Time travel thing - a small preview

[ffutures]

Forthcoming Cruises: Triassic-Cretaceous TS Corinthic, Captain Richard Thorne RNVR, White Star Line: Departs for a four-week cruise to the Triassic-Cretaceous oceans, calling in at London (1588 AD), Vinland (1000 AD), Herculaneum (75 AD; day trip to Pompeii available), Africa (500,000 BC; hunting trips available), Triassic-Cretaceous (circa 150 Million BC). Launched in 1902, the Corinthic is a luxurious new liner of 12,251 tons capable of 14 knots and equipped with the latest Ferguson Chronatron® time displacer and a Babbage-Williamson navigational engine. Excluding stops en-route and any delays to manoeuvre the journey to the Triassic-Cretaceous seas will take approximately a week, with a week spent sight-seeing and hunting in this period before the return journey. Currently all first-class accommodation is reserved, but second and third-class cabins are still available and may be booked via Thomas Cook & Sons and other reputable agents. Corinthic will depart from pier 7, Southampton, at 2.00 PM on Tuesday 11th May.

Okay - showing my crappy maths here. What I need here is a SIMPLE mathematical formula that'll relate the distance travelled in time to the distance at sea, possibly an exponential curve or close to it. The way I want it to work is that you start off slowly but accelerate. A few months in the first few miles, a few years in the next few, and so forth, say 200 million years in a week, and the beginning of the universe in a month or two (assuming you could keep sailing). I can simply give figures that suit me, but it'd be better if I could give a formula that can be used without too much messing around. Any suggestions?

Comments

[karohemd.livejournal.com]

Don't ask me, I'm a linguist, the mathematical side of my brain is the size of a peanut. ;o)

However, I want to book now.

[ffutures.livejournal.com]

No you don't. Trust me on this...

[karohemd.livejournal.com]

Heh.

[drplokta]

Exponential will increase too fast, you're probably better off with cubes or squares.

How about:
1 mile = 1 day
8 miles = 512 days = 1.5 years
16 miles = 4096 days = 12 years
32 miles = 30,000 days = 100 years
64 miles = 750 years
128 miles = 6000 years
256 miles = 50,000 years
512 miles = 400,000 years
1024 miles = 3 million years
2048 miles = 25 million years
4096 miles = 400 million years
8192 miles = 3.2 billion years
16536 miles = 25 billion years -- so back before the big bang.

Time in days is the cube of distance in miles (or kilometres if you want a slightly faster progression).

[ffutures.livejournal.com]

That's actually the first relationship I tried! It's a bit arbitrary, but I agree it's dead easy to calculate.

Okay, let's say I go with that - would the RPG people reading this think that the relationship sounded a bit artificial, or would you be willing to suspend your disbelief?

[cdybedahl.livejournal.com]

The direct relationship between miles and days is too neat for me, but toss in an arbitrary constant (so you get days = constant * miles^3) and it'll look pretty much like stuff you actually find in physics.

[major-clanger.livejournal.com]

OK, let's assume that we're cruising at 15 knots or so. That's 360 nautical miles per day, about 2500 nm per week, or roughly 10,000 nm per month. So we want a function f(d), where roughly speaking:

f(10) = 1
f(100) = 10
f(360) = 1000
f(2500) = 2*10^8
f(10,000) = 10^10

To start with, let's try to find a function where f(10) = 1 and f(10,000) = 10^10. This gives us log(f(10^1) = 0 and log(f(10^4) = 10.

Set d = 10^x, i.e. x = log(d)

log(f(d)) = log(f(10^x)) = 3.33(x-1)

-> f(10^x) = 10^(3.33(x-1))
-> f(d) = 10^(3.33(log(d)-1))

Let's try this out.

f(10) = 1 yr
f(100) = 2150 yrs
f(360) = 154,000 yrs
f(2500) = 98.4 M yrs
f(10,000) = 10 B yrs

...which is sort of what we want, but if anything doesn't rise steeply enough.

How about making the inner function itself rise more steeply. Let's have

log(f(d)) = log(f(10^x)) = ((x-1)^2)+1

(still has 1 -> 1 and 4 -> 10, but with a curved rise in between). Now we get:

-> f(10^x) = 10^(((x-1)^2)+1)
-> f(d) = 10^(((log(d)-1)^2)+1)

Now we get:

f(10) = 1 yr
f(100) = 100 yrs
f(360) = 2640 yrs
f(2500) = 5.62 M yrs
f(10,000) = 10 B yrs

Wa-hey! Just what you're after, I think.

So, the formula for time T in years gone back over distance d nautical miles is

T = 10^(((log(d)-1)^2)+1)

and conversely

d = 10^(sqrt(log(T)-1)+1)

Hope that helps,

MC

[ffutures.livejournal.com]

A bit too complicated, I think, but I've just tried 3*cube of miles = days and it gives pretty much what I want for a 14-knot ship - Triassic-Cretaceous in about a week, 854 million years in two weeks, 6.84 billion in four.

[ffutures.livejournal.com]

Just realised the bleeding obvious, which is that the ship will be a lot slower in the first half hour or so since it has to get moving - either you get up to speed before switching on, or you switch on then start the ship moving, either way it will add significantly to the time it takes for the initial bit of the journey. Which is the way I wanted it to feel - creeping slowly at first then faster and faster, then the "sun whizzing backward across the sky" thing.

[ffutures.livejournal.com]

When did the Earth first have a breathable atmosphere? Anyone know?

[major-clanger.livejournal.com]

This graph suggests that atmospheric oxygen reached about half its current abundance 500-600 MYA, i.e. about the time of the Cambrian Explosion (this is probably not a coincidence). It looks like it reached its current levels about 300 MYA.

MC

[ffutures.livejournal.com]

Thanks - that's very useful. Sorry to have rejected your formula, but the cube one does seem rather easier to work with (apart from needing cube roots to get distances for a given time, which is a PITA).

[drplokta]

But if certain theories are correct, you're going to need to have one hell of an icebreaker at around 600MYA.

[karohemd.livejournal.com]

The atmospher was probably not very stable before the Triassic as there was a huge extinction in the Permian during which the majority of life on Earth died.

[dsample.livejournal.com]

Not all that long ago, relatively speaking.

Cyanobacteria first started producing oxygen about 2.7 billion years ago, but it took about 2 billion years to get the atmosphere up to its current oxygen levels. Multicellular life first appeared about 1.2 billion years ago. Animal life, and green plants appeared on land about 500 million years ago.

[ffutures.livejournal.com]

Just changed the "fudge factor" to one based on the tonnage of the ship:

Time displacement = (tonnage/4050)*distance³

which gives a "bigger is better" effect and adds an easily-grasped complication to the calculation which gamers ought to like. It's no good just being fast, it has to be a BIG ship or you're just too slow.

[dsample.livejournal.com]

So if you could fit your time widget into something like a Nimitz class aircraft carrier, you could really go places. (Twice the displacement of the Titanic, and 30+ knots.)

[ffutures.livejournal.com]

Exactly. Plugging the Nimitz data into the spreadsheet I've written I'm getting:

After 15 minutes - 26.24 years
After an hour - 1,679.22 years
After a day - 23,213,470.23 years
After 2 days - 185,707,761.81 years
After 3 days - 626,763,696.10 years
After a week - 7.96 billion years

etc.

[robertprior.livejournal.com]

What happens if you hit something while the gadget is on? Does it get carried with you in the "time field"?

What is the distance measured relative to? (Do ocean currents have an effect?)

And will you be ignoring "snowball Earth"?

Hm. If continental drift happens in your setting, voyages at higher speeds get interesting :-)

[ffutures.livejournal.com]

Hm. If continental drift happens in your setting, voyages at higher speeds get interesting :-)

I was waiting for someone to spot that one. There are all sorts of problems, that's just one of them.

As for hitting things - still working on that.

[madbaz.livejournal.com]

I have a vision of the ship pouring on the speed to catch the continent, which of course just makes the continent accelerate too. Might have to disengage the temporal drive in a known area of open ocean and travel in real-time. Or just cruise around in circles until the continent gets to you. Also, what's the rate of fuel useage, that'll alter the speed of travel as it gets used and the ship gets lighter won't it?

Can't read some text by the way, the picture is covering it.

[madbaz.livejournal.com]

And of course the Earth, sun, spiral arm, galaxy, local group and supercluster are all moving relative to each other too. Some sort of anchor might be in order.

*Goes off singing*
I'm standing on a planet, a planet that's evolving
and revolving at nine hundred miles and hour....

[ffutures.livejournal.com]

I've edited how the picture width is set - let me know what you think.

[madbaz.livejournal.com]

Yeah, thanks, that works.