by John Wyatt
In one of my technology management classes, part of the MBA program, my normally excellent instructor passed out the most horrific essay I had ever read! He had written it some time ago - and nearly threw it out. However, instead of discarding it, he titled it "One Person's Trash is Another Person's Treasure." In this deplorable paper he had tried to describe what he called "Algorithms of Truth." His hope was that his essay would spark ideas in his hapless students. The spark that it lit in me was to write the story below - namely, how to present the same concepts in a way that the students may actully enjoy reading!
It's a cold, damp twilight; especially inclement weather for mid-May, 1864. The War Between the States has raged for far too long, and now that Grant leads the northern army, the tide is swinging their way.
Earlier, the Yankees had charged the wall and pushed back General Ewell’s boys, but then we charged forward and pushed the Yankees back, but the Yankees had not run. Hancock’s men lay only a breath’s distance away, trapped on the other side of the wall (if that's what you can call a 3 foot mound of dirt and logs). They were too close to us to stand up and run away (they would be running across an open field with us shooting them in the back), and we were too few to jump over the wall and fight hand to hand. So we had all just hunkered down and waited for nightfall.
Would General Early arrive from Spotsylvania Courthouse in time to rescue us, and where was General Lee? In a war that has pitted brother against brother, was even there any Truth remaining at all? I lay here quietly in the damp trenches behind a low wall of dirt and logs, alongside the remnants of the First Virginia Brigade, doing our best to keep our powder dry and our muskets ready in spite of the cold drizzle.
I should have stayed a merchant. I had grown up in Pennsylvania, but my years at Virginia Military Institute had influenced me to join the cause of the South. So, instead of learning how to transform learning into knowledge, and then into technologies (all the rage up North these days); and instead of selling my goods and services for a profit, I’m stuck here, laying in the mud behind a hastily built pile of dirt and logs, waiting for daylight and General Hancock to decide my fate.
“Psstt – Johnny Reb!” a hesitant voice beyond the wall whispered. I nudged the man next to me, hoping his musket was loaded – I ran out of ammunition earlier, chasing the Yankees back across the wall. No response. I think he may have died.
“My name isn’t Johnny.” I whispered back. “If you know what’s good for you, you’ll run back to the woods you all came from and get the hell out of Virginia!” My voice cracked – my bravado didn’t even convince me!
“You got anything to eat, Johnny Reb? I ain’t got no food over here.”
Grumble. Is this guy serious? After charging our wall and killing half the brigade, he has the nerve to lay there and ask me for food!
“I got some,” I whispered back, “but I need something for it. You got any ammunition?”
“What fer? So’s you can shoot me come dawn?”
“That, or run my bayonet through a chink in the wall and get you right now!” I didn’t actually have a bayonet – lots of us didn’t. Them northern boys sure had them, though. Every once in a while a bayonet would come stabbing through a gap in the logs.
“Look,” he whispered back, “there ain’t no use us just layin’ here all night waitin’ to kill each other. What say we pass the time?”
The drizzle had stopped, but now it had turned to a cold fog that was chilling me to the bone. He made sense, kind of. I was too cold and wet to sleep anyway.
“Well, what do you want to do, Yank? Talk about the weather?”
I heard a dry chuckle from the other side of the wall. “It sure is cold for May, ain’t it the God’s truth! And them General’s will get us all killed for sure.”
“Our Cause is just,” I replied, “so God’s Truth is on our side.”
“What truth?” came the response. “There ain’t no real truth – not absolute truth, anyway. I was a school teacher, you know? I taught mathematics at a young boy’s school up in Maine. Mathematics is cold, hard logic, and it says there ain’t no such thing as absolute truth – except for numbers, that is.”
“Hogwash!” I had studied mathematics at VMI, and had won many a debate as well. “Algorithms are pure expressions of Truth. Algorithms are a precise … PRE-CISE set of rules specifying how to solve problems.”
“Hah!” came the retort, “but they say nothing about the nature of Truth!”
“Well then, what is the definition of Truth? I don’t suppose you have a dictionary handy?”
“You kiddin’? We run into battle as soon as we saw you Rebs building your walls. We didn’t bring nothin’ that wasn’t already in our hands. That’s why I’m so darned hungry!”
I began to feel pity, just a little, for this soldier who had found himself trapped, along with so many others, unable to advance and yet unable to retreat.
“Well,” I ventured, “I don’t have one either, but it’s true that the moment you guys stand up to run, you’ll get shot down! Why else are you hiding on the other side of OUR wall!”
Silence ensued, and I began to think he had died or slid away.
“True.” He finally spoke. “It seems like you is speakin’ the truth – meanin’ that it conforms to fact and reality, in accordance with our situation. Yep, I guess that’s what Truth really is – conformity to the rules.”
“Yes, and like I said, an algorithm is a set of rules – and Truth is conformity to the rules.”
“Well, then there ain’t no Truth in me,” the Yankee chuckled. “I ain’t ever conformed to a rule in my life! That’s why I was teaching young boys instead of college – can’t follow rules. So tell me, Johnny Reb, there seems to be two different words used in different ways, but a lot alike in meanin’. You says that an algorithm is a precise set of rules for solving a problem (like getting’ me some food), and Truth relies on conformity to facts, rules, or whatever standards there is. In math terms, we might say that algorithms are closed sets of specific elements that operate on any input that is compatible with their syntax.”
“SIN TAX!” I shouted! Men on either side of me stirred and shushed, with several calls for “Quiet!”
“Sin tax!” I whispered. “You mean you guys just tax the sin and don’t try to stop it?”
More chuckles from the Yankee. “No – not ‘s-i-n t-a-x’. ‘S-y-n-t-a-x’. That’s the way that linguistic elements get put together – like the rules of grammar. I guess it’s kinda like an algorithm that way. ‘Course now, just because Truth is conformity to the rules, that don’t mean that an algorithm can’t describe an untruth just as well. Truth, being an expression of what is genuine, an algorithm may seem like an expression of truth. But they can also say things that just ain’t so, or even things that conflict with themselves!”
Hmmmm, clearly this Yankee was no dullard. “How do you mean?” I queried.
“Well, let’s say we gotta take the square root of X. You know what square roots are, Johnny Reb?”
“Yes I do, and my name isn’t Johnny.”
“Like I says, Johnny Reb, we gotta take this square root of X, and that’s a truth for some values of X (like a ‘2’ or a ‘4’), but it just ain’t true when we tries to make X into a ‘-1’! So see, this here algorithm can express either Truth or Untruth, depending on what we puts into it!”
“You mean, garbage in, garbage out?”
“Yeah!” he replied. “That sounds catchy! Most truths don’t stand up as Universal truths, and those what does is mostly assumptions, axioms, and matters of faith. Describing numbers ain’t hard, but proving their universal truths is somethin’ else. Say, you found anything over there to eat yet? All this talk is makin’ me hungry!”
I felt around and found some hard tack in the pockets of the corpse next to me. “Here,” I call as I toss it over the wall. “The guy who had this doesn’t need it anymore.”
“Thanks! Oh, I see what you mean. I guess lots more of us gonna be eatin’ mana in heaven before this war ever ends.”
“Well, at least us Southern boys will be – I don’t know about you Yankees.”
“Well, you sounds more like a Yankee than I does!”
“That’s because I was raised in Pennsylvania. In fact, some of my countrymen night be over that wall.”
“I don’t think so. Mostly Maine men over here – General Hancock’s boys and some others. Say, ain’t it interesting how our ‘truth’ seems relative to our situation! I wonder how many things we claim is True is really just relative! Like, say me and you was on the same side and we was fightin’ Injuns. An Injun comes a runnin’ at us, whoopin’ and hollerin’ like the Devil was in ‘im, and we both fires our muskets at once. One of us hits a tree right next to the Injun, and the other hits the Injun. Well, whose bullet was movin’ faster?”
I thought on that one, and it didn’t seem like it would make any difference – both bullets would be going at the same speed.
“You might think they’d be both going just as fast,” he continued, “but it depends on your relative position.”
“I don’t see how?” I was confused now.
“You see, the tree ain’t moving, but the Injun is. So by the time the bullet hits the Injun, he’s just a bit closer to us than the tree. So, from the Injun’s point of view, the bullet is going at whatever speed the bullet is, PLUS however fast the Injun is running towards it! But the tree ain’t movin’, so the bullet hits the tree just a split second later and seems to be goin’ slower than it was for the Injun – from the tree’s point of view. But if I was ridin’ on that bullet, like Pecos Bill ridin’ a tornado, both bullets would be goin’ just as fast! So see, it’s all relative to the observer! Truth can be like that. Sometimes we call that ‘conditional truth’.”
Well, this Yankee mathematician certainly had an intriguing line of reasoning! I ventured one step further in my thoughts.
“I begin to see what you mean; geometry also provides examples of relative truth. If I’m in a two-dimensional plane looking at a circle, I cannot know if it is really a sphere, a cone, or a cylinder.”
“Exactly!” came the enthusiastic reply.
Just then another voice whispered loudly to my left. “We live in a universe where we define Truth using binary logic – it either Is or it Isn’t. Yes/No, Win/Lose. Yet, who’s really gonna win this war? It ain’t me, cause no matter what side wins, I ain’t ever gonna be the same.”
“That’s true.” Came another voice from the Yankee side. “The implications of adding a third dimension to our two-dimensional space shows how we view this war, relative to how the generals and congersmen view it. Some of them sure are cone-heads!”
There was subdued laugher along our section of the line.
“So,” I ventured, “although the definitions of ‘algorithm’ and ‘truth’ may overlap, in many situations they are relative, or conditional. Truth then becomes a matter of perspective. Velocities, positions, shapes – all are up for grabs when we change our point of origin. Truth, then, becomes a matter of perspective, and algorithms are simply methods of analysis. They can be used together, but they cannot be considered Algorithms of Truth. At most, they can only be two different tools used by the seeker of a particular truth. Two completely contrary truths could be analyzed using the same algorithm.”
“That’s right, Johnny Reb!” replied the math teacher.
“Remember,” another Yankee spoke, “geometry, logic, and reason are products of Western thought. But they also long claimed that the Earth was flat, with the sun goin’ round it!”
“And,” yet another Yankee spoke, “truth is nearly always conditional! It depends on our perception and connections to other truths. But algorithms are just operators that act without regard for truth or anything else.”
“Like General Grant!”
Laughter rippled down both sides of the wall. The night began to suffuse with a cold glow; the full moon must be rising. The fog covered everything with an icy, penetrating wetness.
“Well,” one voice said, “my powder’s worthless. How’s about yours?” Several voices assented. “You feel like goin’ at it with knives and bayonets come daylight?”
Silence covered the line like a tomb.
“I thought not. What say you Rebs just lets us filter back to our lines real quiet like, and we’ll finish this work another day?”
Mumbled assents rippled across our line. “Sure; you guys be careful though. Don’t make no noise or our pickets might hear you.”
The faint sounds of movement carried over the wall, but were deadened in the heavy morning fog.
“You take care, Yankee.”
“You too, Johnny Reb.”
“My name still isn’t ‘Johnny’.”
“Mine neither. But my brother’s is, and he’s fightin’ with the First Virginia – that’s you guys. So you see, it’s all relative. I hope’s we never meets again.”
Jordan, Thomas. “One Person’s Treasure is Another Person’s Trash.” Feb, 2004. TMGT 540 handout.