User:Ray Calvin Baker/LogicalThing

 This is the "LogicalThing.txt" file, created WED 2011 AUG 10 05:05 PM, revised WED 2011 AUG 10 05:05 PM.

Mister Spock Does the Logical Thing

As I begin this story, I do not know how it will end. I will emulate Mister Spock's logical decision, just as he did it.

Renegade is a science outpost established to study the nearby Von Neuman nebula, a region filled with a variety of unstable stars. This makes it both essential for study, and difficult to approach. Furhermore, as an outpost it has strategic value both for the Federation and for the Romulan Empire. It has not enough strategic value that either side wants to risk all-out war, but the Federation needs to keep sending supply ships, which the Romulans have been attempting to destroy. In fact, each of the last six Federation supply ships has been destroyed, and the scientists at Renegade are in a desparate situation. Hence the current mission of the USS Enterprise.

Science officer Spock has been studying the reports from all successful resupply missions, and the recovered message buoys from all but two of the failed missions. He concludes that there is only one safe way to approach the Renegade station (because of the proximity of unstable stars). He has established that five basic scenarios have been played out, as Federation ships attempt to resupply Renegade. 1. Federation ship approaches in "silent running" mode, finds Romulans waiting in ambush, fires torpedoes, and completes its resupply mission successfully. 2. Federation ship approaches in "silent running" mode, finds Romulans waiting with all weapons at full power, fires torpedoes, but is destroyed by Romulan phaser fire. 3. Federation ship approaches with all weapons at full power. The Romulans see them coming, and lay out a spread of torpedoes. One of these destroys the Federation ship. 4. Federation ship approaches with all weapons at full power, and finds Romulans waiting with all their weapons at full power. The Federation ship gets of the first shot, destroys the Romulan blockade, and resupplies the Renegade base. 5. Any other tactics lead to the destruction of the Federation ship.

"So, you mean to tell me that we have only two choices, "running silent", or "all weapons at full power"? And there's a 50-50 chance we will all be killed? And we'll have only a few seconds to fire if we find the Romulans first?"

"Yes, Captain. That is the situation as I see it."

"Well, Spock, I think the thing for me to do, is: give you full command of the ship so you will have every tactical advantage possible, then, trust your Vulcan logic to 'do the logical thing.'"

"Thank you for your confidence, Captain, But my notes do not indicate any pattern to the Romulan strategy. It seems completly random to me."

"Check your notes again. We're all counting on you to find something."

Spock returns to his science station and begins to review his notes.

"Hmm. This is interesting. The nearby nebula was named after John Von Neuman, who invented something called 'game theory' around the year 1940. Ah! here's something ... 'Theory of Games' ... 'zero-sum games' ... ... payoff matrices ... optimal strategies. Here's a strange strategy for a symmetric, zero-sum game. Yes! the payoff matrix for our situation looks like this:"

\  Federation choices:      | \ "silent     | weapons    | R \ running"    | powered    | O *++ M a|1. Romulan |3.Enterprise| U m| ship      | destroyed; | L b| destroyed; |           | A u| Resupply  | Resupply   | N s| mission   | mission    | h| sucessful | fails      | C +++ H p|2.Enterprise|4.Romulan  | O o| destroyed; | ship      | I w|           | destroyed; | C e| Resupply  | Resupply   | E r| mission   | mission    | S e| fails     | sucessful  | d|           |            | ===+++

"Attention all hands! Mister Spock has command of the Enterprise, until we're all killer, or until we dock at Renegade station in two hours. He says there is a 50% probability for either occurrence. He says he has found the optimum strategy in the archives. I am preparing a message buoy for launch in case the Enterprise is destroyed, so future Federation ships may learn from our experience. If you want to leave any messages for your next-of-kin, use your personal logs, and patch them through to Communications. Mister Spock says he is ready to make his tactical decision in fifteen minutes. I trust he will do the logical thing."

Mister Spock jots down a note: "HT silent running; TH full power". Then he begins talking to himself, "Heads, heads, Inconclusive. Tails, tails, Inconclusive. Tails, heads, full power." He turns on the intercomm, "Attention all hands. This is Mister Spock taking command of the Enterprise, per Captain Kirk's orders. Full power to shields. Full power to all phasor banks. Prepare to fire all phasors as soon as I verify targeting. Course laid in. Steady as she goes."

Spock's targeting of the Romulan vessel is precise. He verifies targeting within two seconds. The Romulan's shields hold for a few seconds, but give way before the Romulan's can return fire. Seconds later, the Romulan ship explodes in a devastating matter-antimatter core breach. The Enterprise shields hold firm, and the inertial dampers buffer the incoming shock wave.

"This is Mister Spock commanding USS Enterprise. Requesting permission to dock."

"Permission granted!" (Wildly enthusiastic cheers in the background.) Boy, are we glad to see you!"

Two hours and ten seconds after he made is original ETA, Spock brings the Enterprise in for a smooth docking. Within minutes, supplies are being unloaded into the Rengade station's storage areas.

"Mister Spock, did I see you tossing a coin while you were working there at the Science station?"

"Yes, Captain, you did. You had asked me to do 'the logical thing,' so I did."

Mister Spock had been concerned that the coin he tossed might be biased, so he took a sensible precaution. This requires some simple calculations to explain. Let's assume a biased coin comes up "heads" 60% of the time. "Heads, heads, probability .6 * .6 = .36, inconclusive." "Tails, tails, probability .4 * .4 = .16, inconclusive." "Heads, tails, probability .6 * .4 = .24, proceed with 'silent running'", but this is not what happened. "Tails, heads, probability .4 * .6 = .24, proceed with all weapons at full power" Each of these last two cases has exactly the same probability, .24, so this eliminates the effect of a biased coin, leaving only the desired 50-50 result.

Spock and the crew of the Enterprise were lucky. But Spock did "the logical thing" under the circumstances. The end.

