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Has anybody read, or does anyone know of, a particular paper on the amount of time humanity has to "wait" before venturing in actual interstellar travel?
It discusses the optimal time to launch our ships and head for the nearest stars. It is basically a "wait" calculation taking into account the growth of our technology, etc. (i.e. flying too soon would mean future generations, with more 'mature' technologies, would eventually catch up to them).
@AnthonyX has found a paper that fits your description, published in JBIS. The paper's citation is:
Kennedy, Andrew. (2006). Interstellar Travel - The Wait Calculation and the Incentive Trap of Progress. Journal of the British Interplanetary Society. 59. 239-246.
and it can be read now at Researchgate.
The Abstract says:
This paper describes an incentive trap of growth that shows that civilisations may delay interstellar exploration as long as voyagers have the reasonable expectation that whenever they set out growth will continue to progress and find quicker means of travel, overtaking them to reach and colonise the destination before they do. This paper analyses the voyagers’ wait calculation, using the example of a trip to Barnard’s Star, and finds a surprising minimum to time to destination at a given rate of growth that affects the expansion of all civilisations. Using simple equations of growth, it can be shown that there is a time where the negative incentive to travel turns positive and where departures will beat departures made at all other times. Waiting for fear future technology will make a journey redundant is irrational since it can be shown that if growth rates alter then leaving earlier may be a better option. It considers that while growth is resilient and may follow surprising avenues, a future discovery producing a quantum leap in travel technology that justifies waiting is unlikely.
I suspect that there is a simple mathematical underpinning to assertion of existence of a time "where departures will beat departures made at all other times." and that is actually an interesting intellectual exercise in itself!
This turns out to be a great question in that the paper is really intriguing!
I'm not the only person to think this. There is an excellent discussion of this paper by Paul Gilster (Planetary Society) in the Centauri Dreams post Barnard’s Star and the ‘Wait Equation’ . Near the end of the post, it says:
This is a rich paper that weaves economic growth patterns with the pace of technology over time and takes a sober look at how our culture might adapt to the possibilities of long-term missions. I wrote in a 2004 entry about van Vogt’s classic “Far Centaurus” story (Astounding, Jan. 1944) as an example of travelers being caught by faster technologies, but there are a number of related scenarios that science fiction writers could mine by pondering the equations in this paper. I was also interested to learn in an e-mail from Kennedy that he has a second paper on the subject in the works. We’ll look at it here when it appears.
There is indeed a second paper:
Kennedy, Andrew. (2013). The Wait Calculation: The Broader Consequences of the Minimum Time from Now to Interstellar Destinations and its Significance to the Space Economy. Journal of the British Interplanetary Society. 96-109.
which can also be read at Researchgate
This paper summarises the wait calculation [1] of interstellar voyagers which spends the minimum time to destination given exponential growth in the rate of travel available to a civilisation. The minimum time obliges stellar system colonisers to consider departure times a significant risk factor in their voyages since a departure then to a destination will beat a departure made at any other time before or after. Generalised conclusions will be drawn about the significant impact that departures to interstellar destinations before, at, or after the minimum time will have on the economic potential of missions and on the inevitability of competition between them. There will be no international law operating in interstellar space and an ability to escape predatory actions en route, or at the destination, can only be done by precise calculations of departure times. Social and economic forces affecting the factors in the growth equation are discussed with reference to the probability of accelerating growth reaching the technological Singularity and strengthening the growth incentive trap. Islamic banking practices are discussed as a credible alternative to compounding interest bearing paper for funding the space economy in the long term and for supporting stakeholder investment in such long term mission development. The paper considers the essential free productivity of the Earth’s biosphere and the capital accumulations made possible by land productivity are essential components to a viable long term space economy and that research into re-creating the costless productivity of the biosphere at a destination will determine both the mission’s ultimate success and provide means of returns for stakeholders during the long build up. Conclusions of these arguments suggest that the Icarus project should ignore a robotic interstellar mission concept and develop a manned colonising mission from now.
