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When you think of spies and secret agents, you might think of lots of things; nifty gadgets, foreign travel, dangerous missiles, fast cars and being shaken but not stirred. You probably wouldn't think of mathematics. But you should.Cracking codes and unravelling the true meaning of secret messages involves loads of maths, from simple addition and subtraction, to data handling and logical thinking. In fact, some of the most famous code breakers in history have been mathematicians who have been able to use quite simple maths to uncovered plots, identify traitors and influence battles.The Roman GeezerLet me give you an example. Nearly 2000 years ago, Julius Caesar was busy taking over the world, invading countries to increase the size of the Roman Empire. He needed a way of communicating his battle plans and tactics to everyone on his side without the enemy finding out. So Caesar would write messages to his generals in code. Instead of writing the letter 'A', he would write the letter thatcomes three places further on in the alphabet, the letter 'D'. Instead of a 'B', he would write an 'E', instead of a 'C', he would write an 'F' and so on. When he got to the end of the alphabet, however, he would have to go right back to the beginning, so instead of an 'X', he would write an 'A', instead of a 'Y', he'd write a 'B' and instead of 'Z', he'd write a 'C'.Complete the table to find out how Caesar would encode the following message:
Treason!If you've got the hang of coding messages by shifting the alphabet forward, then you might have realised that it is actually pretty simple to crack this type of code. It can easily be done just by trial and error. An enemy code breaker would only have to try out 25 different possible shifts before they were able to read your messages, which means that your messages wouldn't be secret for verylong.So, what about coding messages another way Instead of writing a letter, we could write a symbol, or draw a picture. Instead of an 'A' we could write *, instead of a 'B' write + etc. For a long time, people thought this type of code would be really hard to crack. It would take the enemy far too long to figure out what letter of the alphabet each symbol stood for just by trying all the possiblecombinations of letters and symbols. There are 400 million billion billion possible combinations!This type of code was used by Mary Queen of Scots when she was plotting against Elizabeth the First. Mary wanted to kill Elizabeth so that she herself could become Queen of England and was sending coded messages of this sort to her co-conspirator Anthony Babington. Unfortunately for Mary, there is a very simple way of cracking this code that doesn't involve trial and error, but which doesinvolve, surprise, surprise, maths.
In the 1950s, it was established that genetic information is transferred from DNA to RNA, to protein. One sequence of three nucleotides in DNA corresponds to a certain amino acid within a protein. How could this genetic code be cracked After Marshall Nirenberg discovered the first piece of the puzzle, the remainder of the code was gradually revealed in the years that followed. Har Gobind Khorana made important contributions to this field by building different RNA chains with the help of enzymes. Using these enzymes, he was able to produce proteins. The amino acid sequences of these proteins then solved the rest of the puzzle.
Figure 2 Global overview of metabolic changes occurring during the transition from green expanding fruit to ripening processes (from 30 DAA to 60 DAA) in tomato fruit. Names of metabolites in red, green and black indicate increase, decrease or no changes, respectively. Metabolites are analyzed mainly in pericarps. The Figure summarizes data collected by Carrari and Fernie (2006); Gilbert (2009); Mounet et al. (2009); Centeno et al. (2011); Beauvoit et al. (2014); Biais et al. (2014), Van Meulebroek et al. (2015), Van de Poel et al. (2012), and Zhao et al. (2018).
Forty-three years ago, Penn State University played for its first national championship in a football season that began against Temple on Sept. 1, 1978, and ended against second-ranked Alabama, on Jan. 1, 1979. It was the season in which Penn State football became Penn State Football, a season that saw head coach Joe Paterno become an American icon. It was also a season that saw a serial sexual predator attack multiple Penn State students.
His name was Todd Hodne, and he was perhaps the most dangerous predator ever to play college football. \"I have been a prosecutor for nearly 30 years,\" wrote John B. Collins, who prosecuted one of Hodne's crimes, in a letter to a parole board. \"I have prosecuted serial killers and capital cases. Todd Hodne, to this day, remains among the three most dangerous, physically imposing and ruthless excuses for a human being I have ever faced in court.\"
St. Dominic won the state Catholic High School Football League championship in 1975, in Tom Capozzoli's final season as head coach. His son Tony, a senior, was named first-team Parade All-American, and he committed to Penn State as a quarterback and a kicker. Todd Hodne, Dave Smith and John Poggioli had one more season together, and though Hodne and Smith once had a fistfight on the school stairs, Hodne and Poggioli were thought to be best friends. In truth, Poggioli said he remained in the friendship because he didn't know how to get out. He was drawn to Todd Hodne and he was afraid of Todd Hodne in equal measure, and Hodne made him pay every time Poggioli tried to emerge from under his sway. When Poggioli was a junior, he told Hodne that he might try out for the school play; Hodne responded by sneering, \"You're no actor,\" and dumping a pail of water on his head. When Poggioli had a crush on a girl named Janet, he wouldn't dare ask her out because Hodne, though not her boyfriend, had claimed her. \"In my four years at St. Dominic, nobody asked me out because they were so afraid of Todd,\" Janet Shalley remembers now. \"I could only date boys from other schools. And back then, I had it going on.\"
It was not a violent crime. But it was a felony, and Joe Paterno was a coach who called players into his office even when he heard they were not participating in classroom discussions. He was a disciplinarian, and there would have to be discipline. On Aug. 19, 1978, two months after the burglary, Penn State held a scrimmage, and afterward, Paterno told gathered reporters that Todd Hodne had been suspended for the season. But he did not like to give up on his players, and he did not give up on Hodne. In his announcement, Paterno said that Hodne will be able to return to the team \"if he has a good academic year and if he proves to us that [the robbery] was a mistake.\" He also sought to provide Hodne a role model for his sophomore season, and to that end, one of his seniors, Fred Ragucci, was summoned into the football office. Ragucci went to a Catholic high school on Staten Island, and now he played defensive end for Paterno. When Ragucci was told he would have a new roommate in Hamilton Hall, he didn't blink, even though he was two years older than Hodne and was not part of his crowd. Ragucci could figure out easily enough why he wound up in this unlikely pairing: \"I was a pretty good student. I was pretty straight, never in any trouble. Nobody specifically mentioned this to me, but I think they were trying to put people in with people who might be a good influence.\"
Adrienne Reissman was a student at Penn State and a waitress at the Train Station. She kept her car parked close by, in the alley behind the restaurant. One night after work in the fall of 1978, she was walking out to the alley in the dark. She remembers what she was wearing because she has asked herself so many times what she looked like that night, what he might have seen. \"What woman doesn't ask what she looked like\" she asks now. \"Was I a target Was I trashy\" She was wearing \"black slacks and a tan sweater with suede patches at the elbows.\" She was 24 years old. She was 5 feet tall. She was an artist and a self-described hippie. She didn't know the football players who came into the Train Station because she didn't particularly care about them: \"I was not boom-boom rah-rah.\"
These were lies. In the days before turning himself in, Hodne had tried to convince Brickowski to vouch for him regarding one of the nights Musser was interested in. \"Todd tried to tell me, 'That's bulls---, because you and I know we were both at the library that night,'\" remembers Brickowski, who went on to play 13 years in the NBA and whose father had taught Hodne driver's ed in high school. \"And I looked at him. I go, 'What' He says, 'We were at the library that night. Study hall.' And I'm like, 'Todd, we never stayed in study hall.' We would go to study hall, sign in the front and slip out the back and have someone sign our names. And he goes, 'No, no, on this night, we did.' And I go, 'No, we f---ing didn't. And that was the break between him and I.\"
There was an investigation of the attack. \"The police came over,\" she says. \"They were in my apartment for a long time.\" Karen remembers her attacker going through everything, and now the cops were doing the same. Jean remembers seeing smudges of black all throughout their apartment where police had tried to lift fingerprints. Jean also remembers that when Hodne was arrested, Clyde had reminded her that the three of them had run into him at The Saloon a few weeks before the attack. Karen remembers police finding a footprint outside her window. But 43 years later, what Karen remembers most is the sense she had that the police were investigating her as much as they were investigating what happened to her: \"And basically what came out of it was that they told me they didn't have enough information to go to court. And that's what I heard from everyone involved in this: not enough evidence. They had evidence.\" 1e1e36bf2d