Wahrian Time Machine

Wahrian Time Machine
Information
Type	Other
Available on	All planets
Unlocked by	Secrets of Space-Time level 1
Construction
Iron 500.00B (x1.50) Steel 1.00T (x2.00) Titanium 10.00B (x2.20)
Special
Using the time machine will reset your progress converting your Research Points into Technology Points

The Wahrian Time Machine is a building that is unlocked by having at least Level 1 in the Research Secrets of Space-Time (which, in turn, needs Quantum Physics Level 2, Nuclear Physics Level 14, and conquering Xora Tauri).

The Wahrian Time Machine may be constructed on any planet you own (from the "Other buildings" section, where you would also find the options to build Shipyards, Greenhouses, Battery Chargers, and Trade Hubs) and requires 500 billion Iron, 1 trillion Steel, and 10 billion Titanium. One Wahrian Time Machine suffices for the entire empire; however, the number of Orion Cargo ships in the Time Travel fleet that appears on Promision after travelling in time increases as the square root of the number of Wahrian Time Machines throughout your empire.

$N_{OrionShips} = \text{floor}(3.2 * {\sqrt{N_{TimeMachines}}})$

Once constructed, clicking on the Wahrian Time Machine in the Other Buildings section present a new button labeled "Travel in Time". Clicking on this button displays a confirmation dialog where you can confirm or cancel the command. If you confirm, then your game is "reset" back to Promision, Year 1, Day 1. You lose all fleets and conquered territory. Your Research Points (both already spent in Research and points you have not yet spent) are converted into Technology Points according to the following formula:

$\text{TP} = \frac{2}{\ln\left (5 \right )} ~ \times ~ \text{Influence} ~ \times ~ \ln \left (1 + \frac{\text{RP}}{200 ~ \times ~ 10^9} \right )$

In other words, take your sum total of spent and unspent Research Points, divide that by 200 billion (0.2 trillion), add 1, take the natural logarithm, multiply by the Influence of your empire (which is the sum of the individual Influence values of each planet you conquered), multiply by 2, then finally divide by LN(5) ("the natural logarithm of five", which is approximately 1.6094).

Any given level of Research can be purchased with either Research Points or Technology Points; any given single level of Research can NOT be purchased with a combination of RP and TP, but you CAN (for example) buy 5 levels with Technology Points and buy 8 levels with Research Points. The Technology Point costs for a given Research are NOT proportional to the Research Point costs (in most cases), so some Research fields (such as Geology) may have very inexpensive TP costs.

Once you have used a Wahrian Time Machine, you can build up your Empire all over again using the same methods you used to build up your Empire in the first place, only this time assisted by having access to higher levels of Research. You can even re-advance to the point where you build a Wahrian Time Machine AGAIN and Travel in Time AGAIN. In this event, the number of Technology Points you start off with on a subsequent use of the Wahrian Time Machine is the number of Technology Points you started off with at Promision plus the new contribution from your Influence and Research Points. Expressed algebraically:

$\text{TP}_\text{new} ~ = ~ \text{TP}_\text{old} ~ + ~ \left (\frac{2}{\ln(5)} ~ \times ~ \ln \left (1 ~ + ~ \frac{\text{RP}}{200 ~ \times ~ 10^9}\right ) ~ \times ~ \text{influence} \right )$

You can accumulate Technology Points without limit by repeating the cycle of: build up empire, conquer Xora Tauri, build Wahrian Time Machine, Travel in Time, repeat.