Day 85 - Vectors II

If you stand outdoors on a clear starry night with a compass and a protractor you can identify any star. [Polar angle] How far do you have to turn clockwise from North to see the star directly in front of you? [Azimuthal angle] How far above the horizon do you have to lift your head to see it head on. [Radial distance] How far away is it? Wikipedia will show you a lot of Greek symbols and calculus equations but what I just said says the same thing in ordinary language.

Remembering what I said yesterday that qualities can be measured in the same way. Which direction is it and how much of it? Take a baseball and cut it in half. Glue one piece to a thin piece of glass and the other piece on the other side of the glass directly adjacent to the first piece. 360 degrees marked on the glass around the baseball. The angle above or below the class on a protractor. The magnitude measured with a ruler.

Any point on that baseball becomes an object of interest. Chocolate ice cream. If you like it there will be an arrow shooting out from the center of the baseball in the chocolate ice cream direction with a magnitude directly proportional to the amount you like or dislike it. Vanilla ice cream might be right next to it. If you like vanilla it will be longer or shorter than chocolate by the amount you prefer it. If, on the other hand, you don't like vanilla the arrow will shoot out of the baseball on the other side of the glass.

Why does this matter? By the time all the likes and dislikes are aggregated the surface of all the arrow points will appear as a lumpy potato rather than a smooth baseball. That lumpiness defines us in more ways than a simple statistical summation.

I will follow up tomorrow with an interesting algorithm about lumpy potatoes and human personalities.

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Day 84 - Vectors

Visualize a knob that you could turn to indicate how you felt. Zero = apathy. 10 = engagement. Better, imagine that you could turn it in the opposite direction from 0 to -10 to show repugnance. 10 for like, 0 for don't care, -10 dislike.

Expand the scale to 100. 100 = love, 0 = couldn't care less, -100 = hate. Not romantic love but attraction or interest. Positive is interest, negative is detest.

Think of the vast domain of things that this scale could be applied to: people, places, things, …

BBQ ribs = 89, cauliflower = -20.
Bruno Mars = 27, Eazy-E = -74.

Consider a sphere. At the origin there is an infinity of directions an arrow could point. For every direction from the origin there is an opposite direction. For the north pole, there is the south pole opposite it.

Let us postulate that the length of the arrow is analogous to our -100 < 0 < +100 scale. Zero is the origin of the sphere. Thus, anything can be represented by an arrow and a set of coordinates. For taste, BBQ ribs is a long arrow in one direction, while cauliflower is a short arrow in the opposite direction. Perhaps, squash is an arrow of zero length in the same direction.

This arrow can be described in a 3-dimensional model by stating values for x, y, and z coordinates. Another way to describe it would be to state the radial distance (length of the arrow) plus the polar angle and the azimuthal angle (direction of the arrow). In math terms: r, θ, φ.

More on this tomorrow!

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Day 83 - Options

Life is filled with infinite possibilities. What a wonderful fantasy.

From the moment of conception our lives are framed. Not preordained, but bounded by circumstances and the decisions we make.

Only a couple of miles separate Beacon Hill from Fields Corner in Dorchester, yet the spectrum of opportunities offered by each are worlds apart. Infinity is filtered by our origins and our actions.

A decision is to cut off other options. What is decided for us and by us filters future states. Like a map, at each junction a choice is made: north, south, east, or west. Unlike a map, we can not go back in time and undecide. Once made the range of choices is constrained for the next step.

Good choices come from experience,
Experience comes from bad choices.

Good choices can also come from the random luck of coincidence or a serendipitous observation. Entropy can play both for us and against us. The Butterfly Effect suggests that no action is too insignificant to play a role in determining our future.

Plan for the future,
    Live for today,
        Make the best deal you can get!

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Day 82 - Stream

It's easy to float down a stream, a buoy traveling lightly, letting the current take you where it will. No cares, no responsibilities, maybe a bruise or two along the way as you collide with a rock. Nothing to worry about.

It's hard to build a house on the shore. Make decisions about what and where. Lay the foundation, build the structure, put up the roof to protect you from the elements.

Sitting alongside the stream on a sunny day watching the carefree others float by, you wonder whether commitment was the right choice. Sitting inside, watching the storm, the decision seems moot. This is the house, this is the place, no turning back.

Memory of the past is a sly phantasm that tricks you into believing what it wants you to. It's a sucker's game because you want to believe it too. When the going gets tough and the meandering stream beckons, it's hard to stand firm. Yet the words were said, the commitment was made.

That's how a house becomes a home.

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Day 81 - Birthday

Beth's birthday yesterday – totally focused on her. +1 on the end of the challenge. 

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Day 80 - Fail

A whole lot going on yesterday and I went to bed without writing my "100 words"

Not fatal but disappointing - Now it will be 101 day of 100 words. 

Let's see what today brings.

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Day 79 - Contacts

I found an old printout of my contacts dated 5 Aug 1996, a little over 25 years ago.

I married one of them.

I am still in active contact with 15 of them.

I am friends with 12 of them but not actively.

I am not on speaking terms with 3 of them.

I have no idea who 13 of them were.

21 of them have drifted away, probably never to be seen again.

Sadly, 8 of the best of them are dead.

My current contact list has 796 entries.

23 are in my A-List category

55 get Christmas cards.

41 are Motorcycle People

9 are in New York City, 11 in San Diego, 5 in Boston, and 1 in Hong Kong. The rest are scattered around the world.

14 are under the general heading of California.

It's been a slow day obviously. The high point was doing tax preparations. Maybe tomorrow will be more exciting

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Day 78 - Hello

The hardest word in the English language to pronounce is oftentimes “Hello”

Harsh words to a friend, a separated sibling, someone from the past you've lost touch with, all can make saying that word very hard. I've been in that position, I'd moved away and lost contact with a family that befriended when I was young and irresponsible. I wanted to reach out and say Thank You but I didn't know where to start.

I agonized over what to do. What would I say? What would they say? Would they be mad I hadn't been more grateful? I felt guilty for doing nothing.

Finally, I drove to their house and knocked on the door. When they answered I managed “Hello” and waited for the hammer to drop. Instead, they welcomed me into their home as if time had never passed. We sipped coffee and talked about things as if I was there only a week ago.

We make up things in our minds about how it will play out. Too often we borrow trouble before it even happens. It will not turn out well every time but at least that would be closure.

It's an easy thing to put off but imagine if they weren't there when you finally made the call? What if they were no longer there when you tried to say “Hello”?

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Day 77 - Dragons

On the map it says, “Beyond This Place There Be Dragons”. Some would say, “Dragons mean trouble. Best to stay home.” Others would say, “What place is that to stay away from?” A few will wonder, “What kind of dragons might there be?”

A traveler comes by and tells all that over the far ridge the grass is purple. One person replies that he's a damn fool, everyone knows that grass is green. Another remarks that since the traveler has been there and the rest of them haven't, they should take him at his word. That the grass on the other side is different and purple, and since they aren't going there, what difference does it make?

A couple of people venture out and travel over the ridge to see the purple grass. One of them sets up Purple Grass Tours to take people to see the odd colored vegetation. Only a few bob, all meals included.

There is one person that, seeing the purple grass, strikes out to find out what color the grass is beyond the next ridge.

Which person are you?

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Day 76 - Oxymoron

When I read about an “Adventure Tour” I have to wonder what that means. The two words are totally opposed to one another. A “Tour” is a planned route with defined stops and predictable Kodak Moments. Stand here, point your camera there, go home and tell everyone what an adventure you had!

If this is a motorcycle tour then it means that there will be a leader who will tell you what to do and how to do it. Probably a chase vehicle to carry your gear and have the campsite set up with dinner waiting. All very deluxe.

Except where is the adventure? It might be challenging and will likely take you to places you've never been to before but there is no risk involved. It's all handed to you on a platter with all the worry removed.

With no risk there is no adventure! If you are not making decisions for yourself there is no risk. You are paying someone to make sure you have a good time without worrying about how it will all come out.

I had stopped at a gas station to get gas when a bunch of riders on matching BNWs pulled in. They said they were part of an XYZ Tour of the Southwest. One of the riders had gone down and cracked a valve cover or something and was bleeding oil. Not a problem! A van pulled up with XYZ Tours painted on the side. Two guys jumped out and replaced the cover from spares they carried with them. By the time I was gassed up they were ready to roll again.

Great service I thought as I pulled away. That's what they pay the big bucks for. And it's totally worth it for somebody who has limited time and the money to spare. I have no quarrel with it BUT it's not an adventure!

An adventure involves decision making, risk taking, problem solving, and discovery about yourself and the world around you. Sometimes it will be wonderful and sometimes it will go sideways, but it will always be yours to take credit and responsibility for. Pride of accomplishment and confidence in yourself are the rewards.

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Day 75 - Campfire

What makes you go down one road instead of another? What makes you choose an innocuous looking side road? What makes you go a little further than the others?

We left the ranger and with intentions of going to Panamint Springs. However, there was this scenic point that looked like a good place to park on something level and solid, a place to stretch our legs. All well and good except that there was a dirt road running out to the end of the overlook. Nothing you couldn't do in a Camry if you wanted but nobody did. Not the ones in the huge overlander rigs, not the ones in the tricked out jeeps, just the ones in the little red truck who wanted to see what was on the other side of the ridge.

My sister thinks she can see an alligator in the far canyon wall

Back on our way to Panamint Springs I spotted a side road with no markings that seemed to call out to me. Back up, turn right, follow the yellow dust road. We had found a snow storm in Death Valley. Why not a 30' waterfall?

The trail at the end of the road required some scrambling over rocks and boulders but we were rewarded with Darwin Falls. As we were thinking that this was a bit odd in the middle of a desert a group of young (20-something) women joined us. We chatted for a bit and I asked them where they were from. A couple of them answered “San Diego”. When I asked them where in San Diego they mentioned towns in San Diego county. I replied, “I used to live in O.B. And P.B.” and silently added “before you were ever born.” I took their group picture and we parted friends, never to see one another again.

We finally reached Panamint Springs which is a tiny airstrip, a general store, a gas pump, and the ubiquitous RV park. $15 for a tent site, $55 for a tent cabin with cots, or $200 for a real cabin with a bed. We chose the middle ground and found our place for the night. The canvas tent walls flapped in the wind, the cots were lumpy and uneven, BUT were able to stretch out in our sleeping bags and get a pretty good night's rest. And we finally had our campfire!

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Day 74 - Snow

After a night sleeping in the truck with the wind howling outside we woke to freezing gusts that tore at our clothes. We decided that coffee could wait and we would go a little way to warm the engine (and ourselves) while we checked out the road ahead. Lippincott Mine Road was only a few miles long. It would take us down to the valley and out to one of the main roads back into the center of the park. It looked so easy on the map.

We pulled up to the sign that said “4-wheel drive High clearance vehicles only.” With the bliss of the ignorant I said “That’s what we have. Let’s go take a look.” 100 meters further we had no way of turning around.  We were committed!

Luckily it was all downhill and with judicial use of brakes and steering we were able to navigate the many super-pucker moments along the way. Washouts, narrows, and sheer drop offs were around every turn. To say that it was tense would be a major understatement. But we made it and came to an intersection with a much better road.

The Saline Valley Road ran north and south. North, over Jackass Pass was the shortest and looked to be the better option. It was for most of the 11 miles. We rolled across the desert floor with a relatively smooth ride. On the map, it was a long dash road vs the short dash road we had just descended. Long dash = harsh dirt road, short dash = 4x4 only!

We started gaining altitude and entered the cloud cover. Light misty snow was falling but nothing to worry about (yet). As we continued to gain altitude we encountered deeper and deeper snow. 4-wheel drive and good tires kept us going as we advanced up the pass. Only a couple more miles to go!

Sharp turns and the grade were easily navigated until we got stuck. So close to the road and yet so far. Out came the tire chains that went on easier than expected and we were making forward progress again. For a while. Then we were stuck again. Back down 15' and run at it with full throttle to bull our way through. Once, twice, a third time and we were through. We were to encounter many more deep sections like this but luckily the same technique got us through each one.

Finally to the top, only an hour and a half to cover to cover 2 miles, we began to relax. After traveling another couple of miles to convince ourselves that we were really out of harm's way we stopped and took off the chains. A park ranger passed in the opposite direction and waved to us. We laughed that he was going to put up the Road Closed sign.

We entered an amazing Joshua Tree forest that went on for as far as the eye could see. Losing altitude we also came out of the snow and into sunlight. Out came the map. We were looking for the best way back to civilization when the ranger pulled up next to us. He asked where were coming from and just stared at us blankly when we told him. He had turned back when he saw the snow deepening. My sister's joke was that Jackass Pass referred to the drivers not the animals. The ranger thought that was funny with an all knowing smile.

This showed that others had a sense of humor too. After what we had just been through we laughed out loud.

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Day 73 - Cold

Death Valley - The least deadly place on the planet.

Slow start this morning. Breakfast at Mel’s Diner (muy bien) and back to the motel to swap the scooter into the other trailer and load all the gear into the red truck. The U-Haul trailer didn’t have a ramp so one was created out of a milk crate and a couple of concrete blocks. If we had made a video of it we would have a million YouTube hits by now. But it made it and got tied down so all's well that ends well.

Titus Canyon was closed at the entry which was disappointing. However, the exit was open to hikers so we spent a couple of hours examining the geophysical features up close. Very different perspective from the last time when I rode a motorcycle through the canyon

There was a retired guy with a bicycle that he was quite proud of. He showed us all the custom features he had added to the bike. ALL of them. I finally remarked, as politely as possible, that we had to be in Cerro Gordo for sunset and needed to start hiking. He agreed after showing us only two more of his innovations.

After leaving the canyon I decided to try going past Tea Kettle Junction instead of the Cerro Gordo road. It also goes by the Ubehebe Crater and The Racetrack. The crater was pretty amazing. Big and deep. There was a trail to the bottom but it was cold and getting late. The road to the Racetrack was typical high desert with plenty of what I named “pineapple” cactus but I think they were really young Yucca trees. The road climbed into the hills and turned into some brutal washboard.

The Racetrack was underwhelming. Had it not been so late and so cold we might have looked at it more closely but we needed to find a place to camp unless we wanted to set up in the dark. The wind was howling and we barely got the tent erected before we had to tie it to the truck to keep it from blowing away. Dinner was a hurried affair of warmed up pulled pork and then we decided to take down the tent and sleep in the truck. All I can say is that I found a hundred positions that were all uncomfortable.

Temperatures in the 30s did not help although I had climbed into my sleeping bag with all my clothes on. I should have brought my winter bag to The Hottest Place on Earth!

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Day 72 - Lippincott

Out on the desert for the last few days. Some challenges that I had not expected but survived them all. While I pull my notes together I'll share these thoughts.

A “farkle” is an accessory that is supposed to add function to a vehicle but is often just an add-on to increase the style points of the vehicle. If it is chromed it is bling.

An anodized billet brake reservoir cover is such a farkle. It adds no functionality but looks nice. After market oil filler plugs often decrease functionality because they require a wrench where the OEM plug will require only your fingers to remove.

Normally farkles doe no harm to anything except the wallet. Your buddies think they look good and are jealous. Some are very popular among newbies and are big on the look at me scale. Snorkels on Jeeps are high on this list.

However, I came across an instance where a farkle could be deadly. Wheel spacers and offset wheels move the tire away from the axle, ostensibly to allow wider tires to be installed. When you see Jeeps and pickup trucks with their tires sticking out of the wheel wells this is the reason. Macho looks that generally do no harm. Most of these vehicles never see anything more exciting than a gravel driveway.

On the Lippincott Road in Death Valley they could be fatal. The reason being that the road is extremely narrow with steep drop offs on the side. I got on it by mistake and had a mega-pucker ride to the bottom. My truck has stock wheels with slightly over sized tires and it barely stayed on firm ground. Crossing washouts and climbing over boulders was nerve racking and required 100% concentration. Only with experience and patience did I made it to the bottom safely.

On the way out of the valley I came across some young guys in three vehicles that were looking at maps. The farkles on their trucks screamed newbie so I pulled over to ask them where they were going. They said they were planning on Lippincott Road. Not only that, they were planning on going up where I had just come down. Up being significantly harder than Down.

I asked them about their experience and it became obvious that they were Silicon Valley techies who had lots of money and were out for a good time. I suggested that they get some more practice before attempting the road, and when they did they should go downhill rather than uphill. A park ranger pulled up as I was leaving and must have given them the same advice because I saw them turn around and drive away.

It occurred to me later that they all had heavily offset wheels that might not have fit on the road. That would mean either tumbling down a ravine, probably fatally, or attempting to back down the road which would be beyond extremely difficult. Thus, a farkle that could be life threatening. There is a reason that Jeeps are short and narrow.

I took 1½ hours to go 8 miles and was in no hurry to go any faster.

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Day 71 - Road

Michael Time - Michael Trocosso was my roommate when I lived in San Diego. We both liked the same things; girls, partying, traveling, and photography. The last two were combined into many trips that always started the same way.

First we would find an excuse to go somewhere but it didn't have to be much of an excuse. One time it was to go to Montana so that we would be on the axis of a solar eclipse. Another time it was to go skiing in Colorado because we knew somebody there who would let us sleep on their couch. Ensenada was always an instant agreement to pack up and go.

Second we would pick a date and time. The date was easy, there was only one solar eclipse so we had to leave 3 days earlier. The time was always fixed at 8 am which meant we would never leave at 8 am. Every time we would say "8 am for sure this time!" and every time we would get away 2-3 hours later.

We would say, "Since we always say 8 am and finally leave at 10, let's just say 10 am and avoid the stress." We finally got away at noon.

Another time we agreed to sleep in and leave when we were ready. That time we left the next day!

Once we were going to take Michael's pickup but realized that we would never make it past the city limit. So we decided to take VW van. One problem, it would never make it up into the mountains with the slipping clutch so we scurried around to find the parts, pulled the engine, replaced the clutch, and were on our way by 6 pm. 

It was hopeless and we knew it but we always said, "8 am - This time for sure!"

I'm in Beatty Nevada now, eastern gateway to Death Valley. I said "8 am - this time for sure!" knowing in my heart it would be more like 10 am. Sure enough, 10 am turned into noon as I pulled out of the driveway. Michael was riding with me in spirit.

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Day 70 - Routes

So many roads, so many choices. I'm leaving for Death Valley tomorrow and checking the maps to decide what route to take.

Did you know that Google Maps will help you find the Road Less Traveled? Click the Options link and select Avoid Highways. Google will find alternate routes to your destination and list the times and distances.

Another way to plot an interesting route is to grab the line on the map and tow it to another town or junction. Goggle will reroute the rest of the trip to accommodate your new point. Just put the cursor on the trip line, then click and drag it to a new location.

Lastly, you can add destinations in the original menu. Click Add Destination and type in a new way point. A bonus is that you can type in a name from your address book and Google will fill in the address. It also knows the names of national parks and points of interest. Drag any destination up or down to reorder the trip until it's just the way you want it.

Tonopah, NV. Famous for Little Feat's song Willin'

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Day 69 - Walmart

I hear a lot of grumbling about Walmart. The family has too much money, they treat their employees unfairly, they beat up their suppliers, and on and on.

I dropped one of the lug nuts for my trailer into the snow and couldn't find it. I went to the tire center at the local Walmart and asked if they could sell me one. Nope, but they were happy to give me a brand new one for free.

A friend's son is on the spectrum. He's a great person and is fun to be around. He's never going to work for Google or Goldman Sachs but he's bright and energetic in his own way. He went to Walmart for a job but they said they didn't need anyone at the time.

He went home and thought about it. He's ~21 and able to drive. He went back to Walmart the next day and said plainly that while he would be slow at first he was reliable and a hard worker. He told them he would learn fast and get better over time and all he wanted was a chance too prove it. They hired him on the spot and he's advanced to different positions since starting.

Look at the people working at Walmart. Most of them are good people who are never going to get hired at Nordstrom's or the Apple Store. They want to work and Walmart gives them a position that most think of as a “good job.” Walmart is known for working with employees who need flexibility in picking up their kids after school or taking care of a relative. Many want to earn some extra income but don't want to work a full 40 hours.

There was a community outside Denver that was planned to be ultra-green. No big box stores allowed. It was failing to meet its budget and finally relented to adding retail stores. The improved tax base balanced their budget. More importantly, the surrounding communities now had access to better goods at cheaper prices. The study I read acknowledged that the people nearby could buy healthier groceries with less money. There were more jobs available without long commutes. Their standard of living was greatly improved. Besides, if the greenies didn't like the stores they didn't have to shop there. But of course they did.

It's a long running meme that Walmart customers are low class. Funny pictures on the internet belie the fact that virtually all the shoppers are good, honest, working class people who want the best for their families. Moreover, I'm not impressed with the entitled snobbishness of Whole Foods customers who think running into you with their cart is acceptable behavior because they are oh-so-important and in a hurry.

Walmart is a business, not a social service agency. They provide goods and services at the lowest prices by negotiating the best deals with their suppliers. Employees are one group of those suppliers. This is not China, nobody is forcing anyone to work at Walmart. But they never have a shortage of customers or associates so something must be working well for all.

It's the American way!

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Day 68 - More Stuff

The best way to find something you've misplaced is to buy another one. The moment you have two of them the first one will reappear.

The best way to make sure you can't find something is to put it somewhere you can't possibly forget. You'll never see it again until you buy another one.

Getting ready for my camping trip I find that I have seven different cook sets all alike. A couple are different sizes for backpacking or car camping. One is still in the original unopened box and is exactly the same as another set.

I have a pocket stove, a multi-fuel stove, two canister stoves, and a two burner stove. Plus, fire starter in case I want to cook over an open wood fire.

Three sleeping bags with pads and mattresses. Four tents from a small one that fits on the back of my motorcycle to one that has separate rooms for lounging and sleeping.

Water bottles in every color, shape, material, and size you can imagine. Also collapsible water jugs in case I need to carry water from a stream. Only one water filter though.

Waterproof dry bags in multiple sizes from small 10 liter to just plain HUGE! Straps to hold it all together in every size, color, and material.

Where did all this stuff come from? I admit to being a gear junkie but this is a little silly. Having gotten it all out and sorted I think it's time to reduce the herd. I'm sure the kids in the neighborhood would be happy to get some of this for their next overnighter.

And then I'll have room to go buy more!

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Day 67 - Choices

Poignant and thoughtful but not the complete story. 

We all could have made better choices along the way but it's too late now to dwell on our regrets. 

What is truly sad are the people who wish they could go back in time and change something they did as if it would make their life better. Sad because they are admitting that they don't like the life they have now. 

The only happy people are the humble ones who admit their faults and mistakes and yet accept that they are living the life they chose. 

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Day 66 - Cable

5 kids + 2 hours = 1 Mad House

I finally got the new axle installed on the trailer and backed in to take it for a test drive. I wasn't paying attention and backed over the green cable box. The box was shattered into a dozen pieces and the cables inside were ripped apart. No Internet!!

Then I get the call. “Can you watch the kids for a couple of hours?” Sure. Why not? Things have been going so well today that I actually got through getting my driver's license renewed in under 20 minutes. It's time for the train wreck.

I spent over 30 minutes on the phone with Comcast. Once I broke through the auto-response robot answering part that kept telling me to reset my modem and connected with a real person it went well. (Hint: if you're caught in ACD Hell, try hitting 0 about 8-10 times. That will often signal the system that you are unhappy.)

The technician I talked to had a good sense of humor and I have some experience with network cables so we were able to patch together a temporary fix that should hold together until a repair person can come out with another green box and some new cables. We had a good laugh over stories of old ladies calling because they were missing their soap operas.

In the meantime the kids showed up and were unusually boisterous. We fed them ramen noodles and parked them in front of the TV. Immediately there was mayhem over the fact that I called Star Wars 4 “Star Wars 1” and they wanted to watch number 1 not 4. That was settled when I told them they could either watch #4 or watch my choice of movies. They took a vote and decided that #5 (Empire Strikes Back) was what they really wanted and settled down.

Until Olivia decided to climb up on the couch and knocked Alexander's soda over on Ezra who spilled his soda on Caleb. More mayhem ensued. Cleaning up the mess and restarting the movie took a while but eventually everyone was quiet and there were no further disasters.

Olivia decided to come upstairs and play with her cars and balls. She's just past her first birthday and is pretty bright. She doesn't know many words yet but has a whole vocabulary of squeaks and eeks. We were playing fetch with her balls which was fun. It amazes me the way a small child can do the same thing over and over, 37 times, and get such a big kick out of it every time.

I would roll the ball across the floor and she would go get it and bring it back to me. Just like having my very own puppy. Then the ball rolled next to one of the others and she brought back both of them to me. We played several rounds of twosies until they rolled next to a 3^rd ball. She giggled as she ran over and picked up two balls. Then she put one down and picked up the third ball. Then she looked at it, put down one of the balls and picked up the new one.

This cycle repeated itself about 6-8 times. Each time putting down a ball so that she could pick up the other ball and then realizing she was still missing a ball. I just sat there trying to imagine what was going through her mind. Finally, she gave the extra ball a kick and threw down the two she was holding. She'd had enough of the ball paradox and went back to playing with her cars. They seemed to make more sense to her.

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