician. Third paragraph: Physicist. Fourth paragraph: Average Doctor. Apr 9, 2016 at 11:59
No. The interior of the TARDIS occupies a different dimension (it's "dimensionally transcendental"), which is how it packs so much in what to us appears to be a small space.
If we suppose that the quote should be taken at face-value (and personally I choose to believe the Doctor was being hyperbolic), then the TARDIS can be infinitely large in terms of space in the realm it's occupying. That doesn't mean it is infinitely large in terms of space in our universe/dimension.
answered Apr 8, 2016 at 11:26
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3I like the idea of the Doctor being hyperbolic, as opposed to answering "the Doctor lies" all the time to any inconsistency. Apr 8, 2016 at 14:57
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1@MrLister: Yeah I thought that line was getting a little old ;) Apr 8, 2016 at 15:15
I think it's a matter of phrasing.
The Doctor probably intended to convey the idea that the TARDIS is "infinitely expandable" but has not actually expanded very far yet.
It's a similar concept to an empty "basement universe". Not much in there, relatively speaking, but effectively infinite room for expansion.
As evidence, the journey to the center of the TARDIS from the outer door only took a few hours. That indicates that it's in the order of a few Kms at most plus the size of the black hole in the center.
As further evidence, he has previously jettisoned individual rooms to balance his energy needs. That would only make sense if the rooms were of significant size compared to the entire TARDIS.
Also bear in mind he is a notorious braggard and unreliable narrator who claims to also have serious memory loss issues.
As an analogy, consider: the TARDIS is infinite, meaning "its size is not finite" or, in (several) other words, the TARDIS can be whatever size it needs to be to contain whatever it is it needs to contain. If something very large must be brought in, the TARDIS will change its size to contain the item. If said item is removed the TARDIS may choose to adjust its size so that it is no longer large enough to contain the item which is no longer there. If the need arises for an infinitely long corridor or an infinitely large room the TARDIS will supply said space - all while still being inside the TARDIS. Perhaps where we're hung up is on the word "infinite". Perhaps a better term would be "recursive flexibility". :-)
answered Apr 9, 2016 at 11:12
Although the TARDIS is described as infinitely large and seemingly similar to a black hole because of its infinite mass inside of a single telephone box, that does not mean that it contains everything similar to the infinite decimal set between 1.1 and 1.2 which is an infinite set yet most definitely, clearly does not contain every number which is also applicable to the Doctor's TARDIS.
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While correct, this doesn't add much to the answers already posted. However, welcome to SFF Stack Exchange! I hope you'll poke around a bit and find something else here that you can answer :-)– Rand al'Thor ♦Apr 8, 2016 at 22:53