"I prefer diamonds," Stacey jokes.
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We all laugh, then responding to Ralph's gesture I give it a try. "We probably have to look for a more numerical measure. This way we'll be able to arrange the elements without being criticized for subjective preferences."
"Very good," says Ralph. He's probably mistaken us for his kids. "What do you suggest as a suitable measure?" he asks me.
"I didn't take chemistry," I reply, "not even as a minor. How would I know?" But since I don't want to offend Ralph I con- tinue, "Maybe something like specific gravity, electrical conduc- tivity, or something more fancy like the number of calories ab- sorbed or released when the element is combining with a reference element like oxygen."
"Not bad, not bad at all. Mendeleev took basically the same approach. He chose to use a quantitative measurement that was known for each element and which didn't change as a function of the temperature or the state of the substance. It was the quantity known as atomic weight, which represents the ratio between the weight of one atom of the given element and the weight of one atom of the lightest element, hydrogen. This number provided Mendeleev with a unique numerical identifier for each element."
"Big deal," Bob can't hold himself. "Exactly as I suspected, now he could organize all the elements according to their ascend- ing atomic weights, like soldiers in a line. But what good does it do? What practical things can possibly come out of it? Like I said, children playing with lead soldiers, pretending that they do very important work."
"Not so fast," Ralph responds. "If Mendeleev had stopped here, I would accept your criticism, but he took it a step further. He didn't arrange the elements in a line. He had noticed that each seventh soldier represents basically the same chemical be- havior, though with increased intensity. Thus he organized the elements in a table with seven columns.
"In this way all the elements were displayed according to ascending atomic weight, and in each column you find elements with the same chemical behavior in ascending intensity. For ex- ample, in the first column of his table stood lithium, which is the lightest of all metals, and which, when put into water, becomes warm. Right below it is sodium, which when put into water, flames. Then the next one in the same column is potassium, which reacts even more violently to water. The last one is cesium which flames even in regular air."
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"Very nice, but as I suspected it's nothing more than child's play. What are the practical implications?" Down-to-earth Bob.
"There were practical ramifications," Ralph answers. "You see, when Mendeleev constructed his table, not all the elements were already found. This caused some holes in his table that he reacted to by 'inventing' the appropriate missing elements. His classification gave him the ability to predict their weight and other properties. You must agree that's a real achievement."
"How was it accepted by the other scientists of his time?" I ask, curious. "Inventing new elements must have been received with some skepticism."
"Skepticism is an understatement. Mendeleev became the laughing stock of the entire community. Especially when his table was not as neatly arranged as I described it to you. Hydrogen was floating there above the table, not actually in any column, and some rows didn't have one element in their seventh column, but a hodgepodge of several elements crowded into one spot."
"So what happened at the end?" Stacey impatiently asks. "Did his predictions come true?"
"Yes," says Ralph, "and with surprising accuracy. It took some years, but while he was still alive all the elements that Mendeleev predicted were found. The last of the elements that he 'invented' was found sixteen years later. He had predicted it would be a dark gray metal. It was. He predicted that its atomic weight would be about 72; in reality it was 72.32. Its specific gravity he thought would be about 5.5, and it was 5.47."
"I bet nobody laughed at him then."
"Certainly not. The attitude switched to admiration and his periodic table is regarded by students of chemistry today as basic as the ten commandments."
"I'm still not impressed," my stubborn replacement says.
I feel obliged to remark, "The biggest benefit was probably the fact that due to Mendeleev's table people didn't have to waste time looking for more elements." And turning to Bob I say "You see, the classification helped in determining, once and for all, how many elements do exist. Putting any new element in the table would have upset the clear order."
Ralph coughs in embarrassment, "Sorry Alex but that's not the case. Only ten years after the table was fully accepted, several new elements were discovered, the noble gases. It turned out that
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the table should have been constructed to have eight columns, not seven."
"Just as I've said," Bob jumps in a triumphant voice. "Even when it works you still can't trust it."
"Calm down, Bob. You must admit that Ralph's story has a lot of merit for us. I suggest that we ask ourselves what's the difference between Mendeleev's classification of the chemical ele- ments and our many attempts to arrange the colored shapes in order? Why was his so powerful and ours so arbitrary?"
"That's just it," says Ralph, "Ours were arbitrary, and his was..."
"Was what? Not arbitrary?" Lou completes his sentence.
"Forget it." Ralph agrees. "That's not a serious answer. I'm just playing with words."
"What exactly do we mean by arbitrary, and not arbitrary?" I raise the question.
Since nobody answers I continue, "Actually, what are we looking for? We're looking to arrange the facts in some order. What type of order are we seeking? An arbitrary order that we superimpose externally on the facts, or are we trying to reveal an intrinsic order, an order that already exists there?"
"You're absolutely right," Ralph is getting excited, "Mende- leev definitely revealed an intrinsic order. He didn't reveal the reason for that order, that had to wait for another fifty years, when the internal structure of the atoms was found, but he defi- nitely revealed the intrinsic order. That's why his classification was so powerful. Any other classification that just tries to super- impose some order, any order, on the given facts is useful in only one sense-it gives the ability to present the facts in a sequence, tables, or graphs. In other words, helpful in preparing useless, thick reports.
"You see," he continues enthusiastically, "we, in our attempts to arrange the colored shapes, didn't reveal any intrinsic order. Simply because in that arbitrary collection there was no intrinsic order to be revealed. That's why all our attempts were arbitrary, all futile to the same extent."
"Yes, Ralph," Lou says in a cold tone, "But that doesn't mean that in other cases, where intrinsic order does exist, like in man- aging a division, we can't fool ourselves in the same way. We can always procrastinate by wasting our time playing with some artifi- cial, external order. Let's face it, what do you think Alex and I
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would have done with the pile of facts that we suggested he gather. Judging by what we've done for so long here in the plant, probably just that-playing a lot of games with numbers and words. The question is what are we going to do differently now? Anybody got an answer?"