Footnotes

[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 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 effect 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 approach.

[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, C_J was based on today’s money cost, but 𝜔_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 𝛼, resolves this problem.

[11] I have added N_H,F,t and N_H,C,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 − 1/m = 0.9, this implies that 90% of knowledge F is successfully reproduced from t − 1t to t. The greater the ‘rate of remembering,’ the greater the successful knowledge transfer across periods. 1 − 1/m = 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.

[15] I have been encouraged to add commentary on factors, beyond economic considerations, which may influence time travel usage, but a number of early readers, including reviewers and colleagues with whom I have shared this article and the various ideas contained within. A remarkably frequent comment has been that many would time travel for the fun of it--call it chrono-tourism--and that my analysis may miss this point. Hence, the subsequent addition.

[16] I am grateful to the reviewers for this comment.