The Economics of Time Travel

Author: Stuart Mills

Author: Stuart Mills
Date: December, 2023
Text: PDF (https://doi.org/10.53975/7t49-r566)

Abstract

The lack of time travellers visiting us may be seen as evidence that time travel is not possible. In this article, I argue an alternative explanation is that we are not economically important enough to our descendants to justify the costs of time travel. Using a cost-benefit analysis, I elaborate on this argument. I suggest that the major cost of time travel is likely to be the energy cost, whilst the largest benefit of time travel is knowledge which the present possesses, but the future has lost. Focusing on this benefit, I argue it is extremely unlikely that we possess a piece of knowledge which is sufficiently important to a future civilisation (system critical), but also has been lost by said civilisation. This is to say, we may not have been visited by time travellers because we are not important enough.

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Introduction

One experimental way to prove the feasibility of travel forwards and backwards in time (i.e., time travel) would be to stage a large, broadcasted event. The location for such an event should be temporally significant—say, Greenwich—and the advertising for the event should be substantial. By substantial, I mean significant enough to be remembered for all of human history (call this the chrono-permanency criterion). Assuming such a feat of marketing is accomplished, matters turn to the event itself. The event should be a welcoming party for our descendants. It should serve as a message that at the particular moment in history that the event takes place—perhaps New Year’s Eve, 2023?—our descendants are to send a chrononaut to make contact. If no one shows up, this suggests time travel is not possible. If someone shows up, time travel would be demonstrated.

The above experiment builds from a logical argument: that if time travel were possible, we would be awash with time travellers. As we are not, time travel is not possible. Yet, this argument assumes something quite significant: that we, or any civilisation prior to ours, are worth visiting.¹ In this article, I propose an economic cost-benefit analysis of time travel. I argue the main economic benefit which our descendants may receive via time travel is knowledge which we currently possess, but they have lost. Furthermore, this knowledge must be sufficiently critical to our descendants to justify the costs of time travel, which are likely to be dominated by energy costs. I posit that even assuming the energy requirements for time travel are met by a human civilisation in the future, it is highly unlikely that that same civilisation will come to depend on a piece of knowledge which we currently possess, but they have lost and cannot rediscover by other means. In other words, I argue that even assuming time travel is possible, our epoch is unlikely to offer any economic benefit to a future, time travelling civilisation.

The Economics of Time Travel to Date

Various economic perspectives on time travel have been proposed. A notable flurry of commentary, albeit tongue-in-cheek, began in 2006 as Tyler Cowen (2006) began musing on the economics of relativity, drawing on Krugman’s (2010 [1978]) Theory of Interstellar Trade (also see Cowen, 2008a).² Cowen (2008a, 2008b) and others (Gans, 2008; Morehouse, 2012; Whitman, 2008) would build on these ideas further to incorporate labour within ‘transtemporal markets.’ The basic argument of these perspectives is that future epochs would be incentivised to use time travel to exploit the cheaper labour of the past, select epoch-specific legal structures which were beneficial for business, and embrace arbitrage opportunities for resources across time-periods. Gans (2008) is an exception insofar as they are critical of these arguments, and suggest that the clear, overwhelming economic advantage for a time traveller comes from using knowledge of the future to play markets of the past. Indeed, in a recent paper, Swinton (2021) argues that the stock market proves time travel to be impossible, because markets are less rational than would be expected if a flurry of actors with enhanced foresight were actively trading.

What is surprising about this literature (besides its existence) are the dual assumptions that a) time travellers would broadly operate within the same or similar economic system to that of the present; and b) that the past offers efficiencies for this economic system which the present would not. These assumptions are not wholly unjustified. For instance, if time travel were invented tomorrow, any would-be time traveller would have globalised capitalism as their framework of economic reference, and with that in mind, might indeed travel to the past to purchase Apple shares.

But if time travel is invented many years from now, be it centuries or millennia, there is no compelling reason to believe a time traveller of, say, the 41st millennium would behave, economically, like an agent from the 21st century. Globalised capitalism is around 100 years’ old; industrial capitalism perhaps 200; and proto-liberal capitalism maybe only 300 to 400 (Wood, 1999). Human societies have, historically, demonstrated substantial capacity to change in (relatively) little time (Graeber and Wengrow, 2021). I will return to this broad criticism at the end of this article. Furthermore, none of the economic benefits of time travel offered in this literature are exclusive benefits of time travel. The notion of cheaper labour, arbitrage opportunities, or legal opportunities are really all advantages of expansion of the economic domain, much in the same way that colonial expansion, or the expansion of credit and financialisation, have been described (e.g., Arrighi, 2009). This is to say, for a time travelling civilisation, there is little reason to believe the advantages of trading with the past would be greater than trading with other planetary civilisations (or species).³ Even if the arguments stand, they are not really advantages of time travel per se.

A Cost-Benefit Analysis of Time Travel

These criticisms point towards a cost-benefit analysis approach. Time travel may only occur at a historical moment when the necessary components of time travel technology can be assembled. This is to say, only a civilisation that can support the costs of time travel could become time travellers. Furthermore, such a civilisation would only accept these costs for benefits which must be achieved through time travel, and not through alternative means, unless the alternative means were costlier than time travel (which, I would argue, largely depends on the nature of time travel technology itself).

Whilst one may consider a plethora of social and ethical costs associated with time travel, such as the grandfather paradox or post-colonial critiques applied trans-temporally, I argue the overwhelming economic cost of time travel is the energy cost. As others have acknowledged (Cowen, 2008a, 2006; Krugman, 2010 [1978]), near luminal or superluminal travel produces sufficient relativistic effects as to constitute time travel, at least into the future (relative to the slower observer). Achieving such speeds requires a tremendous amount of energy—for superluminal travel, an infinite amount of energy, based on our current understanding.⁴ Black holes—infamous galactic objects which warp spacetime—are formed by the deaths of the most massive of stars. These events involve enormous amounts of energy. Whilst physics has much less to say about the mechanisms for travelling backwards in time⁵, taking forward time travel as a rough guide, it is likely—should it be possible—that the primary constraining factor will also be energy.⁶ I take the notion of warping spacetime and superluminal travel as guides to time travel technology, and not as a presumptive means of time travelling. This is to say, because various theoretical ideas of time travel imply huge amounts of energy would be required, I am assuming a similar amount of energy would be required for time travel by any means.⁷

Energy is also an ideal variable to consider when speculating on the likely stage of civilisational development necessary for time travel. The Kardashev scale, developed by Nikolai Kardashev (1964) measures the development of (inter)planetary civilisations based on the amount of energy they are able to capture. A Type I civilisation is able to harness all the energy of its home star which reaches its planet. A Type II civilisation can capture all the energy of its home star, through innovations such as a Dyson Sphere (Dyson, 1960). A Type III civilisation can capture all the energy of its home galaxy. Current estimates suggest Earth has a Kardashev value of approximately 0.73, based on 2021 energy consumption figures (BP Statistic Review of World Energy, 2021).⁸ Carl Sagan adapted Kardashev’s ‘Types’ into a continuous scale, which is where this non-integer value comes from. Doing so in 1971, Sagan then estimated Earth’s Kardashev value at 0.70, implying human civilisation may reach Type I in around 500 years, assuming linear growth in energy consumption. Given the likely energy demands required for, say, the time-distorting effects of a black hole, time travel is unlikely to be achieved in the next few centuries without a historically monumental increase in energy production.

Turning to the question of benefits, I argue time travel is unlikely to be pursued unless the resource gained through the activity is extremely scarce or difficult to acquire in a future period, but is relatively less scarce (or even abundant) in a previous period. Again, given any time travelling civilisation has likely secured dominion over at least its home star, if not a sizeable proportion of its home galaxy, the notion that such scarce resources would be labour or raw materials seems unfounded. On a galactic scale, raw materials are likely to be abundant, especially given the incomprehensible energy resources available to a time travelling civilisation. Such resources could likely support substantially more labour, meaning labour is unlikely to be scarce either. Instead, the most feasible resource which one may consider abundant today, but scarce in the (far) future, is today’s knowledge.

By ‘today’s knowledge,’ I mean everything which is known, by at least someone or something, today. Whilst this definition is necessarily broad, I will generally focus on knowledge of processes (e.g., programming knowledge, manufacturing knowledge). This is because, given the likely large energy costs, knowledge in the sense of historic knowledge, or whatever might be gleamed through ‘chrono-tourism,’ is unlikely to be sufficiently important to a future society to warrant the use of time travel, at least economically speaking. Whilst I consider ‘today’s knowledge’ to encompass everything which is known today, I will generally focus on ‘system critical’ (SC) knowledge. By this, I mean knowledge which is irreplaceable within systems the future civilisation relies upon for maintaining its way of life. I focus on this type of knowledge for two reasons. Firstly, such SC knowledge is the only subset of ‘today’s knowledge’ which may overcome the likely immense energy costs of time travel, in terms of economic benefit. Secondly, because the recent examples of knowledge loss which exist tend to be SC knowledge.

Knowledge is always being lost. History provides a plethora of examples, such as Greek fire and Roman concrete. Several foundational principles of calculus have been found in works attributable to Archimedes, but which—for one reason or another—were lost for centuries (Flood, 2011). Newton’s work on gravity itself owes much to an almost lost set of astronomical observations made by Jeremiah Horrocks, whose early death meant the observations were only (and luckily) published as an appendix in someone else’s book (Ferguson, 2023). In past decades, one example of SC knowledge which was lost is fogbank, a highly classified ‘ingredient’ within the manufacturing process of the United States’ nuclear warheads. Fogbank was so classified, in fact, that no records of the production process were made, with all individuals formerly familiar with the process either dead, or unable to remember. It took US nuclear engineers over a decade to rediscover how to make fogbank (Lillard, 2009).

The idea that advanced civilisations could come to be reliant on knowledge that they no longer have knowledge of may seem silly, but it is both a complete possibility, and indeed, somewhat evidenced in our own society. Complex systems and processes almost never start off complex. Rather, complexity is almost always the result of additional processes being ‘tacked onto’ existing, simple processes (Frey, 2020). This is common in programming—a simple website may be further developed over time, with more code written to facilitate more features. As computers came to be adopted within the finance industry in the 1960s and 70s, foundational software was written in older programming languages to facilitate basic banking services. Finance, being a SC sector within our civilisation, broadly took the ‘if it ain’t broken, don’t fix it,’ approach to this foundational code, almost never rewriting, updating, or otherwise tweaking the code, but instead, tacking on new code to perform new services. This approach is somewhat understandable. Firstly, when launching a completely new version of a complex system, there is a substantial risk that something does not work, and that spectacular errors arise. Secondly, the costs of updating the whole system rarely outweigh the immediate benefits, meaning cost-constrained organisations, such as banks, may always find incentive to forestall major updates.

Of course, the fragility of old systems supporting new systems is not necessarily a problem if knowledge of the old system remains, even when a newer version would be less fragile, or otherwise better (e.g., more efficient). But as systems become more complex, individual competencies within an organisation tend to ‘specialise,’ with understanding of the whole fading from any one individual’s grasp (Beer, 1993, 1975, 1973; Braverman, 1974). As the workforce composition of an organisation changes, with new employees replacing the retiring, SC knowledge can become eroded through partial knowledge transfer and miscommunication.

It might be hard to imagine that a time travelling civilisation would find itself dependent upon today’s knowledge, and simultaneously ignorant of it. Whilst this is a core aspect of the argument I am to make; it is not wholly unheard of within time travel circles. One of the most infamous stories of time travel found online is that of John Titor, who (in 2001) claimed to be a US army soldier from the year 2036. Titor’s supposed mission was to retrieve an IBM 5100 computer from the 1970s, as various critical systems in 2036 used legacy software which was going to break, less compatible technology was acquired to fix the problem (Dodds, 2015). Whilst likely a fanciful tale concocted for an internet forum, the key premise is telling: time travel may occur when future civilisations lose access to SC knowledge.

The Inequality of Time Travel

Cost-benefit calculations are limited in all manner of ways. For instance, one may overestimate some variable within the analysis, or omit a variable entirely. It is my ambition with the arguments above, and the inequality below, to highlight worthwhile aspects of a cost-benefit analysis of time travel, rather than incorporate all possible considerations (of which there are too many).⁹

Equation (1) presents the basic inequality:

In Equation (1), Cj is the money cost of one Joule of energy, and Ej is the amount of energy, measured in Joules, required for time travel. The left side of the inequality thus captures the energy costs of time travel. On the right side, Pr F is the probability that knowledge F is lost; Pr(SCF) is the probability that knowledge F is system critical; and F is the money benefit of rediscovering knowledge F. A time-travelling civilisation is expected to time travel from time t+n to time t only when the energy costs of doing so are less than the expected payoffs of retrieving knowledge F. alpha is a money cost deflator so the value of money on each side of the inequality is comparable. Where money costs are estimated within the same time period, may be ignored. Likewise, alpha may appear on either side of the inequality, provided the correct adjustment to alpha is made.¹⁰

For discursive purposes, what is worthwhile focusing on are the two probabilities, Pr F and Pr(SCF) , on the right side of Equation (1). One way of modelling Pr F is via Equation (2):

where n is the number of years since knowledge F was discovered, r is the ‘reproduction rate’ of knowledge, or broadly, the number of years within a human generation. m is the number of ‘entities’ with knowledge of knowledge F at time t, per Equation (3):

where N (H, F,t) is the number of humans with knowledge of F at time t, and N(C,F,t) is the number of computers (as well as other records, such as books) with ‘knowledge’ of F at time t.¹¹ Note that Equation (2) uses the reciprocal of m, which might be understood as the ‘rate of forgetting,’ compared to m, which is the ‘rate of remembering.’ Thus, (1-1/m)^n/r describes the probability of F being remembered over n years, hence why one less this is equal to Pr F.¹²

Per Equations (2) and (3), knowledge which is very niche or esoteric is known by few people and recorded in few places. Thus, m will tend to be small, and Pr F will rapidly move towards 1. Inversely, where knowledge is very broad or fundamental, many people will know of it, and there will also be many records of it. Thus, m will tend to be large, and Pr F will very slowly move towards 1.¹³

This is important when considering Pr(SCF) . By definition, Pr(SCF) concerns knowledge which is fundamental to a civilisation. As such, even though Pr(SCF) may be difficult to estimate, one can infer that when Pr(SCF) = 1, m will be very large and thus Pr F ≈ 0. Equally, when Pr F = 1 , Pr (SCF) ≈ 0. This is to say, these two multiplicative probabilities likely have a relationship such that they counteract one another. Only in very particular instances—say, the fogbank incident where fogbank was both critical to the US nuclear arsenal but also highly classified, so few knew of it—will Pr F Pr(SCF) ≈ 0 not be found.¹⁴ Therefore, even allowing F to be arbitrarily large, it is very unlikely that the conditions are met for the inequality to be satisfied.

If on the 31st of December 2023 an event is held to welcome our time travelling descendants, and no one shows up, we need not assume this is because time travel is impossible. Instead, the conditions for it to be economically beneficial for our descendants to visit us may just not be sufficient. Put less politely, we as a civilisation are unlikely to be important enough to warrant visiting.

Is the Future so Utilitarian?

As above, we cannot necessarily assume too much about the values of a future civilisation, or their political and economic arrangements. I have used this argument to critique previous economic musings on time travel. Yet, the same argument applies to this contribution. Indeed, perhaps more so. Whereas previous authors (e.g., Swinton, 2021) have generally assumed near-future time travel, I have made the case that time travel will only be possible to a civilisation in the far future, where more time has elapsed, giving way to more scope in the evolution of their socioeconomic system.

Thus, it is not necessarily reasonable to assume that a future civilisation will undertake the utilitarian calculus of a cost-benefit analysis. Indeed, much of my argument is contingent on only two civilisational developments, energy capture and time travel. Yet, in achieving these developments, others (technological, cultural, political, social, etc.) are almost certain to occur. The near-term likelihood of time travel will also certainly spark a vibrant ethical debate, which may include consideration of issues presented here. For instance, in our own epoch, climate change has led to initiatives like the Svalbard Global Seed Vault to preserve biodiversity in plant life. A civilisation which acquires time travel technology may, even before acquisition, recognise the dangers of losing knowledge and set up initiatives to preserve it, if not whole ethical systems and legislative approaches to regulate the emerging technology’s usage.

Equally, without making such an assumption, there is limited analysis which can be undertaken. Indeed, any speculation about the practices of the future must be caveated with all the problems of prediction or inference. Thus, whilst it is highly unlikely that the exact procedure outlined here will be the decision-making framework of a future civilisation, or that the philosophical basis of such a framework would hold either, it is nevertheless just as good a framework to adopt as any other for the purposes of postulation. Furthermore, the approach outlined here avoids some of the more questionable assumptions of previous authors, such as the assumptions of comparable trade arrangements or arrangements of production. By grounding the discussion only in discussions of energy costs and knowledge (information) benefits, little about, say, the economic system of the future, needs to be assumed.

As a final note, I have generally limited my analysis to questions of economic costs and benefits and have been cautious throughout this article to focus on these economic considerations, whilst offering less comment on—as above—alternative motives which may govern the development and use of time travel. One need only to ask oneself what one would do with the ability to time travel to realise that ‘acquiring lost knowledge,’ is a very niche motivation. Just as people travel the globe, and increasingly beyond, so too wanderlust is likely to extend to time travel. The prospect of visiting epochs radically different to one’s own represents an intrinsic motivation for many. This analysis would likely be incomplete without an acknowledgement of this.

And, perhaps someday, economists will have to calculate the various costs and benefits of chrono-tourism, such as those of cultural exchange, and supplement the model proposed here, assuming it is at all relevant. For instance, the (relatively) recent development of the atomic bomb, space travel, and the internet, may all point to the past century or so as an especially interesting time period for a future civilisation built on these (by their standards) primitive technologies. Thus, non-economic terms should be included in any cost-benefit analysis of time travel. Their omission here is wholly the result of practical limitations.

Conclusion

In this article, I argue that (accepting time travel is possible) time travellers may not have visited us because our present offers little economic benefit to them. I postulate that the major economic cost of time travel is likely to be the energy cost, and this cost is likely to be extremely large. Furthermore, I have argued the major economic benefit of time travel is likely to be today’s knowledge, and specifically, knowledge which is ‘system critical’ for a future civilisation, but which said civilisation has lost. Yet, the likelihood of knowledge being lost and for said knowledge to be system critical is extremely small. Thus, I conclude that there is only a very narrow set of circumstances where the present is a likely destination for any time traveller, economically speaking. Much like a parent or grandparent may lament that their immediate family do not visit often enough, present society may need to entertain the possibility that, from an economic perspective, our descendants do not find us especially important.

Acknowledgements

I am grateful to Kira Rhodes, Richard Whittle, and Adam Davidson for their kind comments and suggestions. All errors are my own.

Gardener Comments

Note: the author has responded to comments in the subsequent section.

Gadi Lifshitz:
While the article is well written, and I think has some interesting insights (and so, worth publishing), in my view focusing only on the economic utility is a bit problematic.

The economics of time travel (well, much like any travel - even travel for work purposes) will definitely be a consideration, but as time travel holds a vast potential for financial gain (According to Einstein, “Compound interest is the eighth wonder of the world"...), there's a good chance it will be secondary to other reasons (many of which were mentioned in the article itself, even if as side notes). It would have been interesting to address both the potential gains and other constraints in more details (maybe in follow up articles).

Arturo Macías (Economist):
The main issue to deal with regarding time travel is what do you expect to be the result of an intervention over the past. What happens when the time traveler goes back and kills baby Hitler? Does a new branch reality appear while the older stays? Does the old reality (including the time traveler and the suffering inflicted by WW2) Vanishes? (as you can imagine, this question suggests that my view is that time travel is not only physically, but ontologically impossible). The ontology of time travel and the consequences of intervention shall be discussed before anything else.

An important consequence of this perspective is that the main reason to travel back in time is to alter the past, a possibility not even discussed, and (depending on your ontology of time travel) with a high potential economic value.

A final remark: if energy costs are the limit to time travel, those costs would probably be proportional to the mass of the time vessel. Miniaturization could make time travel viable, but probably we shall look for ultra-small time travelers.

Srinivas Vamsi Parasa:
It is not clear how the ideas presented in this paper can be 'falsified'. The core idea/hypothesis of this paper is (1) the major economic cost of time travel is the extremely high energy cost (unverifiable claim) (2) major benefit of time travel is the lost 'system critical' knowledge which is of importance to a future civilization (unverifiable claim). Ironically, we would need time travel to the future or an encounter with a person who traveled from the future to make sure these assumptions are indeed correct. Therefore, while the speculations presented in the article sound to be plausible, it is not clear how we can 'falsify' the assumptions and claims made in the paper.

Antonio Hanna-Amodio:
In a world where humans frequently assume an exalted status, this article offers a refreshing alternative perspective: rooted in both empiricism and humility.

Ted Wade:
This is a well-posed, interesting, and novel take on a fascinating question. I can’t see any relevance to current science.

Chronos (Emeritus Professor of Temporal Paradoxes):
Quite right - I spent a fortune to travel back here, and now I'm stuck in 2023!

Joe R:
Suppose Elon Musk had a time machine that cost $10B per trip (~5% of his net worth). What would you have to say to him to convince him not to use it? Does anyone really, sincerely believe that "hey, that's kinda expensive and you probably won't make back costs" would do the trick? This is Elon Musk; he'd just respond with "so what, it's a TIME MACHINE!" And then he'd either make $100B anyway or get eaten by a dinosaur. But the point is, good luck stopping him.

This paper is well-written, but makes enormous assumptions and fails to justify them. I expect its value to science will in fact be net negative, distracting researchers from valuable but less cool-sounding topics and by upholding a subpar standard for argument.

Their main argument seems to be: assuming time travel is possible, the only thing that would justify the energy expenditure is system critical knowledge possessed by the past. We couldn't have any knowledge valuable enough, therefore time travelers wouldn't bother.

This argument makes no sense. For one thing, why is system-critical knowledge the only thing presumed valuable enough? What about untapped physical resources? Genetic samples of extinct species? Anthropological data? The ability to directly observe known supernovae? Status and bragging rights?

For another, why would a future society be concerned solely or even principally with economic benefits? If the future happens to be rich, then people will want to time travel even if it's expensive, the same way people today go on wildly expensive vacations. Suppose Cj and Ej are low enough relative to the energy output of a galaxy-spanning civilization that at least one wealthy or well-connected historian, writer, botanist, evangelist, philanthropist, or dedicated LARPer could afford a trip to the past. Why wouldn't they go? Current humans care about lots of things. Future humans (or whatever we become if we make it that far) probably will to. There could be many reasons to travel to the past. There might be plenty of reasons not to (e.g. paradox, which the author ignores), but I doubt "well, it costs a lot of money" will stop literally everyone from bothering.

The narrowest possible interpretation of this paper is "the past probably contains little to no system-critical knowledge worth time-traveling for". This seems...probably true? And the author makes a decent stab at demonstrating it. But it is a massive and unjustified leap to also claim, as they do in their abstract and conclusion, that such knowledge is the main reason anyone would bother. It's an even more unjustified leap to say "and maybe, instead of physics, economics is why we don't see any time travelers!" The narrow claim is trivial and the broader claims are wrong.

Phil Filippak:
First of all, to rephrase David Deutsch, every next century is the most important one in the history of our civilization. We may be deemed unworthy of visiting but at the same time, any century prior to the one that has time travel discovered, may be. I would assume that future generations may be interested in building a comprehensive understanding of history, and therefore will be inclined to visit most of the previous centuries, if not decades.

At the same time, if they are not only technically but also socially advanced, they may not want to ruin or pollute history with the notion of actual time travel, and so even if they will have traveled to the past, they would do that covertly, and no event will attract them.

Considering energy expenditure, we don't know how much energy will be available to our descendants even in 50 years, not to say anything about thousands of years.

Overall, I believe that the idea of time travel is so rarely used in modern scientific thought that it's worth publishing despite the possible flaws that the paper might contain (and I am definitely in no position to notice and point out those if they are present).

Author’s Response to Comments

One of the major contributions of this article, in my opinion, is to entertain. Whilst I have had discussions with people, many of whom think the argument I propose is strange, or perhaps cold, or perhaps completely wrong, I am pleased that in many instances my conversations about this idea have sparked interest, engagement, and discussion. Being wrong matters little if it results in good conversation, in my opinion.

I give this preface to support me in responding to the general sentiment of those who have responded negatively to this article. I have organised their points as: a) the core idea is poorly thought out, and contains many omissions; b) it is too assumptive; c) the approach cannot be falsified; and d) it makes no contribution to science (and perhaps even hinders it). I will try to take each point in turn.

In the introduction, I offer at least eight alternative explanations for why time travellers may not visit the party in my thought experiment. The article pursues only one. Yes, I concede, I have not gone into such inane detail outlining every possibility, but that is not the objective of the article. It is, as above, to entertain (hence why the eighth argument is that the party might not be that good) whilst, I hope, exploring interesting ideas such as measurement of civilisational development, the role of knowledge and lost knowledge, and the limits of cost/benefit analysis. I am not convinced that by exploring every possible twist and turn in the thought experiment that this article would be improved. I am convinced that it would be less entertaining, though I am of course biased.

It is! Whilst I do not deny that it is a bit of a weak argument, I would point critics to my discussion of the utilitarian assumptions of the article, wherein I note that there is almost no basis for many of the assumptions I am making, but that there is little basis for any possible assumptions. The article is speculating about the decision-making processes of a far future civilisation—yes, my assumptions are going to be on shaky ground. But I am sceptical any steady ground can be found.

This criticism I considered very surprising. If one examines the cost/benefit analysis literature, one finds an endless debate between those who support the approach from a pragmatic perspective, and those who are critical of it from (often) a social perspective. The debate is never that CBA is right, and almost always around the implications of thinking CBA is right. Convincing yourself that a poor model is correct is a dangerous deception, and to this end I have much sympathy with those who are critical of CBA. Equally, I am sympathetic to the argument that even formulating a bad model is worthwhile as an exploratory exercise. I think that is what I am trying to do here. Thus, it has never really occurred to me that some would want a ‘falsifiable’ model, because I have never for a moment conceived of the model as an attempt to get to the ‘right’ answer (or the wrong answer if falsified). I have always approached this article with the perspective that the exercise itself is what matters, and the criticisms of my assumptions is where the value lies. Hence my preface. Or, to put it another way, maybe the real insights were the friends we made along the way. If one wants a falsifiable model, then this contribution clearly fails.

Similarly, to the above point, I was quite put off by this comment, because I conceive of the whole scenario as a vehicle for a discussion of ideas, rather than the scenario itself being the main contribution. As I show in the paper, several authors in economics have engaged in similar, perhaps tongue-in-cheek approaches, to play around with economic ideas. I fail to see the harm in this—as an educator, I can only see the positives of wrapping up intellectual ideas in an accessible format, which I hope I am doing here (though perhaps I am failing). To be accused of making a negative contribution was particularly hurtful, though this comment must be wrong. To be pedantic, this contribution does not destroy knowledge. If it is a distraction, then it only makes the process of discovering new knowledge slower; it does not drive it into the negative.

I would like to thank the ‘gardeners’ for their comments, regardless of any disagreements I may have with them, as they have added to the further development of this article.

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1. This is not the only reason why no one may materialise in our experiment, even assuming time travel is possible. Firstly, the historical record of the event having happened may be lost by the era time travel is invented (i.e., not chrono-permanent). Secondly, time travel may be possible, but not to humans. Those beings that can time travel (call them chrono-kin) may have no interest in us. Thirdly, we might be stuck in a time loop. If we are the first people to try the experiment, there would be no one to visit us. This may lead us to think time travel is not possible, meaning it is never invented, so no one visits the next iteration. For the sake of this article, I will generally avoid discussions of loops and grandfathers. Fourthly, there may be laws or ethical standards in the future which forbid the use of time travel. Our descendants may see us as a temporally linear civilisation which needs to be preserved chronologically. Fifthly, time travel may not work with such accuracy or control. It may not be possible to time travel to a precise date, time, and location. Sixthly, time travel may be a suicide mission. If time travel is possible, but only in one direction (i.e., forwards, or backwards), the experiment is necessarily also a call for someone to abandon their life as they know it. Seventhly, time travel may only affect time, not space. As the Earth is constantly moving around the Sun, and the Solar System shifting around the galaxy, and the galaxy moving throughout the universe, a time traveller may very well travel to attend the party, only to find themselves on the opposite side of the universe. I am grateful to Adam Davidson for this comment. Eighthly, the party may not be that good.

2. For the benefit of the reader, Cowen’s reference to Krugman is to the 1978 draft of Krugman’s 2010 paper. One should not regard this publishing anomaly as evidence that Tyler Cowen can time travel.

3.  Assuming this civilisation has access to these resources and markets, which I implicitly do with my discussion of Kardashev development in the following section.

4.  I generally will assume either a) faster-than-light travel could one day be achieved, or b) time travel will not involve faster-than-light travel. These assumptions are made for the purposes of maintaining the premise of this article. If time travel is not possible, you dear reader might as well stop reading, and I might as well stop writing.

5.  Superluminal travel may be one candidate for backwards time travel, as would an Einstein-Rosen bridge. Both are theoretical concepts at present.

6.  As was suggested to me, an alternative constraining factor might be that time travel requires an extremely rare resource, which cannot be manufactured, and which is destroyed during time travel. For instance, some as yet undiscovered, fundamental particle. This being so, much of what is said about energy can be replaced with discussion of this X particle. Yet, I argue it is less assumptive (though, of course, still assumptive) to assume high energy costs, than to imagine a mysterious particle being crucial to a technology not yet invented.

7.  At the least, this assumption aligns with an argument I think is quite reasonable, namely, that given we do not yet have time travel technology, we likely do not yet possess the resources required for time travel technology.

8.  Specifically, 0.7276 using a power figure (in Watts) of 18.87×10¹², and Sagan’s equation of K=(log10P)-610, where P is power, and K is the Kardashev score.

9.  In this sense, the reader is encouraged to regard the given inequality as a proposal along the lines of the Drake equation for estimating the number of intelligent civilisations in the universe—not necessarily accurate, but sufficient for provoking some thought and discussion.

10.  The deflator arises because money has a different value depending on the time period examined. If, say, CJ was based on today’s money cost, but F was based on the money costs of a different period, these values would not be comparable as $t$t+n. Introducing a deflator, and choosing the appropriate value for , resolves this problem.

11.  I have added NH, F,t and NC, F,t for simplicity, though one may rightly object to this as the ‘rate of forgetting’ is likely different across different mediums.

12. For instance, say m=1000, r=25, and n=500, based on earlier estimates of the time for humanity to become a Type I Kardashev civilisation. Then, Pr F = 0.02, or that knowledge F has a 2% chance of being forgotten.

13. Equation (3) assumes that knowledge is not perfectly transferred from one entity to another. For instance, if 1-1m=0.9, this implies that 90% of knowledge F is successfully reproduced from t-1r to t. The greater the ‘rate of remembering,’ the greater the successful knowledge transfer across periods. 1-1m=0.9 is compounded by the number of transfer periods, hence the exponent nr. For instance, a transfer rate of 90% over two periods would, in the second period, only successfully transfer 90% of the 90% previously transferred, or 81% (i.e., 0.9²) of the total.

14. Another instance, related to skills, may be the complexity of knowledge. Highly complex knowledge will likely be known by fewer people, and may be more sensitive to errors in reproduction.