#9 - Knowing

(This is the final installment of the story from post #8)

"WAIT!!", you cry as your bother heads for the edge. He turns his head to look back and sees you hurdling towards him. He doesn't slow down at all, however, and is about to reach the edge when he sees, out of his downward peripheral vision,  a small jagged rock. It was too late. As his left foot got caught, just for a split-second, underneath the sharp stone, he winced. His body proceeded to launch forward, briefly airborne, before thrashing to the ground. He rolled right onto the edge and then slowly slid off.

You stumbled to the edge and looked down and saw a small speck falling towards the piraña pool. You heard a soft "plop," and stared down for a few seconds. The waters started to get rougher as the ripples attracted the attention of hundreds of pirañas. You closed your eyes, hard. You had no idea what was even happening; you turned away, shocked. You glanced at the relaxed nylon rope strewn about the ledge.

"Why isn't the rope taut?" you thought.

"Did the knot give way?" you asked. 

In fact, it didn't. The knot was still holding firmly around the the waist of your brother. Having been quiet for several moments out of fear, he let out a piercing scream, half in terror, and half in pain. You lunge to the edge to see your brother hanging on to a small branch that extended from the ledge, about five feet below you. Tears streaming down his face, shirt torn up, and without a left shoe, your brother dangled; he was too far down for you to reach without falling off yourself.

"Hellllllllllllp!!" he cried.

You started to panic. Your brother was alive, but you knew he couldn't hang there for long. You had to do something, and fast. You looked around. You didn't see anything that seemed like it would help, only your brother's backpack, the rope, a bunch of rocks, and you were sitting atop the craggy ledge. You stepped back. Took a couple breaths and yelled, "How were you planning to get yourself up?!?"

"I don't.... I don't... know..." your brother gasped, struggling to speak. You could hear the branch crackling, and twisting around. You knew it wasn't going to hold for long. It was just like your brother to do something so utterly rash and destructive that he would find himself in such a situation, but you could hardly believe that it was actually happening. 

"Hold on!!" you yelled. You needed a moment to think. You wished you were back in your room, sitting leisurely at your desk with a pencil and a blank sheet of paper, free from the distractions of the world. You soon realized, however, that this was no such time. You didn't need thought... you needed action. You saw your brother's backpack and noticed that the arm straps had snap-in buckles, and suddenly it came to you. 

"I'll get you right up, just hold on for one minute!" you shouted. 

"Huh, uh... uh.... ok..." your brother said, fighting even to breathe. 

You ran over to his empty bag, picked it up and started filling it with rocks. Lots and lots of rocks. You hardly knew what you were doing, you felt like you were acting out of instinct rather than analysis. You knew that you could barely lift your brother, so you filled the bag with the heavy rocks strewn about the ledge until you couldn't even lift it. 

"I can't... it won't... I... can't hold..." He let out an almost resigning cry.

"YES YOU CAN!! YOU'RE GONNA BE FINE!!" you vociferated. 

Then, pushing it over to the edge, you slid the bag over to the section of the rope that was laxly hovering over the air. You detached the arm buckles of the back pack, fed the rope through, and then re-attached the buckles. Then, with one more hard push, you sent the bag flying off the edge, taking that section of the rope with it. But horror quickly hit you as you realized the error in your plan, the rope wasn't going to pull your brother up like a counterweight like you had thought, it was going to pull him down like... well... like a bagpack full of rocks. But you had one last chance. It hit you that you could take the part of the rope that was in between your brother and the bag and get it around that large boulder, it would work like a counterbalance. You sprinted to that part of the rope, which, in any moment, would be pulled downward like the rest of the rope. You grabbed it, sprinted back to the boulder, and, just as you began to feel resistance from the rope being yanked down by the bag, you threw it over the top of the boulder. The rope landed exactly at the equator of the mighty rock, and cracked hard against the boulder with tautness. You didn't know it, but at that same moment, you're brother's hand slipped. But just at the right moment, the force of the bag sent an impulse through the rope, which went around the boulder and reversed his acceleration, the rope was severed right at the boulder in the process. He was flown up over the ledge, thrown right towards the boulder that you stood in front of... and you caught him. You heard a soft "plop" as the bag of rocks hit the piraña pool. Your brother was gasping for air, tears in his eyes, just like you...

THIS, is what you were missing...

(I hope you enjoyed it! I may be adding an epilogue later, but for now I suggest that you (and I will as well) contemplate the events of this little story)

Certainly yours,

Quentin

#8 - A leap of faith?

(Continuing on Post #7... There's some good words in the mix, so enjoy)

Now you and your brother are walking down the long road toward Know ledge. You can barely process what's going through your own mind, let alone your brother's.

"You're seriously going to jump off that ledge." You say incredulously.

"Sure, with this nylon rope I got from the garage."

"Stop smiling, this isn't funny anymore."

"It kinda is."

"Why?!"

"Dramatic irony... you think you can know everything by deducing it all. You don't realize that you wouldn't be anywhere if it weren't for five things."

"I know what you're gonna say... the senses, right?"

"Exactly. Just think about a world in which we could not see, hear, taste, smell or feel. It would be a pretty boring world. At least, I think so."

"Sure it would be boring. But the thing is that our senses really can't be trusted. When it comes to knowledge - certain knowledge - we can only trust what we can show deductively."

"Oh really?"

You thought for a second. Then you came up with what was sure to hurt his contention:

"Yeah, I mean, I could reproduce the answer to a question a million times using deduction. But no matter how many times you observe something, you can never guarantee that it will happen the next time, can you? The sun has risen every morning, does it mean that it has to rise tomorrow? Every time you drop something it has fallen. Does that mean it will fall the next time? It certainly doesn't. There is no logical reason why we can assume that past observations will hold in the future. For centuries people thought the Earth was flat. They were so sure because of what they saw. And yet, they were still wrong. The past is easy. It's the future that is hard. How do you know that your observations aren't leading to erroneous conclusions, or resting on incomplete data? How can you rely on what's passed in order to justify what you think will happen? In order to make any sort of general conclusion using induction, you have to make a leap of faith."

"Watch me."

You didn't realize it, but while you were intently arguing your point, you both had

arrived at the ledge. He set his stuff down and intently started to rummage through a bag of various things he had brought. The nylon rope was stretched out along the craggy ledge. A small segment was even hovering over the side.

"What if that leap is in a life or death situation? It's certainly quixotic of you to think that your observations will always lead you to the right conclusions."

"Hey, I never said my observations would always lead me to right conclusions." He said as he began tying the rope around the bottom half of a gigantic boulder near the edge.

"Then how can you risk your life knowing that? And doesn't that show that deduction is better since it can, after all, guarantee the right conclusions?"

Your brother paused. He then finished tying an intricate knot around the rock. He paused again as if in deep thought. You thought he wasn't going to respond. It seemed like he had no response he could give. After all, how could he put so much confidence into something he knew was fallible? He proceeded to tie an extra special knot around his waist. A knot that made you think of Alexander the great and the Gordian Knot that he once boldly cut. 

"This amount of rope seems about right," your brother said, completely ignoring the question posed to him. He took a couple steps out towards the edge of the ledge. You saw the wind intermittently blowing his hair from side to side, as if it were desperately gasping for air, as you almost were. Your brother then said,

"The thing is, you don't see how we all need induction every day. Without it, we wouldn't be able to function at all. If we were all to suddenly question everything we we had ever seen, we would never make progress. What if every morning I checked extensively to make sure their wasn't a bomb in my cereal box. Well, that would certainly slow my morning down quite a bit don't you think? What if I was always thinking about the possibility of something not falling when dropped? I would never be able to make any conclusions at all. Always hinging on something which has never been disproved and has always been shown to be true slows down progress. In many cases, progress grinds to a halt because of it. When you solved that problem about how many meters of rope someone would need when jumping of the ledge, you yourself assumed that the person would in fact fall. We need induction." He took another step forward. The wind picked up. "Induction. Experiment. Experience. This is how we learn." He looked around. He seemed confident, like he was doing calculations in his mind about the impending drop and they were all checking out.

"One thing I don't get though..."

"Yeah?"

"Why do you still choose experience over theory, when-"

"Because" he interrupted you, "as I see it, a theory is no good to us if we can't put it into practice. And also, as philosopher David Hume once said, 'The most lively thought is still inferior to the dullest sensation.'"

There was momentary silence, only broken by the pitter-pattering of feet against dirt. He was running for it. Prepared to take the leap, when...

"WAIT!!"

The conclusion is up next. See you soon. (How's that for a cliffhanger?)

Faithfully,

Quentin

#7 - Still on the 'ledge (with a ledger, a pen, and an idea)

Salvete! (Latin for hello [to more than one person])

Let's keep at this and continue on post #6...

Let's say that you're sitting down at your desk. You have your eyes closed, a writing implement, and a something to write on (perhaps your trusty 'ledger?) You're thinking about what would happen if you jumped off a cliff... with a nylon rope tied around your waist (phew, you had me worried for a sec). But the cliff is over a pool filled with lots of hungry pirañas [Oh my god, *gulp*, you know how much I hate.... diacritical tildes! Why can't you just spell it 'piranha'?!? Then it will be less scary!] [NO!]. You want to know exactly how long your rope should be (knowing that the nylon rope stretches a bit with respect to a factor that is a quality of the rope) so you can just barely touch the top of the pool. Well, you do all these calculations and you logically deduce that your rope should be x meters long. Hooray! You just gained some knowledge. Not just any knowledge, a priori knowledge.

A priori (pronounced 'ah pre-or-ee') is an awesome word/phrase that describes reasoning or knowledge that proceeds from theoretical deduction as opposed to experience.

A priori comes directly from Latin and literally means, "from what is before."

Then there's you're little brother. While you're slaving away working to logically deduce knowledge and prove things to be true, he's outside doing just any old random thing - observing the stars, throwing objects in the air, digging for a passageway to China. Stupid brother, he's out doing all these things to see how they work, when you could just show him how they work using your pencil and your trusty 'ledger. He also has a 'ledger for some reason. You don't know why he needs it, he's just taking down any old notes, he's not doing any calculations or logical deductions - he's just writing down what he sees. When he observes a phenomenon regularly and repeatedly, he infers from these particular instances a general conclusion. You do have to concede, however, that his methods for observation are pretty scientific. He is quite good at inducing knowledge. Not just any knowledge, a posteriori knowledge.

A posteriori (pronounced "ah poh-steer-ee-or-ee") is another awesome word/phrase that describes reasoning or knowledge that proceeds from observation or experiences - empirical as opposed to theoretical.

A posteriori comes directly from Latin and literally means, "from what comes after." 

So one day you're all fed up with him and his non-deductive ways:

"Hey, little brother! Get over here!"

"Sure...what is it?"

"How can you honestly expect to gain knowledge while you're outside all day?"

"How can YOU honestly expect to gain knowledge while you're inside all day?"

"Hah, I've learned dozens of things in the last half-hour with nothing more than logical deduction!"

"Well, anything you learn from that, I can learn with nothing more than my senses and observations!"

"Oh yeah? Well how about this: I just showed that you would need exactly x meters of nylon rope to jump off that cliff down the road in order to exactly touch the top of the piraña pool! Show that with your precious observation!"

"You mean that ledge? KNOW Ledge?"

"Yeah I do..."

"Well, okay." And he smiles.

"Okay?"

"Okay." And he smiles some more.

Man this is getting interesting! Part 3 coming soon...

Certainly yours,

Quentin

P.S. Recently learned that 'a priori' and 'a posteriori' have alternate pronunciations I did not know about. Listen to them here and here.

#6 - I'm on the 'ledge (STTA)

Hey ally. (typo - that was supposed to be 'all', not 'ally', but you're probably not an enemy of mine... so I'll leave it)

Shira and I sincerely apologize, as the last couple posts haven't been the most uplifting. (Although, I have to admit, 'catacomb' is endlessly fun to say.) I'll try to right this ship.

And yeah, I've been quite busy. But it has all been in the pursuit of KNOWLEDGE! And that is what I want to talk about for a bit, if you'll indulge me to do so, here's a Something To Think About:

Wow, knowledge. Quite a lofty thing to talk about, don't ya think? In fact, no ledge is loftier than knowledge. It's a pretty craggy ledge - not smooth at all - lots of small and sharp rocks with millions of pebbles and grains of thought sprinkled all over it. Of course, the ledge gets windier and rougher as you approach the edge of the ledge. As you go out farther and farther, you have more of an impulse to turn back. This impulse gets intense at a faster and faster rate as you continue. Each step is more arduous than the previous one, and there's always another step to take.

The one weird thing about this ledge is that no one has ever seen the end of the ledge. Some people argue that there isn't an end to it. Others rebut, "Well, it isn't a ledge, then, is it?"

Some people seem to think that there is only one way to make your way out to the edge of the ledge. Of course, this is not true. Very few paths have been mapped out extensively; and only a handful have been identified as possible routes at all. Even these are nothing but prospective routes. Who is to say that a certain route won't lead to a dead end. After all, no one has seen the end or even knows if one exists.

Many more people seem to think that they must follow paths that have already been marked and mapped out. This is, of course, completely false. There's no guarantee that you will end up where you want to go by following a path, whether it is marked or unmarked. In fact, think of the first person to traverse the path you're on. Did that person follow any marked path? No, they certainly did not. They followed their own path; they stepped in to uncharted waters. You need to find the way down to the edge of the ledge that's yours and yours alone. After all, we have only explored a small subset of the possible paths.

On that introductory note (heh), I want to talk about how we come to know and the words (yes, words! hooray for a blog post that talks about words!) that describe them.

Philosophers tend to agree that we gain knowledge through three fundamental operations of the mind: intuition, deduction, and induction.

Intuition is when we see directly that something is the case or that an immediate thought is absolutely necessarily true. Intuition does not require reasoning.

Deduction is when we move through a series of intuitions to obtain a conclusion that is necessitated (albeit indirectly) by our base intuition. Deduction is reasoning.

Induction is when we take a specific example of something and infer a general conclusion from it. This is also reasoning.

It is interesting to think about when you are deducing knowledge and when you are inducing knowledge...

You know, I was going to continue and give some examples, but I have quite a bit more to say; and I think this is enough to chew on for a bit. Think about it for a while and look for part 2 soon.

Yours by mathematical induction - today, the next day, and the day after that, on to ∞,

Quentin