Absolute Zero

[WP] God has a points system. Positive for good deeds, negative for bad. You die and St. Peter tells you your net points equal 0.


“Next!”

A woman stepped forward nervously. “Here, sir.”

St. Peter glanced at her, then looked down to the computer screen in front of him. “Over two hundred points, well done. Please proceed.” The woman skipped lightly through the Pearly Gates, a blissful smile on her face. As the Gates closed, I saw thousands of other beings inside, welcoming her with open arms.

“Next!”

An old man hobbled forward. He seemed to do so out of habit, though; his balance was perfect and he did not favour either leg.

“Thirty-nine point seven, could be worse. It’s Purgatory for you, until you get those last ten points.” St. Peter waved towards a smaller, more modest door beside the Pearly Gates. The old man hobbled through it, with a final longing look at the Gates.

“Next!”

This man was dressed in a sharp suit, and walked ahead smartly. He bowed to the angel. “Present, Your Honour.”

St. Peter glanced at the screen. “Wow. Okay.” He pulled a lever and the clouds below the man parted. Mr. Suit-And-Tie fell out of sight, screaming all the way down. There was a sizzle and a flash of orange, flickering light. The clouds closed again.

“Next!”

I gulped, stepping forward. I wasn’t proud of my life. I’d done many things, some good, some bad. I’d lifted stuff from the local supermarket once or thrice, but I’d been loyal to my friends and family, helping them out in times of need. Surely family matters would give enough points to outweigh some petty larceny, didn’t it? Well, loyal for the most part. Sometimes I just couldn’t find the energy to deal with their problems. Like the time Janet said “we had to talk”, but I was a little busy at the time playing Halo. But I helped take care of her cat when she was away. Except for that one time when it jumped in my cereal and I screamed and accidentally threw it out of –

“Matthew!” St. Peter called, interrupting my thoughts. “Come take a look at this.”

A bespectacled angel flapped his way over, tilting St. Peter’s screen to get a better view.

“Curious,” he said. He prodded a few keys.

I was growing even more nervous than I had been before. I snuck a look at the leaderboards hanging beside St. Peter. Gandhi and his three thousand points smiled back at me, as did Hitler and his negative nine thousand. I wondered if I had just made it to one of the lists.

Several minutes passed, and the two angels continued to pore at the computer, whispering to each other. I glanced behind me. People in the queue were beginning to get restless.

“Excuse me, sir,” I ventured, “Might I ask what the delay is?”

St. Peter looked up and sighed. “It’s a small technical problem, no worries. We’ll get it sorted out soon.”

Beside him, the angel who was presumably St. Matthew gave a soft snort. “Cloud computing. What a joke.”

Hours passed, but the issue didn’t seem to have been solved. An increasing number of angels began to crowd around St. Peter’s computer terminal. Finally, they seemed to reach a conclusion, and St. Peter strode forward.

“Sorry for the delay,” he said. “There’s been a small issue. You see, we track scores with real numbers — that is, numbers with infinite decimal places. Each good or bad thing you do earns you a decimal score between fifty and negative fifty, and we sum them up to get your final score. If your score is positive, we let you into Purgatory or Heaven; if it’s negative you go straight to Hell.

“Your score seems so far to be zero, so we don’t know where to send you. Yet. Summing numbers with infinite decimal places results in exactly zero with exactly zero probability, so all we need to do is keep scrolling down until we find the first significant digit. Not to worry, we’ve looked through several billion digits already, it won’t be much longer.”

Several hours passed.

Several days passed.

The queue for entrance was now rather long. It stretched out as far as the eye could see. People squatted all over the place, having long given up hope of the line moving forward in the foreseeable future. The woman behind me had grown increasingly frustrated, at one point slipping off to have a whispered conversation with an angel, of which I only caught the words “additional terminals”, “bureaucratic inefficiency”, and “fucking idiot”.

All to naught, though, as nobody had yet found any significant digits. Forty angels had been recruited into the effort, and were now searching various parts of my score in parallel, St. Peter himself continuing the first sequence while others skipped gazillions of digits to search in the middle of my score. All zeroes.

At first, I had been confident that a digit would eventually be found, but confidence tends to wane after several octillion digits of evidence to the contrary. At this rate, I was worried that I had locked everyone out of heaven forever.

After a week had passed, I was positively jittery. The good lady behind me was staring daggers at me whenever I happened to look in her general direction, and the rest of the queue was warming to her attitude. Although I was fairly sure I was now an immortal soul, I had a feeling it couldn’t be much longer before the collective efforts of the Queue managed to find a way to make me disappear, permanently.

I couldn’t stand it any longer.

“St. Peter,” I said. “Can you please just send me to Hell?”

St. Peter lifted his weary face, and removed his spectacles. “Excuse me?”

“Well, I understand that you need certain criteria for letting people enter Heaven, but my being here is preventing everyone else from entering either. Would you please send me to Hell so that everyone else can proceed on to the afterlife?”

St. Peter looked at me thoughtfully. “You are aware that Hell is an eternity of suffering, yes?”

“Yes.”

“And you are willing to bear it, on the behalf of everyone else in the queue?”

I paused. It couldn’t be much worse than an eternity of waiting in a queue, especially one with Ms. Pissed-Off plotting behind my back. “Yes.”

St. Peter nodded slowly. “As you wish.” He reached for the lever he’d pulled earlier to drop Mr. Suit-And-Tie down the gutter. I closed my eyes.

There was an electronic ding, and St. Matthew’s voice cried out, “Wait!”

I opened my eyes. I was still standing on the cloudy ground before the Pearly Gates.

St. Matthew pointed excitedly to the monitor. “Look!”

“Well, I never,” St. Peter exclaimed. “It looks like your act of ultimate personal sacrifice has earned you fifty points! I can let you in now.”

“Uh…” St. Matthew said.

St. Peter waved me toward the small door to Purgatory.

“Uhhh…” St. Matthew said.

“What is it?” St. Peter asked, turning to him.

“He got fifty points, Pete. Fifty point zero. Fifty point zero zero zero zero.”

“Oh.”

“So… should we send him to Purgatory or Heaven?”

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(Short) Sketch

There were no clocks in the basement.

No clocks. No watches. Had it been an hour? A day? It was difficult to tell.

The boy hunched over a wooden desk, soldering iron in hand. The desk was rather shabby, with many chips and scratches, and patches that looked like they might have been scorched. By its side stood a small wooden barred filled with water, half-covered with a metal lid.

There was a soft hiss as the boy welded another pipe onto the small device in his hands. It was curiously formed, a mass of gears and pipes crammed into a tiny space, encapsulated with the beginnings of a protective shell. Some silver, some bronze, and a few dull grey. Most were of different diameters, and showed different amounts of wear.

There was a puff, and vapour began to seep out of the device. The boy sighed, shook the device gently, and a little bronze cylinder fell out. Without looking up, the boy pulled open a drawer by his side, and reached into one of the many small trays, pulling out a replacement.

But something must have gone badly wrong, because the device began to vibrate in his hands. The boy reached over and dropped the device into the barrel of water beside his desk, replacing the lid. A second of silence, and then several simultaneous clangs rang out, exactly as if some sort of device had exploded inside the barrel.

The boy set the lid aside again.

He pulled open two drawers, and counted out a precise number of gears and pipes onto the desk. He could start anew, and would, over and over.

After all, he had all the time in the world.

The End

As I laid the firewood down, the farmer thanked me.

‘Fox’, he said, ‘I cannot repay you for everything you’ve done. I am poor, and all I have are these carrots, but you may take as many of them as you wish.’

I cannot eat carrots, but I know my good friend Rabbit does. There are mountains of carrots, more than you can ever hope to eat. Will you come with me tomorrow?

The rabbit listened, but he knew the fox was cunning and deceitful.

“No, Fox,” the rabbit said, “You have fooled me twice already. I know your ways, and I am blind no longer.”

The rabbit pulled the lever he had hidden in the wall. The ground opened under the fox, and he fell into a pot of boiling water, never to trouble anyone again.

And the rabbit lived happily ever after.

I closed the book. Julie was silent, drawing the slow breaths of deep slumber. I reached over and turned out the light. For a while, I simply sat, watching her.

I heard a creak behind me.

I turned, and there crouched a man in black clothes. He froze when he saw that I had noticed him. He was wearing a black mask — well, it may not have been black, because the lights were off and it was quite dark, but it was some kind of dark colour, maybe blue or brown but you get my meaning — and he was carrying a knife.

I screamed, Julie screamed, and the man fled. I ran after him, grabbing the golf club that I keep in the hallway. I was catching up to him, and he must have panicked because he tripped and fell, hard.

Knowing I was about to catch up to him, the man got desperate, and from his pocket he pulled out a bazooka-

“Wait a moment.” The cop held up his hand, disbelief written all over his face. “A bazooka? Seriously? Don’t fool around. A police report is serious business.”

“What do you mean? Of course I’m serious!”

“A bazooka, taken out from his pocket.”

“Yes.”

“How big was the bazooka?”

“Uh, about thirty centimetres.”

“Long?”

“No, thick. The length was, ah, about two metres.”

“…I’m going to write you up for obstruction of justice.”

The judge pressed a button, and the recording stopped. I held my face in my hands.

“In my defence, Your Honour, I was drunk.”

The judge sighed. “Enough. We will convene again in fifteen minutes.” He tapped his gavel.

That was when I thought, I want to go one layer deeper! But how?

(Short) Vision

“Alright, tell me what you see.”

“I see… a man. He flees a burning city on a dying horse. Blood flows like water, and ash falls like snow. His heart is filled with grief, but in his arms is the child that has the power to end the Dark Lord, for neither can-”

“No, no, what do you see here?” She raps the board. “What letter is this?”

“Oh, er… M.”

“And this?”

“Z.”

“This one?”

“It’s a P.”

“Alright Mr. Collins, your eyesight is perfectly fine.” She glances skeptically at him. “Your third eye, on the other hand, needs some seeing to.”

“Can you recommend a specialist?”

“Next!”

(Short) High Mages

The two men faced each other across an empty plain. Their brows were furrowed in concentration, their eyes, focused and intent. If you paid close attention, you would notice a faint sphere enclosing each of them, swirling and shimmering in different colours.

Every now and then, a ball of fire, or bolt of lightning or whatever, would pop into existence in the air around one of the combatants, speeding for a thinner section of the sphere. But without fail, the other would wave a hand, and the sphere would shift, the fireball smashing to a thousand embers and dispersing harmlessly.

“I’m bored,” the younger combatant announced. He abandoned his dueling stance and straightened, waving off an opportunistic thunderbolt launched by the other. “Battles between High mages are so uneventful. Defence always beats offense. I think we should find another way to settle this.”

“Fine. What do you suggest?”

The young mage pointed into the distance. “If you can take out five of those birds in one try, I’ll acknowledge the loss and turn myself in. But if you can’t, you will return to the Justiciars and say I was too powerful for you.”

The old mage snorted. “Fair enough. You’ll be in the White Court before the day is out, mark my words.” He gazed into the distance, gauging distances and plotting trajectories. A circle of five miniature suns grew in his hands, spinning larger and larger…

… until a spear of rock pierced through his shield and took the old mage straight through the head. His body fell limp, and the five fireballs spun out of control, detonating in an enormous burst of flame and debris.

The young mage turned away from the conflagration. “What an idiot.”

Efficiency of a Gas Cycle

I was reading up on the physics of refrigeration for … reasons … and while working out some of the math, stumbled on something interesting. It’s almost certainly not novel, but I thought I’d write it out anyway. (It might not even be correct, if I’ve made a careless mistake somewhere. I’m cautiously confident it’s right, though.)

Overview

The gist of my “discovery” is that the (non-standard1) efficiency of refrigeration using a gas cycle is a simple ratio of two temperatures.

I’ll define a gas cycle here for convenience. In a gas cycle, a volume of cold gas is placed in thermal contact with a system in order to extract heat from the system. The gas is then separated, compressed to a high temperature, then placed in contact with a heat sink, rejecting the heat into the sink. The gas is then allowed to expand, cooling down in the process, and the cycle starts again.

More technically, a gas starts off at temperature T_N (N for minimum), and is placed in thermal contact with the system to be cooled, its temperature falling isochorically until equilibrium to T_C (C for cold reservoir). The gas is then compressed adiabatically to a new temperature of T_X (X for maximum), where it is then placed in contact with the heat sink and it cools isochorically until equilibrium to temperature T_H (H for hot reservoir). The gas is then allowed to expand adiabatically, reaching the original temperature T_N.

The quantity I’m interested in is :

\frac{T_{extr}}{T_{rej}}

= \frac{n C_V \Delta T_{extr}}{n C_V \Delta T_{rej}}

= \frac{T_C - T_N}{T_X - T_H}

Obviously, not all four temperatures are free variables, otherwise the efficiency could be anything. So, we need to find the relationship between the four temperatures, and plug it into the expression for efficiency.

The Four Temperatures

The core of the relationship lies in the adiabatic transitions from T_C to T_X and T_H to T_N.

We look first at T_C and T_X.

We start with the equation for adiabatic processes:

TV^{\gamma - 1} = constant

and we know that

V_N = V_C and V_H = V_Xbecause the transition between these states is isochoric.

So, from the adiabatic equation, we proceed to isolate the V terms so that we can later eliminate them with the other equations:

T_X V_X^{\gamma - 1} = T_C V_C ^{\gamma - 1}

\implies (\frac{V_C}{V_X})^{1 - \gamma} = \frac{T_C}{T_X}

\implies \frac{V_C}{V_X} = (\frac{T_C}{T_X})^{\frac{1}{1 - \gamma}}

Similarly, for T_N and T_H we obtain

 \frac{V_N}{V_H} = (\frac{T_N}{T_H})^{\frac{1}{1 - \gamma}}

Substituting into V_N = V_C (isochoric transition):

V_H (\frac{T_N}{T_H})^{\frac{1}{1 - \gamma}} = V_X (\frac{T_C}{T_X})^{\frac{1}{1 - \gamma}}

But since V_H = V_X (isochoric), this simplifies down to:

\frac{T_N}{T_H} = \frac{T_X}{T_C}

which is the desired relationship between the four temperatures.

Efficiency

We pick a variable at random and substitute into the expression for efficiency:

\frac{T_C - T_N}{T_X - T_H}

= \frac{T_C - \frac{T_C T_H}{T_X}}{T_X - T_H}

= \frac{T_C}{T_X} \frac{T_X - T_H}{T_X - T_H}

= \frac{T_C}{T_X}

This is the same expression from the earlier section!!

what sorcery is this??

Conclusion

So somehow the efficiency turns out to be this simple ratio.

It’s not completely out of the blue. The ratio structure of the relationship between the four temperatures hinted that it was describing some underlying parameter, but I didn’t expect the constant to be the efficiency of the transfer.

The expression for efficiency also makes some intuitive sense. You would expect that the efficiency goes down if you pump the gas up to higher temperatures. I didn’t expect it to be such a simple relationship, though.

Maybe there’s actually something really simple going on, but a intuitive physical understanding of this system continues to elude me. But whatever the case, the expression for efficiency is certainly one of the most elegant relationships I’ve seen.


  1. Usually, efficiency is defined as the ratio of useful work extracted (in this case, the energy removed from the system to be cooled) to the work input. However, the value I am interested in is the ratio of heat extracted from the system to be cooled to the heat output to the heat sink. There’s no name for this that I know of, so I just use “efficiency” here.