The math of shape


I once worked for a firm of lawyers over the university holidays to earn some extra money. One of my daily chores was to visit the post office to collect mail and send off packages. At the post office worked a woman called Sarah. She had a terrible squint and an overbite of horsey, uneven teeth that were so long that she struggled to close her mouth around them. She looked constantly surprised.

Sadly, her beauty wasn’t skin deep. As far as I could tell, Sarah was a deserted outpost in the hinterland of the intellect. You had to travel past world-class idiots and then across a wide stretch of nothing at all before you got to Sarah. Sarah pushed at the boundaries of stupidity every time I saw her. Behind the clerks was an open area in which she did odd jobs. There was a trapdoor to a basement storage area beneath it. On two separate occasions I watched as Sarah opened this door and then plunged into the basement with a muffled cry a few seconds later. There was also a door to an office beyond the open area, operated with a foot pedal of some kind. I often saw the clerks open it while carrying parcels. Sarah was stumped by this door. She’d kick it until one of the clerks opened it for her. A device that would yield to a foot would not yield to Sarah. Another time I watched as she tried to tape up a box that bore a This Side Up sign. Instead of turning it over, she crouched and taped the underside of the box while she grunted and complained. At first I thought that it already contained something that could not be turned upside down but then one of the clerks went and turned the package over in exasperation. The box was empty. Sarah frowned at it and then turned it back to how it was before she continued to struggle with the tape.

I felt sorry for Sarah. She was doing odd jobs, just like I was. Like me, she did dumb things. I wanted to tell her that I understood and that everything would be OK, even though I knew that they would never be.

There was a single clerk on duty when I arrived one day. After he’d helped another customer, he disappeared through the door with the pedal. I waited at the counter for a minute and then Sarah came over. She held a broom and was slightly out of breath.

“Yeth?” she lisped.

I reflected for a moment on the cruelty of life but she went on.

“What you want?”

“Hello Sarah,” I tried.

“Yeth??” she insisted.

“Everything will be OK,” I purred.

She narrowed her eyes.

“What you want??” she demanded.

“Er—I have to mail these packages. I’ll wait for someone.”

She squared her shoulders.

“Tharah will,” she said.

“It’s OK,” I replied, “really. I’ll wait.”

Sarah held out her free hand and made a low, moaning sound. I gave her my parcels. There were two boxes and a long tube containing a poster. She smiled as she took them. It wasn’t a pretty sight but it made me feel good.

“You don’t have to do this,” I called after her as she waddled to the scale behind her with the first of the boxes and the broom in her other hand. Obviously, once Sarah got busy with something, she didn’t let go.

She put the box on the scale and struggled with her free hand until she’d turned it the right way up. She squinted at the readout and pressed a button which printed a weight label. Then she did the same thing with the second box.

“Why do you turn the box?” I asked as she fetched the tube.

“To make thure it’th right,” she mumbled as she walked away.

She placed the tube on the scale and shook her head.

“Thith one ith wrong,” she declared when she got back.



“What do you mean, wrong?”

“It’th too long for the thcale.”

For a moment I was speechless.

“Thee,” she said and returned to the scale. “It thtickth over.”

She pointed at the ends of the tube which didn’t touch the scale surface and shook her head like a child refusing broccoli.

“Can’t thend thith one,” she concluded.

“What do you mean? Surely the scale is not the length limit?”

Sarah looked at me as though I’d gargled in Greek.

“Why can’t it be longer than the scale?” I tried.

She gave me a weary look.

“Becauth you can’t weigh it,” she sighed.

“Why not?”

She returned to the scale and placed the tube on it again.

“Thee,” she said and pointed at the ends of the tube, “thith and thith. Not on the thcale.”

“You’re joking, right?”

But humour didn’t flower in the barren landscape of Sarah’s mind. She wouldn’t crack a joke if she sat on one.

“They don’t toutth,” she added.

“I know,” I said, “of course they don’t touch. It doesn’t matter.”

“It doeth!”

By now a few people had started to queue with me. The woman behind me smiled wanly and shrugged.

“Look,” I said, “I tell you what. Put one of my boxes onto the scale and let it stick out over the edge a bit. Then we check what it weighs, OK?”

Sarah sighed again.

“That’th not how you thend it,” she explained. “You thend the whole boxth.”

For a moment I was dumbstruck. Clearly, the episode with the tape had been no accident. Sarah dealt in absolutes.

“All you have to do is weigh it,” I tried again.

“It’th bigger than the thcale,” she insisted.

“That doesn’t matter.”

Sarah wrung the handle of the broom.

“The thhape ith wrong,” she said.

“The shape?”

“Yeth,” she said as she mimed her idea of shape. “Thhape.”

“Ah,” I said, sensing a breakthrough, “that’s the thing with mass. It doesn’t care about shape.”


Someone giggled in the queue behind me.

“That’s what the scale tells you,” I ploughed on. “The mass of the thing. By weighing it.”

Sarah shook her head with the air of someone who knew that it was hopeless.

“The thcale tellth you how much the thtampth are,” she said firmly.

“Sure,” I agreed, “I know. I know. But how does it do that?”

Sarah looked at me with pity.

“It meathureth the parthel.”


The woman behind me cleared her throat.

“It checkth how big it ith,” Sarah explained.

She leaned forward to make a point.

“That’th why it mutht fit,” she emphasised.

Things were getting away from me. In a kind of panic I wondered where the real clerk was.

“Of course size matters,” I conceded, “but not for smaller parcels like these. They’re charged by weight. That’s what the scale is for. It measures weight.”

“And yourth ith too big,” Sarah continued. “It thtickth over.”

As long as Sarah refused to understand weight, I was doomed.

“OK,” I tried, “let’s say you’re going to send me somewhere.”

Sarah frowned.

“And you put me on the scale—”

“You’re too big for the thcale.”

“I know,” I pleaded, “just listen. Before you weigh me, you squash me into a box that can fit onto the scale.”

Sarah looked pleased at this prospect.


“Would you weigh me like that?”

She shook her head again. This time it looked as though she’d spotted what the problem was.

“No,” she insisted and wagged her finger. “If I thquath you, you’re different.”

“But I’m different all the time!” I cried. “Look!”

I held my arms out to the sides.

“It’s still me. I weigh the same as before. You can squash me or stretch me.”

Sarah sighed and considered my arms.

“Now you’re thtretthed,“ she remarked.

“Stretched, squashed, it doesn’t matter.”

“It doeth,” she insisted.


“Your armth thtick out like wingth.”

“So what?”

“Wingth make you lighter,” she said with finality. “Birdth can fly.”

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