Down The Rabbit Hole: Complex Theories of Time in Alice’s Adventures in Wonderland

Alice’s Adventures in Wonderland (1865) and Through the Looking-Glass and What Alice Found There (1872) were both published during an uncertain time period. Isaac Newton’s theory of absolute time and space, proposed in 1687, remained the most prominent time theory throughout the nineteenth century despite increasing opposition. Newton defined time and space as a creation of God that was independent, absolute, infinite, and served as a backdrop to everyday life. However, Newton’s theory was never unanimously accepted and faced opposition from other scientists and mathematicians like Gottfried Leibniz. Leibniz argued for relational time concepts founded on mathematics and geometry, which were independent of God (Ray 112). While both Leibniz and Newton employed mathematics to explain time, Leibniz argued that the employment of mathematics confirmed that time was relational (Ray 112). Relative concepts of time, like Leibniz’s, increased in prominence as technology progressed.

The industrial progression of the late nineteenth century also created uncertainty regarding time theories as society progressed away from secular reasoning, which was fundamental to Newton’s theory. According to Peter Galison, Einstein’s Clocks, Poincaré’s Maps: Empires of Time (2003), the conflict between Newton’s theory and the emerging relative theories was essentially ‘a clash between the early modern and the modern: on the one hand, space and time as modifications of the sensorium of God [Newton]; on the other, space and time as given by rulers and clocks’ (38). Despite these challenges, Newton’s theory was not supplanted until 1905 with Albert Einstein’s Theory of Relativity. The Alice texts were published before 1905 and consequently epitomise the uncertainty surrounding time theories in the late nineteenth century.

        Charles Lutwidge Dodgson, pseudonym Lewis Carroll, studied classics and mathematics at Oxford before becoming a mathematician at Christ Church. In Euclid and His Modern Rivals (1879), also penned under Lewis Carroll, Dodgson commended Euclidean geometry which relies on natural or obvious logic; for example, the three angles of a triangle always equal 180°. Dodgson’s promotion of Euclid logic could be considered surprising, particularly when considered with regard to the nonsense associated with the Alice texts. Thus, the Alice texts may, after all, possess logic. Dodgson was extraordinarily versed in logic, specifically as the writer of Symbolic Logic (1896) and The Game of Logic (1886). These texts, aimed at children, explained the fundamentals of logic and provided innumerable puzzles. Bartley, one editor of Symbolic Logic, claimed that Dodgson’s ‘logical insight merged with his literary genius’ because ‘riddles about hypothetical or conditional statements, counterfactual and otherwise, even turn up in some of his children’s stories’ (29). The Alice texts are no exception.

Dodgson attempted to separate himself from Lewis Carroll. In a letter to Alexander Macmillan (1879), Dodgson wrote that ‘the fewer there are who are able to connect my face with the name “Lewis Carroll” the happier for me’ (337). Regardless, intersection between the two lives was unavoidable and some critics were able to connect Dodgson to Lewis Carroll. For example, the ‘John Bull’ (1866) linked Dodgson to Lewis Carroll by stating that ‘the book [Wonderland] furnishes evidence that Mathematics are not inconsistent with writing works of imagination’ (qtd. in Carroll, Letters 85).

The fact that the main character Alice is modelled on Alice Liddell, a child friend of Dodgson’s, suggests that aspects of Dodgson’s life feature in the Alice texts. Arguably, mathematical concepts also appear in the texts, especially since Dodgson simultaneously held the Christ Church Mathematical Lectureship (1855-1881) while writing Wonderland (1865) and Through the Looking-Glass (1872). Dodgson’s prestigious academic career would have, at least, allowed him to understand Newton’s complex theories. In fact, Dodgson references Newton with great respect in a letter to Mrs. F.S Rix (1885) regarding her daughter’s academic progress: ‘thorough mastery, of so much in so short a time, would be (even if she were a female Isaac Newton) out of the question’ (564).

Surprisingly, little criticism exists on mathematical concepts, let alone time theories, in the Alice texts and the existing essays are limited in scope; for example, ‘Time and Stress: Alice in Wonderland’ (1985) by Calvin Petersen at seven pages and ‘Alice in Time’ (2011) by Gillian Beer, the most thorough essay available, at thirteen pages. Instead, most essays focus exclusively on Dodgson’s relationship with Alice Liddell or methods for teaching the text; for example, ‘Back to The Future with Alice in Wonderland’ by Sandy Feinstein (2015). In general, criticisms on the Alice texts are limited and far out-numbered by reproductions including annotated and centenary editions, eighteen different movie versions, numerous songs (e.g. ‘White Rabbit’ by Jefferson Airplane), and merchandise. The Alice texts have, therefore, become firmly cemented in popular culture, while being relatively ignored as an academic text.

Critics may not have focused on time theories in the Alice texts due to the difficulties of their historical position as they were published almost two hundred years after Newton and thirty-three years before Einstein. Nonetheless, the late nineteenth century witnessed an increase in time awareness, which challenged Newton’s concepts of absolute time and created a period of uncertainty. The Alice texts depict this uncertainty through the use of nonsense. Nonsense has been explored by numerous critics; for example, Anna Neil, ‘Developmental Nonsense in the Alice Tales’ (2013), argued that nonsense functions as ‘a complex device for enhancing cognitive and linguistic flexibility’ (384). The Red Queen exemplifies the ‘cognitive and linguistic flexibility’ of nonsense. When Alice states ‘a hill ca’n’t be a valley, you know. That would be nonsense’ the Red Queen replies ‘I’ve heard nonsense, compared with which that would be as sensible as a dictionary [Carroll’s italics]’ (Carroll, Looking-Glass 140). The subjectivity of nonsense is literally revealed through emphasis on personal perspective with italics on I’ve.

Subjectivity is often determined by cultural norms. Cultural norms are social standards that determine inappropriate and appropriate behaviour, values, and beliefs (i.e. sense and nonsense) and can vary between cultures. This variability is precisely Alice’s experience. Alice, according to Hugh Haughton (editor of the centenary edition), is ‘the main critical user of the term [nonsense] in the book. Of the fifteen times “nonsense” appears in the text, nine of them refer to Alice’s judgment on the absurdity of what is being said’ (17n2). Alice’s use of the term positions her as a stranger as she can only view the Wonderland/Looking-Glass culture in opposition to her personal beliefs. The Red Queen invites Alice, and the reader, to reconsider pre-conceived notions like definitions of nonsense by ‘absolutely dissolv[ing] any fundamental distinction between sense and nonsense’ (Haughton 140n6). Through erasing this distinction, the Red Queen promotes conceptual flexibility to create an alternative reality where hills can be valleys and nonsense can be sensible.

Clocks, within Wonderland, indicate the transition between sense and nonsense and incorporate time into the discussion. In the opening pages, it is the White Rabbit’s pocket watch stirs that Alice’s curiosity causing her adventure down the rabbit hole:

When the Rabbit actually took a watch out of its waistcoat-pocket, and looked at it, and then hurried on, Alice started to her feet (Carroll, Wonderland 10).

The White Rabbit’s pocket watch is the only clock that appears before Alice enters Wonderland/Looking-Glass and unlike the Mad Hatter’s watch or the Looking-Glass clock is not broken and does not have an old man’s face. As the only normal and intact symbol of time, the White Rabbit’s pocket watch might represent social conventions. Gillian Beer, one of the few critics to explore the White Rabbit’s pocket watch, states that ‘belatedness, anxiety, physical props like the watch, all bespeak the individual under the cosh of time-regulated society’ (xxviii). The pocket watch is, thus, imbued with social and historical significance, but Beer only examines this significance at surface-level. Nonetheless, the White Rabbit’s pocket watch also reflects deeper psychological changes of the late nineteenth century.

The intellectual ‘time reformation’ that occurred in the late nineteenth century was evident in the commercial dominance of clock companies like Seth Thomas and E Howard, which Alexis McCrossen discusses in ‘”Conventions of Simultaneity” Time Standards, Public Clocks, and Nationalism in American Cities and Towns 1871-1905’ (2007). Seth Thomas and E Howard sold over two thousand clocks between 1871 and 1905 with a majority of purchases made by government institutions (McCrossen 220). This commercial dominance required the pre-existence of psychological conditions such as increased time sensitivity. While Wonderland was published six years prior to Seth Thomas and E Howard’s success, these conditions would have already been established in society.

The increase in time awareness, specifically in relation to government control, is evident in the White Rabbit’s anxiety. According to McCrossen, clocks allowed the government to lay ‘claim to [the] ownership of time’ (221) which is evident in the White Rabbit’s opening line: ‘Oh dear! Oh dear! I shall be too late!’ (Carroll, Wonderland 10) as the Duchess, a traditional government figure, will ‘be savage if I’ve kept her waiting’ (Carroll, Wonderland 17). The Duchess’ ability to cause the White Rabbit anxiety indicates that she controls and owns the White Rabbit’s time. The correlation between the White Rabbit’s anxiety and McCrossen’s article further demonstrates that the White Rabbit represents conventional late nineteenth century attitudes towards time.

McCrossen, regrettably, only references Newton in a brief footnote. However, the wide dispersal of clocks between 1871 and 1905 increased the demand for synchronised time, which consequently challenged Newton’s theory of absolute time. Galison explains that by the 1880s ‘Newton’s absolute, theological time had no place; instead there stood a procedure ’ (44). Engineering common time, a procedure for rationalising and measuring time, had replaced but not disproven Newton’s theory (Galison 44). According to Newton, absolute time could only be understood through advanced mathematics and therefore was generally inaccessible. Laypeople instead relied on relative measurements of time. Newton, Philosophiae Naturalis Principia Mathematica (1689), explained that relative time was a ‘duration by the means of motion, which is commonly used instead of true [absolute] time’ while relative space was a ‘movable dimension or measure of the absolute spaces’ (6). Relative concepts, therefore, made absolute time and space more comprehensible and accessible.

This overlap is one example of the intimate relationship between time and space. Even before Hermann Minkowski’s space-time continuum theory (1907), a mathematical model that fused space and time into a four-dimensional manifold, notions of space and time were often considered and defined in conjunction. For example, clocks (measurements of absolute time) were commonly used to chart maps   and determine longitude and latitude (segments of absolute space). However, Newton only briefly explored relative concepts and instead placed emphasis on the absolute. As society became globalised, flaws in Newton’s theory became apparent as absolute time failed to provide procedures for standardising time, which was necessary for a modern society that needed to regulate railway timetables and more accurately determine longitude and latitude.

Issues of determining longitude and latitude feature in Wonderland, specifically during Alice’s fall down the rabbit hole. The first objects Alice notices are the ‘maps and pictures hung upon pegs’ (Carroll, Wonderland 10), which indicates the geographical focus of the passage. Alice employs knowledge acquired from ‘lessons in the school-room’ to explain her experience such as that the Earth’s centre is ‘four thousand miles’ from the surface (Carroll, Wonderland 11). Typically, the schoolroom serves to disseminate a wide range of concepts including clock-time. Barbara Adams in Timewatch: The Social Analysis of Time (1995) discusses the role of education in cementing commonly accepted concepts:

It is this dominant time, so central to our adult social life, which gets habituated during childhood through the time discipline promoted in education (64).

Since time and space are closely correlated, Adams’ theory can be extended to apply to concepts of space. If Alice’s understanding of space reflects socially prescribed concepts, then her inability to precisely determine longitude and latitude serves the same purpose. Immediately after reciting facts about the Earth’s centre, Alice states ‘”then I wonder what Latitude and Longitude I’ve got to?” Alice had not the slightest idea what Latitude was, or Longitude either’ (Carroll, Wonderland 11). Alice may not have the ‘slightest idea’ what latitude and longitude were as longitude had not yet been accurately fixed.

Maps depended on synchronised clocks, which highlighted the demand for new methods of measuring and thinking about time and space in the eighteenth and nineteenth century. The Longitude Act of 1714 offered substantial financial rewards for practical methods for determining map coordinates (Galison 182). This issue would, however, not be solved until 1897 by Henri Poincaré and would require the aid of the telegraph (Galison 182). Since Wonderland was published almost thirty years earlier, the ordinary individual, like Alice, would have been unable to define their precise position and could only admire that longitude and latitude ‘were nice grand words to say’ (Carroll 11). Therefore, Alice’s fall down the rabbit hole represents the uncertainties surrounding concepts of time and space, specifically longitude and latitude, within society before the late nineteenth century.

The rabbit hole also transports Alice to Wonderland: a land of ‘linguistic and conceptual flexibility’ (Neil 384). As Petersen states, one of the immediate results is ‘the loss of a comprehensible space-time frame of reference’ (427). While Alice’s initial experience is disorientating with regard to space, for example frequent changes in size, the disorientation of time only initially becomes apparent in the chapter ‘A Mad Tea-Party’ with the Mad Hatter. The Mad Hatter represents and literally interprets Newton’s theory of absolute time and space. Newton explained that absolute time ‘flows equably without relation to anything external’ while absolute space ‘remains always similar and immoveable’ (Philosophiae Naturalis 6). The Mad Hatter appears to almost mock Newton’s theory by comparing time to an individual; for example, the pronouns him instead of it or capitalised ‘T’ in Time (Carroll, Wonderland 62). Time, according to the Mad Hatter, can determine his own movements based on personal preference and flights of fancy: ‘now, if you only keep on good terms with him [Time], he’d do almost anything you liked with the clock [my italics]’ (Carroll, Wonderland 63). Since the Mad Hatter has quarrelled with Time, Time ‘won’t do a thing I [he] asks! It’s always six o’clock now’ (Carroll, Wonderland 64).

This personified version of time, similar to absolute time, functions independently without ‘relation to anything external’ and, similar to absolute space, is stubborn and ‘immoveable.’ While it may appear that the Mad Hatter ridicules Newton’s theory of absolute time, this was probably not Carroll’s intention. In a letter to his sister Elizabeth (1894), Carroll writes that his intention is ‘not so much to prove one view of a thing right, and another wrong, as to get both views clearly stated’ (1044). Despite this statement originally concerning religion, Carroll’s intention could be extended to include Newton’s theories. Therefore, the Mad Hatter may also represent and simplify Newton’s more complex theories.

Make-believe worlds, according to Galison, could be beneficial for conveying complex scientific arguments:

It certainly is possible--even productive--to read Einstein and Poincaré as if they were abstract philosophers whose goal was to enforce philosophical distinctions by fabricating hypothetical worlds rich in imaginative metaphors (29).

If this method is beneficial for understanding Einstein and Poincaré, then it is also beneficial for understanding Newton. Carroll persistently advocated that complex concepts should be accessible to children and used ‘hypothetical worlds rich in imaginative metaphors’ to explain complex theories in Symbolic Logic and The Games of Logic.

Carroll plausibly also employed this technique to explain other complex theories such as Newton’s theory of absolute motion. Newton argued that every object has an absolute state of motion that is relative to other objects’ absolute states of motion:

All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be movable, is absurd. These are therefore the absolute places; and translations out of those places, are the only absolute motions (Philosophiae Naturalis 9).

The Mad Hatter’s tea party, similar to absolute space and time, is organised by an order of successions and situations. Newton argued that absolute space and time is segmented into successions and situations by primary or absolute places, which in Wonderland are literally represented by the table places at the tea party. If the table places represent absolute places, then the tea party’s movement around the table, i.e. the ‘translation out of those places,’ represents absolute motion. Since absolute places, or table places, are permanently immoveable, the Mad Hatter can never leave the tea party and is thus never without his tea and bread-and-butter.

However, Alice is skeptical and asks ‘what happens when you come to the beginning again?’ (Carroll, Wonderland 64). As Newton’s universe is infinite and changes to the primary places are ‘absurd,’ this question while logical to Alice is incomprehensible to the Mad Hatter. In a letter to an anonymous agnostic (1897), Carroll explains,

If, in any discussion between two persons, one accepts some axiom needed in the discussion, and the other does not, there is no more to be said: further discussion is useless (1122).

An axiom is a statement that is self-evidently true, but cannot be proven since ‘proof must rest on something already granted’ (Carroll, Letters 1122). Time theories are one example of an axiom since Alice perceives time through relational concepts while the Mad Hatter perceives time as absolute. According to Newton, laypeople, like Alice, were incapable of understanding absolute time as ‘common people conceive these quantities under no notion, but the relation they bear to sensible objects’ (Philosophiae Naturalis 7).

Alice depends on her relationship to sensible objects like ‘beat[ing] time’ to music or clocks that ‘tell what o’clock it is’ to understand time (Carroll, Wonderland 65). Since the concepts represented by the Mad Hatter are inaccessible to laypeople, including Alice, Alice dismisses the tea party as ‘the stupidest tea-party I ever was at in all my life’ (Carroll, Wonderland 67). Therefore, as Carroll states ‘there is no more to be said’ between Alice and the Mad Hatter and ‘further discussion is useless’ (Letters 1122).

One of the greatest challenges to Newton’s theory were relational theories like those presented by Ernst Mach (1893), Leibniz  (1715-16), Bishop George Berkeley (1721), and to a degree Einstein (1905). Relational theorists argued that time and space was only meaningful in relation to objects or events and, hence, dismissed absolute time. For example, Bishop George Berkeley in De Motu (1721) argues that ‘since space and time have no foundation in our sense experience’ they are meaningless (qtd. in Ray 116). Mach’s text The Science of Mechanics (1893), which greatly influenced Einstein, built upon Berkeley’s argument to directly challenge Newton:

No one is competent to predict things about absolute space and absolute motion; they are pure things of thought, pure mental constructs, that cannot be produced in experience (229).

Therefore, Mach argues that absolute time is a mere ‘metaphysical concept’ with ‘neither a practical or scientific value’ (224). While Mach’s text was published twenty-one years after Through the Looking-Glass, the debate between relational and absolute theories dates back to antiquity.

Through the Looking-Glass engages in this debate through the concept of Looking-Glass time, which the White Queen describes as ‘living backwards’ or the inverted flow of time (Carroll, Looking-Glass 170). One example of ‘living backwards’ is the White Queen’s concept of today, tomorrow, and yesterday or in other words present, future, and past. The White Queen declares that Alice may have  ‘jam to-morrow and jam yesterday—but never jam to-day’ since ‘it’s jam every other day: to-day isn’t any other day’ (Carroll, Looking-Glass 171). This raises the philosophical question of the movement of time. If time’s passage is linear, then when does yesterday become today? How are temporal changes determined? If the White Queen constantly lives in the present then yesterday never happened, tomorrow will never come, and she will never have to give Alice jam. Therefore, the very definitions that are used to define time are contradictory and paradoxical, which Newton addresses in De Gravitatione:

The parts of duration are individuated by their order, so that (for example) if yesterday could change places with today and become the later of the two, it would lose its individuality and no longer be yesterday, but today (25).

Since Newton considers it absurd for durations to change places, time cannot be inverted. Nonetheless, this philosophical question was increasingly discussed throughout the late nineteenth and twentieth century giving rise to alternative theories regarding the passage of time.

Theories of time travel while not actually proposed until after Einstein’s Theory of Relativity, were however present within novels of the nineteenth century including The Time Machine (1895) and Rip Van Winkle (1819). While Through the Looking-Glass does not specifically address time travel, it does engage with similar concepts through backward causation. Backwards causation or backwards living is the reversal of the temporal order of cause and effect. Philosophers that supported backwards causation, like Michael Dummet and Anthony Flew (1950s), suggested that time can move in both directions (Ray 120). Jan Faye, ‘Backward Causation’ (2015), suggested that while this theory primarily appeared in the mid-twentieth century, earlier traces of this concept existed within the work of David Hume an eighteenth century philosopher.

The White Queen exemplifies backwards causation as her ‘memory works both ways’ (Carroll, Looking-Glass 171) and the sequencing of events occurs backwards. For example, the White Queen plasters her finger, screams, catches her broach, and then pricks her finger (Carroll, Looking-Glass 173). Roger Holmes, one of the few critics to discuss Looking-Glass time, considers it plausible that ‘one might live in a world in which screams and pain came before the pinprick’ (147). However, Holmes considers Looking-Glass cake, another example of backwards causation, illogical. In ‘The Lion and the Unicorn’ chapter, the Unicorn instructs Alice to ‘hand it [the cake] round first, and cut it afterwards,’ which Alice deems nonsense (Carroll, Looking-Glass 203). This is, however, indeed how Looking-Glass cake works and as Alice ‘carried the dish round, the cake divided itself into three pieces’ (Carroll, Looking-Glass 203).

Holmes claims that Looking-Glass cake, unlike the White Queen’s injury, couldn’t occur because it is ‘an action that looks greedily to the future; reverse it and you get nonsense’ (146). However, Holmes has forgotten that only Alice considers this nonsense. The other characters consider backward causation normal since this, as the White Queen states, is ‘the way things happen here’ (Carroll, Looking-Glass 173). Within this context, Looking-Glass cake and screams and pain before the pinprick are equally plausible.

The Alice texts can be employed to explore the time theories spanning from Newton’s theory in the seventeenth century to backwards causation in the mid-twentieth century. This multi-century investigation reveals the uncertainty surrounding time theories, regardless of date. Throughout the Alice texts, Alice and the reader are consistently challenged with maintaining an open mind while exploring new worlds full of new concepts. Open-mindedness is promoted, throughout the Alice texts, by the characters Alice encounters in Wonderland and the Looking-Glass:

Alice laughed. ‘There’s no use trying.’ She said: ‘one can’t believe impossible things.’

‘I daresay you haven’t had much practice,’ said the [White] Queen. ‘When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast’ (Carroll, Looking-Glass 174).

Believing the impossible is a task that Alice repeatedly faces and, unlike many of the other characters, is utterly unable to accept. Alice journeys through the text as a passive passer-by who only records her adventures. It then becomes the reader’s responsibility to cultivate the wonder and curiosity that Carroll so strongly promoted. Nonsense may, contrary to Alice’s opinion, be sensible or at very least possible with some practice.

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