Most of the anger and bluster had drained away, and Brother Matthew no longer shouted his innocence. He sat with his large frame sagging and his normally round face drawn and sallow. It was as if the flame inside him was now burning low and flickering as badly as the oil lamp on Mendel's desk.

Brother Gregory had given him the news and brought him up to date with his latest discoveries, but Klacel, usually so alive and interested in everything, just sat on his crate and nodded. Nothing Mendel said seemed to affect him, even the fact that he, and the Abbot, now considered him innocent only raised a faint smile. Proving it, he said softly, was another matter.

Sadly, Brother Gregory left his friend to his meal, skipped going to Vespers despite the wrath of the Prior, and went back, alone, to his rooms. There he collected some blank pieces of paper, a new pen, a full inkwell, and started writing down in as logical manner as possible, all the evidence he had collected.

As he had done when trying to work out the meaning of his hybrid pea crosses some years ago, Mendel returned to the kind of thinking he had been taught at the University in Vienna. Under the tutelage of a new breed of scientists such as Doppler, Unger and Schleiden, he and their other undergraduates had been shown how to move away from the Greek way of thinking and towards the newer, modern way of examining scientific evidence.

For, at the time Mendel was in college, most philosophers still worked in the way first discovered by the Greeks over 2,000 years before. It was an attractive system. About 300 BC Euclid had used geometry to produce the most elegant examples of this method; axioms followed by deduction. This approach depended on statements of truth so obvious they were acceptable to all and therefore were unquestioned. These were called axioms. Euclid collected the best of these axioms, such as "the shortest distance between two points is a straight line", and from them deduced a set of theorems that became "Euclidean Geometry".

Greek science depended on deduction. They started with the axioms and deduced a whole body of knowledge based on them. In geometry this approach met with considerable success and even today Euclidean Geometry is taught in schools, but, after their initial successes, the Greeks went seriously wrong.

They considered deduction the only way of gaining new knowledge. They ignored, where ever they could, direct observation and measurement. It was considered shameful to study nature or collect facts, except when it could not be avoided. Thinking was the highest form reason, and the Greeks seriously undervalued anything that was too closely related to everyday life. A gap opened up between what the Greeks saw (when they bothered to look) and what they thought about it.

They also began to think of axioms as "absolute truths", and as they, and later scientists, began to think of other areas of knowledge outside of geometry, they made some serious mistakes. It was "axiomatic" that the sun revolved around a stationary earth, it was obvious, everyone could see it with their own eyes. Unfortunately the axiom was wrong, so all their deduced astronomy and their pictures of spheres of the heavens were wrong as well. Starting with axioms and deducing outcomes only works if the axioms were correct in the first place.

"So what am I doing wrong?" Mendel asked himself as he sat looking at the neatly written evidence before him. "What axiom are we all using in this case?"

It seemed so obvious that no one had questioned it; the axiom was that a Czech Hussite had broken into the Obserstleutnant's room to carry out acts of sabotage. The deductions that everyone had drawn from this axiom were; that the burning of the lists and the breaking of the beaker were acts of vandalism designed to bring publicity to their cause; that Klacel was a known Czech Hussite; that Klacel was the only person at the monastery with such a motive and opportunity.

Therefore, ergo, Brother Matthew was guilty even if no one had seen him do it, he had denied it strenuously, and it was an act totally out of character.

But Mendel now knew that the axiom on which all this deduction was based, could be wrong, or at least the deduction from the axiom had to be wrong. He had evidence which said that Brother Matthew could not have left the dirt in the fire place hearth, as it contained pollen that would have made him very sick. This was the new way of thinking he had been taught at University. First experiment and measure the real world. In his case he had found the pollen in the dirt and also the strange refractive index of the glass. Then use "induction" as a logical means of arriving at "generalizations" about the experimental situation. Although these generalizations are only imperfect pictures, or visions, of the reality that underlies a phenomenon, they are a start.

To Mendel there was no Greek, "perfect truth", only observations, induction and a strengthening confidence in the mathematical principles that formed the basis of the phenomenon. But how was that going to help his friend get out of trouble?

Slowly he spread the papers around him and went over, yet again, all the evidence he had collected. A locked door; how had the saboteur gained entrance? Burnt lists; how and when had the fire started? A broken glass beaker; why?

If he took the axiom that Brother Matthew was a violent Czech nationalist, all these facts and questions supported only one deduction; he was guilty. But, if you threw away that axiom, and the deductions based on it, what could you substitute?

It only made sense to burn the conscript lists if you were trying to prevent fellow Czechs from being drafted into the regiment and sent off to war - didn't it? Or did it? What other possible reason could there be? No one else could profit or have a motive for burning those names beginning with the letter 'S'? Or could they?

Questions, questions and more questions; they hammered around Brother Gregory's brain like the sounds of thunder that had swept over the monastery a few nights before. Once, several years before, he had asked himself the same kinds of questions about a stack of data. Then, on the desk before him, there had been sheets of numbers collected by himself and Brother Joseph concerning the offspring hybrids of various pea plants.

Those numbers had not made any sense at all in their raw state, and it was not until, late one night, that he had arrived at the simple idea of converting them into ratios that the true pattern emerged. The simple act of taking one set of data, dividing it by a second set, and always getting the ratio 3:1, three is to one, that a mathematical solution to the complex biological problem of heredity sprang out at him.

All the confusion of columns of numbers became an obvious mechanism whereby controlling 'elements' were inherited by offspring in predictable ways from both parents. It was a vision of nature's profound beauty that no one had seen or realized before, and all revealed by looking at the data in a new way, and recognizing a pattern in the numbers. Now, what was the pattern in the evidence against Klacel?

For about another hour nothing suggested itself. The human brain often works the slowest when driven the hardest, and it wasn't until he felt exhausted and was about to give up for the night that Brother Gregory's brain flicked itself over two of the least obvious facts before it - and made a connection!

At first the connection seemed, to his tired mind, an absurd one. He took off his spectacles and rubbed his eyes, but the two small facts continued to bounce, rub off one another, and stretch out tentacles of induction that grew until they began to envelop all the other facts and evidence spread out on the table. Without the numbing axiom that the whole incident had been driven by a demented Czech nationalist, a lot of the facts began to support a different, much clearer vision and quite a different hypothesis.

With growing confidence, Brother Gregory started asking questions of his new hypothesis. Suddenly, looked at in this new way, the answer to the question 'why burn only four pages of the conscription list?' was obvious! But the answer to the question 'why break the glass beaker?' was so clever, so devious and so - imaginative - it took his breath away. If he was right in his hypothesis, he was dealing with a highly intelligent person who had gone to a lot of trouble to remain undetected in his crimes.

This person would be hard to catch, and his crime might still be laid at Brother Matthew's door, as all Mendel had done so far was re-arrange the facts to fit a different hypothesis. Now, how could he prove it?

Across the monastery the Compline bell sounded as the geneticist monk turned his mind to solving that problem. He would get little sleep that night. Tomorrow was Monday and the tribunal met to judge Brother Matthew the day after. He must try and find a way to test the hypothesis before then.