An Irrefutable Case (Loose Lawyers Book 1)
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We can zero in on the art of persuasion, relegating even the most emotional, human performances to the sidelines. Sharpness in argument, free of temperance from blind faith and desperate hope, to convince, illuminate the most skeptical mind is the beautiful potential of our minds. Whenever it appears, in life and fiction, we take notice and applaud. Unfortunately, even the idiom, without a shadow of a doubt , cannot be quantified. For what if one could have a doubt was even smaller than this figurative guideline? Those words seem strangely light-hearted when possibly dealing with the life of another human being.
It just has the traction of having been around in our language regarding uncertainty since the 19th century. There is never a guarantee that truth will be paid handsomely with the correct verdict. In the end, it comes down to something that is both a human blessing and curse — hope. There is, however, a standard of proof that goes well beyond what a courtroom could ever hope for.
It will always have a 1. Any flaw of even the tiniest amount will render its currency as valuable as a three dollar bill. We are talking about mathematical proof. QED is Latin for quod erat demonstrandum. It is found at the very end of many mathematical proofs and philosophical arguments. It signals in no uncertain terms that whatever was needed to be proven, has been done so. Often found in many academic writings during the Renaissance era, the notation has always carried some intellectual swagger.
Most frequently terms
It is with no surprise then that marinating in the soup of social media that the phrase is now punctuated with profanity — to underscore some kind of the personal verbal jousting victory. Whether it is a mathematical proof or some form of airtight reasoning, QED is, however, the checkmate of the clearest thinking — that you are correct, the game is over, and the prize of irrefutable argumentation belongs to you.
Proof is the lifeblood of mathematics. It is not sufficient to cite one million cases where your idea works.
It has to work in the infinite arena of every case. Bridging that daunting gap, however, is not for the weak, as failure is what will most often greet you — over, and over and over again. The greatest mathematicians were not necessarily separated by ability; they were separated by courage.
Thinking is exhausting. Thinking in isolation without notoriety or success is a recipe for emotional collapse — for almost everyone. In the Boston Marathon, around the 20 mile mark, there is a rather short ascent of only 88 feet that occurs over a distance of just under half a mile. However, this is a point the race where the glycogen storage in muscles is most likely depleted — or, what runners like to refer to as hitting the wall. Heartbreak Hill, just outside of Boston College, has been historically named because of how many runners basically succumb to this challenging climb.
The world of proof — especially the famous solved and unsolved ones — is all Heartbreak Hill. That is why the great 20th century mathematician, Paul Erdos, surmised whimsically that all the great proofs must be in a book contained by God.
- Fantazia of foure Parts in A Minor!
- Loraine and the Little People (Illustrated);
- Jaime Lea and the Bumblebee.
Erdos called this book simply The Book. A direct and roundabout way of saying you better believe in God. He must have been channeling some amalgam of Lewis Carroll and Yogi Berra! Like with everything in life, not everything is good just because it exists.
Master List of Logical Fallacies
It should be susceptible to being critiqued for pleasing aesthetics, and eventually gain universal approval — or disapproval. As such, not all proofs are treated the same.
Most people have some thankfully vague memories of doing those horrendously uninspiring two-column proofs where one had to prove one triangle was exactly the same as another triangle. If that was your introduction to proof, then you should not be blamed for losing your appetite for not only proofs, but for mathematics as well. It almost destroyed my interest in mathematics. I was good at them, but for me, it represented the nadir of mathematics.
Triangles that nobody cares about.www.networking4acure.com/wp-content/2293-como-rastrear.php
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Notation and formalization that reeked of some pedantic precision. If you could bottle this scent, it would have been called eau du unnecessary surgery , smelling of sterilized operating rooms.
I will say often in this book that mathematics is an art form. If it had to classify the proofs that Lockhart is referring to, then it would be paint-by-numbers, 17 shades of grey, of a wall. We spent a week showing how one triangle was congruent to another. It was the longest month of my life….
The best proofs are elegant because of their balance of creative genius and economy. But, before we enter the sacred domain of world class proofs and their intrepid curators, it is important to rewind the clock back to when we began school. Then, like with many of the topics left until high school, is when we should have got our feet wet with logic, reasoning, and proof. No triangles or dispiriting jargon! Only simple examination of endearing stories. The following is a nursery rhyme that we know all too well:. Jack and Jill went up the hill to fetch a pail of water.
Jack fell down and broke his crown, and Jill came tumbling after. But, even a simple childhood story can serve as a bedrock for logic and reasoning. Here are some statements. Which ones are true and which ones are false? Which ones are unfounded assumptions? All of a sudden there is curiosity and interest in discussing the validity of each of these events.
Having children trying to defend or deny each statement related to a familiar context is how the long road to rigorous proofs should begin. Hansel and his sister, Gretel, were lost in the woods. They walked and walked, and finally saw a lovely house made of gingerbread.
Not knowing the house belonged to the witch, they walked up to the house and knocked at the door. No one answered the door, and they went inside. Being very hungry, they looked for something to eat. They opened the over door to see if there was any food inside, whereupon the witch sneaked up behind them and shoved them both in the oven.
Again, which statements are true and which ones are false? Notice how there is an increased level of ambiguity now. However, that does not change the ability to assign truth or falsehood or assumption to any of the preceding statements. That is how we fold in proof into our children. Let them reason with the familiar, so they can naturally weave in their own interest to the fabric of proof.
Once this is established, careful guidance — hold on to the ropes, kids — into reasoning ideas about numbers can take place. At some point, all kids should see and marvel at one of the cheekiest proofs ever — the proof that there are an infinite number of prime numbers. For one, kids would learn about the building blocks of numbers, prime numbers — numbers that can only be evenly divided by 1 or itself. Two, the concept of infinity, which is usually a tough beast to slay, will be shown to be brought down in a few clever stabs of logical thinking.
And, of course three, highlighting how the idea to prove it for the general case is the end game always. Case by case is not only impossible, but as will be seen, can lead to false conclusions. Here are all the prime numbers under a hundred:. Numbers go on forever. Prime numbers do as well. In the first one hundred numbers, they appear in healthy amounts — even beside each other twin primes like 17, 19; 41, 42 and 71, However, they get rarer and rare as you count to a maddening infinity.
Taking a giant and perhaps incomprehensible leap into numbers that are up digits long, only 0. While it definitely appears that finding prime numbers in the stratospheric range of large numbers is extremely rare, they will go on forever. If you think of prime numbers as a heart beat, primes seem to be full of life early on.
We can hear their pulse often enough.
But, as we move steadily towards infinity, there is almost deathly silence. And, only in the rarest moments do we get reminded that primes never die — they just get fainter, fading endlessly into the oblivion of infinity. There is a sweet sadness to this that I think plays right to the our heart. Things can be almost gone, but ironically always still there. So, when the largest prime number ever found in September, , there was a small celebration in the math community.
It has over 17 million digits! If you have already established rapport with the jurors, when you use these behaviors they will begin to pace you. Of course, this is the true test of your being able to lead the jurors. If you want jurors to experience a particular state as you are presenting your opening or closing statement, for example, you need to use those behaviors vocal, verbal, and nonverbal cues that correspond with the particular drama that you are trying to create.
Too often trial attorneys will deliver a very emotional argument in terms of the verbal content and not use the correct vocal and nonverbal behav-iors.