Three Hats, a Blind Man and a Dime

The Webster stories, "Webster's Diction" , are best read in order.

This story is lecture #3, part of a series of lectures given by Professor Webster, in "Webster's Diction" . Lecture #1 is "The Color of God"  and #2 is "Silence in G Minor" 

Three Hats, a Blind Man and a Dime

“I had a dream!”

‘What is Webster up to this time, a cheap imitation of Dr. King?’ Carlisle thought, knowing full well that he wasn’t alone in this speculation, for the several sideways turned heads and raised brows revealed a telepathic shock through the room.

“I had a dream that a three-headed man came into my hat shop and asked for three of my finest hats. I jumped, of-course, such a fine customer as this cannot be kept waiting. I was also quite disappointed that this was the first three-headed customer I’d seen all year.” Webster continued into an audience of cocked eyebrows and Elvis lips. “Why is it that all the one-headed bums come to my shop? I work so hard, for a third the sales.” Webster says, holding out his hand, with a small space between his thumb and forefinger, as if to indicate something less than an extended palm. “A white hat and two black hats, I would have gone all black myself, but I shook his hands anyway, all four of them, even gave him a 20% discount, and told him to tell his friends. My business would triple. Maybe I could sell gloves, and it would quadruple. What about earmuffs, think of the mathematical possibilities.”

“What kind of herbal tea did you say you’ve been drinking sir?” Carlisle said, with no attempt at concealing his wise-crack, for Webster appeared in a jovial mood today.

“No tea, son, no tea. But I did have a slight fever.” Webster holds a palm to his forehead, unsure if it had dissipated. “Nothing like a fever dream - Mother Nature’s compensation for all those aches and pains.”

“Cogito, ergo sum. Remember that? I think, therefore I am.” Webster said, with one finger tapping his temple. “Well, last night I was deceived into thinking I was a hat salesman, with visions of grandeur. After all, I was going to multiply my business, many times over.” Webster held his hands out, as if lying about the size of a fish he caught. “Foolish, isn’t it? I mean, to think that my hat customers would be interested in gloves, or earmuffs. That’s what fever does to you.” Everyone chuckled, somewhat hesitantly however, for no-one was quite sure of Webster’s sanity.

“Sanity. It’s like loose change in my pocket. I’ve always got some, I just don’t know how much.” Webster said, digging deep into his pocket, hoping to hear a jingle.

‘He reads minds too,’ Gupta cautioned Carlisle, with a crossways glance.

“Forty seven cents, not even enough for a cup of tea.” Webster looks disappointed.

“Si fallor, sum.” St. Augustine had Descartes beat by a few centuries, though most of the students took this as proof that Webster was, indeed, short-changed. “If I am deceived, I exist. Still Latin, Mr. Gupta, still Latin.” Gupta was preparing his shoulders for their usual disclaimer.

“So, I sell hats to a three-headed customer, and, with any luck, I’ll sell him two pairs of gloves as well. But he’ll pay me in large bills, and I have no change. So he winks his left eyes and he says, ‘Merry Christmas’ as fireworks light up the sky.” There was scarcely a breath now.

“But the math works, my dear friends, the math always works.” Webster proclaimed, still jingling the change in his left hand, failing to notice a dime had dropped by his feet.

Putting thirty seven cents back in his pocket, he calls for volunteers. “Mr. Gupta, Ms. Cole and Ms. Lauren, you are hereby volunteered into my hat shop.” The volunteers approach cautiously, Gupta picks up the dime and hands it to Webster, thinking he could hardly spare it.

“Deduction, Descartes said, is the other path to knowledge.” Webster stops as Gupta hands him a dime. “Thank you Mr. Gupta, fifty seven cents, enough for my Earl Grey, and a few pennies to spare.” Gupta didn’t have the heart to tell him differently. “We are going to play a little game today. A little game of deductive reasoning.” Webster says, as he lines his three-headed specimen, one behind the other, with Ms. Lauren in front:

Gupta (rear)
Cole (middle)
Lauren (front)

He then brings out a box, which he places behind Gupta. Gupta is afraid to turn around and hopes that Webster is as afraid of snakes as he is, after all, Webster seems a little insane today, who knows what’s in the box. “Rest easy, Mr. Gupta, there’s no Jack in this box.”

“In this box there are five hats, three black and two white.” Webster displays three fingers, followed by two, as if to add credibility to his experiment. “ In a couple of minutes I will place a hat on each of the heads of this fine customer. No-one will know the color of the hat upon his, or her, own head, they will only know the color of the hat on the head, or heads, in front of them.”

“ Ms. Lauren, I’m sorry, but you will be at a distinct disadvantage, for there is no-one ahead of you.” Webster seemed delighted with the game, which he had not played since old Hammel put him in the front of the line, some thirty years ago. Webster had worked himself into a tizzy last night, trying to remember how it went, its no wonder he dreamt what he did.

“Before I place the hats upon their furrowed brows, we will make a little wager, my friends. A gentlemen’s wager, for I can only carry so much change, and you all must eat today, I’m sure.” Webster was giddy again, remembering how Hammel had walked away with lunch money for a week. But those were different days then, when ‘a penny for your thoughts’ was a fair exchange.

“All right, I want you all to write down who it is you expect will be the first to guess the color of the hat upon their head, and place your paper face down on your desk.”

Once he was convinced of their resolution, Webster placed the hats upon his pupils, black, white and black again:

Gupta (Black)
Cole (White)
Lauren (Black)

He rubbed his hands together, like a three year old who scammed an extra cookie, and he waited.

It only took a minute, or so, for Lauren to say, “there’s a black hat on my head.”

“Of course, there is my dear, of course there is.” Webster pronounces, as he flips his own paper over, revealing, ‘LAUREN’ to have been his choice. What goodies would he have had for lunch, if he were Hammel, what goodies.

“Deduction. The blind man’s option.” Webster declared, as each student looked to their own proclamations in disbelief, some having chosen Gupta, for his obvious advantage, and others having chosen Cole for she was the undisputed Webster brainiak. But none, not one of them, had chosen Lauren, that is to say none, but the professor, whose odd smile only gave credit to those who thought he had gone insane.

“Deduction!” Webster said triumphantly. “Close your eyes, if you want to see.”

“At least you leave here knowing you exist, that’s something, isn’t it?” he says almost apologetically, as they file out, staring at their papers, as if the answer would jump out like a jack-in-the-box.

Webster will head straight to the teacher’s lounge, where you can still get a cup of tea for fifty cents, and he will be dumbfounded that he’s three cents short.


[I see you stayed behind to try to figure out why Lauren, after hearing nothing but silence, was able to declare that her hat was black. Go ahead, take your time. Then check out ‘Gupta’s Notes,’ for you know, Ms. Cole, the brainiak, is likely to explain it.]


Gupta’s Notes:

Gupta, of course, took notes only during the first part of the lecture and, though they were neat, they were nonetheless incomplete. As for the game they played, he was still unsure as to why he lost and, more importantly, why they played it. Well, let truth be told, even if he was as clear as a moon-filled night on Kerala bay, he would still ask for Cole’s help, for, as we now know, Cole’s presence sends waves through his body and lights up the sky like the fireworks of Diwali.

Cole had already worked the equation in her head and was ready for Guptas’s first question, “why did Lauren win?” She touched Gupta’s forearm as she explained, which, of course, made Gupta totally deaf, but he smiled attentively nonetheless.

“It goes like this,” she said, still holding Gupta’s arm, “There were three black hats and two white hats, right? So, you, being at the back of the line, would have called your own hat ‘black’ if you saw two white hats in front of you, since any of the remaining hats would have been black, right?” Gupta wished he had paid more attention at the time, but her soft white nape made his body tingle all over.

“You remained quiet, so I assumed you did not see two white hats.” She continued, her hands moving as if she were conducting the gaze of his eyes. “You must have seen either two black hats, in which case your own hat could have been white or black, or you saw a black hat and a white hat, in which case your hat could still have been white or black. So, you were unsure of the color of your hat, look,” she draws it out for him:

The possibilities Gupta can see ahead of him –

possibility #1
Cole (Black)
Lauren (Black)


Or

possibility #2
Cole (White)
Lauren (Black)


Or

possibility #3
Cole (Black)
Lauren (White)

“so, your silence told me you were faced with three possibilities ahead of you. Again you could not have seen two white hats, or you would have known your hat was black.”

“Of course, I was only able to see Lauren’s hat.” Cole continues to mesmerize Gupta. “If her hat had been white, I would have called my hat black,” she refers to ‘possibility #3’ in her drawing, to show that only a white hat ahead of her would give her certainty about the color of the hat on her head. “But, Lauren’s hat was black. So,” this time she refers to ‘possibility #1 and #2, in her drawing, “my hat could have been black or white, I could not be sure. So I said nothing.”

“Lauren, of course, knows as much of this as we do.” Cole was being overly optimistic about Gupta’s understanding. “ So, she knows that my silence means I am looking at a black hat – and she calls ‘black’. Simple, you see.” Gupta, of course, wanted her to repeat it, for her soft voice made him feel like every cell on his skin was changing places with another.

“What does this have to do with dreams, I don’t get it.”

“Well, his dream was simply setting up the game, but he was also saying, ‘the math always works,’ I think he is telling us that we can be deceived in our understanding of 'truths,' when we rely on our senses, but certain truths are always salient, like math. No matter how many heads and hands we are deceived into believing are real, they always add up to the same number, whether we are dreaming nonsense, or counting our change.”

“What about the hand gestures? What was that all about?” Gupta says, hoping she will move her long slender fingers in ways that always captivate him.

“I think he was trying to tell us that even in dreams an open palm means more than a pinch. You know what I mean?”

“And the game? I mean it was fun and all, but why?” Gupta wishes she would go on forever.

“Deduction, get it? He is telling us that deduction can tell us truths, even when we don’t see them. Deduction, is clarity of the mind.”

“But a blind man’s option, what does he mean?”

“Well, a blind man is not deceived by what he sees. You see, the classroom could have been blindfolded, and, if they just gave it a little time, like Lauren did, they would all have guessed correctly. They might even have been disadvantaged by what they saw.” Gupta closes his eyes, and proves her right on all counts, for he is now more certain he loves her than he’s ever been.


If you enjoy this type of story, please read professor Webster's other stories, which I will add to from time to time, in "Webster's Diction" .The Next Story is "Aristotle’s Pigeons" .